diff --git "a/docs.json" "b/docs.json" new file mode 100644--- /dev/null +++ "b/docs.json" @@ -0,0 +1 @@ +[{"doc_id": 1, "text": "experimental investigation of the aerodynamics of a\nwing in a slipstream .\n an experimental study of a wing in a propeller slipstream was\nmade in order to determine the spanwise distribution of the lift\nincrease due to slipstream at different angles of attack of the wing\nand at different free stream to slipstream velocity ratios . the\nresults were intended in part as an evaluation basis for different\ntheoretical treatments of this problem .\n the comparative span loading curves, together with\nsupporting evidence, showed that a substantial part of the lift increment\nproduced by the slipstream was due to a /destalling/ or\nboundary-layer-control effect . the integrated remaining lift\nincrement, after subtracting this destalling lift, was found to agree\nwell with a potential flow theory .\n an empirical evaluation of the destalling effects was made for\nthe specific configuration of the experiment ."}, {"doc_id": 2, "text": "simple shear flow past a flat plate in an incompressible fluid of small\nviscosity .\nin the study of high-speed viscous flow past a two-dimensional body it\nis usually necessary to consider a curved shock wave emitting from the\nnose or leading edge of the body . consequently, there exists an\ninviscid rotational flow region between the shock wave and the boundary\nlayer . such a situation arises, for instance, in the study of the\nhypersonic viscous flow past a flat plate . the situation is somewhat\ndifferent from prandtl's classical boundary-layer problem . in prandtl's\noriginal problem the inviscid free stream outside the boundary layer is\nirrotational while in a hypersonic boundary-layer problem the inviscid\nfree stream must be considered as rotational . the possible effects of\nvorticity have been recently discussed by ferri and libby . in the\npresent paper, the simple shear flow past a flat plate in a fluid of small\nviscosity is investigated . it can be shown that this problem can again\nbe treated by the boundary-layer approximation, the only novel feature\nbeing that the free stream has a constant vorticity . the discussion\nhere is restricted to two-dimensional incompressible steady flow ."}, {"doc_id": 3, "text": "the boundary layer in simple shear flow past a flat plate .\nthe boundary-layer equations are presented for steady\nincompressible flow with no pressure gradient ."}, {"doc_id": 4, "text": "approximate solutions of the incompressible laminar\nboundary layer equations for a plate in shear flow .\n the two-dimensional steady boundary-layer\nproblem for a flat plate in a\nshear flow of incompressible fluid is considered .\nsolutions for the boundary-\nlayer thickness, skin friction, and the velocity\ndistribution in the boundary\nlayer are obtained by the karman-pohlhausen\ntechnique . comparison with\nthe boundary layer of a uniform flow has also\nbeen made to show the effect of\nvorticity ."}, {"doc_id": 5, "text": "one-dimensional transient heat conduction into a double-layer\nslab subjected to a linear heat input for a small time\ninternal .\n analytic solutions are presented for the transient heat\nconduction in composite slabs exposed at one surface to a\ntriangular heat rate . this type of heating rate may occur, for\nexample, during aerodynamic heating ."}, {"doc_id": 6, "text": "one-dimensional transient heat flow in a multilayer\nslab .\n in a recent contribution to the readers'\nforum wassermann gave analytic\nsolutions for the temperature in a double\nlayer slab, with a triangular heat\nrate input at one face, insulated at the other,\nand with no thermal resistance\nat the interface . his solutions were for the\nthree particular cases..\ni propose here to give the general solution\nto this problem, to indicate\nbriefly how it is obtained using the method of\nreference 2, and to point out\nthat the solutions given by wassermann are\nincomplete for times longer\nthan the duration of the heat input ."}, {"doc_id": 7, "text": "the effect of controlled three-dimensional roughness\non boundary layer transition at supersonic speeds .\n experiments were performed in the 12-in. supersonic wind\ntunnel of the jet propulsion laboratory of the california\ninstitute of technology to investigate the effect of three-dimensional\nroughness elements (spheres) on boundary-layer transition on a\ntained at local mach numbers of 1.90, 2.71, and 3.67 by varying\ntrip size, position, spacing, and reynolds number per inch .\nthe results indicate that (1) transition from laminar to turbulent\nflow induced by three-dimensional roughness elements begins\nwhen the double row of spiral vortices trailing each element\ncontaminates and breaks down the surrounding field of vorticity, (2)\ntransition appears rather suddenly, becoming more violent with\nincreasing roughness height relative to the boundary-layer\nthickness, (3) after the breakdown of the vorticity field, the strength\nof the spiral vortices may still persist in the sublayer of the\nensuing turbulent flow, (4) lateral spacing of roughness elements has\nlittle effect upon the initial breakdown (contamination) of the\nlaminar flow, and (5) the trip reynolds number where u\nand v are the velocity and kinematic viscosity at the outer edge of\nthe boundary layer and k is roughness height, such that transition\noccurs at the roughness position, varies as the position reynolds\nnumber to the one-fourth power, viz., where x is\ntrip position ."}, {"doc_id": 8, "text": "measurements of the effect of two-dimensional and three-dimensional\nroughness elements on boundary layer transition .\nin his study of the effect of roughness on transition, h. l.\ndryden found, on the basis of available data, that the effect\nof a two-dimensional roughness element such as a /trip wire/\ncould be represented reasonably well in terms of a functional\nrelation between and, where is the reynolds number\nof transition based on distance from the leading edge, is the\nheight of the roughness element, and is the boundary-layer\ndisplacement thickness at the position of the element . at his\nsuggestion some additional data were obtained, primarily to\nextend the range to higher values of, during the course of an\ninvestigation of transition on a flat plate conducted at the\nnational bureau of standards . after the results on the two-\ndimensional roughness elements were obtained, it appeared to be\ndesirable to see whether a row of three-dimensional roughness\nelements would behave in the same way ."}, {"doc_id": 9, "text": "transition studies and skin friction measurements on\nan insulated flat plate at a mach number of 5.8 .\n an investigation of transition and skin friction on an insulated\nflat plate, 5 by 26 in., was made in the galcit 5 by 5 in.\nhypersonic wind tunnel at a nominal mach number of 5.8 .\n the phosphorescent lacquer technique was used for transition\ndetection and was found to be in good agreement with total-head\nrake measurements along the plate surface and pitot boundary-\nlayer surveys . it was found that the boundary layer was\nlaminar at reynolds numbers of at least 5 x 10 . transverse\ncontamination caused by the turbulent boundary layer on the\ntunnel sidewall originated far downstream of the flat plate leading\nedge at reynolds numbers of 1.5 to 2 x 10, and spread at a\nuniform angle of 5 compared to 9 degree in low-speed flow .\n the effect of two-dimensional and local disturbances was\ninvestigated . the technique of air injection into the boundary\nlayer as a means of hastening transition was extensively used .\nalthough the onset of transition occurred at reynolds numbers\nas low as 10, a fully developed turbulent boundary layer was\nnot obtained at reynolds numbers much below 2 x 10\nregardless of the amount of air injected .\n a qualitative discussion of these results is given with emphasis\non the possibility of a greater stability of the laminar boundary\nlayer in hypersonic flow than at lower speeds .\n direct skin-friction measurements were made by means of the\nfloating element technique, over a range of reynolds numbers\nverified as being laminar over the complete range . with air\ninjection, turbulent shear was obtained only for reynolds\nnumbers greater than 2 x 10, this value being in good agreement with\nearlier results of this investigation . the turbulent skin-friction\ncoefficient was found to be approximately 0.40 of that for\nincompressible flow for a constant value of r, and 0.46 for an effective\nreynolds number between 5 and 6 x 10 ."}, {"doc_id": 10, "text": "the theory of the impact tube at low pressure .\n a theoretical analysis has been made for an impact tube of the\nrelation between free-stream mach number and the impact and\nfree-stream pressures and densities for extremely low pressures .\nit is shown that the results differ appreciably from the\ncorresponding continuum relations ."}, {"doc_id": 11, "text": "similar solutions in compressible laminar free mixing\nproblems .\nthere are in supersonic aerodynamics many situations of\npractical interest wherein streams of different velocities and,\nin general, different stagnation pressures mix with one another .\nin the majority of these problems the interaction between the\ntwo streams takes place in the presence of an axial pressure\ngradient . its effect on the characteristics of the mixing may\ninfluence significantly the performances of the devices wherein\nthe phenomena cited above occur . a theoretical and\nexperimental program of research to study mixing in the presence of\naxial pressure gradients is being carried on at the polytechnic\ninstitute of brooklyn ."}, {"doc_id": 12, "text": "some structural and aerelastic considerations of high\nspeed flight .\n the dominating factors in structural design of high-speed\naircraft are thermal and aeroelastic in origin . the subject\nmatter is concerned largely with a discussion of these factors and\ntheir interrelation with one another . a summary is presented\nof some of the analytical and experimental tools available to\naeronautical engineers to meet the demands of high-speed flight\nupon aircraft structures . the state of the art with respect to\nheat transfer from the boundary layer into the structure, modes\nof failure under combined load as well as thermal inputs and\nacrothermoelasticity is discussed . methods of attacking and\nalleviating structural and aeroelastic problems of high-speed\nflight are summarized . finally, some avenues of fundamental\nresearch are suggested ."}, {"doc_id": 13, "text": "similarity laws for stressing heated wings .\n it will be shown that the differential equations for a heated\nplate with large temperature gradient and for a similar plate at\nconstant temperature can be made the same by a proper\nmodification of the thickness and the loading for the isothermal plate .\nthis fact leads to the result that the stresses in the heated plate\ncan be calculated from measured strains on the unheated plate by\na series of relations, called the /similarity laws ./ the\napplication of this analog theory to solid wings under aerodynamic\nheating is discussed in detail . the loading on the unheated analog\nwing is, however, complicated and involves the novel concept\nof feedback and /body force/ loading . the problem of stressing\na heated box-wing structure can be solved by the same analog\nmethod and is briefly discussed ."}, {"doc_id": 14, "text": "piston theory - a new aerodynamic tool for the\naeroelastician .\n representative applications are described which illustrate the\nextent to which simplifications in the solutions of high-speed\nunsteady aeroelastic problems can be achieved through the use of\ncertain aerodynamic techniques known collectively as /piston\ntheory ./ based on a physical model originally proposed by\nhayes and lighthill, piston theory for airfoils and finite wings\nhas been systematically developed by landahl, utilizing\nexpansions in powers of the thickness ratio and the inverse of the\nflight mach number m . when contributions of orders and\nare negligible, the theory predicts a point-function\nrelationship between the local pressure on the surface of a wing and the\nnormal component of fluid velocity produced by the wing's\nmotion . the computation of generalized forces in aeroelastic\nequations, such as the flutter determinant, is then always\nreduced to elementary integrations of the assumed modes of motion .\n essentially closed-form solutions are given for the bending-\ntorsion and control-surface flutter properties of typical section\nairfoils at high mach numbers . these agree well with results of\nmore exact theories wherever comparisons can be fairly made .\nmoreover, they demonstrate the increasingly important influence\nof thickness and profile shape as m grows larger, a discovery that\nwould be almost impossible using other available aerodynamic\ntools . the complexity of more practical flutter analyses-e.g., on\nthree-dimensional wings and panels-is shown to be substantially\nreduced by piston theory . an iterative procedure is outlined, by\nwhich improved flutter eigenvalues can be found through the\nsuccessive introduction of higher-order terms in and .\n other applications to unsteady supersonic problems are\nreviewed, including gust response and rapid maneuvers of elastic\naircraft . steady-state aeroelastic calculations are also discussed,\nbut for them piston theory amounts only to a slight modification\nof ackeret's formulas .\n suggestions are made regarding future research based on the\nnew aerodynamic method, with particular emphasis on areas where\ncomputational labor can be reduced with a minimum loss of\nprecision . it is pointed out that a mach number zone exists where\nthermal effects are appreciable but nonlinear viscous interactions\nmay be neglected, and that in this zone piston theory is the logical\nway of estimating air loads when analyzing aerodynamic-\nthermoelastic interaction problems ."}, {"doc_id": 15, "text": "on two-dimensional panel flutter .\n theory and experiments of the flutter of a buckled plate are\ndiscussed . it is shown that an increase in the initial deviation\nfrom flatness or a static pressure differential across the plate\nraises the critical value of the /reduced velocity ./\n the applicability of the galerkin method to the linearized\nproblem of flutter of an unbuckled plate has been questioned by\nseveral authors . in this paper the flutter condition was\nformulated in the form of an integral equation and solved numerically\nby the method of iteration and the method of matrix\napproximations, thus avoiding the constraint of assumed modes . for a\nplate (with finite bending rigidity) the results confirm those\ngiven by the galerkin method .\n an approximate analysis of the limiting form and amplitude of\nthe flutter motion for a buckled plate is presented ."}, {"doc_id": 16, "text": "transformation of the compressible turbulent boundary\nlayer .\n the transformation of the compressible turbulent boundary-\nlayer equations to their incompressible equivalent is\ndemonstrated analytically . the transformation is essentially the same\nas that for the laminar layer, first given by stewartson, except\nthat the explicit relation between the viscosity and temperature\nis not required . a key point in the analysis is the modification\nof the stream function to include a mean of the fluctuating\ncomponents and the postulate that the apparent turbulent shear,\nassociated with an elemental mass, remains invariant in the\ntransformation .\n the values of the incompressible friction coefficients and of\npressure rise causing separation thus transformed show good\nagreement with the experimentally measured and independently\nreported results . an application of the transformation to the\nself-preserving boundary layers and to the computations of\ngeneral boundary-layer flow is shown ."}, {"doc_id": 17, "text": "remarks on the eddy viscosity in compressible mixing flows .\nin connection with a study of the wakes behind bodies in hypersonic flow\ncarried out for the missile and space vehicle division of the general\nelectric company, it was desired to estimate the eddy viscosity in\naxisymmetric, compressible wakes . because of the lack of applicable\nexperimental data, it was found necessary to make such an estimate by\nrationally extending the few available data for incompressible flows to\nthe compressible case . this suggested the application and extension of\nthe transformations applied to turbulent boundary layers in reference\ninfinitesimal mass are invariant with transformation, mager showed that\nthe partial differential equations for the compressible turbulent\nboundary layer can be transformed to incompressible form . the validity of\nthis assumption and of the transformations was established for several\nboundary-layer flows by comparison with experiment ."}, {"doc_id": 18, "text": "the flow field in the diffuser of a radial compressor .\nthis note discusses the two-dimensional diffuser flow field\nin a radial compressor outside the impeller wheel . it is\nassumed that the diffuser has guide vanes arranged in a circular\nrow at a radius . the impeller wheel has the radius (see\nfig. 1) . the flow in the diffuser starts at the circle with the\nradius . the velocity components, and in the r and\ndirections of the velocity vector on this circle are prescribed\ntogether with the thermal state of the gas . the flow so prescribed\non the radius will, if no disturbances are present (i.e., no\nboundary conditions in the flow other than zero velocity at\ninfinity are to be fulfilled), develop in a spiral flow ."}, {"doc_id": 19, "text": "an investigation of the pressure distribution on conical bodies in\nhypersonic flows .\na large amount of work on conical flow fields without axial symmetry\nat supersonic speed is presently available . however, no apparent\nhypersonic approximation has yet been derived . in this note,\nexperimental data on two elliptical cones at m = 6 are presented and a\nhypersonic approach obtained from physical considerations is suggested ."}, {"doc_id": 20, "text": "generalised-newtonian theory .\n author generalizes lees's (amr 10(1957), rev. 2601)\nmodification of newtonian theory for blunt-nose bodies to apply to pointed-\nnose bodies as well . the result is expressed by\nsin where is the local inclination of the body\nsurface and the subscript /max/ refers to the maximum local\ninclination and pressure coefficient . for blunt-nose bodies\nand the generalized theory reverts to lees's blunt-nose\nmodification with given by normal shock relations . author shows,\nby comparison of newtonian and generalized-newtonian theory\nwith exact solutions, the superiority of generalized-newtonian\ntheory . he also shows that both two-dimensional and\naxisymmetric shapes are correlated by this generalization . results are\npresented in two figures that support author's generalization and\nindicate the independence of the correlation from variations in\nboth the hypersonic similarity parameter k = m(d1) and the ratio\nof specific heats y .\n reviewer believes this generalization should be of interest to\nthose engaged in development of hypersonic hardware as well as\ntheory ."}, {"doc_id": 21, "text": "on heat transfer in slip flow .\na number of authors have considered the effect of slip on the heat\ntransfer and skin friction in a laminar boundary layer over a flat plate .\nreference 1 considers this by a perturbation on the usual laminar\nboundary-layer analysis while some other studies.dash e.g., reference\nthe impulsive motion of an infinite plate ."}, {"doc_id": 22, "text": "on slip-flow heat transfer to a flat plate .\n assuming that continuum flow energy equation in a boundary\nlayer remains valid well into slip region and taking account of the\ntemperature jump in a moving rarefied gas and for influence of\nlarge mean free path through appropriate boundary conditions, a\nsolution is found for the temperature gradient in the slip region .\nthen from maslen expression (j. aero. sci. 25, 6, 400-401, june\nslipping fluid to a flat plate, and behavior confirms results for\nsmall values of knudsen number ."}, {"doc_id": 23, "text": "skin-friction and heat transfer characteristics of\na laminar boundary layer on a cylinder in axial incompressible\nflow .\n a solution is given for the case of the laminar boundary layer\nof an incompressible fluid of constant properties on the exterior\nof a cylinder with flow parallel to the cylinder axis . this case\ndiffers from the blasius solution for flow along a flat plate by\nconsidering the effect of the curvature in a plane transverse to\nthe flow direction . the local skin-friction and heat-transfer\ncoefficients for a prandtl number of 0.715 are evaluated and\ncompared to the similar magnitudes for flat plate flow, and the\neffect of the curvature is shown to be significant in some practical\ncases . recovery factors are evaluated, and this quantity is\nfound to be insensitive to the effect of curvature of the boundary ."}, {"doc_id": 24, "text": "theory of stagnation point heat transfer in dissociated\nair .\n the boundary-layer equations are developed in general for the\ncase of very high speed flight where the external flow is in a\ndissociated state . in particular the effects of diffusion and of atom\nrecombination in the boundary layer are included . it is shown\nthat at the stagnation point the equations can be reduced exactly\nto a set of nonlinear ordinary differential equations even when the\nchemical reactions proceed so slowly that the boundary layer is\nnot in thermochemical equilibrium .\n two methods of numerical solution of these stagnation point\nequations are presented, one for the equilibrium case and the\nother for the nonequilibrium case . numerical results are\ncorrelated in terms of the parameters entering the numerical\nformulation so as not to depend critically on the physical assumptions\nmade .\n for the nonequilibrium boundary layer, both catalytic (to\natom recombination) and noncatalytic wall surfaces are\nconsidered . a solution is represented which shows the transition\nfrom the /frozen/ boundary layer (very slow recombination\nrates) to the equilibrium boundary layer (fast recombination rates) .\na recombination rate parameter is introduced to interpret the\nnonequilibrium results, and it is shown that a scale factor is\ninvolved in relating the equilibrium state of a boundary layer on\nbodies of different sizes .\n it is concluded that the heat transfer through the equilibrium\nstagnation point boundary layer can be computed accurately by\na simple correlation formula and that the heat\ntransfer is almost unaffected by a nonequilibrium state of the\nboundary layer provided the wall is catalytic and the lewis\nnumber near unity ."}, {"doc_id": 25, "text": "inviscid hypersonic flow over blunt-nosed slender bodies .\n at hypersonic speeds the drag area of a blunt nose is much\nlarger than the drag area of a slender afterbody, and the energy\ncontained in the flow field in a plane at right angles to the flight\ndirection is nearly constant over a downstream distance many\ntimes greater than the characteristic nose dimension . the\ntransverse flow field exhibits certain similarity properties directly\nanalogous to the flow similarity behind an intense blast wave\nfound by g. i. taylor, s. c. lin, and a. sakurai . a comparison\nwith the experiments of hammitt, vas, and bogdonoff on a\nflat plate with a blunt leading edge at in helium shows\nthat the shock-wave shape is predicted very accurately by this\nsimilarity analysis . the predicted surface pressure distribution\nis somewhat less satisfactory . experimental results on a\nhemisphere-cylinder obtained at in the galcit air tunnel\nindicate that not only the shock-wave shape but also the surface\npressures for this body are given very closely by the similarity\ntheory, except near the hemisphere-cylinder junction .\n energy considerations combined with a detailed study of the\nequations of motion show that flow similarity is also possible for\na class of bodies of the form, provided that,\nwhere for a two-dimensional body and for a\nbody of revolution . when the shock shape is not\nsimilar to the body shape, and the entire flow field some\ndistance from the nose must depend to some extent on the details\nof the nose geometry .\n by again utilizing energy and drag considerations one finds\nthat at hypersonic speeds the inviscid surface pressures\ngenerated by a blunt leading edge are larger than the pressures\ninduced by boundary-layer growth on an insulated flat surface\nfor an insulated blunt-nosed slender body of revolution the\ncorresponding distance is given by . (here\nis free-stream reynolds number based on leading-edge\nthickness, or nose diameter .) in free flight these constants are\nreplaced by 1,700 and 20, respectively, so that viscous\ninteraction effects are important over the forward portion of a blunt-\nnosed slender body only for relatively low values of .\nhowever, /far downstream/ of the nose the inviscid over-pressure is\nsmall and viscous interaction phenomena will have to be taken\ninto account ."}, {"doc_id": 26, "text": "inviscid leading-edge effect in hypersonic flow .\ncurrent interest in the problem of inviscid-viscous\ninteraction has led to the realization of the significant effect of\nthe leading-edge thickness in hypersonic flow . the purpose\nof this note is to give an account of the downstream influence\nof the blunt leading edge on the basis of the hypersonic small\nperturbation theory ."}, {"doc_id": 27, "text": "newtonian flow theory for slender bodies .\n as an aid to the aerodynamieist in the design of air frames for\nhypersonic speeds (speeds faster than about mach 5), newtonian\nflow theory is examined from the point of view of gas dynamics\nand hypersonic small-disturbance theory . the usual theory is\nshown to result as the first approximation of an expansion valid\nfor small . a basic similarity parameter\nis introduced . a general solution\nof the first approximation for the flow past slender bodies (bodies\nwhich cause only a small disturbance to the stream) at zero angle\nof attack is given . an important condition which limits the\napplication of the theory is noted-namely, that the pressure\ncoefficient on the surface not fall to zero . the theory is then\napplied to cones and to bodies whose shape is ."}, {"doc_id": 28, "text": "a note on the explosion solution of sedov with application\nto the newtonian theory of unsteady hypersonic flow .\nan exact analytical solution of the equations of inviscid\ncompressible unsteady flow has been given by sedov (reference\nto the solution may be made through hayes and probstein) .\nthis solution is the similarity solution for a constant-energy point\nexplosion . in view of the recent work on problems of hypersonic\nflow in the limiting form of the ratio of specific heats near 1\nsolution in this limit and inquire what form such a solution would\ntake . einbinder, in a recent note, has examined the solution for\nvarious but does not mention the interesting case of .\nit may be shown that the convergence to the limit is nonuniform\nover the flow field . it is also not difficult to show that the non-\nuniform behavior exhibited here is that which one would expect\nfrom the newtonian formulation as derived in reference 3 ."}, {"doc_id": 29, "text": "a simple model study of transient temperature and thermal\nstress distribution due to aerodynamic heating .\n the present work is concerned with the determination of\ntransient temperatures and thermal stresses in simple models intended\nto simulate parts or the whole of an aircraft structure of the built-\nup variety subjected to aerodynamic heating .\n the first case considered is that of convective heat transfer\ninto one side of a flat plate, representing a thick skin, and the\neffect of the resulting temperature distribution in inducing\nthermal stresses associated with bending restraint at the plate edges .\nnumerical results are presented for the transient temperature\ndifferentials in the plate when the environment temperature first\nincreases linearly with time and then remains constant, the\nperiod of linear increase representing the time of acceleration of\nthe aircraft . corresponding thermal stress information is\npresented .\n the second case is that of the wide-flanged i-beam with\nconvective heat transfer into the outer faces of the flanges . numerical\nresults are presented for transient temperature differentials for a\nwide range of values of the applicable parameters and for an\nenvironment temperature variation as described above .\ncorresponding thermal stresses in a beam of infinite length are\ndetermined . a theoretical analysis of the stress distribution in a beam\nof finite length is carried out and numerical results obtained for\none case . an experimental investigation of temperatures and\nstresses in such a beam is described, and results are presented\nwhich indicate good agreement with corresponding theoretical\nresults ."}, {"doc_id": 30, "text": "photo-thermoelastic investigation of transient thermal\nstresses in a multiweb wing structure .\n photothermoelastic experiments were performed on a long\nmultiweb wing model for which a theoretical analysis is available in\nthe literature . the experimental procedures utilized to simulate\nthe conditions prescribed in the theory are fully described .\n correlation of theory and experiment in terms of dimensionless\ntemperature, stress, time, and biot number revealed that the\ntheory predicted values higher than the experimentally observed\nmaximum thermal stresses at the center of the web . detailed\ntemperature measurements in the flange suggested that the major\nsource of this discrepancy can be traced to the one-dimensional\nheat conduction analysis of the flange employed in the theory ."}, {"doc_id": 31, "text": "thermal buckling of supersonic wing panels .\n the temperature and thermal stress distributions are analyzed\nin multicellular supersonic wing structures . a buckling criterion\nis established for the panels of cover plates subjected to thermal\nstresses ."}, {"doc_id": 32, "text": "the dynamic motion of a missile descending through\nthe atmosphere .\n a method is presented for computing rapidly, yet accurately,\nthe dynamic motion of a ballistic-type missile descending through\nthe atmosphere . the equations of motion are separated into a\nset of /static/ trajectory equations (zero angle of attack) and a\nset of /rotational/ equations describing the oscillatory motion\nof the missile about its center of gravity . a transformation\nallows the rotational equations to be written in a manner\nanalogous to the equation for an undamped oscillating spring mass\nsystem with the mass equal to unity and a time variable spring\nconstant . for given initial conditions this equation can be\nsolved to obtain the envelope of maximum angle of attack . an\nadditional transformation allows the calculation of the complete\noscillatory motion at any time during the trajectory as a function\nof the maximum angle of attack at that time .\n this solution shows that the maximum angle of attack of a\nmissile descending through the atmosphere at relatively constant\nspeed is reduced even when the aerodynamic damping is neglected ."}, {"doc_id": 33, "text": "the prospects for magneto-aerodynamics .\n the equations describing the flow of an electrically conducting\nfluid in the presence of electric and magnetic fields are written\ndown with the aid of certain simplifications appropriate to\naeronautical applications . in order to estimate the probable\nsignificance of magneto-aerodynamic effects, some data on\nconductivity of pure and /seeded/ air are first examined .\ndimensionless quantities representing the ratios of forces and of\ncurrents are then formed and their values studied for conditions\nof flight in the atmosphere .\n some examples of magneto-hydrodynamic and magneto-\ngasdynamic effects in simple flows are given . these include\ntwo cases of poiscuille flow of conducting liquids with applied\nmagnetic fields and the case of quasi-one-dimensional gas flow\nwith applied electrical and magnetic fields . in the last case,\nattractive possibilities are found for controlled acceleration or\ndeceleration of gas at subsonic and supersonic speeds, even in\nconstant-area channels . the behavior of the flow is\ncharacteristically different in different regimes of mach number and flow\nspeed relative to certain /significant speeds/ that are dependent\non the ratio of electrical to magnetic field strengths . these\nare studied, and a chart is constructed to relate the length to\nthe speed ratio of a maximum-acceleration constant-area channel .\n it is concluded that the advantages that may accrue from\nmagneto-aerodynamic methods are sufficiently attractive to\njustify the considerable research and engineering development\nthat will be required . among the unsolved engineering problems\nare the reduction of surface resistance of electrodes in contact\nwith a conducting gas, development of techniques for seeding,\nand provision of the required magnetic fields in flight ."}, {"doc_id": 34, "text": "constant-temperature magneto-gasdynamic channel flow .\nin the course of investigating boundary-layer flow in\ncontinuous plasma accelerators with crossed electric and\nmagnetic fields, it was found advantageous to have at hand simple\nclosed-form solutions for the magneto-gasdynamic flow in the\nduct which could serve as free-stream conditions for the boundary\nlayers . nontrivial solutions of this sort are not available at\npresent, and in fact, as in the work of resler and sears, the\nvariation of conditions along the flow axis must be obtained\nthrough numerical integration .\n consequently, some simple solutions of magneto-gasdynamic\nchannel flow were sought, possessing sufficient algebraic simplicity\nto serve as free-stream boundary conditions for analytic\ninvestigations of the boundary layer in a physically reasonable accelerator .\nin particular, since the cooling of the accelerator tube is likely to\nbe an important physical problem because of the high gas\ntemperatures required to provide sufficient gaseous conductivity,\nchannel flow with constant temperature appears interesting .\nsome simple algebraic solutions for the case of a constant\ntemperature plasma are developed in the following paragraphs ."}, {"doc_id": 35, "text": "stagnation point of a blunt body in hypersonic flow .\n the purpose of this paper is to present a method of calculation\ndevised to yield all the important information on the symmetric\ninviscid hypersonic flow in the stagnation point region of a blunt\nbody . the problem is the same as that considered by hayes\nwho used a slightly different approach . it is demonstrated that\nhayes' results are valid in the stagnation point region and can\nhence be considered a basis for constructing less restricted\nsolutions .\n equations are presented giving velocity, pressure, detachment\ndistance, and vorticity . the values of shock detachment\ndistance and body pressure coefficient are compared with\nexperimental data for spheres . the pressure comparison shows that\nthe results of hayes and the theory presented herein represent a\nbetter approximation than the newtonian impact theory for\nhypersonic mach numbers .\n in conclusion, the possibility of refinements to this analysis is\ndiscussed ."}, {"doc_id": 36, "text": "supersonic flow around blunt bodies .\nthe newtonian theory of impact has been shown to be\nuseful for pressure calculations on the forward facing part\nof bodies moving at high speed . it is now a familiar practice\nto use this information to calculate nonviscous velocities at the\nwall and then to estimate rates of heat transfer . this\nprocedure is perhaps open to question,. heat-transfer rates depend\non velocity gradients which are not given by the newtonian\nanalysis . nor can one obtain information on boundary-layer\nstability or all the body stability derivatives . it seems,\ntherefore, inevitable that, as design proceeds with these hypersonic\nmissiles, there will be a greater need for more accurate\naerodynamic theories either to predict what will happen in unfamiliar\nflight conditions or to effect an extrapolation from a known test\nresult to the design condition ."}, {"doc_id": 37, "text": "a new technique for investigating heat transfer and\nsurface phenomena under hypersonic flow conditions .\non the forebody of many practically interesting hypersonic\nvehicles, there is little interaction between the inviscid\nflow field and the boundary layer . therefore, inviscid flow theory\ncan be used to determine, independent of surface phenomena,\nthe physically interesting quantities such as shock shape, shock\ndetachment distance, sonic line shape, and pressure distribution .\nfurthermore, the pressure distribution so determined can then be\nused for the study of heat transfer, materials behavior, and other\nsurface phenomena . thus, for these bodies, the prandtl\nboundary-layer concept can be utilized for the calculation of both the\ninviscid flow and the boundary-layer behavior .\n it is the purpose of this note to point out that this concept can\nalso be applied experimentally in order to provide, in\nconjunction with a conventional hypersonic wind-tunnel air supply, a\nmeans for investigating hypersonic heat transfer and surface\nphenomena under conditions of flight reynolds numbers ."}, {"doc_id": 38, "text": "on the prediction of mixed subsonic/supersonic pressure\ndistributions .\n high-speed wind-tunnel results are analyzed to derive a\nsemiempirical scheme for the prediction of transonic pressure\ndistributions . the supersonic and subsonic parts of the flow are\ntreated separately, and then linked by an empirical shock\npressure rise relation . the significance of the empirical results is\nconsidered in relation to the physical mechanism of transonic\nflows . it is also shown that theoretical solutions can be\nimproved by introducing the empirical shock relation ."}, {"doc_id": 39, "text": "on the flow of a sonic stream past an airfoil surface .\n this study of the flow about an airfoil in a near-sonic stream\nindicates the important factors determining the pressure\ndistribution on the airfoil . analysis of the mach wave pattern\nsuggests that the supersonic domain of the flow can be derived\nfrom two simple-wave flows, one arising from the mach waves\nreflected at the sonic line and the other from the changes in\nairfoil surface slope . the compressive effect of the reflected mach\nwaves is determined quantitatively as a function of airfoil\nleading-edge geometry from an analysis of measured pressure\ndistributions for uncambered airfoils,. and it is shown how this can\nbe superimposed on the wave system from the curved surface to\ngive an equivalent simple-wave flow over the airfoil .\n an application of this scheme to the calculation of the pressure\ndistribution over an airfoil in a sonic stream gives results in good\nagreement with experiment ."}, {"doc_id": 40, "text": "experiments on boundary layer transition at\nsupersonic speeds .\n tests were conducted in the 12-in. continuous supersonic wind\ntunnel of the jet propulsion laboratory, california institute of\ntechnology, to determine the effects of surface cooling on\nboundary-layer transition at supersonic speeds . the effects of\ncooling were investigated at test section mach numbers of 1.97,\nsmooth cone in the presence of three levels of supply-stream\nturbulence (0.4, 2, and 9 per cent) and several single-element\nroughnesses at fixed axial location . transition data were obtained\noptically by means of a magnified-schlieren system . the results,\nfor the range of mach number investigated, indicate that (1)\ntransition on a smooth cone can definitely be delayed by surface\ncooling, (2) transition promoted by either supply-stream\nturbulence or surface roughness can also be delayed by surface cooling\ndepending upon degree of turbulence or relative roughness\nrespectively, and (3) the adverse effects of increased turbulence and\nroughness decrease with increasing mach number ."}, {"doc_id": 41, "text": "on transition experiments at moderate supersonic speeds .\n studies of transition over a flat plate at mach number 1.76\nwere carried out using a hot-wire anemometer as one of the\nprincipal tools . the nature and measurements of free-stream\ndisturbances at supersonic speeds are analyzed . the\nexperimental results are interpreted in the light of present overall\ninformation on transition at supersonic speeds and conclusions as\nto further fruitful experiments are drawn ."}, {"doc_id": 42, "text": "the gyroscopic effect of a rigid rotating propeller\non engine and wing vibration modes .\n in many wing vibration analyses it is found necessary to take\ninto account the effect of flexibly mounted engines . hence,\nit is reasonable to ask what vibratory gyroscopic effect this\nflexibility may give rise to when propellers are whirling . an engine\nmount may be thought of as a horizontal beam cantilevered\nfrom the wing, having both horizontal and vertical flexibility .\nif this beam were infinitely rigid horizontally, then, when it\nvibrated, the gyroscopic moments induced in the propeller due\nto the resultant pitching motion of its axis would not produce\npropeller axis yaw . however, engine-mount lateral stiffness\ntical stiffness, so that gyroscopic effects will play a role as the\npropeller axis undergoes pitching vibrations at the tip of the\ncantilever engine mount . the purpose of this paper is to\ninvestigate this role under the assumption that the propeller itself\nis a rigid disc .\n the paper is divided into four parts . part (1) deals briefly\nwith classical gyroscope theory . part (2) presents engine\nvibration mode studies-experimental photographic techniques on a\nmodel gyroscope mounted at the ends of two different cantilever\nbeams . part (3) presents the theory of the coupled motion of\nan elastic wing upon which a gyroscope is mounted to simulate\nan engine-propeller system on an airplane . part (4) consists\nof an example of the theory of part (3), in which, by taking\nwhat are thought to be reasonable parameters, results are\nobtained showing how the whirling of a rigid propeller may\nmaterially affect wing normal mode shapes and frequencies ."}, {"doc_id": 43, "text": "the relation between wall temperature and the effect\nof roughness on boundary layer transition .\nthe experimentally demonstrated rise and subsequent\nfall of transition reynolds number with decreasing wall-\nto-ambient temperature ratio has been the subject of two recent\nnotes . in both cases it was argued that the increased\neffectiveness of roughness due to wall cooling was not sufficient to\nexplain the transition-reversal phenomenon on nominally smooth\nbodies . in one case, the criterion for transition reversal was\ntaken to be and in the other values of as low as\neter is a reynolds number formed from velocity and\nkinematic viscosity based on calculated conditions at the height of\nroughness element k in the undisturbed, laminar boundary layer\nat the station of roughness location . the present note is\nsubmitted to show that another method for evaluating the effect\nof roughness on transition leads to an opposite conclusion ."}, {"doc_id": 44, "text": "tip-bluntness effects on cone pressures at m=6.85 .\nthere is, at present, considerable interest in the\ncharacteristies of blunted bodies from both an aerodynamic and a\nheat-transfer standpoint . the use of blunt shapes is\ncontemplated to reduce the heat-transfer problem at body noses, but\nthere are also applications for blunt noses which occur from\nmainly aerodynamic considerations . an actual reduction in\ndrag may be the beneficial result of blunting the nose of a cone\nor a similar slender shape under certain conditions . although\nthe sphere has received considerable treatment, the nose shapes\nare not necessarily tangent spheres . in the case, let us say, of a\ntotal head tube situated in the nose of a given body, the blunting\nmay be quite flat, and nose sections blunter than spherical shape\nmay conceivably be desirable, in some cases, from the heat-\ntransfer standpoint .\n the purpose of the present investigation is to examine the\naerodynamic effect of a simple type of nose blunting on a basic\nbody .\nthe incompressible flow of an electrically conducting fluid\npast a porous plate y = 0 with constant suction velocity in\nthe presence of a transverse uniform strength has recently\nbeen investigated by gupta . in this note, the problem is\ngeneralized to take into account the effect of free convection, when a\nbody force g per unit mass is acting in the negative x-direction\nparallel to the wall . the fluid is assumed to be semi-\nincompressible as usual . in addition to the obvious practical\nsignificance, this problem is also interesting in the sense that it\nprovides another exact solution of the magnetohydrodynamic\nequations, since the only electromagnetic assumptions involved\nare constant properties and freedom from excessive charges ."}, {"doc_id": 45, "text": "an investigation of separated flows, part ii: flow\nin the cavity and heat transfer .\n the first portion of this paper describes studies of the internal\nstructure of the separated flow in a notch at a free-stream mach\nnumber of 3 . observations include.. flow visualization, spark-\nschlieren pictures of the fluctuations of the free shear layer, and\nstudies of the diffusion of heat from sources placed in the\nseparated region . the second part describes measurements of local\nheat transfer to the wall .\n the external mach number, the length-to-depth ratio of the\ncavity, the ratio of the oncoming boundary layer thickness to the\nnotch depth (in the turbulent flow region), the thermal\nto-momentum thickness ratio of the boundary layer and, finally,\nthe geometry of the internal boundary of the separated region\nare varied as systematically as possible . on the basis of these\nobservations, a simple model of the flow in and the heat transfer\nacross the separated region is formulated ."}, {"doc_id": 46, "text": "some comments on the inversion of certain large matrices .\nthe subject of matric structural analysis has been treated in two\nrecently published papers in the journal . the authors of these papers\nhave made a number of statements about the inversion of certain large\nmatrices . it is the purpose of this note to bring to the attention of\nthe reader certain facts that shed new light on this important problem .\nit is shown here that the situation is not as hopeless as the above-\nmentioned authors intimate ."}, {"doc_id": 47, "text": "analysis of low-aspect-ratio aircraft structures .\n two methods are presented for the analysis of complex low-\naspect-ratio aircraft structures . both methods provide for\narbitrary external loading, are general with respect to the\norientation of structural members, and permit arbitrary boundary\nconditions . for purposes of analysis a structure is idealized as a\nnetwork of flexural members with interconnected torsion boxes .\n in the first method, sets of linear equations are obtained by\nexpressing boundary conditions, member deflection equations,\nequilibrium requirements, and slope-compatibility relationships\nin terms of deflections and internal forces . the solution for\ndeflections and internal forces is then formed as the product of an\ninverse structural matrix and a column matrix of load functions .\n in the second method, the conditions at a given boundary are\nassembled as a column matrix and are transferred in a step\nby-step fashion over the entire structure to an opposite boundary .\nthe transfer is accomplished by successive multiplications of\nsquare matrices composed independently for the different\ntransfer ranges . the final operation is the inversion of a relatively\nsmall matrix and provides the solution for the unknown boundary\nconditions .\n comparisons of theoretical results with experimental data and\nelectric-analog solutions are favorable ."}, {"doc_id": 48, "text": "supersonic flow at the surface of a circular cone at\nangle of attack .\n formulas for the inviscid flow properties on the surface of a\ncone at angle of attack are derived for use in conjunction with\nthe m.i.t. cone tables . these formulas are based upon an\nentropy distribution on the cone surface which is uniform and\nequal to that of the shocked fluid in the windward meridian\nplane . they predict values for the flow variables which may\ndiffer significantly from the corresponding values obtained\ndirectly from the cone tables . the differences in the magnitudes\nof the flow variables computed by the two methods tend to\nincrease with increasing free-stream mach number, cone angle\nand angle of attack ."}, {"doc_id": 49, "text": "temperature and velocity profiles in the compressible\nlaminar boundary layer with arbitrary distribution\nof surface temperature .\n an analysis is presented which enables the temperature\nprofiles, veiocity profiles, heat transfer, and skin friction to be\ncalculated for laminar flow over a two-dimensional or axially\nsymmetric surface without pressure gradient but with an arbitrary\nanalytic distribution of surface temperature . the general theory is\napplicable to a gas of any prandtl number, although the\nnumerical results given herein have been computed for air .\nthe predictions of the theory for the special case of constant\nsurface temperature are compared with the calculations of crocco .\non the basis of this comparison, it is inferred that the present\ntheory enables heat-transfer and skin-friction calculations\naccurate to within about 5 per cent to be made for flight conditions\nup to mach numbers near 5 and to within about 1 or 2 per cent\nfor supersonic wind-tunnel conditions up to considerably higher\nmach numbers .\n a particular effort has been made to present the results, which\nare simple considering their generality, in a form that can be used\nreadily in practical applications . from the mathematical point\nof view, the theory is applicable to an arbitrary analytic\ndistribution of surface temperature, but in any given practical case it is\nnecessary that the surface-temperature distribution be\napproximated by a polynomial . the only unknowns in the final\nequations developed are the coefficients of this polynomial, so that the\nwork involved in applying the theory in any given case depends\nentirely on the work involved in approximating a given surface-\ntemperature distribution by a polynomial .\n an example is worked out in detail which illustrates some of the\nprincipal effects of variable surface temperature . it is shown\nthat both positively infinite and negatively infinite heat-transfer\ncoefficients can occur . the anomaly of infinite and negative\nheat-transfer coefficients is discussed and attributed to the\ncustomary definition of the heat-transfer coefficient, which is shown\nto be fundamentally inappropriate for flows with variable surface\ntemperature . in the particular example considered, a\nconventional method for calculating the net heat transferred yields\ncompletely incorrect results . a brief qualitative discussion of the\npossible effects of the heat transfer on flow separation is given .\nin order to facilitate the use of the results, all of the principal\nequations developed are collected and summarized in the section\nentitled /practical use of results ./"}, {"doc_id": 50, "text": "investigation of laminar boundary layer in compressible\nfluids using the crocco method .\n in the present investigation of the flow of air in a thin laminar\nboundary layer on a flat plate, the crocco method has been used to solve\nthe simultaneous differential equations of momentum and energy involved\nin such flow . the crocco method was used because it gave accurate\nresults for arbitrary prandtl number near unity . the prandtl number\nwas taken at 0.75, the specific heat was held constant, and the\nsutherland law of viscosity-temperature variation was assumed to\nrepresent the viscosity data starting with an initial ambient\ntemperature of -67.6 f . the main results presented here are the\nskin-friction and heat-transfer coefficients as functions of reynolds number,\nmach number, and wall-to-free-stream temperature ratio . variations of\nshear, velocity, temperature, and mach number across the boundary layer\nare included . the crocco method is discussed in detail ."}, {"doc_id": 51, "text": "theory of aircraft structural models subjected to aerodynamic\nheating and external loads .\n the problem of investigating the simultaneous effects of transient\naerodynamic heating and external loads on aircraft structures for the\npurpose of determining the ability of the structure to withstand flight\nto supersonic speeds is studied . by dimensional analyses it is shown\nthat ..\nconstructed of the same materials as the aircraft will be thermally\nsimilar to the aircraft with respect to\nthe flow of heat through the structure\nwill be similar to those of the aircraft when the structural model is\nconstructed at the same temperature as the aircraft .\nexternal loads will be similar to those of the aircraft .\nsubjected to heating and cooling that correctly simulate the aerodynamic\nheating of the aircraft, except with respect to angular velocities and\nangular accelerations, without requiring determination of the heat flux\nat each point on the surface and its variation with time .\nacting on the aerodynamically heated structural model to those acting\non the aircraft is determined for the case of zero angular velocity and\nzero angular acceleration, so that the structural model may be subjected\nto the external loads required for simultaneous simulation of stresses\nand deformations due to external loads ."}, {"doc_id": 52, "text": "procedure for calculating flutter at high supersonic\nspeed including camber deflections, and comparison\nwith experimental results .\n a method which may be used at high supersonic mach numbers is\ndescribed for calculating the flutter speed of wings having camber in\ntheir deflection modes . the normal coupled vibration modes of the wing\nare used to derive the equations of motion . chord deflections of the\nvibration modes are approximated by polynomials . the wing may have a\ncontrol surface and may carry external stores although no aerodynamic\nforces on the stores are presented . the aerodynamic forces that are\nassumed to be acting on the wing are obtained from piston theory and\nalso from a quasi-steady form of a theory for two-dimensional steady\nflow . airfoil shape and thickness effects are taken account of in the\nanalysis .\n the method is used to calculate the flutter speed of some wings\nwhich had been previously tested at mach numbers of 1.3 to 3.0 .\ncomparison of the calculations and experiment is made for flat-plate 60\nand 45 delta wings and also for an untapered 45 sweptback wing ."}, {"doc_id": 53, "text": "transition reynolds numbers of separated flows at\nsupersonic speeds .\n experimental research has been conducted on the effects of wall\ncooling, mach number, and unit reynolds\nnumber on the transition reynolds\nnumber of cylindrical separated boundary\nlayers on an ogive-cylinder model .\nresults were obtained from pressure and temperature measurements and\nshadowgraph observations . the maximum\nscope of measurements encompassed\nmach numbers between 2.06 and 4.24, reynolds numbers (based on length of\nseparation) between 60,000 and 400,000,\nand ratios of wall temperature to\nadiabatic wall temperature between 0.35 and 1.0 .\nwithin the range of the\npresent tests, the transition reynolds number was observed to decrease\nwith increasing wall cooling, increase with increasing mach number, and\nincrease with increasing unit reynolds number . the wall-cooling effect\nwas found to be four times as great when the attached boundary layer\nupstream of separation was cooled in conjunction with cooling of the\nseparated boundary layer as when only the separated boundary layer was\ncooled . wall cooling of both the\nattached and separated flow regions also\ncaused, in some cases, reattachment in the otherwise separated region .\ncavity resonance present in the separated region for some model\nconfigurations was accompanied by a large decrease in transition reynolds\nnumber at the lower test mach numbers ."}, {"doc_id": 54, "text": "method for calculation of compressible laminar boundary\nlayer characteristics in axial pressure gradient with\nzero heat transfer .\n the karman-pohlhausen method is extended primarily to sixth-degree\nvelocity profiles for determining\nthe characteristics of the compressible\nlaminar boundary layer over an adiabatic\nwall in the presence of an axial\npressure gradient . it is assumed that the prandtl number is unity and\nthat the coefficient of viscosity varies linearly with the temperature .\na general approximate solution which permits a rapid determination of\nthe boundary-layer characteristics for any given free-stream mach number\nand given velocity distribution at the outer edge of the boundary layer\nis obtained . numerical examples indicate that this solution will in\npractice lead to results of satisfactory\naccuracy, including the critical\nreynolds number for stability . for the special purpose of calculating\nthe location of the separation point in an adverse pressure gradient, a\nshort and simple method, based on the use of a seventh-degree velocity\nprofile, is derived . the numerical example given here indicates that\nthis method should in practice lead to sufficiently accurate results .\nfor the special case of flow near a forward stagnation point it is shown\nthat the karman-pohlhausen method with the usual fourth-degree profiles\nleads to results of adequate accuracy, even for the critical reynolds\nnumber ."}, {"doc_id": 55, "text": "separation, stability and other properties of compressible\nlaminar boundary layer with pressure gradient and heat\ntransfer .\n a theoretical study is made of the effect of pressure gradient,\nwall temperature, and mach number on laminar boundary-layer\ncharacteristics and, in particular, on the skin-friction and heat-transfer\ncoefficients, on the separation point in an adverse pressure gradient,\non the wall temperature required for complete stabilization of the\nlaminar boundary layer, and on the minimum critical reynolds number for\nlaminar stability . the prandtl number is assumed to be unity and the\ncoefficient of viscosity is assumed to be proportional to the\ntemperature, with a factor arising from the sutherland relation . a simple and\naccurate method of locating the separation point in a compressible flow\nwith heat transfer is developed . numerical examples to illustrate the\nresults in detail are given throughout ."}, {"doc_id": 56, "text": "an analysis of the applicability of the hypersonic\nsimilarity law to the study of the flow about bodies\nof revolution at zero angle of attack .\n the hypersonic similarity law as derived by tsien has been\ninvestigated by comparing the pressure distributions along bodies of\nrevolution at zero angle of attack . in making\nthese comparisons, particular\nattention was given to determining the limits of mach number and fineness\nratio for which the similarity law applies . for the purpose of this\ninvestigation, pressure distributions\ndetermined by the method of\ncharacteristics for ogive cylinders for\nvalues of mach numbers and fineness\nratios varying from 1.5 to 12 were compared .\npressures on various cones\nand on cone cylinders were also compared in this study .\n the pressure distributions presented demonstrate that the hypersonic\nsimilarity law is applicable over a\nwider range of values of mach numbers\nand fineness ratios than might be expected from the assumptions made in\nthe derivation . this is significant since within the range of\napplicability of the law a single pressure\ndistribution exists for all similarly\nshaped bodies for which the ratio of\nfree-stream mach number to fineness\nratio is constant . charts are presented\nfor rapid determination of\npressure distributions over ogive cylinders for any combination of mach\nnumber and fineness ratio within defined limits ."}, {"doc_id": 57, "text": "applicability of the hypersonic similarity rule to\npressure distributions which include the effects of\nrotation for bodies of revolution at zero angle of\nattack .\n the analysis of technical note 2250, 1950, is extended to include\nthe effects of flow rotation . it is\nfound that the theoretical pressure\ndistributions over ogive cylinders can be related by the hypersonic\nsimilarity rule with sufficient accuracy for most engineering purposes .\n the error introduced into pressure distributions and drag of ogive\ncylinders by ignoring the rotation term in the characteristic equations\nis investigated . it is found that\nthe influence of the rotation term on\npressure distribution and drag depends only upon the similarity\nparameter k (mach number divided by fineness ratio) .\nalthough the error in\ndrag, due to neglect of the rotation term, is negligible at k=0.5, the\nerror is about 30 percent at k=2.0 .\n charts are presented for the rapid determination of pressure\ndistributions for rotational flow over\nogive cylinders for all values of\nthe similarity parameter between 0.5 and\nof mach number and fineness ratio ."}, {"doc_id": 58, "text": "pressure measurements on sharp and blunt 5 and 15 half-angle\ncones at mach number 3.86 and angles of attack to\n100 .\n measured pressure distributions on cones are compared with modified\nnewtonian theory . deviations as large as 14 percent of the stagnation\npressure behind a normal shock are found .\nby combining empirical results\nfor cylinders normal to the flow with\nnewtonian concepts, a method of\ncalculating pressures on cones at high angles\nof attack is developed .\ncalculations by this method differ from the\nexperimental results on sharp cones\nby only 2 percent of the stagnation\npressure behind a normal shock . for\nblunted cones, additional deviations\nup to 8 percent are noted near the\nnose .\n schlieren pictures of the flow show an attached shock on the sharp\nof attack . detachment of the shock\nappears to be associated with the\nattainment of sonic speed immediately\nbehind the shock .\n an orifice size effect is found which can increase the indicated\npressure above the true value, if\nthe orifice width is greater than\none-tenth the local radius of curvature ."}, {"doc_id": 59, "text": "tables of exact laminar-boundary layer solutions when\nthe wall is porous and fluid properties are variable .\n the three partial differential equations of the laminar boundary\nlayer for two-dimensional steady-state compressible flow have been\ntransformed into two ordinary differential equations by the method of\npohlhausen, falkner, and skan . the ordinary equations include\nparameters for expressing the simultaneous effects of pressure gradient in\nthe main-stream flow through a porous wall and property changes in the\nfluid due to large temperature differences between the wall and the\nfree stream .\n a total of 58 cases have been solved numerically by the method of\npicard . the euler number (nondimensional pressure-gradient parameter)\nranges in value from 1 (stagnation-point value) to the negative values\nfound at the laminar separation points . three rates of flow through\nthe porous wall were considered (including the impermeable case where\nthe flow rate is 0) . five temperature ratios (stream temperature\ndivided by wall temperature) were used .. the uncooled and unheated\ncase (temperature ratio of 1), two cooled cases (temperature ratios of\nture ratios of and ) . velocity, weight-flow, and temperature\ndistributions are tabulated as are the dimensionless stream function of\nfalkner and skan and its derivatives and the dimensionless temperature\nfunction of pohlhausen and its derivatives .\n for each case, displacement, momentum, and convection thicknesses,\nas well as nusselt number and coefficient of friction at the wall, were\ncomputed ."}, {"doc_id": 60, "text": "estimation forces and moments due to rolling for several\nslender tail configurations at supersonic speeds .\n the velocity potentials, span loadings, and corresponding force\nand moment derivatives have been theoretically evaluated for a number\nof slender-tail arrangements performing a steady rolling motion at\nsupersonic speeds .\n the method of analysis is based upon an application of\nconformal-transformation techniques . the utilization of these techniques allows\nthe simple determination of the complex potentials for various types\nof two-dimensional boundary-value problems .\n in addition, two simple and often-used approximations to the\nrolling derivatives have been compared with the corresponding exact\nvalues determined by the method presented in this report .\n in order to show the importance of wing-tail interference, the\neffect of the flow field behind a rolling wing on the tail\ncharacteristics has been illustrated for a simple wing-tail arrangement ."}, {"doc_id": 61, "text": "on flow of electrically conducting fluids over a flat\nplate in the presence of a transverse magnetic field .\n the use of a magnetic field to control the motion of electrically\nconducting fluids is studied . the boundary-layer solutions are found\nfor flow over a flat plate when the magnetic field is fixed relative to\nthe plate or to the fluid . the\nequations are integrated numerically for\nthe effect of the transverse magnetic\nfield on the velocity and temperature\nprofiles, and hence, the skin friction and rate of heat transfer .\n it is concluded that the skin friction and the heat-transfer rate are\nreduced when the transverse magnetic\nfield is fixed relative to the plate\nand increased when fixed relative to the fluid . the total drag is\nincreased in all the cases studied ."}, {"doc_id": 62, "text": "similar solutions for the compressible laminar boundary\nlayer with heat transfer and pressure gradient .\n stewartson's transformation is applied to the laminar compressible\nboundary-layer equations and the\nrequirement of similarity is introduced,\nresulting in a set of ordinary nonlinear differential equations\npreviously quoted by stewartson, but unsolved . the requirements of the\nsystem are .. prandtl number of 1.0, linear viscosity-temperature\nrelation across the boundary layer, an\nisothermal surface, and the particular\ndistributions of free-stream velocity\nconsistent with similar solutions .\nthis system admits axial pressure\ngradients of arbitrary magnitude, heat\nflux normal to the surface, and arbitrary mach numbers .\n the system of differential equations is transformed to an integral\nsystem, with the velocity ratio as\nthe independent variable . for this\nsystem, solutions are found for pressure gradients varying from that\ncausing separation to the infinitely favorable gradient and for wall\ntemperatures from absolute zero to twice the free-stream stagnation\ntemperature . some solutions for separated flows are also presented .\n for favorable pressure gradients, the solutions are unique . for\nadverse pressure gradients, where the solutions are not unique, two\nsolutions of the infinite family of possible solutions are identified as\nessentially viscid at the outer edge of the boundary layer and the\nremainder essentially inviscid . for\nthe case of favorable pressure gradients\nwith heated walls, the velocity within\na portion of the boundary layer is\nshown to exceed the local external velocity .\nthe variation of a reynolds\nanalogy parameter, which indicates the ratio of skin friction to heat\ntransfer, is from zero to 7.4 for a surface of temperature twice the\nfree-stream stagnation temperature, and from zero to 2.8 for a surface\nheld at absolute zero where the value 2 applies to a flat plate ."}, {"doc_id": 63, "text": "hypersonic viscous flow over slender cones .\n viscous self-induced pressures on 3 -semivertex-angle cones were\nmeasured over the range 3.7 free-stream mach number 5.8 and 0.5\nviscous-interaction parameter 2.3 . the data were found to be in good\nagreement with results obtained by talbot on 5 cones in the range\nrameter 3.5 . all these data were correlated reasonably well by the\nviscous-interaction parameter, which is defined as\nwhere and are the mach number and reynolds number based on\nideal taylor-maccoll flow conditions and c is the chapman-rubesin\nfactor .\n a new method for calculating self-induced pressures is presented\nwhich takes into account the interaction between boundary-layer growth\nand the inviscid-flow field at the outer edge of the boundary layer .\npressures calculated by this method were only 10 to 20 percent higher\nthan the measured values ."}, {"doc_id": 64, "text": "unsteady oblique interaction of a shock wave with plane\ndisturbances .\n analysis is made of the flow field produced by oblique impingement\nof weak plane disturbances of arbitrary\nprofile on a plane normal shock .\nthree types of disturbance are considered ..\nmoves . the sound wave refracts either\nas a simple isentropic sound wave\nor as an attenuating isentropic pressure wave, depending on the angle\nbetween the shock and the incident\nsound wave . a stationary vorticity\nwave of constant pressure appears behind the shock .\nreflects as a sound wave, and a stationary vorticity wave is produced .\nthe shock . the incident wave refracts as a stationary vorticity wave,\nand either a sound wave or attenuating pressure wave is also produced .\n computations are presented for the first two types of incident wave,\nover the range of incidence angles, for shock mach numbers of 1, 1.5,\nand ."}, {"doc_id": 65, "text": "convection of a pattern of vorticity through a shock\nwave .\n an arbitrary weak spatial distribution of vorticity can be\nrepresented in terms of plane sinusoidal shear waves of all orientations and\nwave lengths (fourier integral) . the analysis treats the passage of a\nsingle representative weak shear wave through a plane shock and shows\nrefraction and modification of the shear wave with simultaneous\ngeneration of an acoustically intense sound\nwave . applications to turbulence\nand to noise in supersonic wind tunnels are indicated ."}, {"doc_id": 66, "text": "some effects of joint conductivity on the temperature\nand thermal stresses in aerodynamically heated skin-stiffener\ncombinations .\n temperatures and thermal stresses in typical skin-stiffener\ncombinations of winglike structures subjected to aerodynamic heating have\nbeen obtained with the aid of an electronic differential analyzer .\nvariations were made in an aerodynamic\nheat-transfer parameter, in a joint\nconductivity parameter, and in the ratio\nof skin width to skin thickness .\nthe results, which are presented in nondimensional form, indicate that\ndecreasing the joint conductivity parameter lowers both the interior\nand the average temperature ratios, increases the peak thermal stress\nratios in the skin, and may considerably increase the peak stiffener\nstress ratios,. increasing the aerodynamic heat-transfer parameter\ndecreases the interior and average temperature ratios, increases the\npeak skin stress ratios somewhat,\nbut greatly increases the peak\nstiffener stress ratios,. and increasing the ratio of skin width to skin\nthickness produces only moderate decreases in the peak skin stress\nratios while moderately increasing the peak stiffener stress ratios ."}, {"doc_id": 67, "text": "dynamic stability of vehicles traversing ascending\nor descending paths through the atmosphere .\n an analysis is given of the oscillatory motions of vehicles which\ntraverse ascending and descending paths through the atmosphere at high\nspeed . the specific case of a skip path is examined in detail, and\nthis leads to a form of solution for the oscillatory motion which should\nrecur over any trajectory . the distinguishing feature of this form is\nthe appearance of the bessel rather than the trigonometric function as\nthe characteristic mode of oscillation ."}, {"doc_id": 68, "text": "some aspects of air-helium simulation and hypersonic\napproximations .\n some illustrations of the differences that may be expected between\nresults obtained in hypersonic wind tunnels that employ air and results\nobtained in those that employ helium as the test medium (imperfect-gas\neffects are not considered) are compiled and presented herein . simple\nexpressions are presented that demonstrate the possibility of simulating\nair results in helium tests and of transforming helium data to\nequivalent air data . nonviscous and viscous simulations are considered . in\nmost cases, the methods and the general forms of the expressions for\nsimulation that are derived are applicable to any two ideal gases having\ndifferent ratios of specific heats ."}, {"doc_id": 69, "text": "predicted shock envelopes about two types of vehicles\nat large angles of attack .\n methods based on oblique- and normal-shock relationships and the\ncontinuity of mass flow through suitably chosen volume elements between\nthe shock and body were developed to predict shock envelopes about two\ntypes of vehicles being considered for atmosphere entry . one type is a\nhigh-drag capsule shape . the other type is essentially a slender\ntriangular wing capable of providing high lift or high drag, depending on\nthe angle of attack . predicted and measured shock envelopes were\ncompared for a mach number range of 3 to 15 for vehicles at high angles of\nattack,. good agreement was found . most of the available experimental\ndata were in a speed and temperature range in which no important\nreal-gas effects occurred ."}, {"doc_id": 70, "text": "a study of flow changes associated with airfoil section\ndrag rise at supercritical speeds .\n a study of experimental pressure distributions and section\ncharacteristics for several moderately thick airfoil sections was made . a\ncorrelation appears to exist between the drag-divergence mach number\nand the free-stream mach number for which sonic velocity occurs at the\nairfoil crest, the chordwise station at which the airfoil surface is\ntangent to the free-stream direction . it was found that, since the\nmach number for which sonic velocity occurs at the airfoil crest can be\nestimated satisfactorily by means of the prandtl-glauert rule, a method\nis provided whereby the drag-divergence mach number of an airfoil\nsection at a given angle of attack can be estimated from the low-speed\npressure distribution and the airfoil profile . this method was used\nto predict with a reasonable degree of accuracy the drag-divergence\nmach number of a considerable number of airfoil sections having diverse\nshapes and a wide range of thickness-chord ratios .\n the pressure distributions and section force characteristics of\nseveral moderately thick airfoil sections at mach numbers above the\ndrag-divergence mach number were analyzed . some of the characteristics\nof the flow over these airfoils at supercritical mach numbers are\ndiscussed ."}, {"doc_id": 71, "text": "laminar boundary layer behind shock advancing into\nstationary fluid .\n a study was made of the laminar compressible boundary layer induced\nby a shock wave advancing into a stationary fluid bounded by a wall .\nfor weak shock waves, the boundary layer is identical with that which\noccurs when an infinite wall is impulsively set into uniform motion\nshocks .\n velocity and temperature profiles, recovery factors, and\nskin-friction and heat-transfer coefficients are tabulated for a wide range\nof shock strengths ."}, {"doc_id": 72, "text": "boundary layer behind shock or thin expansion wave\nmoving into stationary fluid .\n the boundary layer behind a shock or thin expansion wave advancing\ninto a stationary fluid has been determined . laminar and turbulent\nboundary layers were considered . the wall surface temperature behind\nthe wave was also investigated . the assumption of a thin expansion\nwave is valid for weak expansions but becomes progressively less\naccurate for strong expansion waves .\n the laminar-boundary-layer problem was solved by numerical\nintegration except for the weak wave case,\nwhich can be solved analytically .\nintegral (karman-pohlhausen type)\nsolutions were also obtained to provide\na guide for determining expressions\nwhich accurately represent the\nnumerical data . analytical expressions\nfor various boundary-layer parameters\nare presented which agree with the\nnumerical integrations within 1 percent .\n the turbulent-boundary-layer problem was solved using integral\nmethods similar to those employed for the\nsolution of turbulent compressible\nflow over a semi-infinite flat plate .\nthe fluid velocity, relative to\nthe wall, was assumed to have a\nseventh-power profile . the blasius\nequation, relating turbulent skin friction\nand boundary-layer thickness, was\nutilized in a form which accounted for compressibility .\n consideration of the heat transfer to the wall permitted the wall\nsurface temperature, behind the wave,\nto be determined . the wall\nthickness was assumed to be greater than the\nwall thermal-boundary-layer\nthickness . it was found that the wall\ntemperature was uniform (as a\nfunction of distance behind the wave)\nfor the laminar-boundary-layer case\nbut varied with distance for the turbulent-boundary-layer case ."}, {"doc_id": 73, "text": "investigation of the stability of the laminar boundary\nlayer in a compressible fluid .\n in the present report the stability of two-dimensional laminar\nflows of a gas is investigated by the method of small perturbations .\nthe chief emphasis is placed on the case of the laminar boundary layer .\n part 1 of the present report deals with the general mathematical\ntheory . the general equations governing one normal mode of the small\nvelocity and temperature disturbances are derived and studied in great\ndetail . it is found that for reynolds numbers of the order of those\nencountered in most aerodynamic problems, the temperature disturbances\nhave only a negligible effect on those particular velocity solutions\nwhich depend primarily on the viscosity coefficient (/viscous\nsolutions/) . indeed, the latter are actually of the same form in the\ncompressible fluid as in the incompressible fluid, at least to the first\napproximation . because of this fact, the mathematical analysis is\ngreatly simplified . the final equation determining the characteristic\nvalues of the stability problem depends on the /inviscid solutions/ and\nthe function of tietjens in a manner very similar to the case of the\nincompressible fluid . the second viscosity coefficient and the\ncoefficient of heat conductivity do not enter the problem,. only the\nordinary coefficient of viscosity near the solid surface is involved .\n part 2 deals with the limiting case of infinite reynolds numbers .\nthe study of energy relations is very much emphasized . it is shown\nthat the disturbance will gain energy from the main flow if the gradient\nof the product of mean density and mean vorticity near the solid surface\nhas a sign opposite to that near the outer edge of the boundary layer .\n a general stability criterion has been obtained in terms of the\ngradient of the product of density and vorticity, analogous to the\nrayleigh-tollmien criterion for the case of an incompressible fluid .\nif this gradient vanishes for some value of the velocity ratio of the\nmain flow exceeding 1-1/m (where m is the free stream mach number) ."}, {"doc_id": 74, "text": "an experimental study of the turbulen coundary layer\non a shock tube wall .\n interferometric measurements were made of the density profiles of\nan unsteady turbulent boundary layer on the flat wall of a shock tube .\nthe investigation included both subsonic and supersonic flow (mach\nnumbers of 0.50 and 1.77) with no pressure gradient and with heat transfer\nto a cold wall . velocity profiles and average skin-friction\ncoefficients were calculated . effects on the velocity profile of\nsurface roughness and flow length are examined ."}, {"doc_id": 75, "text": "studies of structural failure due to acoustic loading .\n some discussion of the acoustic fatigue problem of aircraft\nstructures is given along with data pertaining to the acoustic inputs from\nsome powerplants in common use . comparisons are given for results of\nsome fatigue tests of flat panels and cantilever beams exposed to both\nrandom- and discrete-type inputs . in this regard it appears that both\nthe stress level of the test and the type of model are significant,.\nhence, no generalization can be made at this time . with regard to\nincreasing the fatigue life, it was noted that increased stiffening of\na panel due to curvature and pressure differential is particularly\nbeneficial ."}, {"doc_id": 76, "text": "flight measurement of wall pressure fluctuations and\nboundary-layer turbulence .\n the results are presented for a flight test program using a fighter\ntype jet aircraft flying at pressure altitudes of 10,000, 20,000, and\napparatus was used to measure and record the output of microphones and\nhot-wire anemometers mounted on the forward-fuselage section and wing of\nthe airplane . mean-velocity profiles in the boundary layers were\nobtained from total-pressure measurements .\n the ratio of the root-mean-square fluctuating wall pressure to the\nfree-stream dynamic pressure is presented as a function of reynolds\nnumber and mach number . the longitudinal\ncomponent of the turbulent-velocity\nfluctuations was measured, and the turbulence-intensity profiles are\npresented for the wing and forward-fuselage section .\n in general, the results are in agreement with wind-tunnel\nmeasurements which have been reported in the literature . for example, the\nvariation of (is the root mean square of the wall-pressure\nfluctuation, and q is the free-stream dynamic pressure) with reynolds\nnumber was found to be essentially constant for the forward\nfuselage-section boundary layer, while variations at the wing station were\nprobably unduly affected by the microphone diameter, which was\nlarge compared with the boundary-layer thickness ."}, {"doc_id": 77, "text": "a comparative analysis of the performance of long range\nhypervelocity vehicles .\n long-range hypervelocity vehicles are studied in terms of their\nmotion in powered flight, and their motion and aerodynamic heating in\nunpowered flight . powered flight is\nanalyzed for an idealized propulsion\nsystem which rather closely approaches\npresent-day rocket motors .\nunpowered flight is characterized by a return\nto earth along a ballistic, skip,\nor glide trajectory . only those\ntrajectories are treated which yield the\nmaximum range for a given velocity at the end of powered flight .\naerodynamic heating is treated in a manner\nsimilar to that employed previously\nby the senior authors in studying ballistic missiles (naca tn 4047),\nwith the exception that radiant as well as convective heat transfer is\nconsidered in connection with glide and skip vehicles .\n the ballistic vehicle is found to be the least efficient of the\nseveral types studied in the sense\nthat it generally requires the highest\nvelocity at the end of powered flight in order to attain a given range .\nthis disadvantage may be offset, however, by reducing convective heat\ntransfer to the re-entry body through\nthe artifice of increasing pressure\ndrag in relation to friction drag - that\nis, by using a blunt body . thus\nthe kinetic energy required by the vehicle at the end of powered flight\nmay be reduced by minimizing the mass of coolant material involved .\n the glide vehicle developing lift-drag ratios in the neighborhood\nof and greater than 4 is far superior\nto the ballistic vehicle in ability\nto convert velocity into range . it has the disadvantage of having far\nmore heat convected to it,. however, it has the compensating advantage\nthat this heat can in the main be radiated\nback to the atmosphere .\nconsequently, the mass of coolant material may be kept relatively low .\n the skip vehicle developing lift-drag ratios from about 1 to 4 is\nfound to be superior to comparable ballistic and glide vehicles in\nconverting velocity into range . at\nlift-drag ratios below 1 it is found to\nbe about equal to comparable ballistic\nvehicles while at lift-drag ratios"}, {"doc_id": 78, "text": "an analytical treatment of aircraft propeller precession\ninstability .\n an analytical investigation is made of a precession-type instability\nwhich can occur in a flexibly supported aircraft-engine-propeller\ncombination . by means of an idealized\nmathematical model which is comprised\nof a rigid power-plant system flexibly\nmounted in pitch and yaw to a fixed\nbackup structure, the conditions required for neutral stability are\ndetermined . the paper also examines the sensitivity of the stability\nboundaries to changes in such parameters\nas stiffness, damping, and\nasymmetries in the engine mount, propeller\nspeed, airspeed, mach number,\npropeller thrust, and location of pitch and yaw axes . stability is found\nto depend strongly on the damping and stiffness in the system .\n with the use of nondimensional charts theoretical stability\nboundaries are compared with experimental results obtained in wind-tunnel\ntests of an aeroelastic airplane model . in general, the theoretical\nresults, which do not account for wing response, show the same trends\nas observed experimentally,. however,\nfor a given set of conditions\ncalculated airspeeds for neutral stability\nare consistently lower than the\nmeasured values . evidently, this result is due to the fact that wing\nresponse tends to add damping to the system ."}, {"doc_id": 79, "text": "effects of extreme surface cooling on boundary layer\ntransition .\n an investigation was made to determine the combined effects of\nsurface cooling, pressure gradients, nose blunting, and surface finish on\nboundary-layer transition . data were obtained for various body shapes\nat a mach number of 3.12 and reynolds\nnumbers per foot as high as 15x10 .\n previous transition studies, with moderate cooling, have shown\nagreement with the predictions of stability theory . for surface roughnesses\nranging from 4 to 1250 microinches the location of transition was\nunaffected with moderate cooling . with extreme cooling, an adverse effect\nwas observed for each of the parameters investigated . in general, the\ntransition reynolds number decreased with\ndecreasing surface temperature .\nin particular, the beneficial effects of a favorable pressure gradient\nobtained with moderate cooling disappear with extreme cooling, and a\ntransition reynolds number lower than\nthat observed on a cone is obtained .\nfurther, an increase in the nose bluntness decreased the transition\nreynolds number under conditions of extreme cooling ."}, {"doc_id": 80, "text": "effect of distributed three-dimensional roughness and\nsurface cooling on boundary layer transition and lateral\nspread of turbulence at supersonic speeds .\n an investigation was made in the langley 4 by 4-foot supersonic\npressure tunnel at mach numbers of 1.61 and 2.01 to determine (1) the\neffect of distributed roughness on boundary-layer transition with the\nmodel surface at adiabatic wall temperature and cooled and (2) the\neffect of surface cooling on the lateral spread of turbulence . both\ndistributed granular-type and single spherical roughness particles were\nused, and transition of the boundary layer was determined by hot-wire\nanemometers . the transition-triggering mechanism of the\nthree-dimensional roughness at supersonic speeds appeared to be the same as\nthat previously observed at subsonic speeds . in fact, the critical\nvalue of the roughness reynolds number parameter (that is,\nthe value at which turbulent spots are initiated by the roughness) was\nfound to be approximately the same at supersonic and subsonic speeds\nwhen complete local conditions at the top of the roughness, including\ndensity and viscosity, were considered in the formulation of the\nroughness reynolds number . for three-dimensional roughness at a reynolds\nnumber less than its critical value, the roughness introduced no\ndisturbances of sufficient magnitude to influence transition . surface\ncooling, although providing a theoretical increase in stability to small\ndisturbances, did not increase to any important extent the value of the\ncritical roughness reynolds number for three-dimensional roughness\nparticles . cooling, therefore, because of its effect on the\nboundary-layer thickness, density, and viscosity actually promoted transition due\nto existing three-dimensional surface roughness for given mach and\nreynolds numbers . the measured lateral spread of turbulence in the\nboundary layer appeared to be unaffected by the increased laminar\nstability derived from the surface cooling ."}, {"doc_id": 81, "text": "compressible laminar flow and heat transfer about a\nrotating isothermal disk .\n the flow and heat transfer about a rotating isothermal disk are\nre-examined to include the effects of compressibility and property\nvariations . if viscous dissipation is neglected,\nthe compressible problem is\ncorrelated to the incompressible problem by assuming linear variations\nof viscosity and thermal conductivity with temperature . certain\ninaccuracies in several previous incompressible solutions are noted and\ncorrected herein . the effect of compressibility appears as a\ndistortion of the normal coordinate and normal velocity component and as\na multiplicative factor in the heat-transfer coefficient, the nusselt\nnumber, and in the expressions for the skin-friction components and\ntorque required to rotate the disk ."}, {"doc_id": 82, "text": "theoretical investigation of the ablation of a glass-type\nheat protection shield of varied material properties\nat the stagnation point of a re-entering irbm .\n the melting-type heat protection at the stagnation point of a\nre-entering irbm is treated by employing homogeneous, opaque, and\nnondecomposing glass shields which do not exceed a temperature of\nsome effects due to variations of the glass properties . the ballistic\nre-entry vehicle has a nose diameter of 0.635 m, a ballistic factor\nof 3.5 x 10, a re-entry angle of 124.9 (from the\nvertical) at an altitude of 100 km, and a re-entry speed of 4.5 .\nthe performance of 36 different glass shields with assumed\ncombinations of material properties is investigated by employing a\ncalculation method which yields practically exact, transient solutions\nfor the problem . as a corollary, results for a certain steady flight\nstate are also given . the discussions made it possible to derive\nunder realistic flight conditions some thermal characteristics for the\nemployment of thin, or light-weight, glass shields .\n investigation of these hypothetical glass shields leads to the\nconclusion that a low thermal conductivity and a high specific heat,\nand thus, a small thermal diffusivity are most desirable . a small\nthermal diffusivity yields high surface temperatures, causing a high\nradiative heat transfer out of the shield,. and steep temperature\nprofiles normal to the surface, causing a small thermal penetration across\nthe shield with little total ablation of the shield . results show that\nfor the assumed irbm re-entry, the necessary thickness of the employed\nglass shields increases monotonically with thermal diffusivity which is\nthe only material parameter affecting this thickness .\n a high viscosity level and a high emissivity constant of the\nsurface of the supposedly opaque shield are also desirable,. although,\nthese two properties exert a comparatively small influence on the\noverall performance when disregarding glass shields with an extremely\nlow viscosity level ."}, {"doc_id": 83, "text": "discussion of solar proton events and manned space\nflights .\n as a result of studies made during the\ninternational geophysical year (igy) and the\ninternational geophysical cooperation (igc),\nit is known that a considerable fraction of\nlarge solar flares give rise to almost pure\nstreams of protons which reach the earth and\ncontinue to arrive for as long as 11 days .\nthe energies of these particles lie within a\nvery steep spectrum extending from 20 to\nleast 500 mev . because of the frequency\nof large flares during times of high solar\nactivity, and owing to the long duration of each\nsolar proton emission, these particles were\npresent in detectable intensity near the top\nof the earth's atmosphere for about 15 percent\nof the time from 1957 to 1960 . the number\nof large flares that accelerated and released\nthese particles during this three-year period was about 30 .\n the event that began on august 22, 1958\ncontributed greatly toward the understanding\nof the solar and terrestrial sequence of events,\nand in addition provided the first\nidentification of the emitted particles . a flare on may\nof protons in the neighborhood of the earth that\nthis phenomenon was recognized as an\nadditional radiation hazard to manned vehicles\nin the high atmosphere and in most parts\nof the solar system . the three very intense\nevents that occurred in july, 1959 further\nsupported this conclusion, and the possibility\nof predicting such events became an\nimportant consideration . in addition to its value\nin the protection of human beings, effective\nforecasting clearly would be of great value in\nthe detailed scientific study of this\nphenomenon .\n this paper presents a preliminary\ndiscussion of some aspects of predicting the\narrival of protons at the earth following the\nappearance of solar activity features and,\nequally important, of forecasting the periods\nwhen this penetrating radiation is unlikely\nto occur ."}, {"doc_id": 84, "text": "experimental investigation of the downstream influence\nof stagnation point mass transfer .\n this report presents the results of an experimental\ninvestigation of the downstream influence of localized mass transfer in the\nstagnation region of a blunt body under hypersonic flow\nconditions . the coolant is injected through a porous plug coaxial\nwith the centerline of symmetry of the model . the tests were\ncarried out in a wind tunnel with a mach number of 6.0,\nstagnation temperatures of approximately 1,600 r., and a stagnation\npressure of approximately 600 psia . four different gases were\ninjected over a range of mass flows . the heat transfer on the\nimpermeable section was measured under isothermal wall\nconditions,. for the higher rates of mass flow, adiabatic surface\ntemperatures were also determined . the theoretical analysis of the\nboundary-layer flow is investigated in order to establish the\nsimilarity parameters for the flow system . these parameters permit\nthe extrapolation of the test results to other flow conditions,\nprovided that laminar flow prevails . helium is found to be the\nmost efficacious coolant ."}, {"doc_id": 85, "text": "on trails of axisymmetric hypersonic blunt bodies flying\nthrough the atmosphere .\n the trail left in the atmosphere by a body moving at hypersonic\nspeeds is the subject of theoretical treatment . the times\nrequired for ionization and dissociation (and their inverse processes)\nto go to completion, when compared to the flow times of a gas\nparticle, are important in determining the observable effects of\nhypersonic trails-i.e., emitted thermal radiation and reflection\nof electromagnetic waves from the trail .\n in order to simplify the theoretical treatment, the trail is\ndivided into two regions .. (1) the expansion-controlled trail,\nwhich treats the behavior of the wake behind the body up to a\npoint, along the direction of flight, where the pressure decays to\nthe free-stream value and cooling is controlled principally by the\nexpansion of the flow, and (2) the conduction-controlled trail,\nwhere the trail cools mainly by diffusion of heat away from the\nhigh-temperature core .\n the influence of the details of the body shape on the\nobservables are discussed and a simple computational procedure for\nthe behavior of the conduction-controlled trail is developed based\non integral methods . results of calculations that assume\nthermodynamic equilibrium of the flow field give the values of the\nthermodynamic variables in the trail of a sphere, axial\ndistributions of emitted thermal radiation, and maps of electron density\ndistribution . it is shown that the cooling of the\nconduction-controlled trail is essentially due to conduction of heat and that\nviscous effects are not important . it is found that this portion\nof the trail does not widen as one proceeds downstream . flight\nvelocities considered vary between 15,000 and 35,000 ft sec and\naltitudes range between 100,000 and 250,000 ft ."}, {"doc_id": 86, "text": "inviscid-incompressible flow theory of static peripheral\njets in proximity to the ground .\n an /exact/ flow theory of peripheral jets issuing\nsymmetrically from a hovering aerial-ground vehicle is presented . the\ntheory is exact insofar as no simplifying assumptions have been\nmade in obtaining a solution of the governing inviscid,\ntwo-dimensional hydrodynamical flow equations . the results are\nvalid for all jet thickness vehicle height ratios . the limit of\napplicability of existing theories (very low thickness height\nratios) are defined . jet reaction, lift, and power coefficients for\nstatic conditions are introduced and computed . lift\naugmentation and lift power ratios are also calculated .\n applications to three-dimensional vehicles with rotational\nsymmetry are indicated ."}, {"doc_id": 87, "text": "free-convection magnetohydrodynamic flow past a porous flat plate .\nthe incompressible flow of an electrically conducting fluid past a\nporous plate with constant suction velocity in the presence of a\ntransverse uniform strength has recently been investigated by gupta . in\nthis note, the problem is generalized to take into account the effect of\nfree convection, when a body force is acting parallel to the wall . the\nfluid is assumed to be semi-incompressible as usual . in addition to\nthe obvious practical significance, this problem is also interesting in\nthe sense that it provides another exact solution of the\nmagnetohydrodynamic equations, since the only electromagnetic assumptions involved\nare constant properties and freedom from excessive charges ."}, {"doc_id": 88, "text": "magnetohydrodynamic free-convection pipe flow .\nit has been shown that transverse magnetic fields of practical\nstrengths exert considerable influence on liquid-metal,\nfree-convection, vertical, flat-plate and parallel-plate flow fields .\nthe extent of influence was determined by the magnitude of a\nnondimensional parameter a which is the ratio of the hartmann\nnumber to the fourth root of the grashof number, and is a\nmeasure of the relative influence of the magnetic and buoyant\nforces . in this note the steady, fully developed, laminar,\nfree-convection flow of a fluid of electrical conductivity through\na fully submerged, open-ended, constant-temperature, vertical\npipe located in a transverse magnetic field of strength is\nanalyzed in terms of the same parameter . the magnitude of\nits influence on the velocity and temperature profiles, the surface\nshear and heat transfer, and the volumetric flow rate is\ndetermined ."}, {"doc_id": 89, "text": "an investigation of separated flows, part i: the pressure\nfield .\n the present article describes an investigation of several types of\nseparated regions such as blunt-base wakes and cavities formed\nin cutouts in the boundaries and ahead of or behind two\ndimensional steps in supersonic (mach numbers 2 to 4) and\nsubsonic flow . the conditions for the existence, the geometry,\nand the pressure field are described in this paper .\n a second article (to be published) will describe investigations of\nthe internal flow and the heat transfer across such separated\nregions .\n it is found that there is a maximum (critical) ratio of the length\nof the separated free-shear layer to the depth of the depression\nin the boundary beyond which the cavity collapses, leaving\nmutually independent separated regions at each protrusion .\nthis critical length changes greatly upon laminar-turbulent\ntransition in the oncoming boundary layer,. in either laminar or\nturbulent flow it is approximately independent of mach and\nreynolds numbers . a semiempirical correlation predicting the\nconditions under which the flow will span a depression of arbitrary\ndepth is proposed .\n detailed pressure distributions along the boundaries of a\ncavity (in turbulent flow) are presented as a function of the ratio\nof the cavity length to the critical length, which is found to be\nthe pertinent similarity parameter . for short notches\nthe impact pressure due to the reversal of the inner portion\nof the shear layer at recompression tends to thicken the shear\nlayer and a type of boundary layer-free stream interaction\ngoverns the pressure field . the pressure in the cavity is nearly\nconstant and can be higher than free-stream . in long notches\nthe shear layer bends inward at separation and\ncurves back gradually ahead of the recompression point . the\nfloor-pressure variation is pronounced and the recovery pressure\nat reattachment is small . the variation of the drag coefficient\nwith mach number reflects the change from one to the other\nmechanism of recompression .\n detailed surveys of the mach-number distributions in a\nblunt-body wake and the mixing region behind its throat, as\nwell as in the shear layer spanning a cutout in a wall, are presented\nand analyzed . it is found that, in general, the assumptions of\nthe simple supersonic-wake models which rely on a principle of\nsteady flow with mass conservation in the cavity are not adequate\nfor cavities in which there is recompression against a boundary .\n results showing the influence of the thickness of the initial\nboundary layer (in the range of 0.3 to 3 times the notch depth)\nand of the geometry of the notch are also presented ."}, {"doc_id": 90, "text": "periodic temperature distributions in a two-layer composite\nslab .\nan investigation to determine the feasibility of using an\ninsulating thermal barrier to protect exposed solid\npropellant motors from atmospheric or environmental temperature\nvariations has recently been completed . in one portion of this\nstudy, a solution was developed for the periodic temperature\ndistribution in a two-layer composite slab . one exposed surface of\nthis composite slab was adiabatic, and the other exposed surface\nwas subjected to a sinusoidal temperature variation . the\ntechnique used in the analysis was similar to that of grober . in this\nnote, pertinent features of the development of the solution are\ngiven ."}, {"doc_id": 91, "text": "periodic temperature distribution in a two-layer composite slab .\nin a recent contribution to the reader's forum, under the above title,\nstonecypher outlined a method for finding the periodic temperature\ndistribution in a two-layer composite slab, one exposed surface of the slab\nbeing insulated and the other subject to a sinusoidal temperature\nvariation . perfect thermal contact between the two layers, and constant\nthermal properties were assumed .\ntwo years ago i drew attention in these pages to a method for\ndetermining the transient temperature in such a two-layer slab resulting from a\ntriangular heat-input pulse . i should like to point out that this same\nmethod also is applicable to the case where one external face is given\na sinusoidal temperature variation with time . the method is based on\nthe analogy between one-dimensional heat flow and the flow of an\nelectric current in a simple transmission line having only series resistance\nand parallel capacitance ."}, {"doc_id": 92, "text": "the analysis of redundant structures by the use of\nhigh-speed digital computers .\n large-scale redundant structure analyses are currently\nfeasible by the use of modern high-speed digital computers .\nthis capability opportunely meets the urgent need to solve\ncomplex problems which otherwise would be hopelessly beyond\nthe capacity of the hand desk computer . however, the difficulties\nhave now shifted from tedious hand computations to the problems\nof adequately representing the structure by a model and\nof the peculiarities of irregular geometrical configurations .\n a wide scope of problem types can be handled by a generalized\nprogram approach . matrix formulation is used for the organization\nof input data and for handling data transfer in the large\ncomplex of subroutines, including the formation of equilibrium\nand continuity conditions to the final loads and deflections .\nsimultaneous treatment of thermal expansions and plasticity\nis included .\n the use of minimum-size redundant systems is emphasized,\nstarting from the philosophy of cutting members to provide a\nstatically determinate structure . improved numerical accuracy\nand problem size capacity is gained for a given computer .\nexamples are discussed ranging from simple plane-load diffusion\nproblems to pressurized fuselage cutouts and complex\nwing-fuselage-shell intersection-type problems ."}, {"doc_id": 93, "text": "the supersonic blunt body problem - review and extensions .\n a survey of existing analytical treatments of the supersonic or\nhypersonic blunt-body problem indicates that none is adequate\nfor predicting the details of the flow field . reasons are given for\nthe failure of various plausible approximations . a numerical\nmethod, which is simpler than others proposed, is set forth for\nsolving the full inviscid equations using a medium-sized electronic\ncomputer . results are shown from a number of solutions for\nbodies that support detached shock waves described by conic\nsections ."}, {"doc_id": 94, "text": "the transverse curvature effect in compressible axially\nsymmetric laminar boundary layer flow .\n the viscous transverse curvature effect in compressible axially\nsymmetric laminar boundary-layer flow has been investigated,\nand it is found that the effect is characterized by the parameter\nwhich is essentially the ratio of the boundary-layer thickness\nto body radius . it is shown that the busemann and crocco\nintegrals of the two-dimensional energy equation for are\nstill valid for axially symmetric flow in which the transverse\ncurvature effects are considered . by a generalization of\nmangler's transformation it is then shown that the boundary-layer\nequations are reducible to an almost two-dimensional form,\nmaking the analysis simpler for two asymptotic flow regions\ncharacterized by and less than or of the order of unity .\nit is with the latter region that the present paper is primarily\nconcerned, and for this case it is shown that the additional term\nin the momentum and energy equations, which differentiates them\nfrom the two-dimensional form, behaves like an external\nfavorable pressure gradient .\n except for certain special cases it is necessary to obtain the\nof the order of unity by means of asymptotic expansions in\nascending powers of a parameter that is small compared to unity\nbut proportional to . it is shown how the asymptotic\nsolutions can be found for (1) the velocity and temperature\ndistributions for the compressible zero pressure gradient case when the\nbody shapes are given by and and (2) the\nvelocity distribution for incompressible flow with an external\nvelocity of the form past a body given by . the\nzeroth approximation is the mangler result . for the cases of a\nlinear external velocity distribution, similar profiles can be found\nfor all values of . more generally it is shown that similar\nprofiles exist if the exponents n and m satisfy the condition that .\nhere, similar is used in the restricted meaning\nthat the distributions are derivable from ordinary differential\nequations .\n in the case of the cone and cylinder with zero pressure gradient\nwhere the equations have been numerically integrated for,\nthe first-order correction to the mangler formulation shows that\nthe effect on both the skin-friction coefficient and heat-transfer\nrate can become appreciable in the range where is less than\nor of the order of unity . at a constant, the effects are\nincreased in magnitude when either the ratio of wall to free-stream\ntemperature, or mach number, is increased . also, all other\nconditions being equal, for the same value of the skin-friction\ncoefficient and heat-transfer increase on the cylinder is greater\nthan that on the cone .\n for flows with pressure gradient, the transverse curvature term\nbehaves again like a favorable pressure gradient and tends to\ndelay both separation and transition when compared with axially\nsymmetric flows in which the transverse curvature effect is\nneglected ."}, {"doc_id": 95, "text": "temperature distribution and thermal stresses in a\nmodel of a supersonic wing .\n the transient temperature distribution and the thermal\nstresses in an idealized wing structure considered by hoff and\ntorda in reference 1 are determined . only the effects of\naerodynamic heating and of heat conduction are included,. radiation\nand convection effects are neglected . the present work differs\nfrom that of reference 1 in that the conduction from the cap to\nthe web is considered when the temperature of the cap is\ncalculated, and the spar cap temperature is assumed to be a function\nof both space and time . graphs of temperature and thermal\nstress distributions are presented, and the results are compared\nwith those of reference 1 ."}, {"doc_id": 96, "text": "review of published data on the effect of roughness on transition from\nlaminar to turbulent flow .\na review is presented of the published data on the effect of roughness,\nespecially single roughness elements, on transition from laminar to\nturbulent flow, in which an attempt is made to reanalyze and correlate the\navailable information . the reanalysis shows that the transition\nreynolds number of a flat plate with zero pressure gradient is a\nfunction of the ratio of the height of the roughness element to the\ndisplacement thickness of the boundary layer at the element, this functional\nrelation being a better representation of the data than a constant\ncritical reynolds number of the roughness element . other data show that the\neffects of roghness are similar in streams of different initial\nturbulence and that a plot of the ratio of transition reynolds number of the\nrough plate to that for the smooth plate against the ratio of the height\nof the roughness element to displacement thickness of the boundary layer\nat the element gives good correlation of all the data for a given shape\nwhen transition occurs downstream from the\nroughness element . at a certain value of the height-thickness ratio\ndependent on the stream speed, location of roughness element, and\nairstream turbulence, the transition position reaches the element and\nremains there as the height or the stream speed is further increased .\nthe paper also discusses available data on the effect of distributed\nroughness on transition on a flat plate, as well as some of the\npublished data on roughness effects on transition on air-foils ."}, {"doc_id": 97, "text": "a mixing theory for the interaction between dissipative\nflows and nearly isentropic streams .\n by means of a simplified theoretical /model,/ the present paper\ntreats the general class of flow problems characterized by the\ninteraction between a viscous or dissipative flow near the surface\nof a solid body, or in its wake, and an /outer/ nearly isentropic\nstream . for the present, the external flow is taken to be a plane,\nsteady, supersonic flow, which makes a small angle with a plane\nsurface or plane of symmetry, although the methods used can be\nextended to curved surfaces, to axially symmetric supersonic\nflows, and also to subsonic flows . the internal dissipative flow\nis regarded as quasi-one-dimensional and parallel to the surface\non the average, with a properly defined mean velocity and mean\ntemperature . the nonuniformity of the actual velocity\ndistribution is taken into account only approximately by means of a\nrelation between mean temperature and mean velocity .\nmixing, or the transport of momentum from outer stream to\ndissipative flow, is considered to be the fundamental physical process\ndetermining the pressure rise that can be supported by the flow .\nwith the aid of this concept, a large number of flow problems is\nshown to be basically similar, such as boundary-layer\nshockwave interaction, wake flow behind blunt-based bodies (base\npressure problem), flow separation in overexpanded supersonic\nnozzles, separation on wings and bodies, etc ."}, {"doc_id": 98, "text": "heat transfer by laminar flow to a rotating plate .\n an exact solution of the heat-transfer problem for the von\nkarman example of the laminar flow of a viscous fluid over a\nrotating plate is given in dimensionless form and physically\ndiscussed . the solution is explicitly given for a constant\ntemperature on the plate with viscous dissipation included . the\nnumerical results are given for prandtl numbers from 0.5 to 10 ."}, {"doc_id": 99, "text": "the fundamentals of the statistical theory of turbulence .\nstatistical theory in general considers mean values of certain\nquantities . in the case of the turbulent motion one is interested in mean\nvalues of velocities and of their derivatives, and in mean values of\nsquares and products of velocities and their derivatives . it was o.\nreynolds who first expressed the so-called apparent or turbulent\nstresses by the mean values of the products of the velocity components . the\ndifferent theories suggested so far have as their common objective the\nestablishment of relations between certain mean values, e.g. between the\nturbulent shear stresses given by the mean products of velocity\nfluctuations and the derivatives of the mean velocities, i.e. the measured mean\nvelocity gradients . in this sort of investigations the conception of\nthe /correlation/ is of paramount importance . the late a. friedman\ntried to introduce the correlations as unknown variables in the\nhydrodynamic equations., however, he could not carry his investigations to\npractical results, i.e., to results which can be compared with the\nexperimental evidence . recently, g. i. taylor had success in his\nanalysis of /isotropic/ turbulence by means of correlation calculations, and\nwas able to discuss, theoretically, the problem of the decay of\nturbulence in a windstream behind a turbulence producing device . his theory\nraised considerable interest because it is concerned with the important\nproblem of wind-tunnel turbulence and its results could be compared\ndirectly with experimental work done by dryden in this country and by\nfage, townend and simmons in england .\nthe present paper is concerned with two fundamental problems.. with\nuniform isotropic turbulence and with the turbulent friction in a\nparallel stream . first, the general theory of isotropic turbulence is\ndeveloped . this general theory includes taylor's consideration as a\nspecial case . however, it"}, {"doc_id": 100, "text": "vibration isolation of aircraft power plants .\nvibration in aircraft structure can almost\nalways be traced to vibratory forces originating\nfrom the power plant . these forces are transmitted\nto the aircraft in two ways .. (1) by the action of air\nforces upon the surfaces of the aircraft in, or adjacent\nto, the slip stream of the propeller, and (2) by direct\ntransmission of unbalanced forces from the power\nplant through the engine mounting . the latter has\nalways caused the preponderance of disturbance .\nvibratory stresses induced in the engine mounting\nstructure occasionally produce fatigue failures in the\nassociated parts, and always shorten the useful life\nof the entire aircraft structure . more important,\nhowever, are the psychological and physiological\neffects of continuous vibration and its attendant noise\non the passengers and crew . this may very likely\nbe the major source of the rapid fatigue which is so\nintimately associated with flying . the importance\nand desirability of drastically reducing vibration can\nhardly be questioned .\n this paper is limited to a consideration of the\ndirectly transmitted forces and, further, considers the\npower plants as rigid bodies attached by flexible means\nto the aircraft which is also considered as a rigid body\nof relatively large mass . it is also limited to the case\nof engines and engine supporting structures having\naxial symmetry (radial engines), although the methods\nemployed could easily be extended to other cases ."}, {"doc_id": 101, "text": "laminar heat transfer over blunt-nosed bodies at hypersonic flight\nspeeds .\nthis paper deals with two limiting cases of laminar heat transfer over\nblunt-nosed bodies at hypersonic flight speeds, or high stagnation\ntemperatures.. (a) thermodynamic equilibrium, in which the chemical\nreaction rates are regarded as /very fast/ compared to the rates of diffusion\nacross streamlines., (b) diffusion as rate-governing, in which the\nvolume recombination rates within the boundary layer are /very slow/\ncompared to diffusion across streamlines . in either case the gas density\nnear the surface of a blunt-nosed body is much higher than the density\njust outside the boundary layer, and the velocity and stagnation\nenthalpy profiles are much less sensitive to pressure gradient than in the\nmore familiar case of moderate temperature differences . in fact, in\ncase (a), the nondimensionalized enthalpy gradient at the surface is\nrepresented very accurately by the /classical/ zero pressure gradient\nvalue, and the surface heat-transfer rate distribution is obtained\ndirectly in terms of the surface pressure distribution . in order to\nillustrate the method, this solution is applied to the special cases\nof an unyawed hemisphere and an unyawed, blunt cone capped by a\nspherical segment .\nin the opposite limiting case where diffusion is rate-controlling the\ndiffusion equation for each species is reduced to the same form as the\nlow-speed energy equation, except that the prandtl number is replaced\nby the schmidt number . the simplifications introduced in case (a) are\nalso applicable here, and the expression for surface heat transfer rate\nis similar., the maximum value of the ratio between the rate of heat\ntransfer by diffusion alone and by heat conduction alone in the case of\nthermodynamic equilibrium is given by.. (prandtl no./schmidt no .)\nwhen the diffusion coefficient is estimated by taking a reasonable value\nof atom-molecule collision cross section this ratio is 1.30 .\nadditional theoretical and (especially) experimental studies are clearly\nrequired before these simple results are accepted ."}, {"doc_id": 102, "text": "advantages and limitations of models .\nsummary .. the use of models for structural test investigations in the\npresence of kinetic heating effects is examined . the principal\nfeatures of the complex process to be\nrepresented are discussed under the classifications\nexternal air flow, internal heat transfer,\nelastic response . of these the second is found\nto influence most model design, and an\nanalysis of a typical structure is included to\nillustrate the various contributions to\ninternal heat transfer ."}, {"doc_id": 103, "text": "theory of mixing and chemical reaction in the opposed\njet diffusion flame .\n an idealization of the flow system used by potter\nand butler is analyzed . the differential\nequation of mixing is solved exactly, to give the location\nof, and burning rate in, the flame . the solutions\nto the chemical kinetic differential equation\nare discussed, relations being derived between the jet\nflow rate at extinction, the chemical kinetic\nconstants and the laminar flame speed in premixed\ngases . it is shown that the jet flow rate at\nextinction is independent of the transport properties .\ncomparison is made with the experimental\ndata of potter, heimel and butler . it is argued that\nexperiments must be carried out at higher\nreynolds numbers if the measurements are to be\nquantitatively analyzable ."}, {"doc_id": 104, "text": "similar solutions of a free convection boundary layer\nequation for an electrically conducting fluid .\n author investigates the existence of a class of similar solutions\nfor free convection from a vertical flat plate, such as are known for\nfree convection in a nonconducting fluid . the magnetic field acts\ntransversely to the fluid motion and is assumed to remain constant\nin the direction perpendicular to the plate . this introduces into\nthe momentum equation a retarding force which is a function only\nof x, the distance along the plate length . for similarity it is\nfound that the magnetic inductance must vary as . if\nthe plate temperature is constant . if n = 0, the magnetic\ninductance is constant while the plate temperature increases linearly\nwith x ."}, {"doc_id": 105, "text": "the asymptotic boundary layer on a circular cylinder\nin axial incompressible flow .\n in this paper the incompressible boundary layer over a\ncircular cylinder in an axial flow is investigated far from the\nleading edge . if u and v are the velocity components in the\nx and r direction respectively and a stream function is\nintroduced by and, then\nfor a constant free-stream velocity has the\nfollowing asymptotic form ..\nwhere the p's are determined successively, first for s=1 and\nall t, then s=2 and all t, etc., from ordinary differential\nequations . here and log c=euler's\nconstant . it is shown that the effect of the curvature of the\nbody (in planes perpendicular to the flow) is to increase\nthe skin friction . also the case in which the free-stream\nvelocity is proportional to (at the\nmethod breaks down), is studied . it is concluded that the\neffect of the curvature of the cylinder, when the boundary\nlayer has a thickness comparable with its radius of\ncurvature, is to delay separation ."}, {"doc_id": 106, "text": "the transverse potential flow past a body of revolution .\n it is shown that in the potential flow of\nan incompressible inviscid fluid past a\nbody of revolution set with its axis at right\nangles to the stream, the velocity\ncomponents at the surface along and perpendicular\nto the meridians vary with azimuthal\nangle round the body in a simple manner .\nthis is shown by entirely elementary\nconsiderations ."}, {"doc_id": 107, "text": "on the mixing of two parallel streams .\n using the techniques of boundary-layer theory, the proper third\nboundary condition for the mixing of two parallel streams is\nderived from the compatibility condition of the higher order\napproximation . it is shown that the commonly adopted third boundary\ncondition of balancing of transverse momentum is correct only for\nthe mixing problem of two semi-infinite incompressible streams .\nfor the fulfillment of the proper third boundary condition, the\npossibility of introducing the similar solution of blasius type is\nexamined for various cases ."}, {"doc_id": 108, "text": "properties of the confluent hypergeometric function .\nthe confluent hypergeometric functions have proved useful in many\nbranches of physics . they have been used in such problems involving\ndiffusion and sedimentation, as isotope separation and protein molecular\nweight determinations in the ultracentrifuge . the solution of the\nequation for the velocity distribution of electrons in high frequency\ngas discharges may frequently be expressed in terms of these functions .\nthe high frequency breakdown electric field may then be predicted\ntheoretically for gases by the use of such solutions together with kinetic\ntheory .\nthis report presents some of the properties of the confluent\nhypergeometric functions together with six-figure tables of the functions ."}, {"doc_id": 109, "text": "the production of uniform shear flow in a wind tunnel .\n a nearly uniform shear flow was obtained in the working\nsection of a wind tunnel by inserting a grid of parallel rods with\nvarying spacing .\n the function of such a grid is to impose a resistance to the\nflow, so graded across the working section as to produce a linear\nvariation in the total pressure at large distances downstream\nwithout introducing an appreciable gradient in static pressure near\nthe grid . a method of calculating a suitable arrangement of the\nrods is described . although this method is strictly applicable\nonly to weakly sheared flows, an experiment made with a grid\ndesigned for a shear parameter as large as 0.45 gave results in\nclose agreement with the theory . there was no evidence from\nthe experiment of any large-scale secondary flow accompanying\nthe shear--a danger inherent in an empirical attempt to grade the\nresistance of the grid--nor was any tendency observed for the\nshear to decay with increasing distance from the grid ."}, {"doc_id": 110, "text": "dynamics of a dissociating gas .\n this is a lucid introduction to the effects of dissociation\nin gas dynamics . the problem in view is that of air flow\npast a bluff body at speeds somewhat above 2 km sec .\nthermodynamic equilibrium is assumed,. theories of near\nequilibrium for transport properties and of large\ndepartures from equilibrium being promised in parts 2 and 3 .\n following a survey of the equilibrium statistical\nthermodynamics of a pure dissociating diatomic gas, a\nnew model is introduced . this /ideal dissociating gas/ is\ncharacterized by only three constants, the characteristic\ntemperature, density and internal energy for dissociation .\nphysically, it may be regarded as having its vibrational\nmodes always just half excited (so that at low\ntemperatures the ratio of specific heats approaches 4 3 rather\nthen 7 5) . thermodynamic properties of the ideal gas\nare derived, and the oblique shock wave relations\ndeduced in the /strong-shock/ approximation (including an\nelegant relation between the principal curvatures of any\nbow shock and the subsequent vorticity) . useful relations\nare given for the isentropic changes that take place along\nstreamlines between shocks .\n various of these results are applied to the problem\ntypified by a sphere flying at high mach number . the\nnewtonian impact theory and its empirical modification\nare dismissed as lacking theoretical basis, in favor of the\nlimit for large values of both mach number and density\nratio across the shock . it is suggested that the zero\nsurface pressure sometimes predicted by the latter theory\ncorresponds to separation not of the flow but of the shock\nwave from the surface . an estimate is given for the\nsubsequent shape of the shock . finally, another\napproximation is applied to the region near the stagnation\nstreamline . the fluid is assumed incompressible, but rotational\nin accord with the shock relations,. and it is shown that a\nspherical shock corresponds to a concentric spherical body .\nthe resulting surface pressure is within 1 per cent of that\npredicted by freeman's second approximation based on\nthe newtonian-plus-centrifugal solution (same j. 1 (1956),"}, {"doc_id": 111, "text": "the laminar boundary layer equation: a method of solution\nby means of an automatic computer .\n a method, very suitable for use with an automatic computer,\nof solving the hartree-womersley approximation to the\nincompressible boundary-layer equation is developed .\nit is based on an iterative process and the choleski method\nof solving a simultaneous set of linear algebraic equations .\nthe programming of this method for an automatic computer is\ndiscussed . tables of a solution of the boundary-layer\nequation in a region upstream of the separation point are\ngiven . in the upstream neighbourhood of separation\nthis solution is compared with goldstein's\nasymptotic solution and\nthe agreement is good ."}, {"doc_id": 112, "text": "steady motion of conducting fluids in pipes under transverse\nmagnetic fields .\n this paper studies the steady\nmotion of an electrically conducting, viscous fluid\nalong channels in the presence of an imposed\ntransverse magnetic field when the walls do not\nconduct currents . the equations which determine\nthe velocity profile, induced currents and\nfield are derived and solved exactly in the case\nof a rectangular channel . when the imposed\nfield is sufficiently strong the velocity profile is\nfound to degenerate into a core of uniform flow\nsurrounded by boundary layers on each wall .\nthe layers on the walls parallel to the imposed\nfield are of a novel character . an analogous\ndegenerate solution for channels of any symmetrical\nshape is developed . the predicted pressure\ngradients for given volumes of flow at various field\nstrengths are finally compared with experimental results for square and\ncircular pipes ."}, {"doc_id": 113, "text": "acoustical signal detection in turbulent airflow .\n improvement in detected signal-to-noise ratio is obtained\nfor a periodic signal masked by additive noise\nand turbulent noise backgrounds . comparisons are made\nbetween autocorrelation, crosscorrelation, and a\ncombination of frequency filtering and crosscorrelation .\nalthough the latter method provided the greatest\nimprovement, the crosscorrelation technique was the\nmost successful single method . it turned out that\nthe maximum improvement obtainable was limited by\nthe dynamic range of the correlator computer and\nnot by errors due to finite averaging time and scanning\nthe delay . the improvement for signals masked by\nturbulent noise was found to be about 5 db less than that\nobtained for additive noise ."}, {"doc_id": 114, "text": "response of plates to a decaying and convecting randon\npressure field .\n following the methods of lyon, an analysis of the\nvibratory response of a plate to a random pressure\nfield is given . the pressure correlation of the random\nfield is assumed to have a scale small compared to\nthe plate size, to decay exponentially, and to convect\nwith constant speed over the plate . two cases are\nconsidered, one in which the convection speed is much\nless than the speed of free flexural waves in the plate,\nthe other in which the convection speed is the same\norder as the flexural wave speed . the mean square plate\ndisplacement is shown to be relatively independent\nof convection for speeds much less than the flexural\nwave speed, and to increase significantly for speeds in\nthe order of the flexural wave speed . it is shown that\ndamping is usually, but not always, an effective means\nof vibration reduction . in the case of convection\nspeeds much smaller than the flexural speed, the use of\nhysteretic damping for reduction of the displacement\nresponse is shown to be limited by the decay of the\nassumed random pressure field ."}, {"doc_id": 115, "text": "on turbulent lubrication .\nthe paper concerns the hydrodynamic turbulent\nmotion in the lubricant layer . proceeding\nfrom the reynolds equations and introducing\nthe approximations currently used in\nlubrication problems, owing to the lubricant film\nthickness, the general motion equations for\nturbulent lubrication are written .\n using the prandtl mixing length hypothesis,\nexact and approximate solutions are\nobtained for the velocity distribution into the\nlubricant layer . the results are discussed by\npointing out the pressure gradient and the\nreynolds number influence on the velocity\ndistributions, as well as the differences with\nrespect to the laminar flow .\n in order to obtain simple formulae, the\nexact dependence of the rate of flow on the\npressure gradient into a dimensionless form\nis replaced by a linear relation, the slope of\nwhich depends on the reynolds number .\nthis approximation allows the obtainment of\nthe pressure differential equation under a\nsimple form . the pressure equation is integrated\nin case of journal bearings, by assuming a\nconstant or a variable viscosity of the lubricant .\n the results are compared to the experimental\ndata obtained by m. i. smith and d. d.\nfuller and the good qualitative agreement is pointed out ."}, {"doc_id": 116, "text": "the elliptic cylinder in a shear flow with hyperbolic\nvelocity profile .\n the stream function for the shear flow with hyperbolic\nvelocity profile past an elliptic cylinder has been determined\nas an infinite series of mathieu functions . it is found that\nthe stagnation streamline of the flow is displaced towards\na region of higher velocity, this displacement increasing\nthe main stream, (2) as the stream becomes progressively\nnon-uniform, (3) with increase of minor axis length when\nthe major axis length remains invariant . in each case the\ndisplacement reaches a limiting value as the cylinder moves away\nfrom the axis of symmetry of the stream . these limiting\nvalues are reached at critical distances from the axis of symmetry,\nwhich decrease as the stream becomes progressively non-uniform,\nbut these distances are approximately independent of incidence .\n the pressure coefficients and the resultant force and moment\ncoefficients associated with the cylinder have also been obtained,\nand investigated numerically for the flat plate type of cylinder ."}, {"doc_id": 117, "text": "the motion of a viscous liquid past a paraboloid .\n an approximate solution for the steady\nflow of incompressible viscous liquid past\na paraboloid of revolution is described .\nan assumption is made for the form of the\nstokes stream function and substituted\ninto the navier-stokes equations using\nparaboloidal coordinates . after making\nsuitable approximations, a non-linear\ndifferential equation for a function f is\ndeduced . the solutions of this equation\ndepend on the reynolds number of the\nflow considered . examples found by\nnumerical integration are given to illustrate\nthe properties of the function f for\nreynolds numbers varying from 0.0001 to\nis found, and it is shown that this approximate\nsolution tends to the perfect fluid\nflow away from the boundary, allowance\nbeing made for the displacement effect of\nwhat may be called the boundary layer ."}, {"doc_id": 118, "text": "the transonic flow of a compressible fluid through\nan axially symmetrical nozzle .\n by a method similar to that developed by s. tomotika\nand k. tamada (quart. appl. math. 7, 381-397 (1950),.\nthese rev. 11, 275) for computing two-dimensional mixed\nisentropic flows in the sonic region, the flow in the vicinity\nof the throat of an axially symmetrical nozzle is studied .\nseveral exact solutions to von karman's equation for axially\nsymmetrical transonic flows are obtained and the one that\ngives flows through a converging and diverging nozzle is\nconsidered in detail . this solution consists of four branches\nof which two are rejected because of singularities . of the\nremaining two branches, one gives pure supersonic flow and\nthe other gives taylor's type of flow with a local supersonic\nregion in the throat . by varying a parameter, the latter\nbranch approaches two asymptotes which yield meyer's\ntype of asymmetrical flows ."}, {"doc_id": 119, "text": "conduction of fluctuating heat flow in a wall consisting\nof many layers .\n van gorcum has pointed to interesting and important analogies\nbetween the theory of a passive four-pole and the conduction of heat\nwaves through stratiform bodies . this paper generalizes in certain\nregards van gorcum's ideas and draws their consequences for the case of\na solid, bounded by two infinite parallel planes and consisting of any\nnumber of layers made from different materials ."}, {"doc_id": 120, "text": "measurement of convective heat transfer by means of\nthe reynolds analogy .\npreston's method for measuring skin friction in pipes has\nbeen extended to include non-uniform flow, with and\nwithout pressure gradients, over flat surfaces . by means of a\nmodified form of the reynolds analogy, the local\nconvective heat transfer coefficient can be related to the skin\nfriction, and it is proposed that the method be used in\naerodynamic models of furnaces and in heat transfer plant\nof simple geometry . more investigations are required of\nthe effects of fluid turbulence, surface roughness and\nsurface curvature on convective heat transfer and skin\nfriction ."}, {"doc_id": 121, "text": "a theory for base pressures in transonic and supersonic\nflow .\n a physical flow model is devised based on the concepts of\ninteraction between the dissipative shear flow and the\nadjacent free stream and the conservation of mass in the\nwake . four flow components are integrated in the model,.\nnamely, the flow approaching the trailing edge, the\nexpansion around the trailing edge, the mixing within the\nfree-jet boundary, and the recompression at the end of the\nwake . a unique and stable solution results for the base\npressure . theoretical results obtained for thin\napproaching boundary layer do not require empirical information\nand are, therefore, best suited to evaluate the merits of the\ntheory . here emphasized is the case of isoenergetic\nconstant-pressure mixing in the turbulent free-jet boundary\nand agreement is found between theory and experimental\ndata ."}, {"doc_id": 122, "text": "a simplified approximate method for the calculation of the pressure\naround conical bodies of arbitrary shape in supersonic and hypersonic\nflow .\nexact conical-flow solutions are available only for circular cones at\nzero angle of attack . for nonaxisymmetric cones or cones at angle of\nattack, only approximate methods exist . these methods are generally\nquite complicated and further limited to certain body shapes or certain\nmach-number ranges . a great need was therefore felt for a simple\napproximate method applicable to any arbitrarily shaped conical body at\nzero incidence as well as at angle of attack .\nsuch a method has been developed recently at lockheed and is presented\nhere in abbreviated form . the method is based on the /equivalent-cone/\ntheory . this theory determines the pressure on a conical body\nutilizing information for a symmetric cone at zero angle of attack with the\nsame normal component of the free stream with respect to the surface as\nthe local element of the body considered . this method works relatively\nwell at high mach numbers . however, it is quite inconsistent at lower\nmach numbers, especially for bodies which deviate considerably from\ncircular cones . the equivalent-cone method does not give satisfactory\nresults, mainly due to the fact that it considers only the local surface\nelement on the body independent of the other body elements in the\nnewtonian-theory manner ."}, {"doc_id": 123, "text": "the downstream influence of mass transfer at the nose\nof a slender cone .\n the influence of localized mass transfer at the nose of a slender\ncone under hypersonic flow conditions has been studied by\nexperimental and theoretical means . two gaseous coolants, nitrogen\nand helium, are injected through a porous plug subtending a\nhalf angle of 30 . the effect of the mass transfer on the shock\nshape, pressure distribution, heat transfer, and transition are\ninvestigated . the experimental work involved tests in the\nmach-number-8.0 tunnel at pibal . the theoretical analysis involved\na study of the effect of mass transfer on the shock stand-off\ndistance and leads to an inviscid-flow parameter permitting the\nexperimentally determined shock shape and pressure distribution\nto be extrapolated to other than test conditions and to other\ncoolant gases . there is obtained the maximum value of this\nparameter resulting in no significant alteration of the pressure\ndistribution on the cone and thus defining the flows in which\nboundary-layer-type similarity applies .\n significant reductions in heat transfer are obtained with\ninjection . indeed, with small amounts of helium injection the\npeak heating is found to occur downstream on the cone and to be\nan order of magnitude less than would occur at the stagnation\npoint without mass transfer . with nitrogen early transition is\nfound to occur, so that local heating rates are actually increased\nover those prevailing at the same reynolds number without\ninjection ."}, {"doc_id": 124, "text": "a summary of the supersonic pressure drag of bodies\nof revolution .\n a number of approximate theories for supersonic and\nhypersonic flow over bodies of revolution at zero angle of attack are\nappraised by a critical comparison with characteristics and\nsecond-order results, with the use of hypersonic similarity as a\nbasis for the comparison . most of the approximate theories\nare inadequate except over very limited ranges of fineness ratio\nand mach number . the combination of second-order\nsupersonic theory and second-order shock-expansion theory provides\nconsistently good results throughout the supersonic speed range .\n on the basis of exact (or nearly exact) supersonic solutions and\na limited amount of test data and theory in the transonic region,\nsummary design curves are developed that give the pressure\ndrag of conical and ogive noses and conical and ogive boattails\nover the complete range of transonic, supersonic, and hypersonic\nmach numbers . other shapes can be analyzed in the same\nmanner, provided that an equivalent amount of data is available .\n the analysis is made with the assumption of inviscid flow,\nso that the effects of boundary-layer growth, shock\nboundary-layer interaction, and flow separation are not included . the\npresent correlations provide a sound basis of inviscid-flow results\nfrom which these additional viscous effects can be evaluated ."}, {"doc_id": 125, "text": "measurements of skin friction of the compressible turbulent\nboundary layer on a cone with foreign gas injection .\n measurements of average skin friction of the turbulent\nboundary layer have been made on a 15 total included angle cone with\nforeign gas injection . measurements of total skin-friction drag\nwere obtained at free-stream mach numbers of 0.3, 0.7, 3.5, and\nx 10 with injection of helium, air, and freon-12\nthrough the porous wall . substantial reductions in skin\nfriction are realized with gas injection within the range of mach\nnumbers of this test . the relative reduction in skin friction is\nin accordance with theory--that is, the light gases are most\neffective when compared on a mass flow basis . there is a marked\neffect of mach number on the reduction of average skin friction,.\nthis effect is not shown by the available theories . limited\ntransition location measurements indicate that the boundary layer\ndoes not fully trip with gas injection but that the transition point\napproaches a forward limit with increasing injection . the\nvariation of the skin-friction coefficient, for the lower injection rates\nwith natural transition, is dependent on the flow reynolds\nnumber and type of injected gas,. and at the high injection rates the\nskin friction is in fair agreement with the turbulent\nboundary-layer results ."}, {"doc_id": 126, "text": "an investigation of two-dimensional supersonic base\npressures .\n an investigation of the base pressure behind wedges at mach\nnumbers 2 and 3 in the laminar and the transitional regime is\nreported . temperature and velocity traverses through the\nmixing zone are shown and exploratory investigations of the\nwake vortex by use of hot wires and flow-visualization techniques\nare described . it is found that the laminar two-dimensional base\npressure agrees well with chapman's theoretical predictions .\nthe shear layer exhibits gross velocity distributions\ncharacteristic of the free jet mixing zone, but also shows disturbances that\noriginate in the expansion-turning of the oncoming boundary\nlayer . an interesting trailing vortex is observed, which is\nexplained in terms of nonuniform mixing rate in the wake ."}, {"doc_id": 127, "text": "supersonic axially symmetric nozzles .\n at each of twenty-one exit mach numbers, ranging\nfrom 1.008 to 8.238, ten supersonic axially symmetric\nnozzle shapes with plane sonic surfaces have been computed\non the eniac by the method of characteristics . the\nboundary of the shortest of each group of ten has a\nsharp edge at the sonic plane, while the others have\nsmooth boundaries . this report describes the computational\nprocedures and presents a sample of the results for twenty\nnozzles .\n more extensive and elaborate tables of the results of the\nentire computations are available at the ballistic\nresearch laboratories . nozzle contours can be obtained\naccurately from them by interpolation for exit mach numbers\nbetween 1.479 and 8.238 for a wide range of ratios of nozzle\nlength to throat diameter ."}, {"doc_id": 128, "text": "effects of free stream vorticity on the behaviour of\na viscous boundary layer .\n theoretical investigation is considered of the two-dimensional\nsteady flow field at large distance from a finite object set in a\nviscous incompressible fluid . study is made of coordinate-type\nexpansions for pressure and velocity for large r, uniformly in, for\nfixed reynolds number, assuming exact boundary conditions at\ninfinity and regularity of flow with zero net mass flow across a\nsimple curve enclosing the object .\n mathematical nature of the distinction between parameter and\ncoordinate-type expansions is discussed with description of inner\nand outer expansions and matching techniques .\n a feature of the expansion procedure is the introduction of an\nartificial parameter . inner and outer expansions are matched with\nthe aid of known solutions of the navier-stokes equations .\nanalysis requires simple consideration of the heat and laplace\nequations without resort to special methods .\n paper is worth studying by those interested in asymptotic\nexpansion procedures ."}, {"doc_id": 129, "text": "an investigation of the noise produced by a subsonic air jet .\nto investigate the theoretical predictions of lighthill on aerodynamic\nsound, measurements have been made of the sound field of a 1 in. air jet\nissuing from a long pipe . the measurements have been made over a wide\nfrequency band (30 to 10,000 cycles/sec.) and in one-third octave bands\nin this frequency range . the mean mach number at the pipe orifice was\nvaried from 0.3 to 1.0 .\nthe dependence of the apparent position of the noise sources on\nfrequency and jet speed was investigated . at a given frequency a source is\nsituated farther from the jet orifice the higher the jet speed . lower\nfrequency sources appear farther downstream than ones of higher\nfrequency, consistent with their association with larger eddies . the\ndirectional characteristics of the sound field at different frequencies\nand jet speeds are illustrated by means of scale diagrams showing lines\nof constant sound intensity . these sound fields are analyzed in terms\nof the moving quadrupole sources of lighthill's theory and good\nagreement obtained . it is shown that the apparent spread of the sources at\nlow frequencies is due to the doppler effect . at low frequency\nrelative to the frequency of maximum power output) the radiation is\npredominantly that of three mutually orthogonal longitudinal quadrupoles\nwhich, except for the effect of convection upon it, has a sound field\nlike a monopole source . at higher frequencies the sound fields of\nlateral and longitudinal quadrupoles predominate ."}, {"doc_id": 130, "text": "the behaviour of non-linear systems .\n many of the phenomena that occur in the world around us are\ngoverned by nonlinear relationships . in the development of the\nmathematical sciences, the difficulties of nonlinear analysis have\nhindered the formulation of nonlinear concepts that would\npermit us to understand such phenomena . in the present article,\nour progress in understanding the behavior of nonlinear systems\nis reviewed and an attempt is made to present the resulting\nconcepts in such a way that they may be applied with some\ngenerality to other problems ."}, {"doc_id": 131, "text": "two-dimensional jet mixing of a compressible fluid .\n the mixing and divergence of a supersonic jet exhausting into\na supersonic stream are investigated theoretically .\n in the first part of this paper, the flow is assumed to be laminar .\nwhen the velocity and temperature in the jet are different\nslightly from those of the surrounding stream, by the method of\nsmall perturbations and under ordinary boundary layer\nassumptions, the equation of motion of two-dimensional flow will be\nreduced to a form of the well-known equation of heat conduction,\nwhose solution is known for any given boundary conditions . it\nhas also been shown that the exact solution of the two\ndimensional jet mixing of viscous compressible fluids can be obtained\nby successive approximations starting with the solution of small\nperturbations .\n velocity and temperature distributions for two cases--one is\nthe mixing of two-uniform flows and the other is the mixing of a\njet of compressible fluid from a two-dimensional nozzle with full\nexpansion exhausting into a supersonic stream--have been\ncalculated . the properties of the jet mixing depend mainly on the\nmomentum of the jet regardless of whether the change of\nmomentum is due to the change of velocity or the change of\ntemperature--i.e., the change of density . compressibility has a\nconsiderable effect on the properties of the jet .\n in the second part, the cases of turbulent flow are investigated .\nby means of reichardt's theory of free turbulence, the turbulent\nshearing stress may be expressed as\n it has been shown in this paper that\nwhere is a constant that can be determined experimentally .\nthe value of n lies between 0 and 1 . the exact value of n\ndepends on the condition of mixing .\n when the expression of turbulent shearing stress given above\nis used instead of the viscous stress in the equation of motion,\nby suitable transformation of variables, it has been shown that\nthe equation of two-dimensional turbulent jet mixing is identical\nto that of the laminar case . hence, the solution of the first part\nof this paper can be applied to the turbulent case, provided that\nthe characteristic constants and n have been properly chosen ."}, {"doc_id": 132, "text": "viscosity effects in sound waves of finite amplitude:\nin survey in mechanics .\n this article has as its subject /the conflicting influence on\nsound propagation of convection on the one hand, and of diffusion\nand relaxation on the other/, whose importance in the\ndetermination of the structure of shock waves was first appreciated clearly\nby sir geoffrey taylor . as an essential introduction to the main\ntopics, author gives an exceptionally clear and valuable account\nof the physical mechanisms of viscosity, thermal conductivity, and\nother diffusion effects, including relaxation . the classical theory\nof shock-wave formation is then discussed, and some extensions\nare made .\n the remainder of the article is based on the demonstration that\nthe nonlinear equation for plane progressive sound waves, in which\nconvection and diffusion are taken into account to a first\napproximation, can be transformed into burgers's equation, the general\nsolution of which was given by hopf and cole . this approach, in\nwhich all flows are continuous (they become discontinuous at\nshock waves in the limit as viscosity, etc., tend to zero), allows\nthe author to re-derive and extend whitham's theory of the\nformation and decay of weak plane shock waves, and to derive many\nnew results, such as the velocity distributions during the union\nof two shock waves and during the formation of a shock wave .\nthe application of the same idea to non-plane shock waves is\nalso discussed, but more briefly,. in these cases, burgers's\nequation is not quite such a good approximation as before .\n the article concludes with sections on sound waves whose\nreynolds numbers based on the length scale of the flow and the\nvelocity amplitude are comparable with unity, and on the effects\nof relaxation on the properties of shock waves . the whole is\nmuch more than a survey, and represents a very substantial\nadvance in the theory of sound waves . it is the finest possible\ntribute to sir geoffrey taylor that he should be able to inspire\narticles such as this and the others in this volume ."}, {"doc_id": 133, "text": "some effects of surface curvature on laminar boundary\nlayer flow .\n the laminar flow of a viscous incompressible fluid over a\ntwo-dimensional curved surface is investigated for two cases, one in\nwhich the curvature is /large/ and the other in which it is\ncases are obtained as approximations from the exact equations of\nmotion by an order-of-magnitude analysis . these equations are\nsolved for flow over a particular surface with zero surface pressure\ngradient . in this analysis, the pressure gradient normal to the\nsurface is included, and the outer boundary conditions are\nmodified in accordance with the requirements of flow over a curved\nsurface .\n the results indicate that for equal reynolds numbers, the\nstress on convex surfaces is less than the flat-plate value, while\nthe stress on concave surfaces is greater than for a flat plate . the\nmost important effect of surface curvature, for the cases\nconsidered, is the modification of the shape of the velocity profile\nnear the /outer edge/ of the boundary layer . the requirement\nthat a smooth transition exist between the viscous flow and the\npotential flow at the outer edge of the layer causes the profile to\nhave a negative slope near the outer edge for convex surface\ncurvature and a positive slope for concave surface curvature ."}, {"doc_id": 134, "text": "note on an interaction between the boundary layer and the inviscid\nflow .\naccording to the classical boundary-layer theory the flow about bodies\nat reynolds numbers of aeronautical interest can be considered as\ncomposed of two regimes.. an outside inviscid flow and a thin\nboundary-layer region adjacent to the body . this point of view leads to the\napproximation that, on a slightly curved surface, throughout the layer\nis negligibly small . the additional assumption that the inviscid flow\nis irrotational leads to the requirement that is zero at the outer edge\nof the boundary layer . in this theory any interaction between the two\nregimes is accountable by a simple correction to the body shape based on\nthe boundary-layer displacement thickness .\nrecently, in connection with hypersonic laminar boundary layers, this\nclassical point of view has been modified., an interaction between the\ntwo flow regimes leading to a self-induced axial pressure gradient has\nbeen considered . it is the purpose of the present note to point out\nanother type of interaction which may be of practical importance and of\nfundamental interest even at mach numbers below those considered in the\nhypersonic boundary-layer theory and which may have to be considered in\nthat theory ."}, {"doc_id": 135, "text": "the calculation of wall shearing stress from heat-transfer measurements\nin compressible flows .\nit has been shown by ludwieg that the wall shearing stress of a laminar\nor turbulent boundary layer in an incompressible flow can be determined\nfrom a heat-transfer measurement at the surface . the instrument\nused in that investigation was essentially a small, locally insulated,\nheating element embedded in the test surface . the size of the\ninstrument was restricted by the condition that the thermal boundary layer\ngenerated by the heating element be contained locally within the laminar\nsublayer . in the present analysis ludweig's theory for such an\ninstrument is extended to compressible flow over an insulated flat plate .\nwith the same limitations on the design and operation of the instrument\nas mentioned above, it can also be assumed for compressible laminar\nand turbulent boundary layers that only the flow in the immediate\nvicinity of the wall or the laminar sublayer will be affected in the region\nof the heated element . this assumption then permits the use of the\nlaminar boundary-layer equations as the governing equations for this\nanalysis for both laminar and turbulent boundary layers ."}, {"doc_id": 136, "text": "recent developments in rocket nozzle configurations .\n existing configurations of supersonic portion of rocket nozzles\nare described and compared . survey covers bell-type conical and\ncontoured nozzles, annular nozzles, plug nozzles, and the author's\nown /e-d/ (expansion-deflection) nozzle . the latter is a\nbell-type nozzle in which the gases are first deflected radially outward\nby a small central plug, then expanded radially inward around the\nbase of the plug, and finally deflected back to a nearly axial\ndirection by the nozzle wall, in compressive turning ."}, {"doc_id": 137, "text": "the generation of sound by aerodynamic means .\n a summary is given of some of the more important experimental results\nrelating to the noise radiated from a cold subsonic turbulent jet .\nthese are then related to the predictions of lighthill's general theory\nof aerodynamic noise ."}, {"doc_id": 138, "text": "wakes in axial compressors .\nthe tendency in the past has been to assume that\nwhen wakes or non-uniform total head profiles are\nfed into an axial compressor then substantially constant\nstatic pressure prevails at the entry, the variations in total\nhead appearing as variations in velocity . this variation\nin velocity causes variation in incidence on the early stage\nblade rows and thus can give rise to excitation of blade\nvibration . this assumption is implicit, for instance, in\nreferences 1 and 2, but we think has been a common\nassumption by most of the people working in this field .\n where the compressor is fed by a duct of substantially\nparallel walls for a reasonable length ahead, such an\nassumption appeared justifiable . such a duct when given\nan air flow test with its outlet discharging, for instance,\nto atmosphere instead of to the compressor, then the\ndistribution assumed would normally be obtained and in fact\nmany surveys of such ducts have been represented in this\nfashion . the object of this note is to show that, in fact,\nthis distribution will not normally occur when the\ncompressor is present and we may normally expect much more\nnearly a constant velocity into the compressor with\nattendant static pressure distributions to match with the total\nhead variations ahead of the intake, with of course, the\nattendant curved flow to support the static pressure\ngradients ."}, {"doc_id": 139, "text": "viscous effects on pitot tubes at low speeds .\n measurements were made of the pressure in a blunt-nosed pitot\ntube, in an air stream at reynolds numbers from about 15 to 1000 .\nthe results are expressed in terms of a pressure coefficient\ndensity of the fluid, and p and v are the static pressure and\nvelocity in the undisturbed stream . as found in previous\ninvestigations, becomes greater than 1 at low reynolds numbers, the\nincrease being about at a reynolds number of 50 (based\non external tube radius) . in disagreement with the work of hurd,\nchesky, and shapiro, no decrease of below 1 was found at any\nreynolds number .\n when the values of found by various experiments are\nplotted against reynolds numbers based on internal tube radius,\nit is found that the curves are in closer agreement than when the\nexternal radius is used ."}, {"doc_id": 140, "text": "the determination of turbulent skin friction by means\nof pitot tubes .\n a simple method of determining\nlocal turbulent skin friction on a smooth\nsurface has been developed which utilises a\nround pitot tube resting on the surface .\nassuming the existence of a region near the\nsurface in which conditions are functions\nonly of the skin friction, the relevant physical\nconstants of the fluid and a suitable length,\na universal non-dimensional relation is\nobtained for the difference between the total\npressure recorded by the tube and the static\npressure at the wall, in terms of the skin\nfriction . this relation, on this assumption,\nis independent of the pressure gradient .\nthe truth and form of the relation were first\nestablished, to a considerable degree of\naccuracy, in a pipe using four geometrically\nsimilar round pitot tubes--the diameter\nbeing taken as representative length . these four\npitot tubes were then used to determine\nthe local skin friction coefficient at three stations\non a wind tunnel wall, under varying\nconditions of pressure gradient . at each station,\nwithin the limits of experimental\naccuracy, the deduced skin friction coefficient was\nfound to be the same for each pitot\ntube, thus confirming the basic assumption and\nleaving little doubt as to the correctness\nof the skin friction so found . pitot traverses\nwere then made in the pipe and in the\nboundary layer on the wind tunnel wall . the results\nwere plotted in two non-dimensional\nforms on the basis already suggested and they\nfell close together in a region whose\nouter limit represented the breakdown of the\nbasic assumption, but close to the wall\nthe results spread out, due to the unknown\ndisplacement of the effective centre of a\npitot tube near a wall . this again provides\nfurther evidence of the existence of a\nregion of local dynamical similarity and of the\ncorrectness of the skin friction deduced\nfrom measurements with round pitot tubes on\nthe wind tunnel wall . the extent of the\nregion in which the local dynamical similarity\nmay be expected to hold appears to vary\nfrom about to of the boundary-layer\nthickness for conditions remote from,\nand close to, separation respectively ."}, {"doc_id": 141, "text": "free-flight techniques for high speed aerodynamic research .\n the development rocket-borne and rocket-launched high-speed\nairplane model test is described . details of airborne components,\ntelemetering units, tracking, and their calibration are also discussed .\ntests on controls, drag measurements, longitudinal stability\nevaluations, lift measurements, pressure measurements, aeroelastic\nestimations, and sonic bang recordings are effected . the reynolds numbers\ninvolved are much higher than are usual in the wind tunnel, and\nextensions of mach numbers are obtained beyond the tunnel limits, both free\nof the tunnel wall interference ."}, {"doc_id": 142, "text": "the problem of aerodynamic heating .\n paper is a good review of knowledge to date on convective heat\ntransfer to objects moving through air at low and high speeds .\ntheoretical and experimental information is given on recovery\nfactors and heat-transfer coefficients for isothermal surfaces of\nunswept flat plates, wedges and cones with attached shock waves,\nand stagnation points of blunt bodies of revolution, for both\nlaminar and turbulent boundary layers . a convenient nomograph for\ncalculating flat plate turbulent boundary-layer heat-transfer\ncoefficients is given . effects of surface cooling, surface roughness,\nand supply stream turbulence on transition are discussed and\nshown graphically ."}, {"doc_id": 143, "text": "interplanetary orbits .\n the basic equations under simplified\nconditions for interplanetary flight are derived .\nfor a voyage from planet to planet an\nunlimited number of orbits is possible . in\norder to give a clear survey of these possible\norbits a diagram is developed from which the\napproximate energy-requirement, the duration,\nand other particulars of a voyage can be\neasily found ."}, {"doc_id": 144, "text": "heat flow in composite slabs .\n this paper presents the solution of the heat flow\nproblem in composite walls under heat transfer conditions\nwhich are typical of uncooled rocket engine walls .\nanalytic expressions in the form of fourier sums are obtained\nfor the temperature distribution in a composite wall\nconsisting of an inner (refractory) medium and an outer\nmetallic) medium under newtonian heat transfer into the\nfirst medium with negligible heat transfer from the\nsecond medium to the exterior . the expressions obtained\nare based on a plane parallel composite slab as a\nrepresentative model for relatively thin cylindrical walls, with\nthickness-to-radius ratio not exceeding 0.2 . the general\nresults for the composite slab are simplified for the limiting\ncases of a thin refractory shield with a thick shielded\nmedium and a thick refractory shield with a thin shielded\nmedium ."}, {"doc_id": 145, "text": "skin friction in the laminar boundary layer in compressible\nflow .\n from an analysis of the work of\ncrocco and others, semi-empirical formulae\nare derived for the skin friction on a\nflat plate at zero incidence with a laminar\nboundary layer . these formulae are\nfor the general case of heat transfer, and\nwhen there is no heat transfer .\n the problem of heat transfer and\nthe effect of radiation are discussed in the\nlight of these formulae . the second\nformula is then utilised in the development of\nan approximate method for solving the\nmomentum equation of the boundary layer\non a cylinder without heat transfer .\nthe method indicates that with increase of\nmach number there is a marked forward\nmovement of separation from a flat plate\nin the presence of a constant adverse velocity gradient ."}, {"doc_id": 146, "text": "supersonic flow past slender bodies with discontinuous\nprofile slope .\n ward's slender-body theory is extended to derive first\napproximations to the external forces on slender\nbodies of general cross section\nwith discontinuous profile slope . two\nclasses of body are considered ..\nbodies whose profile (typified by the local\nradius) is continuous between the\nnose and base, and certain bodies whose\nprofile is discontinuous, such as\nbodies with annular or side air intakes and\nwing-bodies on which the wing\nhas an unswept leading edge . (where air\nintakes are concerned, it is\nassumed that they are sharp-edged and that\nthere is no /spillage/ of the\ninternal flow) .\n the following conclusions apply to\nthe former class of bodies . the\nvariation of drag with mach number is\nfound to depend only on the\ndiscontinuities in the longitudinal rate of change\nof the cross-sectional area, and is\nthus independent of cross-sectional shape .\nthe drag itself is unchanged if\nthe direction of the flow is reversed . the\nexpressions for lift and moment\nassume the same forms as for smooth pointed\nbodies, the lift depending only\non conditions at the base of the body .\n the general theory is applied to\nwinged bodies of revolution with an\nunswept wing leading edge .. the results\nbear a marked resemblance to those\nobtained by ward . the results for wings\nalone are seen to be applicable,\nwith one modification, to subsonic as well as to supersonic speeds ."}, {"doc_id": 147, "text": "supersonic flow past slender pointed wings with ?similar?\ncross sections at zero lift .\n some recent theoretical work on slender pointed wings at zero lift is\nco-ordinated and extended . the wings\nconsidered may have any pointed plan\nform shape, provided that the trailing\nedge is straight and unswept . the root\nsection profile and cross-section shapes\nare arbitrary, provided that, on any\none wing, the latter are /descriptively\nsimilar/ (diamond or parabolic biconvex\nfor instance), though not necessarily\ngeometrically similar . the chief aim of\nthe work is to find wings with simple\ngeometry, low wave drag and pressure\ndistributions which are unlikely to be\nseriously affected by viscous effects .\nwave drag and pressure distributions\nare calculated by slender-wing theory .\ngeneral formulae, which are both simple\nand instructive, are given for the wave\ndrag and the overall pressure distribution,\nwith particular emphasis on the root\npressure distribution . results for a number\nof wings of special interest are\npresented and discussed ."}, {"doc_id": 148, "text": "on displacement thickness .\n four alternative theoretical treatments of 'displacement\nthickness', and, generally, of the influence of boundary layers\nand wakes on the flow outside them, are set out, first for\ntwo-dimensional, and then for three-dimensional, laminar or turbulent,\nincompressible flow . they may be called the methods of 'flow\nreduction', 'equivalent sources', 'velocity comparison' and\n the principal expression obtained for the displacement\nthickness in three-dimensional flow may be written\nif, as orthogonal coordinates (x,y) specifying position on the\nsurface, we choose x as the velocity potential of the external\nflow, and y as a coordinate, constant along the external-flow\nstreamlines, such that h dy is the distance between (x,y) and\nz is the distance from the surface, u and v are the x and y components\nof velocity, and u takes the value u just outside the boundary layer ."}, {"doc_id": 149, "text": "expansions at small reynolds number for the flow past\na sphere and a circular cylinder .\n this paper is concerned with the problem of obtaining higher\napproximations to the flow past a sphere and a circular cylinder\nthan those represented by the well-known solutions of stokes\nand oseen . since the perturbation theory arising from the\nconsideration of small non-zero reynolds numbers is a singular\none, the problem is largely that of devising suitable techniques for\ntaking this singularity into account when expanding the solution\nfor small reynolds numbers .\n the technique adopted is as follows . separate, locally valid\nthe regions close to, and far from, the obstacle . reasons are\npresented for believing that these 'stokes' and 'oseen' expansions\nare, respectively, of the forms\nwhere are spherical or cylindrical polar coordinates made\ndimensionless with the radius of the obstacle, r is the reynolds\nnumber, and and vanish with r . substitution\nof these expansions in the navier-stokes equation then yields a\nset of differential equations for the coefficients and, but\nonly one set of physical boundary conditions is applicable to each\nexpansion (the no-slip conditions for the stokes expansion, and\nthe uniform-stream condition for the oseen expansion) so that\nunique solutions cannot be derived immediately . however, the\nfact that the two expansions are (in principle) both derived from\nthe same exact solution leads to a 'matching' procedure which\nyields further boundary conditions for each expansion . it is thus\npossible to determine alternately successive terms in each\nexpansion .\n the leading terms of the expansions are shown to be closely\nrelated to the original solutions of stokes and oseen, and detailed\nresults for some further terms are obtained ."}, {"doc_id": 150, "text": "integration of the boundary layer equations .\nthe equations of the boundary layer\nare integrated by an expression of the form\nwhere f(x) is a positive function with x=0\nas the stationary point,. (x) is slowly varying,.\nthe integral contains an unknown parameter\nwhich is found from the condition .\n the integral is evaluated by the method of\nsteepest descent . the expressions obtained are\nusually divergent, except in few cases which\ninclude blasius's equation,. the divergent\nexpressions are summed by euler's transformation .\n to check the procedure it is applied to falkner\nand skan's equation . the results obtained\nare very striking,. few terms in the expansions\nare sufficient to obtain close agreement with\nhartree's laborious numerical computations .\n the method is also applied to the general\nboundary-layer equation for the case of flow past\nan elliptic cylinder, measured by schubauer .\nthe results obtained are in close agreement\nwith schubauer's measurements for the velocities,\nalmost up to separation, for the position of\nthe separation point,. and in satisfactory agreement downstream of\nseparation ."}, {"doc_id": 151, "text": "the generation of noise by isotropic turbulence .\na finite region, with fixed boundaries, of an\ninfinite expanse of compressible fluid is in\nturbulent motion . this motion generates noise\nand radiates it into the surrounding fluid .\nthe acoustic properties of the system are studied\nin the special case in which the turbulent\nregion consists of decaying isotropic turbulence .\nit is assumed that the reynolds number\nof the turbulence is large, and that the mach number is small .\n the noise appears to be generated mainly\nby those eddies of the turbulence whose\ncontribution to the rate of dissipation of kinetic\nenergy by viscosity is negligible .\n it is shown that the intensity of sound at large\ndistances from the turbulence is the same\nas that due to a volume distribution of simple acoustic\nsources occupying the turbulent region .\nin this analogy, the whole fluid is to be regarded\nas a stationary and uniform acoustic\nmedium . the local value of the acoustic power output\np per mass of turbulent fluid is given\napproximately by the formula\nwhere a is a numerical constant, u is the\nmean-square velocity fluctuation, is the time, and\nc is the velocity of sound in the fluid . the\nconstant a is expressed in terms of the well-known\nvelocity correlation function f(r) by\nassuming the joint probability distribution of the\nturbulent velocities and their first two\ntime-derivatives at two points in space to be\ngaussian . the numerical value is\nthen obtained by substituting the form of f(r)\ncorresponding to heisenberg's theoretical\nspectrum of isotropic turbulence .\n it is found that the effects of decay make\nonly a small contribution to the value of a, and\nthat the order of magnitude of a is not changed\nwhen widely differing forms of the function\nf(r) are used ."}, {"doc_id": 152, "text": "on the flow of compressible fluid past an obstacle .\nit is well known that according to classical hydrodynamics a steady\nstream of frictionless incompressible fluid exercises no resultant\nforce upon an obstacle, such as a rigid sphere, immersed in it . the\ndevelopment of a /resistance/ is usually attributed to viscosity, or\nwhen there is a sharp edge to the negative pressure which may accompany\nit (helmholtz) . in either case it would seem that resistance involves\nsomething of the nature of a wake, extending behind the obstacle to an\ninfinite distance . when the system of disturbed velocities, although\nit may mathematically extend to infinity, remains as it were attached to\nthe obstacle, there can be no resistance .\nthe absence of resistance is asserted for an incompressible fluid., but\nit can hardly be supposed that a small degree of compressibility, as in\nwater, would affect the conclusion . on the other hand, high relative\nvelocities, exceeding that of sound in the fluid, must entirely alter\nthe conditions . it seems worth while to examine this question more\nclosely, especially as the first effects of compressibility are amenable\nto mathematical treatment ."}, {"doc_id": 153, "text": "on the steady motion of viscous, incompressible fluids,\nwith particular reference to a variation principle .\n except in exceptional cases, it is not possible to represent the\nmotion of a viscous incompressible liquid by means of a variation\nprinciple, but all cases of such motion that have yet been discovered\nbelong to this class of /exceptional cases ./ the appropriate functions\nare given ."}, {"doc_id": 154, "text": "velocity and temperature distributions in the turbulent\nwake behind a heated body of revolution .\nrecently (see abstract 954 (1938)) goldstein made calculations based\non theories of vorticity transfer, of the distributions of velocity and\ntemperature in the turbulent wake behind a heated body of revolution,\nand the present authors now record an experimental determination of\nthese distributions in a low-turbulence wind tunnel . difficulty was\nexperienced in obtaining a truly symmetrical wake and observations\nhave been reduced to mean values, curves of which are given ."}, {"doc_id": 155, "text": "on the solution of the laminar boundary layer equations .\nthe problem of the flow along a flat plate\nplaced edgewise to a steady stream,\nwhen a retarding pressure gradient\nvarying linearly as the distance x\nfrom the leading edge of the plate\nis superposed is discussed . if y denotes\ndistance measured perpendicular to\nthe plate, a solution is obtained in the\nform of a power series in x where\ncoefficients are functions of .\ndifferential equations are obtained for these\ncoefficients . seven of the coefficients\nhave been obtained with reasonable\naccuracy, and the eighth and ninth\nroughly . unfortunately it appears\nthat about eight more terms are\nrequired to carry the solution to\nthe point of separation,. the work\ninvolved in their determination is\nprohibitive . two approximate methods\nhave been developed for determining\nthe error when the first seven terms\nof the series are used as an approximation .\nthese methods lead to the\ndetermination of the point of separation\nand are in agreement as to its\nposition . if is the velocity at the\nedge of the boundary layer at the\nleading edge of the plate and is the\nvelocity gradient, separation is found\nwhen . a method is\ndeveloped for the solution of the\nboundary layer equations in any retarded region .\nit is obtained by\nreplacing the velocity distribution at the edge\nof the boundary layer by a\ncircumscribing polygon of infinitesimal sides and\napplying the preceding solution\nto each of these sides, making the\nmomentum integral continuous at each\nvortex . the problem is thereby\nreduced to the solution of a first order\ndifferential equation ."}, {"doc_id": 156, "text": "the effect of shallow water on wave resistance .\n the general character of experimental\nresults dealing with the effect of\nshallow water on ship resistance may be\nstated briefly as follows ..--at low\nvelocities the resistance in shallow\nwater is greater than in deep water, the\nspeed at which the excess is first\nappreciable varying with the type of vessel .\nas the speed increases, the excess\nresistance increases up to a maximum at a\ncertain critical velocity, and then\ndiminishes . with still further increase of\nspeed, the resistance in shallow\nwater ultimately becomes, and remains, less\nthan that in deep water at the same speed .\nthe maximum effect is the more\npronounced the shallower the water .\nfor further details and references one\nmay refer to standard treatises, but one\nquotation may be made in regard to\nthe critical velocity .. /this maximum\nappears to be at about a speed such\nthat a trochoidal wave travelling at this\nspeed in water of the same depth is\nabout times as long as the vessel .\nit was at one time supposed\nthat the speed for maximum increase\nin resistance was that of the wave of\ntranslation . this, however, holds only\nfor water whose depth is less than\nfor greater depths the speed of the\nwave of translation rapidly becomes\ngreater than the speed of maximum\nincrease of resistance ./ in a recent\nanalysis of the data, h. m. weitbrecht\nexpresses a similar conclusion by stating\nthat for each depth of water there is\na critical velocity, but that the critical\nvelocity does not vary as the square\nroot of the corresponding depth ."}, {"doc_id": 157, "text": "the hodographic transformation in transonic flow .\n the author studies the problem of finding the shape of a\nsymmetrical nozzle with the velocity along the axis (x-axis)\nspecified . the velocity along each streamline is assumed to\nincrease steadily . the singularity at the sonic velocity and\nto the axis of the nozzle) is first studied in the physical\nplane by using a power series in . in the hodograph plane,\nthe two characteristics of the hodograph differential\nequation passing through the sonic point and are lines\nof branch points . the region between these lines is a\nregion of triple-valuedness for the stream function .\noutside this region is single-valued . there are also\nsingularities at the sonic point and the point corresponding to\nthe specified condition at the exit of the nozzle . the author\nthen proposes to construct in the hodograph plane by\nat the exit velocity and (3) a finite sum regular throughout ..\nsin, where r is the square of the velocity\nand the are hypergeometric functions . the a's are\nfixed by the required approximation to the specified velocity\ndistribution along the axis . this solution is single-valued,\nconvergent and represents except a region near the sonic\npoint in the nozzle . for this excluded region, the author\ninverts the solution to obtain a power series in for 0 . this\nis shown to be convergent for the region of interest . the\ntype of solution considered by the author gives a nozzle\nhaving an infinitely long supersonic part ."}, {"doc_id": 158, "text": "temperature charts for induction and constant temperature\nheating .\n charts are presented for determining complete\ntemperature historics in spheres, cylinders, and plates . it\nis shown that for values of the dimensionless time ratio\nx greater than 0.2 the heating equations reduce to such\na simple form that for each shape two charts which give\ntemperatures at any position within the heated or cooled\nbodies can be plotted . it is also shown that the usual\nsimple heating and cooling charts can also be used for the\ndetermination of temperatures and heating times in\nbodies heated by a constant rate of heat generation at\nthe surface (induction heating) . finally, a two\ndimensional chart is given for finding heating times in short\ncylinders, thereby eliminating the trial-and-error\nsolution that is necessary when heating times are found from\nthe present one-dimensional charts ."}, {"doc_id": 159, "text": "numerical methods for transient heat flow .\n this paper deals with the application of numerical\nmethods for the solution of heat-conduction problems,\ntheir generality being extended in the following ways ..\nmay proceed most rapidly to a solution, or may proceed\nmore slowly and with greater precision,. (b) criteria are\ndeveloped for the choice of modulus to insure convergence .\nthis is most important at a convective surface,. (c) a\nmethod is developed for handling k and c when these\nproperties vary independently with temperature . a\ncomprehensive appendix gives the derivations, and the use of\nequations and charts is demonstrated by typical\nexamples ."}, {"doc_id": 160, "text": "approximate analytical solutions for hypersonic flow\npast slender power-law bodies .\napproximate analytical solutions are presented\nfor two-dimensional and axisymmetric\nhypersonic flow over blunt-nosed slender bodies whose\nshapes follow a power law variation . in particular,\nthe body shape is given by where is the\ntransverse body ordinate, is the streamwise distance\nfrom the nose, and m is a constant in the range .\nboth zero-order\nsolutions and first-order (small but nonvanishing values\nof solutions are presented, where m is the\nfree-stream mach number and is a characteristic\nbody or streamline slope . the zero-order shock shape\nis similar to the body shape for these flows . the\nsolutions are found within the framework of\nhypersonic-slender-body theory .\n the limiting case m=1 corresponds to a wedge\nor cone flow . the limiting case\ncorresponds to a constant-energy flow .\nthe latter cases are included\nso that the present study may be applied to all flows\nwherein the zero-order shock shape is given by\nwith m in the range . flow\nfields associated with shock shapes having values of m\noutside this range are also discussed . for all values\nof, except m=1, certain portions of the flow field\nriolate the hypersonic-slender-body approximations,\nwhile other portions are consistent with these\napproximations . for m=1, all portions of the flow field\nare consistent with the approximations .\n the approximate solutions are found as follows .\nthe asymptotic form of the flow in the vicinity of the\nbody surface is used as a guide to write approximate\nexpressions for the dependent variables . these\nexpressions exactly satisfy the continuity and\nenergy equations and contain arbitrary constants\nwhich are evaluated so as to satisfy boundary\nconditions at the shock . the approximate solutions do\nnot satisfy the lateral momentum equation except at\nthe shock and (for the first-order problem) at the body\nsurface .\n the results of the approximate solutions are\ncompared with numerical integrations of the\nequations of motion for various values of m and (ratio\nof specific heats) . good agreement is noted,\nparticularly when m and are both near one . the\nshock is relatively close to the body for the latter\ncases . sufficient results are presented to evaluate\nthe accuracy of the approximate method for various\nvalues of m and ."}, {"doc_id": 161, "text": "supersonic flow past a family of blunt symmetric bodies .\n some 100 numerical computations have been\ncarried out for unyawed bodies of revolution with\ndetached bow waves . the gas is assumed perfect\nwith . free-stream mach numbers\nare taken as 1.2, 1.5, 2, 3, 4, 6, 10, and . the\nresults are summarized with emphasis on the sphere\nand paraboloid ."}, {"doc_id": 162, "text": "nearly circular transfer trajectories for descending\nsatellites .\n simplified expressions describing the transfer\nfrom a satellite orbit to the point of atmospheric\nentry are derived . the expressions are limited to\naltitude changes that are small compared with the\nearth's radius, and velocity changes small compared\nwith satellite velocity . they are further restricted\nto motion about a spherical, nonrotating earth .\n the transfer orbit resulting from the application\nof thrust in any direction at any point in an elliptic\norbit is considered . expressions for the errors in\ndistance (miss distance) and entry angle due to an\ninitial misalinement and magnitude error of the\ndeflecting thrust are presented .\n the largest potential contributing factor towards\na miss distance stems from the misalinement of the\nretrovelocity increment . if this velocity increment is\npointed in direct opposition to the flight path, a 1\nmisalinement leads to a miss distance of 34.5 miles .\nhowever, it is shown that this error can be avoided\nby applying the velocity increment at an angle\nbetween 120 and 150 below the flight-path direction .\n the guidance and accuracy requirements to\nestablish a circular orbit, in addition to the corrections\napplied to transform elliptic orbits into circular\nones, are also discussed ."}, {"doc_id": 163, "text": "an analysis of the corridor and guidance requirements\nfor supercircular entry planetary atmospheres .\n an analysis is presented of supercircular entry\ninto a planet's atmosphere giving particular attention\nto the corridor through which spacecraft must be\nguided in order to accomplish various maneuvers .\na dimensionless parameter based on conditions at\nthe conic perigee altitude is introduced for\ncharacterizing supercircular entries and conveniently\nprescribing corridor widths associated with elliptic,\nparabolic, or hyperbolic approach trajectories . the\nanalysis applies to vehicles of arbitrary weight, shape,\nand size . illustrative calculations are made for\nvenus, earth, mars, jupiter, and titan .\n for nonlifting vehicles having fixed aerodynamic\ncoefficients, curves are presented of dimensionless\nparameters from which can be calculated the maximum\ndeceleration, maximum rate of laminar convective\nheating, and total laminar heat absorbed during\nsingle-pass entry at velocities up to twice circular\nvelocity . for lifting vehicles, curves are presented of\nthe maximum deceleration and overshoot boundary\nof an entry corridor,. equations are presented for\nestimating laminar aerodynamic heating from the\nmaximum deceleration . it is shown that the corridor\nwidth is independent of vehicle weight, dimensions,\nand drag coefficient, provided these are the same at\nthe overshoot boundary as at undershoot . the\ncorridors of certain planets can be broadened\nmarkedly by the application of aerodynamic lift,. for\nexample, the 10-earth-g corridor width for\nsingle-pass, nonlifting, parabolic entry is increased from\nto 52, 51, and 52 miles, respectively, by employing a\nlift-drag ratio of 1 . the use of aerodynamic lift\ndoes not increase appreciably the corridors of mars\nand titan . all corridor widths decrease rapidly\nas the entry velocity is increased .\n terminal guidance requirements on accuracy of\nvelocity and flight path angle for successfully entering\nvarious corridors are compared with analogous\nrequirements for putting a satellite into orbit, for\nhitting the moon from the earth, and for achieving\nicbm accuracy . consideration is given to the\nterminal guidance problem involved in using a\nplanet's atmosphere--rather than rocket fuel--to\neffect orbital transfers from heliocentric to\nplaneto-centric motion, thereby converting a hyperbolic\napproach trajectory to an elliptic orbit about the\ntarget planet . this fuel saving maneuver appears\ntechnologically feasible for certain planetary voyages,\nand implies the possibility of achieving a large\nreduction in required earth lift-off weight of chemical\npropulsion systems ."}, {"doc_id": 164, "text": "an approximate analytical method for studying entry\ninto planetary atmospheres .\n the pair of motion equations for entry into a\nplanetary atmosphere is reduced to a single, ordinary,\nnonlinear differential equation of second order by\ndisregarding two relatively small terms and by\nintroduring a certain mathematical transformation . the\nreduced equation includes various terms, certain of\nwhich represent the gravity force, the centrifugal\nacceleration, and the lift force . if these particular\nterms are disregarded, the differential equation is\nlinear and yields precisely the solution of allen and\neggers applicable to ballistic entry at relatively steep\nangles of descent . if all the other terms in the basic\nequation are disregarded (corresponding to negligible\nvertical acceleration and negligible vertical component\nof drag force), the resulting truncated differential\nequation yields the solution of sanger for equilibrium\nflight of glide vehicles with relatively large lift-drag\nratios .\n a number of solutions for lifting and nonlifting\nvehicles entering at various initial angles also have\nbeen obtained from the complete nonlinear equation .\nthese solutions are universal in the sense that a\nsingle solution determines the motion and heating\nof a vehicle of arbitrary weight, dimensions, and\nshape entering an arbitrary planetary atmosphere .\none solution is required for each lift-drag ratio .\nthese solutions are used to study the deceleration,\nheating rate, and total heat absorbed for entry into\nvenus, earth, mars, and jupiter . from the\nequations developed for heating rates, and from\navailable information on human tolerance limits\nto acceleration stress, approximate conditions for\nminimizing the aerodynamic heating of a trimmed\nvehicle with constant lift-drag ratio are established\nfor several types of manned entry . a brief study\nis included of the process of atmosphere braking for\nslowing a vehicle from near escape velocity to near\nsatellite velocity ."}, {"doc_id": 165, "text": "skin-friction measurements in incompressible flow .\nexperiments have been conducted to measure in\nincompressible flow the local surface-shear stress\nand the average skin-friction coefficient for a turbulent\nboundary-layer on a smooth flat plate having zero pressure gradient .\nthe local surface-shear stress was measured by a floating-element\nskin-friction balance and also by a calibrated total head\ntube located on the surface of the test wall . the\naverage skin-friction coefficient was obtained from\nboundary-layer velocity profiles . the\nboundary-layer profiles were also used to determine the location\nof the virtual origin of the turbulent boundary layer .\ndata were obtainec for a range of reynolds numbers\nfrom 1 million to about 45 million with an attendant\nchange in mach number from 0.11 to 0.32 .\n the measured local skin-friction coefficients\nobtained with the floating-element balance agree\nwell with those of schultz-grunow and kempf\nfor reynolds numbers up to 45 million . the\nmeasured average skin-friction coefficients agree\nwith those given by the schoenherr curve in the\nranges of reynolds numbers from 1 to 3 million\nand 30 to 45 million . in the range of reynolds\nnumbers from 3 to 30 million the measured values\nare less than those predicted by the schoenherr curve .\nthe results show that the /univeral skin-friction constants/\nproposed by coles appraoch asymptotically\na constant value at reynolds numbers exceeding\nmentioned constants and the limited reynolds\nnumber range of the present investigation, there is some doubt\nas to the validity of any turbulent\nskin-friction law written on the basis of the present\nresults . hence, no new friction law is proposed .\n the frictional resistance of a flat plate was\ncalculated by means of the momentum method and\nalso the integrated measured local surface shear .\nfor reynolds numbers from 14 million to 45 million\nboth methods give about the same result,. whereas\nat lower values of reynolds number the momentum\nmethod based on velocity profiles uncorrected for\nthe effects of turbulence results in a frictional\nresistance as much as 4 percent higher than that\nof the integrated shear .\nthe measurement of local surface shear by a\ncalibrated preston tube appears to be accurate\nand inexpensive . the calibration as given by\npreston must be modified slighlty, however, to yield the\nresults obtained from the floating-element\nskin-friction balance ."}, {"doc_id": 166, "text": "flow of chemically reacting gas mixtures .\n suitable forms of the equations\nfor the flow of an inviscid,\nnon-heat-conducting gas in which chemical\nreactions are occurring are derived .\nthe effects of mass diffusion and\nnon-equilibrium amongst the internal\nmodes of the molecules are neglected .\n special attention is given to\nthe speeds of sound in such a gas\nmixture and a general expression for\nthe ratio of frozen to equilibrium\nsound speeds is deduced . an example\nis given for the ideal dissociating\ngas . the significance of the velocity\ndefined by the ratio of the convective\nderivatives of pressure and density is\nexplained . it is the velocity\nwhich exists at the throat of a\nconvergent-divergent duct under maximum\nmass flow conditions, and it is shown that\nthis velocity depends on the\nnozzle geometry as well as on the 'reservoir' conditions .\n as an illustration the phenomena of\nsound absorption and dispersion are\ndiscussed for the ideal dissociating gas .\nthe results can be concisely\nexpressed in terms of the frozen and\nequilibrium sound speeds, the\nfrequency of the (harmonic) sound\nvibration and a characteristic time for\nthe rate of progress of the reaction ."}, {"doc_id": 167, "text": "linearized flow of a dissociating gas .\nthe equations for planar two-dimensional\nsteady flow of an ideal dissociating gas\nare linearized, assuming small disturbances\nto a free stream in chemical\nequilibrium .\n as an example of their solution, the\nflow past a sharp corner in a supersonic\nstream is evaluated and the variations\nof flow properties in the relaxation zone\nare found . numerical illustrations are\nprovided using an 'oxygen-like' ideal gas\nand comparisons made with a characteristics\nsolution . the flow past a sharp\ncorner can be studied in a conventional\nshock tube and it may be possible to\nverify the present theory experimentally .\nin particular it may prove feasible to\nuse the results to obtain a measure of the\nreaction rates in the gas mixture ."}, {"doc_id": 168, "text": "heat conduction through a gas with one inert internal\nmodel .\n the rate of energy transfer between\nparallel flat plates is evaluated\nwhen the (stagnant) gas between them is\npolyatomic with one inert internal\nmode . deviations of the thermal\nconductivity from the complete equilibrium\nof the inert mode relaxation time\nand the effectiveness of the walls in\nexciting or de-exciting this mode .\nthe results are obtained via a linear\ntheory consistent with small\ntemperature differences between the plates .\n it is found that the eucken-value\nof conductivity could be exceeded\nif the relaxation times are non-zero and\nthe plates very effective in\nexciting the inert mode . when relaxation\ntimes are very short the effect\nof the walls on the energy transfer rate\nis small, but the walls make\ntheir presence felt by distorting the\ntemperature profiles in /boundary\nlayers/ adjacent to the walls which are\nof order in thickness\ntime) . this result is\nanalogous to hirschfelder's (1956) for the\ncase of chemical reactions .\n for experimental measurement of\nconductivity in a hot wire cell type\nof apparatus it is shown that extrapolation\nof measured reciprocal\nconductivities to zero reciprocal pressure\nshould load to the full eucken\nvalue . it is also shown that the slope of\nreciprocal apparent (measured)\nconductivity versus reciprocal pressure\ncurves is a function of relaxation\ntime as well as of the accommodation\ncoefficients . it is quite possible\nthat the relaxation effect here is\ncomparable with the temperature jump\neffects, even for rotation in diatomic molecules ."}, {"doc_id": 169, "text": "on the sudden contact between a hot gas and a cold solid .\nthe flow induced by the sudden contact between a semi-infinite expanse\nof gas and a solid, initially at different temperatures, is examined on\nthe basis of a linear continuum theory . for times large compared with\nthe mean time between molecular collisions in the gas, the velocity\nand pressure disturbances are found to be concentrated around a wave\nfront propagating out from the interface at the ambient isentropic sound\nspeed, whilst, near to the interface, these disturbances are small and\nthe gas temperatures are nearly equal to those predicted by the\nclassical constant pressure heat conduction theory .\nthe possible significance of these results in connection with\nreflected shock wave techniques to measure high temperature gas properties is\ncommented upon ."}, {"doc_id": 170, "text": "the interaction of a reflected shock wave with the\nboundary layer in a shock tube .\n ideally, the reflection of a shock\nfrom the closed end of a shock\ntube provides, for laboratory study,\na quantity of stationary gas at\nextremely high temperature . because\nof the action of viscosity, however,\nthe flow in the real case is not\none-dimensional, and a boundary layer\ngrows in the fluid following the initial shock wave .\n in this paper simplifying assumptions\nare made to allow an analysis\nof the interaction of the shock reflected\nfrom the closed end with the\nboundary layer of the initial shock\nafterflow . the analysis predicts\nthat interactions of several different\ntypes will exist in different\nranges of initial shock mach number .\nit is shown that the cooling\neffect of the wall on the afterflow\nboundary layer accounts for the change\nin interaction type .\n an experiment is carried out which\nverifies the existence of the\nseveral interaction regions and shows\nthat they are satisfactorily\npredicted by the theory . along with these\nresults, sufficient information\nis obtained from the experiments to make\npossible a model for the\ninteraction in the most complicated case .\nthis model is further verified\nby measurements made during the experiment .\n the case of interaction with a\nturbulent boundary layer is also\nconsidered . identifying the type of\ninteraction with the state of\nturbulence of the interacting boundary\nlayer allows for an estimate of the\nstate of turbulence of the boundary\nlayer based on an experimental\ninvestigation of the type of interaction ."}, {"doc_id": 171, "text": "a low density wind tunnel study of shock wave structure\nand relaxation phenomena in gases .\n the profiles and thicknesses\nof normal shock waves of moderate\nstrength have been determined\nexperimentally in terms of the variation\nof the equilibrium temperature\nof an insulated transverse cylinder in\nfree-molecule flow . the shock\nwaves were produced in a steady state in\nthe jet of a low-density wind\ntunnel, at initial mach numbers of 1.72\nand 1.82 in helium and 1.78,\nthe shock thickness, determined\nfrom the maximum slope of the cylinder\ntemperature profile, varied from\nmean free path in the supersonic\nstream . a comparison between the\nexperimental shock profiles and various\ntheoretical predictions leads to the\ntentative conclusions that .. (1)\nthe navier-stokes equations are adequate\nfor the description of the shock\ntransition for initial mach numbers up\nto 2, and (2) the effects of\nrotational relaxation times in air can be\naccounted for by the introduction\nof a /second/ or /bulk/ viscosity\ncoefficient equal to about two-thirds\nof the ordinary shear viscosity ."}, {"doc_id": 172, "text": "some aerodynamic considerations of nozzle afterbody\ncombination .\n the aerodynamic problems associated with\npropulsion-system installations have assumed a role\nof vital importance in the development of supersonic\naircraft . although air-induction systems have received\nmoderate attention in the literature, considerably less\ninformation can be found on the design and installation\nof turbojet exit nozzles . this condition should not be\ninterpreted to indicate a lack of problems in jet-exit\ndesign .\n as flight speeds reach supersonic levels, it becomes\nincreasingly difficult to achieve nozzle installations\nwhich are efficient over the entire speed range . the\ndifficulties largely stem from the fact that the goals of\nhigh jet thrust and low afterbody drag are not always\ncompatible . in many of the compromise solutions, it\nis generally unsatisfactory to examine isolated nozzle\nand afterbody performance . rather they must be\ntreated as a unit, and the complex effects of jet\ninteraction with the external stream must be taken into\naccount . to accomplish this, the nozzle and air-frame\ndesigners must closely coordinate their efforts .\n some of the aerodynamic problems of nozzle\nafterbody combinations are outlined in this report .\nparticular attention is devoted to the influence of the\njet-stream interaction on both nozzle thrust and\nafter-body drag . for this purpose, use is made of shock-\nboundary-layer-interaction concepts . this approach,\nalthough not precise, correctly predicts many trends\nand is generally enlightening ."}, {"doc_id": 173, "text": "the effect of a central jet on the base pressure of\na cylindrical afterbody in a supersonic stream .\n this report describes an experimental investigation\nof the factors affecting the base flow and\njet structure behind a cylindrical after-body with a central nozzle .\nseven interchangeable nozzles were tested .\nsix of these were convergent-divergent, with a design mach\nnumber of 2.0, jet base diameter ratios ranging\nfrom 0.2 to 0.8 and nozzle divergence angles ranging from\nconvergent with a jet base diameter ratio of 0.6 .\n in the main experimental programme the free-stream\nmach number was 2.0 and the boundary layer was\nturbulent both on the after-body and in the nozzle .\nmeasurements were made of the base pressure, the surface\npressure distribution inside the nozzle, the overall thrust\nand the nozzle mass flow, over a range of jet pressures .\nthis programme was supplemented by comparative\ntests with the jet exhausting into still air (static tests) .\nreadings were taken of the internal nozzle pressures\nand the jet thrust at different jet pressures . schlieren\nphotography was used extensively throughout .\n the results of the tests with external flow are\npresented in the form of curves showing the separate effects\nof jet pressure ratio, jet base diameter ratio, nozzle\ndesign mach number and nozzle divergence angle on the\nbase pressure and overall thrust . the special case\nof base bleed is discussed separately . similar curves are\nincluded for the static tests . these show the effect\nof jet pressure ratio and nozzle geometry on the jet thrust .\n a general method of correlating data on annular\nbase pressures is proposed and discussed . essentially, this\nmethod compares the pressure on an annular\nbase with the calculated pressure on the corresponding\ntwo-dimensional base . it correlates the present\nresults reasonably well, but is less successful when applied\nto more extensive data ."}, {"doc_id": 174, "text": "investigation at supersonic speeds of the effects of\njet mach number and divergence angle of the nozzle\nupon the pressure of the base annulus of a body of\nrevolution .\n an investigation has been conducted\nin the langley 9-inch supersonic\ntunnel to determine the jet effects for\nvarying jet mach number and\nnozzle divergence angle upon the pressure\non the base annulus of a model with\na cylindrical afterbody . the tests\nwere conducted over a wide range of\njet static pressure ratios and at a\nreynolds number of approximately\nfree-stream mach numbers of 1.62, 1.94,\nand 2.41 . all testing was conducted\nwith an artificially induced\nturbulent boundary layer along the model .\n in the lower range of jet static\npressure ratios, jet flow from a\nsonic or supersonic nozzle affected\nthe pressure acting on the base\nannulus in essentially the same manner\nas shown in naca rm e53h25 which covers\njet static pressure ratios up to about\npresent results showed that the base\npressure tends to level off with\nincreasing jet static pressure ratio,\nand at the extreme static pressure\nratios reached in tests with sonic\nnozzles the base pressure began to\ndecrease . except in the lower range\nof jet static pressure ratios,\nnozzle divergence angle generally had a\nlarger effect on the base pressures\nthan nozzle mach number,. the increase\nin base pressure for a change in\ndivergence angle from 0 to 10 was\nsmall compared to the increase when\nthe divergence angle was changed from\nand other data indicates that the effects\nof divergence angle were reduced\nwhen the ratio of jet exit diameter to base\ndiameter was decreased . jet\nmach number effects increased with increase in stream mach number ."}, {"doc_id": 175, "text": "experiments with static tubes in a supersonic airstream .\n systematic tests have been made at a mach\nnumber of 1.6 on a family of static tubes . the variables\nwhich have been investigated are the shape of the nose, the\ndistance of the holes downstream, and the inclination of\nthe tube to the flow . pressure measurements have also been\nmade in the vicinity of a shock wave and close to a wall ."}, {"doc_id": 176, "text": "base pressure at subsonic speeds in the presence of\na supersonic jet .\n this paper presents the results of an experimental investigation\ninto the effect of supersonic jets upon the base pressure of a bluff\ncylinder in a uniform subsonic flow . the ratio of jet diameter to base\ndiameter was 0.1875 .\n jet stagnation pressures giving slight under-expansion of the jet\ncause an increase in the base pressure but for larger jet stagnation\npressures the base pressure is again reduced .\n a simple theory, based on a momentum integral, shows the dependence\nof the base drag upon the jet and free stream speeds and upon the\ndimensions of the jet and the base ."}, {"doc_id": 177, "text": "the mixing of free axially-symmetrical jets of mach number 1.40 .\naxially-symmetrical, supersonic, fully-expanded jets of diameter\nabout 0.75 in. and of mach number 1.40 issuing into an atmosphere\nat rest were investigated by schlieren and shadow photography and\nby pressure traversing . the development of the jets was found to\ndepend critically on the strength of the shock waves in the core of the\njet at the nozzle exit . with strong shock waves present the jet spread\nvery rapidly and was very unsteady . the jet did in some cases break up\ninto large eddies of the same size as the diameter of the jet . when\nno disturbances were present in the core of the jet the spreading\nwas far more gradual and the jet showed only slight unsteadiness .\nthe turbulent mixing region of the first part of the jet with strong\nshock waves was investigated in detail by pitot tubes . the first\ninch was found to correspond to a two-dimensional half-jet . the\nvelocity profiles were similar and well represented by the error\nintegral . the rate of spreading was only half the value for\nlow-speed flow . by integrations across the mixing region the\nentrainment and the loss of kinetic energy were determined .\nthese quantities were found to agree well with the values estimated by\nassuming an error-integral velocity profile ."}, {"doc_id": 178, "text": "on full dispersed shock waves in carbon dioxide .\n it is pointed out that, for shock mach numbers between 1 and\nthat the adjustments in the energy in all the degrees of freedom\nproceed slowly and in parallel and occur over a distance large\ncompared with the mean free path . theoretical velocity profiles\nfor such shock waves are given and found to be in excellent\nagreement with interferometric shock-tube observations ."}, {"doc_id": 179, "text": "an analysis of base pressure at supersonic speeds and\ncomparison with experiment .\n in the first part of the\ninvestigation an analysis is made of base\npressure in an inviscid fluid,\nboth for two-dimensional and\naxially-symmetric flow . it is shown that\nfor two-dimensional flow, and also for\nthe flow over a body of revolution\nwith a cylindrical sting attached to\nthe base, there are an infinite\nnumber of possible solutions satisfying\nall necessary boundary conditions\nat any given free-stream mach number .\nfor the particular case of a body\nhaving no sting attached only one\nsolution is possible in an inviscid\nflow, but it corresponds to zero\nbase drag . accordingly, it is concluded\nthat a strictly inviscid-fluid\ntheory cannot be satisfactory for practical applications .\n since the exact inviscid-fluid\ntheory does not adequately describe\nthe conditions of a real fluid flow,\nan approximate semi-empirical theory\nfor base pressure in a viscous fluid\nis developed in a second part of the\ninvestigation . the semi-empirical\ntheory is based partly on\ninviscid-flow calculations, and is restricted\nto airfoils and bodies without\nboat-tailing . in this theory an attempt\nis made to allow for the effects of\nmach number, reynolds number, profile\nshape, and type of boundary-layer\nflow . the results of some recent\nexperimental measurements of base\npressure in two-dimensional and\naxially-symmetric flow are presented for\npurposes of comparison . some\nexperimental results also are presented\nconcerning the support interference\neffect of a cylindrical sting, and\nthe interference effect of a reflected\nbow wave on measurements of base\npressure in a supersonic wind tunnel ."}, {"doc_id": 180, "text": "boundary layer over a flat plate in presence of shear\nflow .\n the governing equations of an incompressible\nboundary layer over a flat plate in the presence of a\nshear flow with finite vorticity are derived . for large\nvorticity, a similarity solution is obtained . for\nmoderate vorticity, one of the governing equations\nis replaced by an approximate one for which\nsimilarity solutions exist ."}, {"doc_id": 181, "text": "some problems on heat conduction in stratiform bodies .\n problems on heat conduction in multilayer bodies lead usually to\ncomplicated calculations . the present paper gives an idea of specific\ndifficulties arising in the case of infinite composite solides .\ngeneral deductions are applied to a special class of questions ."}, {"doc_id": 182, "text": "effect of roughness on transition in supersonic flow .\n further experiments carried out in the 12-inch supersonic wind tunnel\nof the jet propulsion laboratory of\nthe california institute of technology\nto investigate the effect of\nthree-dimensional roughness elements (spheres)\non boundary-layer transition on a 10\ntransfer are reported herein . the\nlocal mach number for these tests was\nminimum (effective) size of trip\nrequired to bring transition to its\nlowest reynolds number varies as the\none-fourth power of the distance from\nthe apex of the cone to the trip .\nuse of available data at other mach\nnumbers indicates that the mach\nnumber influence for effective tripping\nis taken into account by the\nsimple expression ."}, {"doc_id": 183, "text": "properties of impact pressure probes in free molecule\nflow .\n an expression has been derived for the mass flow through\na circular tube in free molecule flow when the tube and gas are in\nrelative motion . the gas entering the tube is assumed to have a\nmaxwellian distribution function and the molecular reflection process\nat the wall is assumed to be diffuse .\n the theory has been used to determine the pressure read\nby an impact probe in free molecule flow . although the general\nexpressions derived apply to any value of gas velocity and tube size,\nthe detailed calculations for the pressure probe are difficult except\nfor the case of low speeds and long tubes .\n an experimental check of the theory has been carried out\nusing impact probes in a whirling arm apparatus and in the utia low\ndensity wind tunnel . agreement between theory and experiment is\nquite satisfactory ."}, {"doc_id": 184, "text": "scale models for thermo-aeroelastic research .\n an investigation is made of the\nparameters to be satisfied for\nthermo-aeroelastic similarity . it is concluded\nthat complete similarity obtains\nonly when aircraft and model are identical\nin all respects, including size .\n by limiting consideration to\nconduction effects, by assuming the major\nload carrying parts of the structure\nare in regions where the flow is either\nentirely laminar, or entirely turbulent,\nand by assuming a specific\nrelationship between reynolds number and nusselt\nnumber, an approach to similarity can\nbe achieved for small scale models .\nexperimental and analytical work is\nrequired to check on the validity of these assumptions .\n it appears that existing hot wind\ntunnels will not be completely\nadequate for thermo-aeroelastic work, and\naccordingly a possible layout for\nthe type of tunnel required is described .\nautomatic programmed control of\nthe tunnel would appear to be necessary ."}, {"doc_id": 185, "text": "some possibilities of using gas mixtures other than in\naerodynamic research .\na study is made of the advantages that can be realized in\ncompressible-flow research by employing a substitute heavy gas in place of air .\nmost heavy gases considered in previous investigations are either toxic,\nchemically active, or (as in the case of the freons) have a ratio of\nspecific heats greatly different from air . the present report is based\non the idea that by properly mixing a heavy monatomic gas with a\nsuitable heavy polyatomic gas, it is possible to obtain a heavy gas\nmixture which has the correct ratio of specific heats and which is\nnontoxic, nonflammable, thermally stable, chemically inert, and\ncomprised of commercially available components .\ncalculations were made of wind-tunnel characteristics for 63 gas pairs\ncomprising 21 different polyatomic gases properly mixed with each of\nthree monatomic gases (argon, krypton, and xenon) . for a given\nmach number, reynolds number, and tunnel pressure, a gas-mixture\nwind tunnel having the same specific-heat ratio as air would be\nappreciably smaller and would require much less power than a\ncorresponding air wind tunnel . analogous though different advantages\ncan be realized in compressor research and in firing-range research .\nthe most significant applications, perhaps, arise through selecting and\nproportioning a gas mixture so as to have at ordinary wind-tunnel\ntemperatures certain dimensionless characteristics which air at\nflight temperatures possesses but which air at ordinary wind-tunnel\ntemperatures does not possess . characteristics which involve the\nrelaxation time (or bulk viscosity), the variation of viscosity with\ntemperature, and the variation of specific heat with temperature fall\nwithin this category . other applications arise in heat-transfer\nresearch since certain gas mixtures can be concocted to have any prandtl\nnumber in the range at least between 0.2 and 0.8 ."}, {"doc_id": 186, "text": "base pressure in supersonic flow .\n the problem of accurately predicting the pressure and wake\nconfiguration at the base of bodies in supersonic flow is an\nextremely important one inasmuch as a sizeable portion of the total\ndrag of a given body may be attributable to the low pressure in\nthis region . although a great deal of theoretical and experimental\nwork has been done in this field, there does not yet exist a\nsatisfactory method for accurate predictions .\n this paper represents an excellent effort to experimentally\nconfirm analytically deduced concepts . a large amount of\nexperimental data on body shapes such as wedges, cones, and\ncone-cylinders has been obtained over a range of mach numbers up to 4 .\nthe data are thoroughly discussed with respect to analytical\ndeductions . on the basis of the evidence accumulated it is\nconcluded that the boundary-layer thickness has only a small effect\non the base pressure for axisymmetric bodies and for\ntwo-dimensional bodies when the base height-to-chord ratios are of\nthe order .\n reviewer believes this report is a significant contribution in the\nfield of base pressure and wake flow phenomena ."}, {"doc_id": 187, "text": "investigation of separated flows in supersonic and subsonic\nstreams with emphasis on the effect of transition .\nexperimental and theoretical research has been conducted on\nflow separation associated with steps, bases, compression corners,\ncurved surfaces, shock-wave boundary-layer reflections, and\nconfigurations producing leading-edge separation . results were\nobtained from pressure-distribution measurements,\nshadow-graph observations, high-speed motion pictures, and oil-film\noptics . the maximum scope of measurement encompassed\nmach numbers between 0.4 and 3.6, and length reynolds\nnumbers between 4000 and 5000000 .\n the principal variable controlling pressure distribution in\nthe separated flows was found to be the location of transition\nrelative to the reattachment and separation positions .\nclassification is made of each separated flow into one of three regimes ..\nand /turbulent/ with transition upstream of separation .\nby this means of classificaiton it is possible to state rather\nliteral results regarding the steadiness of flow and the influence\nof reynolds number within each regime .\nfor certain pure laminar separations a theory for calculating\ndead-air pressure is advanced which agrees well with subsonic\nand supersonic experiments . this theory involves no empirical\ninformation and provides an explanation of why transition\nlocation relative to reattachment is important . a simple analysis\nof the equations for interaction of boundary-layer and external\nflow near either laminar or turbulent separation indicates the\npressure rise to vary as the square root of the wall shear stress\nat the beginning of interaction . various experiments substantiate tnis\nvariation for most test conditions . an incidental\nobservation is that the stability of a separated laminar mixing\nlayer increases markedly with an increase in mach number .\nthe possible significance of this observation is discussed ."}, {"doc_id": 188, "text": "an analysis of base pressure at supersonic velocities and\ncomparison with experiment .\n in the first part of the investigation an analysis is made of\nbase pressure in an inviscid fluid, both for two-dimensional and\naxially symmetric flow . it is shown that for two-dimensional\nflow, and also for the flow over a body of revolution with a\ncylindrical sting attached to the base, there are an infinite\nnumber of possible solutions satisfying all necessary boundary\nconditions at anh given free-stream mach numger . for the\nparticular case of a body having no sting attached only one\nsolution is possible in an inviscid flow, but it corresponds to\nzero base drag . accordingly, it is concluded that a strictly\ninviscid-flow theory cannot be satisfactory for practical\napplications .\n an approximate semi-empirical analysis for base pressure\nin a viscous fluid is developed in a second part of the\ninvestigation . the semi-empirical analysis is based partly on\ninviscid-flow calculations . in this theory an attempt is made to allow\nfor the effects of mach number, reynolds number, profile shape,\nand type of boundary-layer flow . some measurements of base\npressure in two-dimensional and axially symmetric flow are\npresented for purposes of comparison . experimental results\nthen are presented concerning the support interference effect\nof a cylindrical sting, and the interference effect of a reflected\nair wave on measurements of base pressure in a supersonic wind tunnel ."}, {"doc_id": 189, "text": "experimental investigation of base pressure on blunt-trailing-edge\nwings of supersonic velocities .\n measurements of base pressure are presented for 29\nblunt-trailing-edge wings having an aspect ratio of 3.0 and various\nairfoil profiles . the different profiles comprised thickness\nratios between 0.05 and 0.10, boattail angles between --2.9\nand 20, and ratios of trailing-edge thickness to airfoil thickness\nbetween 0.2 and 1.0 . the tests were conducted at mach numbers\nof 1.25, 1.5, 2.0, and 3.1 . for each mach number, the reynolds\nnumber and angle of attack were varied . the lowest reynolds\nnumber investigated was 0.2 x 10 and the highest was 3.5 x 10 .\nmeasurements on each wing were obtained separately with\nturbulent flow and laminar flow in the boundary layer .\nspan-wise surveys of the base pressure were conducted on several\nwings .\n the results with turbulent boundary-layer flow showed only\nsmall effects on base pressure of variations in reynolds number,\nairfoil profile shape, boattail angle, and angle of attack . the\nprincipal variable affecting the base pressure for turbulent flow\nwas the mach number . at the highest mach number\ninvestigated (3.1), the ratio of boundary-layer thickness to\ntrailing-edge thickness also affected the base pressure significantly .\n the results obtained with laminar boundary-layer flow to\nthe trailing edge showed that the effect of reynolds number on\nbase pressure was large . in all but a few exceptional cases\nthe effects on base pressure of variations in angle of attack and\nin profile shape upstream of the base were appreciable though\nnot large . the principal variable affecting the base pressure\nfor laminar flow was the ratio of boundary-layer thickness to\ntrailing-edge thickness .\n for a few exceptional cases involving laminar flow to the\ntrailing edge, the effects on base pressure of variations in profile\nshape, boattail angle, and angle of attack were found to be\nunusually large . in such cases the variation of base pressure\nwith angle of attack was discontinuous and exhibited a\nhysteresis . stroboscopic schlieren observations at a mach number\nof 1.5 indicated that these apparently special phenomena were\nassociated with a vortex trail of relatively high frequency ."}, {"doc_id": 190, "text": "on magnetohydrodynamic shock waves .\n in the earlier attempts at finding the jump conditions\nacross a hydromagnetic shock wave (1, 2, 3)\nvarious simplifying assumptions\nregarding the shape of the shock and the\ndimensions and the character of the\nmotion are made . from that analysis it\nis possible to write down the jump\nconditions in a higher degree of generality (4) .\n the shock conditions for magnetohydrodynamic\nflows can, however, be\nderived in their full generality with the help\nof the transport equation as used by\nthomas (5) in the derivation of shock conditions\nin conventional gas dynamics .\n the purposes of this paper are ..\ncover the present more general case .\nthat every flow and field quantity\ndownstream from the shock wave is\nexpressible separately in terms of\nthe known values of these quantities\nupstream from the shock wave .\nin this rearranged form of the equations,\nvarious effects of the shock\nwave can be easily read off .\nthe shock conditions along the same\nlines as in conventional gas dynamics ."}, {"doc_id": 191, "text": "a theory for the core of a leading edge vortex .\n in the flow past a slender delta wing\nat incidence can be observed a\nroughly axially symmetric core of spiralling\nfluid, formed by the rolling up\nof the shear layer that separates from a\nleading edge . the aim in this\nreport is to predict the flow field within\nthis vortex core, given\nappropriate conditions at its outside edge .\n the basic assumptions are\ncore .\nin addition it is assumed that the flow\nis axially symmetric and incompressible .\ntogether, these admit outer and inner\nsolutions for the core from the equations\nof motion .\n for the outer solution the sub-core\nis ignored, and the flow is taken to\nbe inviscid (but rotational) and conical .\nthe resulting solution consists of\nsimple expressions for the velocity components\nand pressure . for the inner\nsolution, which applies to the diffusive\nsub-core, the flow is taken to be\nlaminar, and approximations, some based on\nthe boundary conditions and some\nanalogous to those of boundary layer theory,\nare made . the solution obtained\nin this case is a first approximation, and is\npresented in tabular form .\n a sample calculation yields results\nwhich are in good qualitative and\nfair quantitative agreement with experimental measurements ."}, {"doc_id": 192, "text": "on the hypersonic viscous flow past slender bodies\nof revolution .\n a similar solution of the hypersonic viscous flow past slender bodies\nof revolution is deduced for a special case when the radial coordinate\nof the body surface at section x is proportional to x, where the radial\ncoordinate have the comparable order value with the thickness of the\nboundary layer . here, /similar/ is used in the direct meaning that\ndistributions in the boundary layer keep the similar form lengthwise .\ncalculations are accomplished for the region of strong interaction\nbetween the boundary layer and the shock wave . from several calculations\nit may be expected that if the thickness of the body becomes small, the\nthickness of the layer in which the longitudinal velocity component u is\nrapidly decreased also becomes small, and in the major part of the\nboundary layer, only the normal component v is increased . further if\nthe thickness of the body is increased, then, the height of the shock\nwave, the pressure on the wall, and the shear stress at the wall are\nalso increased while the boundary layer thickness is decreased . the\nnose region is excluded by the reason that the ordinary boundary layer\ntheory will be invalid there ."}, {"doc_id": 193, "text": "a study of inviscid flow about air foils at high supersonic\nspeeds .\nsteady flow about curved airfoils at high supersonic speeds is\ninvestigated analyticially . with the assumption that air behaves\nas a diatomic gas, it is found the the shock-expansion\nmethod may be used to predict the flow about curved airfoils up to\nextremely high mach numbers, provided the flow deflection\nangles are not too close to those corresponding to shock\ndetachment . this result applies not only to the determination of the\nsurface pressure distribution, but also to the determination of the\nwhole flow field about an airfoil . verification of this observation\nis obtained with the aid of the method of characteristics by\nextensive calculations of the pressure gradient and shock-wave\ncurvature at the leading edge, and by calculations of the pressure\ndistribution on a 10-percent-thick biconvex airfoil at 0 angle of\nattack .\nan approximation to the shock-expansion method for thin\nairfoils at high mach numbers is also investigated and is found\nto yield pressures in error by less than 10 percent at mach\nnumbers above three and flow deflection angles up to 25 . this\nslender-airfoil method is relatively simple in form and thus may\nprove useful for some engineering purposes .\neffects of caloric imperfections of air manifest in disturbed\nflow fields at high mach numbers are investigated, particular\nattention being given to the reduction of the ratio of specific\nheats . so long as this ratio does not decrease appreciably below\nto include the effects of these imperfections, should be substantially\nas accurate as for ideal-gas flows . this observation is\nverfied with the aid of a generalized shock-expansion method and a\ngeneralized method of characteristics employed in forms applicable\nfor local air temperatures up to about 5000 rankine .\nthe slender-airfoil method is modified to employ an average\nvalue of the ratio of specific heats for a particular flow field .\nthis simplified method has essentially the same accuracy for\nimperfect-gas flows as its counterpart has for ideal-gas flows .\nan approximate flow analysis is made at extremely high mach\nnumbers where it is indicated that the ratio of specific heats may\napproach close to 1 . in this case, it is found that the\nshock-expansion method may be in considerable error,. however, the\nbusemann method for the limit of infinite free-stream mach\nnumber and specific-heat ratio of 1 appears to apply with\nreasonable accuracy ."}, {"doc_id": 194, "text": "general theory of airfoil sections having arbitrary\nshape or pressure distribution .\n in this report a theory of thin airfoils of small camber is\ndeveloped which permits either the velocity distribution\ncorresponding to a given airfoil shape, or the airfoil shape\ncorresponding to a given velocity distribution to be calculated . the\nprocedures to be employed in these calculations are outlined and\nillustrated with suitable examples ."}, {"doc_id": 195, "text": "correlation of theoretical and photo-thermoelastic\nresults on thermal stresses in idealized wing structure .\nafter a rather complete exploratory program\ndescribed in previous papers, the\nphoto-thermoelastic method was applied to the\nexperimental evaluation of the thermal-stress\ntheories . the new technique was correlated\nwith several theories which analyzed the\ntransient thermal stresses in idealized wing\nstructures of high-speed aircraft . various\ntheories were investigated which represented\nthe same idealized wing models and\ndiffered from each other only in the simplifying\nassumptions regarding the temperature\ndistributions in skin and webs . the theories\nwere evaluated by duplicating the boundary\nand initial conditions on plastic models and\nthen by correlating the theories with the\nobserved fringe orders in nondimensional form .\na significant general conclusion was\nreached after correlating the available theories\nand experimental results . owing to\nsimplifying assumptions concerning the thermal\nbehavior in the flanges, thermal\nstresses predicted by the available theories are all\nhigher than the experimental\nobservation . in some cases the discrepancy is as great as 30 per cent ."}, {"doc_id": 196, "text": "pressure distributions . axially symmetric bodies in\noblique flow .\n a simple picture, known from the work of i. lotz, of the flow over\nthe forward part of a body of revolution in oblique flow is derived\nhere from entirely elementary considerations . the pressure at any\npoint of the (forward part of the) body at any angle of incidence\ndepends on three parameters whose values vary along the body . the\nvariation of these parameters along the body can be determined from a\nrelatively small number of wind tunnel or water tunnel measurements .\nthe necessary water tunnel measurements have been made for four axially\nsymmetric head shapes . additional measurements have been made to\nillustrate the theoretical conclusions . the data for each head shape\nare adequate for a determination of the pressure coefficient at any\npoint on the head shapes at any angle of incidence (up to 6, say) .\nin particular they can be used to determine the peak suction at any\nangle of incidence and so the conditions for the onset of cavitation\non the head ."}, {"doc_id": 197, "text": "pressure distributions on three bodies of revolution\nto determine the effect of reynolds number up to and\nincluding the transonic speed range .\n this paper presents the results of an investigation conducted in\nthe langley 16-foot transonic tunnel to determine the effects of varying\nreynolds number on the pressure distribution on a transonic body of\nrevolution at angles of attack through the transonic speed range . the\neffect of a change in sting cone angle on the pressure distributions\nand a comparison of experimental incremental pressures with theory is\nalso included .\n the models were tested through a mach number range from 0.60 to 1.09 .\nthe reynolds number range based on body length was from 9 x 10 to 39 x\ndiameter was 1.3 x 10 to 4.53 x 10 for the model at 8 angle of attack .\n an increase in reynolds number from 9 x 10 to 39 x 10 affected\nthe longitudinal pressure distributions very slightly . these effects\nwere of such a nature as to cause an increase of 0.05 in the\nnormal-force coefficient of the body when tested in the subcritical cross-flow\nreynolds number range . this increase is in agreement with theoretical\napproximations .\n a comparison between experimental and theoretical values of the\nincremental pressure coefficient due to angle of attack indicated good\nagreement except at angles where separated flow areas existed over the\nbody .\n the effect of a change in sting-cone angle from 5 to 9 on the\npressure distribution of the 120-inch model was negligible up to a\nmach number of 1.05 . at this mach number the effect was to cause a\nsmall increase in the velocity over the rear of the body ."}, {"doc_id": 198, "text": "investigation of a systematic group of naca 1 - series\ncowlings with and without spinners .\n an investigation has been conducted in the langley\npropeller-research tunnel to study cowling-spinner combinations based\non the naca 1-series nose inlets and to obtain systematic\ndesign data for one family of approximately ellipsoidal spinners .\nin the main part of the investigation, 11 of the related spinners\nwere tested in various combinations with 9 naca open-nose\ncowlings, which were also tested without spinners . the effects\nof location and shape of the spinner, shape of the inner surface\nof the cowling lip, and operation of a propeller having\napproximately oval shanks were investigated briefly . in addition, a\nstudy was conducted to determine the correct procedure for\nextrapolating design conditions determined from the low-speed\ntest data to the design conditions at the actual flight mach\nnumber .\n the design conditions for the naca 1-series cowlings and\ncowling-spinner combinations are presented in the form of\ncharts from which, for wide ranges of spinner proportions and\nrates of internal flow, cowlings with near-maximum pressure\nrecovery can be selected for critical mach numbers ranging from\nspinners and the effects of the spinners and the propeller on\nthe cowling design conditions are presented separately to\nprovide initial quantitative data for use in a general design\nprocedure through which naca 1-series cowlings can be\nselected for use with spinners of other shapes . by use of this\ngeneral design procedure, correlation curves established from\nthe test data, and derived compressible-flow equations relating\nthe inlet-velocity ratio to the surface pressures on the cowling\nand spinner, naca 1-series cowlings and cowling-spinner\ncombinations can be designed for critical mach numbers as\nhigh as 0.90 ."}, {"doc_id": 199, "text": "measurement of two dimensional derivatives on a wing-aileron-tab\nsystem .\n measurements have been made of the direct\ntwo-dimensional damping and stiffness derivatives for a\nin incompressible flow .\n corrections arising from the apparatus are discussed and\nreference is made to an attempt to measure the direct\ntab derivatives .\n the effects are shown of frequency parameter, amplitude of\noscillation, reynolds number, aileron angle and position\nof transition on the wing .\n variation with frequency parameter is substantially the\nsame as for vortex-sheet theory and variation of amplitude\nproduces little change in both derivatives . at the lowest\nreynolds number there is little change in both derivatives\nwith variation of aileron angle for the condition of natural\ntransition, but at higher reynolds numbers the stiffness\nderivatives increase at .\n a forward movement of transition reduces the stiffness\nderivatives at the smaller aileron angles, but at,\nat the lowest reynolds number, an increase results .\n similar trends are observed for the damping derivatives above .\n comparison with vortex-sheet theory shows that the\nmeasured values of the stiffness and damping\nderivatives are approximately 0.6 of the theoretical values .\n measurements have been made of the direct\ntab derivatives and cross aileron-tab derivatives for a\nper cent aileron and 4 per cent (approx.) tab . in addition\nsome measurements of the direct aileron derivatives have been\nmade for comparison with earlier results together with a\nnumber of static derivatives for the wing and controls .\n the influence is shown of frequency parameter, reynolds\nnumber, position of transition, mean tab angle and sealing\nof the control hinge gaps . some tests have been made with\nthe ailcron set at minus 8 deg and the tab at plus 12 deg\nfor which condition the hinge moment on the aileron was zero .\n reasonable agreement with the values given by the /equivalent\nprofile/ theory is shown for both direct damping\nderivatives and for the direct tab stiffness derivative . the direct\naileron stiffness derivative shows some departure from\nthe theoretical value when .\n at and the natural transition, comparison\nwith the values given by flat-plate theory gives the\nfollowing approximate factors, where suffix denotes the\ntheoretical values .."}, {"doc_id": 200, "text": "calculation of derivatives for a cropped delta wing\nwith subsonic leading edges oscillating in a supersonic\nairstream .\n the lift, pitching moment and full-span\nconstant-chord control hinge-moment are derived for a cropped\ndelta wing describing harmonic plunging and pitching\noscillations of small amplitude and low-frequency parameter in\na supersonic air stream . it is assumed that (a) the wing\nhas subsonic leading edges, (b) the wing is sufficiently thin\nand the mach number sufficiently supersonic to permit the\nuse of linearised theory .\n expressions for the various derivative coefficients are\nobtained for a particular delta wing of aspect ratio 1.8 and\ntaper ratio these are avaluated and tabulated for mach\nnumbers 1.1, 1.15, 1.2, 1.3, 1.4, 1.5, 1.6 and 1.944 ."}, {"doc_id": 201, "text": "supersonic flow past oscillating airfoils including\nnonlinear thickness effects .\n a solution to second order in thickness is derived for\nharmonically oscillating two-dimensional airfoils in supersonic\nflow . for slow oscillations of an arbitrary profile, the result is\nfound as a series including the third power of frequency . for\narbitrary frequencies, the method of solution for any specific\nprofile is indicated, and the explicit solution derived for a single\nwedge .\n nonlinear thickness effects are found generally to reduce the\ntorsional damping, and so to enlarge the range of mach numbers\nwithin which torsional instability is possible . this\ndestabilizing effect varies only slightly with frequency in the range\ninvolved in dynamic stability analysis, but may reverse to a\nstabilizing effect at high flutter frequencies . comparison with\na previous solution exact in thickness suggests that nonlinear\neffects of higher than second order are practically negligible .\n the analysis utilizes a smoothing technique that replaces\nthe actural problem by one involving no kinked streamlines .\nthis stratagem eliminates all consideration of shock waves\nfrom the analysis, yet yields the correct solution for problems\nthat actually contain shock waves ."}, {"doc_id": 202, "text": "aircraft flutter .\n the term flutter is used here to denote maintained or\nviolent oscillations of a structure due to aerodynamic forces\nacting in conjunction with both elastic and inertial forces .\nattention is restricted to this particular branch of the more\ngeneral field of aeroelasticity, which embraces buffeting,\ndivergence, and reversal of control, as well as flutter,. airscrew\nflutter is not specifically considered . the monograph is\ndivided into three main parts, each of which has been made\nself-contained for the convenience of readers .\n in the first part, general methods for the investigation\nof aircraft flutter, by theoretical analysis and by experiments\non flutter models, are set out and discussed . a detailed\naccount of the aerodynamic theory of wings in non-uniform\nmotion is not included, since this has already been provided\nelsewhere, but methods for the evaluation of the aerodynamic\nforces required in a theoretical flutter analysis are logically\ndeveloped, and a bibliography of researches on the\naerodynamic theory is given in the appendix . investigations\non specific types of aircraft flutter--namely wing flutter,\ncontrol surface flutter, and tab flutter--are discussed in part\nthese various types of flutter are considered, but the practical\ndetails of flutter-prevention devices are omitted . finally,\nin part 3, methods for the experimental determination of\nairloads on oscillating aerofoil systems are described, and\navailable airload measurements are analysed and compared\nwith theoretical results .\n an attempt has been made to refer in the text to all relevant\nbritish work reported by the early part of 1947 . foreign\nwork has been mentioned in parts 1 and 2 only where necessary\nfor the sake of completeness, but in part 3 and the\nappendix all relevant foreign references known to the author have\nbeen included .\n matrix notation has been used for the theoretical treatment in\npart 1, but otherwise its use has been avoided ."}, {"doc_id": 203, "text": "calculated velocity distributions and force derivatives\nfor a series of high-speed aerofoils .\n the polygon method of woods is used to\ncalculate the velocity distribution over a number of\ntwo-dimensional aerofoils at low incidence, subcritical flows only\nbeing considered . lift slopes and aerodynamic centres\nat zero lift are also calculated .\n some comparisons with experimental results are made, and\nthese show good agreement at zero incidence ."}, {"doc_id": 204, "text": "a study of the application of airfoil section data\nto the estimation of the high subsonic speed characteristics\nof swept wings .\n estimates of the variation with\nmach number of the aerodynamic\ncharacteristics of swept wings are made\non the basis of airfoil section\ndata combined with span-loading theory .\nthe analysis deals with\nexaminations of some 26 wings and wing-body\ncombinations ranging in sweep\nangle from 30 to 60 and for mach\nnumbers between 0.6 and 1.0 .\n results of the study indicate\nthat the two-dimensional section data\nafford good qualitative information\nfor such high-speed aerodynamic\ncharacteristics as the variation with\nmach number of drag, zero-lift\npitching-moment coefficient, and lift\ncoefficient for flow separation .\nquantitative estimates of the force\nand moment divergence mach numbers\ncould not be made with any degree of\ncertainty from the airfoil data\nalone . somewhat improved quantitative\nestimates for a given\nconfiguration were obtainable by basing the\nestimates on the measured\ncharacteristics for a wing of similar plan form\nbut different section, and\nadjusting for the effects of differences in\nsection on the basis of section data ."}, {"doc_id": 205, "text": "a correlation of airfoil section data with the aerodynamic\nloads measured on a 45 sweptback wing at subsonic mach\nnumbers .\n an investigation has been made of the possibility of correlating\nairfoil section data with measured pressure distributions over a 45\nsweptback wing in the mach number range from 0.50 to 0.95 at a\nfree-stream reynolds number of approximately 2 million .\nthe wing had an aspect ratio\nof 5.5, a taper ratio of 0.53, naca 64a010 sections normal to the\nquarterchord line, and was mounted on a slender body of revolution .\n at mach numbers of 0.85 and below, and for wing normal-force\ncoefficients below the maximum normal-force coefficient for an\ninfinite-aspect-ratio wing yawed 45 to the flow (derived from airfoil section\ndata by simple sweep relations), good correlation was obtained over most\nof the wing between wing-section and two-dimensional-airfoil pressure\ndistributions . for greater normal-force coefficients lateral\nboundary-layer flow permitted the inboard wing sections to rise to high maximum\nsection normal-force coefficients . the effectiveness of this lateral\nboundary-layer flow disappeared towards the tip . for all mach numbers,\nthe influence of plan-form effects on the pressure distributions limited\nthe quality of the correlation at the 20- and 95-percent-semispan\nstations . above a mach number of about 0.85 the shock waves\noriginating at the juncture of the body and the wing trailing edge spread over\nthe span, preventing further application of two-dimensional data .\n the spanwise load distributions at moderate normal-force coefficients\ncould be predicted from span-loading theory for the entire mach number\nrange of the tests ."}, {"doc_id": 206, "text": "the applications of the polygon method to the calculation\nof the compressible subsonic flow round two-dimensional\nprofiles .\n this paper sets out the method now used by the author of\napplying the polygon method to the calculation of the compressible\nsubsonic flow round two-dimensional aerofoils . tables have been\nconstructed which can be used for all aerofoil shapes, putting the\npolygon method on the same footing numerically as goldstein's\nmethod has the advantage over approximation 3 that it can be applied in\nthe following cases which are beyond the scope of goldstein's method ..\nconventional aerofoils, (b) the low-speed flow about very thick\naerofoils, e.g., in reference 3 it is applied to circular cylinders, (c)\nthe flow about symmetric aerofoils between either straight or constant\npressure walls, (d) flow in asymmetric channels,\nand (e) more difficult problems\nof the flow about aerofoils in the presence\nof one or two constraining\nwalls (to be published) . a method of\ncalculating lift and moment\ncoefficients, and their rates of change\nwith incidence (a) is also\ngiven in the paper .\n as an example the velocity distribution and the rates of\nchange of the lift and moment coefficients with a are calculated for\nthe aerofoil r.a.e.104 at values of m (mach number at infinity) of 0,\nand 0.7, for various values of the incidence, a . the velocity\ndistributions for zero incidence are found to be in fair agreement with\nthe corresponding experimental results . the results at incidence are\nin satisfactory agreement with the experimental results, not for the\nsame incidence, but for the same lift coefficient . it is found, for\nexample, that at m = 0.7 the theory for a = 0.8 agrees best\nwith experiment for a = 1.0, when the lift coefficients are\napproximately the same ."}, {"doc_id": 207, "text": "laminar boundary layer oscillations and transition\non a flat plate .\n this is an account of an investigation in which oscillations\nwere discovered in the laminar boundary layer along a flat plate .\nthese oscillations were found during the course of an experiment\nin which transition from laminar to turbulent flow was being\nstudied on the plate as the turbulence in the wind stream was\nbeing reduced to unusually low values by means of damping\nscreens . the first part of the paper deals with experimental\nmethods and apparatus, measurements of turbulence and\nsound, and studies of transition . a description is then given\nof the manner in which oscillations were discovered and how\nthey were found to be related to transition, and then how\ncontrolled oscillations were produced and studied in detail . the\noscillations are shown to be the velocity variations\naccompanying a wave motion in the boundary layer, this wave motion having\nall the characteristics predicted by a stability theory based on\nthe exponential growth of small disturbances . a review of this\ntheory is given . the work is thus experimental confirmation\nof a mathematical theory of stability which had been in the\nprocess of development for a period of approximately 40 years,\nmainly by german investigators ."}, {"doc_id": 208, "text": "the hall effect in the viscous flow of ionized gas\nbetween parallel plates under transverse magnetic field .\n the electrical conductivity of an ionized\ngas is anisotropic in the\npresence of magnetic field (hall effect) .\nthe conductivity is expressed by\na tensor in the same form for both fully\nand partially ionized gases . by\nthe use of modified ohm's law and\nconventional magnetohydrodynamical\nequations the incompressible viscous\nflow between parallel plates under\nthe transverse magnetic field is analyzed\nand an exact solution is obtained\nwhen the magnetic reynolds number\nis small . the numerical results\nreveal a remarkable effect of anisotropy\nof conductivity . the acceleration\nand deceleration of viscous ionized\ngas under combined electric and\nmagnetic fields are also calculated ."}, {"doc_id": 209, "text": "boundary layer induced noise in the interior of aircraft .\n at high speeds the turbulent boundary layer washing the\nairplane fuselage excites appreciable skin vibration, promoting strong\nnoise in the interior . the fluctuating exciting pressure distribution\ncan be represented as a pattern of moving waves (fourier integral) .\na running ripple in the skin follows underneath each wave, and the noise\nis ultimately due to these ripples .\n the acoustic effects of the running ripples are calculated\nfor an infinite sheet,. this is considered the main result of the\npaper . supersonically moving ripples radiate strong sound in the form\nof mach waves,. subsonically moving ripples radiate no sound . formulas\nfor the mean square surface pressure and the energy flux are obtained\nfor an assumed idealized turbulent pressure spectrum .\n the results are adapted to provide a tentative estimate of\nthe noise generated at subsonic speeds in a practical fuselage . the\nrunning ripples are almost noise-free, but multiple reflections at the\nframes and stringers promote standing waves . an assumption is used\nto link the two kinds of waves, and this leads to provisional\ncalculations of noise level .. on this basis the noise level is\npredicted to vary as for thin boundary layers, changing\nprogressively to for thick layers ( = external air\ndensity, = speed, = layer thickness, = panel thickness) . some\ncomparisons are made with experiment . finally, an idea for\nminimizing the noise is presented ."}, {"doc_id": 210, "text": "propeller in yaw .\n it was realized as early as 1909 that a propeller in yaw\ndevelops a side force like that of a fin . in 1917, r. g. harris\nexpressed this force in terms of the torque coefficient for the\nunyawed propeller . of several attempts to express the side\nforce directly in terms of the shape of the blades, however, none\nhas been completely satisfactory . an analysis that\nincorporates induction effects not adequately covered in previous work\nand that gives good agreement with experiment over a wide\nrange of operating conditions is presented herein . the present\nanalysis shows that the fin analogy may be extended to the form\nof the side-force expression and that the effective fin area may\nbe taken as the projected side area of the propeller . the\neffective aspect ratio is of the order of 8 and the appropriate dynamic\npressure is roughly that at the propeller disk as augmented by\nthe inflow . the variation of the inflow velocity, for a\nfixed-pitch propeller, accounts for most of the variation of side force\nwith advance-diameter ratio v nd .\n the propeller forces due to an angular velocity of pitch are\nalso analyzed and are shown to be very small for the pitching\nvelocities that may actually be realized in maneuvers, with the\nexception of the spin .\n further conclusions are .. a dual-rotating propeller in yaw\ndevelops up to one-third more side force than a single-rotating\npropeller . a yawed single-rotating propeller experiences a\npitching moment in addition to the side force . the pitching\nmoment is of the order of the moment produced by a force equal\nto the side force, acting at the end of a lever arm equal to the\npropeller radius . this cross-coupling between pitch and yaw\nis small but possibly not negligible .\n the formulas for propellers in yaw derived herein (with the\nexception of the compressibility correction) and a series of\ncharts of the side-force derivative calculated therefrom have been\npresented without derivation in an earlier report ."}, {"doc_id": 211, "text": "effect of slight blunting of leading edge of an immersed\nbody on the flow around it at hypersonic speed .\n manufacturing and maintainance of ideally sharp leading edges\nand noses is practically impossible, hence a discrepancy arises\nbetween the theory established for sharp edges and actual flow\naround slightly blunted edges, where a detached shock is formed\nwith a subsonic adjacent region . semi-empirical method is worked\nout showing that the pressure distribution in the vicinity of the\nleading edge is the same for different thin profiles having the same\nshape of bluntness on their edges or noses . the data for a flat\nplate can be used for all of them . for moderate supersonic speed\nthe pressure on the remaining body is practically unaffected by the\nnose bluntness, and can be computed from a sharp-edge theory .\nfor high supersonic speed a slight blunting of the edge can\nconsiderably alter the pattern of flow over a large region . the method\nconsists in replacing blunted edge by action of concentrated\nforces on the flow,. it is applied to blunted wedge where it shows\ndoubling of the drag computed by classic theory, and to cones,\nwhere the drag of a blunted cone may become smaller than that of\na sharp one ."}, {"doc_id": 212, "text": "theory and tunnel tests of rotor blade for supersonic\nturbines .\n in special circumstances where a large work\noutput is required from a turbine in a single stage\nit is necessary to use high pressure ratios across the\nnozzle blades, thus producing supersonic velocities at\ninlet to the rotor . as part of an investigation into such\nturbines, several designs for the inter-blade passages of\nthe rotor have been tested in a two-dimensional tunnel,\na design theory being developed concurrently .\n the first design, featuring constant passage width\nand curvature as in steam-turbine practice, but having\nthin leading and trailing edges, was found to suffer from\nfocusing of the compression waves from the concave\nsurface, with consequent flow separation from the\nopposite convex surface . it gave a velocity coefficient of\nmeasured at an inlet mach number of 1.90 and turning\nangle of 140 deg . the measured value compares favourably\nwith values from previous steam tests, where the\nresults have been in the range from 0.65 to 0.92 .\n from theoretical reasoning, and from additional test\nobservations, a subsequent passage was designed\nhaving an inlet transition length of small curvature, leading\nto a free-vortex passage of double the transition\ncurvature,. a small amount of contraction was incorporated .\nschlieren photographs showed the flow in this\npassage to be almost shock free . a thin region of low-energy\nair existed close to the convex surface, but\nliquid-injection tests located only one small bubble of reversed flow .\npressure traverses at exit indicated a velocity\ncoefficient of 0.952, based on the area-mean total pressure .\nwhen allowance is made for turning angle and\nreynolds number this result appears to compare quite favourably\nwith previous work .\n it would seem that the optimum blade pitching in a turbine\nwould be about 20 to 30 per cent closer than in a\ntwo-dimensional cascade . however, the resultant pitching\ntends to become very close, except at very large\nturning angles, with the result that in some applications\ndifficulties could arise in the practical design and\nmanufacture .\n several uncertainties remain and the present design must be regarded\nas still experimental ."}, {"doc_id": 213, "text": "the performance of supersonic turbine nozzles .\n an investigation has been conducted\nat the national gas turbine establishment into the\nperformance of turbines having high pressure ratios\nper stage . the present report discusses the mode of\noperation of supersonic nozzles for such turbines,\nand describes a cascade experiment . both theory and\nexperiment demonstrate that the conditions imposed\nupon the supersonic flow immediately downstream\nof the nozzles (e.g., by a following row of rotor blades)\nexert an overriding influence upon the nozzle outlet\nflow angle, and hence upon the maximum pressure\nratio obtainable across the nozzle--providing that the\naxial component of velocity is subsonic . this is an\nimportant difference from the more familiar flow of\nsubsonic turbine nozzles, where, for example, the\ndownstream gas angle is controlled predominantly by the\nnozzle blade shape and spacing . a suitable test technique\nusing a closed-jet tunnel is demonstrated .\n the particular nozzles tested, of convergent-divergent\nform, had a straight-sided divergent portion of\nto axial direction) and a design mach number of 2 .\nthe flow was found to be well behaved as regards shock\npattern, losses, and starting over the range of pressure\nratios tested--between 9 1 and 19 1 . in particular the\nefficiency at the design pressure ratio of 16.6 1 was\nhigh, the velocity coefficient calculated from traverses of\npitot and static tubes being 0.98 .\n for the conversion of pitot to total pressure at a mach\nnumber of 2.5 a high accuracy is important in the\nmeasurement of the static pressure,. nevertheless readings\nfrom a conventional four-hole instrument appear to\nbe reliable ."}, {"doc_id": 214, "text": "on the testing of supersonic compressor cascades .\n to facilitate the development of high speed axial-flow compressors,\nan investigation was made into the possibility of measuring blade\nperformance in a stationary cascade at supersonic speeds . a suitable\ntechnique was developed and the losses in a variety of cascades were\nmeasured, but these losses were too high for the blading to have any\npossible application . it was concluded that if a useful compressor is\nto result, it is essential to test the cascades at mach numbers close to\nthe existing technique was suitable only for zero incidence tests, and\nthus a new approach is necessary .\n some of the fundamentals of this cascade testing at low supersonic\nspeeds are discussed in the light of the current understanding of the\nmode of operation of supersonic compressors at transonic speeds ."}, {"doc_id": 215, "text": "the test performance of highly loaded turbine stages\ndesigned for high pressure ratio .\n a blade design for a highly loaded two-stage\nturbine is described and the test performance of\nthe turbine is presented .\n some of the factors affecting the performance and matching\nof turbine blade rows operating at supersonic\ngas velocity are discussed and investigated by means of tests\non a three-dimensional nozzle cascade tunnel\nand on a variety of single-stage turbine builds ."}, {"doc_id": 216, "text": "the supersonic axial flow compressor .\n an investigation has been made to explore the possibilities of\naxial-flow compressors operating with supersonic velocities into\nthe blade rows . preliminary calculations showed that very\nhigh pressure ratios across a stage, together with somewhat\nincreased mass flows, were apparently possible with\ncompressors which decelerated air through the speed of sound in their\nblading . the first phase of this investigation, which has been\nreported in naca acr l5d20, was the development of efficient\nsupersonic diffusers to decelerate air through the speed of sound .\nthe present report is largely a general discussion of some of the\nessential aerodynamics of single-stage supersonic axial-flow\ncompressors . in the supersonic flow about isolated bodies,\nlarge energy losses usually occur due to wave systems which\nextend far from the bodies . supersonic flow entering a cascade\nis considered and, in this case, the possibility of entirely\neliminating this extended wave system is demonstrated,. thus, no\nreason for supersonic compressors to be necessarily inefficient\nis apparent . the conditions that occur as the flow through the\ncompressor is being started are discussed and a hypothesis as\nto the type of transonic flow which will be encountered is\nproposed .\n as an approach to the study of supersonic compressors, three\npossible velocity diagrams are discussed briefly . because of\nthe encouraging results of this study, an experimental\nsingle-stage supersonic compressor has been constructed and tested in\nfreon-12 . in this compressor, air decelerates through the\nspeed of sound in the rotor blading and enters the stators at\nsubsonic speeds . a pressure ratio of about 1.8 at an efficiency\nof about 80 percent has been obtained ."}, {"doc_id": 217, "text": "flow pattern in a converging-diverging nozzle .\n the present report describes a new method for the prediction\nof the flow pattern of a gas in the two-dimensional and axially\nsymmetrical case . it is assumed that the expansion of the gas is\nadiabatic and the flow stationary . the several assumptions\nnecessary on the nozzle shape effect, in general, no essential\nlimitation on the conventional nozzles . the method is applicable\nthroughout the entire speed range,. the velocity of sound itself\nplays no singular part . the principal weight is placed on the\ntreatment of the flow near the throat of a converging-diverging\nnozzle . for slender nozzles formulas are derived for the\ncalculation of the velocity components as function of the location ."}, {"doc_id": 218, "text": "intensity, scale and spectra of turbulence in mixing\nregion of free subsonic jet .\n the intensity of turbulence, the longitudinal and lateral\ncorrelation coefficients, and the spectra of turbulence in a 3.5\ninch-diameter free jet were measured with hot-wire anemometers at\nexit mach numbers from 0.2 to 0.7 and reynolds numbers from\n the results of these measurements show the following .. (1)\nnear the nozzle (distances less than 4 or 5 jet diam downstream\nof the nozzle) the intensity of turbulence, expressed as percent\nof core velocity, is a maximum at a distance of approximately\nincreasing mach and or reynolds number . at distances greater\nthan 8 jet diameters downstream of the nozzle, however, the\nmaximum intensity moves out and decreases in magnitude until\nthe turbulence-intensity profiles are quite flat and approaching\nsimilarity . (2) the lateral and longitudinal scales of\nturbulence are nearly independent of mach and or reynolds number\nand in the mixing zone near the jet vary proportionally with\ndistance from the jet nozzle . (3) farther downstream of the\njet the longitudinal scale reaches a maximum and then decreases\napproximately linearly with distance . (4) near the nozzle the\nlateral scale is much smaller than the longitudinal and does not\nvary with distance from the centerline, while the longitudinal\nscale is a maximum at a distance from the centerline of about\nmum moves out from the centerline . (6) a statistical analysis\nof the correlograms and spectra yields a /scale/ which, although\ndifferent in magnitude from the conventional, varies similarly\nto the ordinary scale and is easier to evaluate ."}, {"doc_id": 219, "text": "on the strength distribution of noise sources along\na jet .\n the spatial distribution of noise sources along a jet is\ninvestigated by application of lighthill's\ntheory to regions of 'similar'\nprofiles . the analysis refers to the\nnoise power emitted by a 'slice' of\njet (section between two adjacent planes\nnormal to the axis) as a function\nof distance x of the slice from the nozzle .\nit is found that this power\nis essentially constant with x in the initial\nmixing region (x law), then\nfurther downstream (say 8 or 10 diameters\nfrom the nozzle) falls off\nextremely fast (x law or faster) in the\nfully developed jet . because\nof this striking attenuation of strength\nwith distance, it is concluded that\nthe mixing region produces the bulk of\nthe noise and must dominate in\nmuffler behavior,. conversely, the 'fat'\npart of the jet must contribute\nmuch less to the total noise power than is commonly supposed .\n powell's experiments on the effects of nozzle velocity\nprofile on total noise power are interpreted\nqualitatively . the behavior of\nmultiple-nozzle or corrugated mufflers,\nboth as to overall quieting and\nfrequency-shifting, is also interpreted\nin the light of the results . the\npossibility emerges that such mufflers\nmay be improved without serious\nthrust loss by the addition of a sound-attenuating shroud ."}, {"doc_id": 220, "text": "a general purpose analogue correlator for the analysis of\nrandom noise signals .\na large proportion of the current research programme of the\ndepartment of aeronautics and astronautics is concerned with the\nstudy of jet noise and boundary layer pressure fluctuations and\ntheir effect on aircraft structures . early in the work it was\ndecided that for a complete description of the random processes\ninvolved it would be necessary in the experimental programme to\nmake correlation measurements in addition to the more standard\nspectrum and amplitude distribution measurements . it was also\nfelt that it would be desirable from the university point of view\nto construct a general purpose correlator which could later be\nused on other types of work . to this end it was decided to give\nthe correlator a wider bandwidth than might strictly have been\nnecessary for the problems on hand . subsequent development work\nhas amply justified this decision ."}, {"doc_id": 221, "text": "a theoretical study of annular supersonic nozzles .\n this paper is concerned with the design\nof annular supersonic nozzles to produce uniform\nflow in supersonic wind tunnels which are axi-symmetrical\nand which have an internal coaxial circular cylinder\nthroughout . symmetrical two-dimensional and conventional\naxi-symmetrical nozzles are special cases of\nannular nozzles .\n proposals are made for design criteria sufficient to\nensure that the flow inside a nozzle is free from limit\nlines and shock waves,. the criteria for (symmetrical)\ntwo-dimensional and (conventional) axi-symmetrical\nnozzles are new . the two outstanding procedures for\ndesigning two-dimensional and axi-symmetrical nozzles\nare generalised to apply to annular nozzles . one of the\ndesign procedures is mainly analytical and the other is\nmainly numerical,. the analytical expressions in both\nprocedures are made much more complicated by the\npresence of the internal cylinder but the numerical process\ncriteria and the mainly numerical design procedure are\nsuccessfully applied to the design of a particular\nannular nozzle ."}, {"doc_id": 222, "text": "the flow over delta wings at low speeds with leading\nedge separation .\n a low speed investigation of the flow over a 40 apex angle delta\nwing with sharp leading edges has been made in order to ascertain\ndetails of the flow in the viscous region near the leading edge of the\nsuction surface of the wing . a physical picture of the flow was\nobtained from the surface flow and a smoke\ntechnique of flow visualization,\ncombined with detailed measurements of total\nhead, dynamic pressure, flow\ndirections and vortex core positions in the flow above the wing .\n surface pressure distributions were also measured and integrated\nto give normal force coefficients .\n the results of this investigation were compared with those of other\nexperimental investigations and also with various theoretical results .\nin particular, the normal force coefficients, vortex core positions and\nattachment line positions were compared with the theoretical results of\nmangler and smith, reference 19 . it was found that ..\nexist on the upper surface of the wing outboard of and below\nthe main vortices . these secondary vortices are formed as a\nresult of separation of the boundary layers developing outboard\nof the top surface attachment lines ."}, {"doc_id": 223, "text": "a note on the theory of the stanton tube .\n existing theories for the stanton tube are\ncritically reviewed, and the paper then outlines a\nsimple method which predicts the calibration function\nat high reynolds numbers to the right order of\nmagnitude ."}, {"doc_id": 224, "text": "quasi-cylindrical surfaces with prescribed loadings\nin the linearised theory of supersonic flow .\n a formula for the velocity field in terms of a given surface\ndistribution of vorticity is applied to points\nlying on the surface . an equation\ngiving the shape of a quasi\ncircular-cylindrical surface in terms of a\nprescribed loading is derived . as an\nexample a half ring wing with prescribed\nloading is discussed ."}, {"doc_id": 225, "text": "elliptic cones alone and with wings at supersonic speeds .\n to help fill the gap in the knowledge\nof aerodynamics of shapes\nintermediate between bodies of revolution\nand flat triangular wings, force\nand moment characteristics for elliptic\ncones have been experimentally\ndetermined for mach numbers of 1.97 and\nsectional axis ratios from 1 through 6\nand with lengths and base areas\nequal to circular cones of fineness\nratios 3.67 and 5 have been studied\nfor angles of bank of 0 and 90 .\nelliptic and circular cones in\ncombination with triangular wings of aspect\nratios 1 and 1.5 also have been\nconsidered . the angle-of-attack range\nwas from 0 to about 16, and the\nreynolds number was 8x10, based on\nmodel length . in addition to the\nforces and moments at angle of attack,\npressure distributions for elliptic\ncones at zero angle of attack have been determined .\n the results of this investigation\nindicate that there are distinct\naerodynamic advantages to the use of\nelliptic cones . with their major\ncross-sectional axes horizontal, they\ndevelop greater lift and have higher\nlift-drag ratios than circular cones\nof the same fineness ratio and volume .\nin combination with triangular wings\nof low aspect ratio, they also develop\nhigher lift-drag ratios than circular\ncones with the same wings . for\nwinged elliptic cones, this increase\nin lift-drag ratio results both from\nlower zero-lift drag and drag due to\nlift . visual-flow studies indicate\nthat, because of better streamlining\nin the crossflow plane, vortex flow\nis inhibited more for an elliptic cone\nwith major axis in the plane of the\nwing than for a circular cone with the\nsame wing . as a result, vortex\ndrag resulting from lift is reduced .\nshifts in center of pressure with\nchanges in angle of attack and mach\nnumber are small and about the same\nas for circular cones .\n comparisons of theoretical and\nexperimental force and moment\ncharacteristics for elliptic cones indicate\nthat simple linearized (flat plate)\nwing theory is generally adequate even\nfor relatively thick cones .\nzero-lift pressure distributions and drag\ncan be computed using van dyke's\nsecond-order slender-body theory .\nfor winged circular cones, a\nmodification of the slender-body theory of\nnaca rep. 962 results in good agreement\nof theory with experiment ."}, {"doc_id": 226, "text": "aerofoil theory of a flat delta wing at supersonic\nspeeds .\n lift, drag, and pressure distribution of a triangular\nflat plate moving at a small incidence at supersonic\nspeeds are given for arbitrary mach number and aspect ratio .\nthe values obtained for lift and drag are compared with\nthe corresponding values obtained by strip theory . the\npossibility of further applications of the analysis leading up\nto the above results is indicated ."}, {"doc_id": 227, "text": "a technique for improving the predictions of linearised\ntheory on the drag of straight edge wings .\n the curve of drag against mach number for straight-edged wings,\ncalculated by using the linearised theory of supersonic flow, displays\ndiscontinuities in slope at the various mach numbers for which the edges\nare sonic . these features, which are not observed in practice, are due\nto the fact that linearised theory predicts an infinite pressure along\na subsonic or sonic edge . it is shown that if the linearised equation\nof supersonic flow is used to determine the flow over straight-edged\nwings, but the linearised boundary condition is replaced by the full\nplaced by plausible values . on this basis a simple method is derived\nfor improving the linearised predictions of the drag of straight-edged\nwings which exhibits satisfactory agreement with experimental results .\n while the technique is not directly applicable to ridge lines, an\nartifice renders them amenable to similar treatment ."}, {"doc_id": 228, "text": "navier-stokes solutions at large distances from a finite body .\nthis paper is concerned with a theoretical investigation of the flow\nfield at large distances from an object moving through a viscous fluid .\nthe discussion will be restricted to the case of two-dimensional\nstationary incompressible flow . the object will be assumed to be of\nfinite size . the domain of the fluid is infinite and it is assumed\nthat there are no other boundaries for the fluid except that of the\ngiven object . the reynolds number will be assumed to have a fixed\nvalue., thus we shall not consider the limiting cases of the reynolds\nnumber tending to zero or to infinity ."}, {"doc_id": 229, "text": "interference between the wings and tail surfaces of\na combination of slender body, cruciform wings and\ncruciform tail set at both incidence and yaw .\n the interference between the wings and the tail surfaces of a\ncombination of circular body, low aspect ratio cruciform wings and\ncruciform tail in an inviscid flow is analysed using the slender body\ntheory . the system may be subjected to both incidence and yaw and,\nin general, the tail fins may be staggered angularly with respect to\nthe main wings .\n the method is a development of that used by owen and maskell in\nr.a.e. report no. aero.2441 to analyse similar effects on a system set\nat zero yaw .\n simple expressions to determine the strengths and positions of\nthe trailing vortices (supposed to be rolled-up) downstream of the main\nwings are given, and from them the forces on the tail are deduced .\nwhen the tail surfaces are triangular and of low aspect ratio an exact\nsolution is obtained from slender body theory .. but for rectangular\ntail surfaces of moderate or high aspect ratio, it is suggested that the\nchanges in lift and sideforce on the tail caused by the wing vortex\nfield can be estimated approximately from the mean upwash and sidewash\nangles evaluated over the respective tail spans . formulae for these\nmeans angles are presented ."}, {"doc_id": 230, "text": "interference between the wings and tail plane of a\nslender wing-body tailplane combination .\n an approximate method of predicting the interference between\nthe wings and the tailplane of a slender wing-body-tailplane\ncombination in an inviscid flow is developed, in order to explain the change\nin centre of pressure position with incidence which has been found to\noccur in wind tunnel and flight tests on guided weapons . incidence\nchanges in one plane only, normal to the plane containing the wings\nand the tail surfaces, have been considered .\n the method is based on slender body theory and the assumption\nthat the wing trailing vortices roll-up completely before they reach\nthe tailplane,. it is, therefore, applicable to weapons equipped with\nlow aspect ratio wings far separated from the tail surfaces . when\nthe tail surfaces are triangular and of low aspect ratio, an\nanalytical solution is given for the effect of the wing downwash field on\nthe tail lift . for high aspect ratio, rectangular tail surfaces it\nis suggested by comparison with experimental data, that the tail lift\nmay be estimated approximately from the value of the mean downwash\nangle across the tail span .\n a summary of the method is given in para.5 which, in conjunction\nwith the introduction, may be read independently of the rest of the\nreport ."}, {"doc_id": 231, "text": "practical calculation of second-order supersonic flow\npast non-lifting bodies of revolution .\n calculation of second-order supersonic flow past bodies of\nrevolution at zero angle of attack is described in detail, and reduced to\nroutine computation . use of an approximate tangency condition is shown\nto increase the accuracy for bodies with corners . tables of basic\nfunctions and standard computing forms are presented . the procedure is\nsummarized so that one can apply it without necessarily understanding\nthe details of the theory . a sample calculation is given, and several\nexamples are compared with solutions calculated by the method of\ncharacteristics ."}, {"doc_id": 232, "text": "accuracy of approximate methods for predicting pressure\non pointed non-lifting bodies of revolution in supersonic\nflow .\n the accuracy and range of applicability of the linearized theory,\nsecond-order theory, tangent-cone method, conical-shock-expansion theory\nand newtonian theory for predicting pressure distributions on pointed\nbodies of revolution at zero angle of\nattack are investigated . pressure\ndistributions and integrated pressure\ndrag obtained by these methods are\ncompared with standard values obtained\nby the method of characteristics\nand the theory of taylor and maccoll .\nthree shapes, cone, ogive, and a\nmodified optimum body, are investigated\nover a wide range of fineness\nratios and mach numbers .\n it is found that the linearized\ntheory is accurate only at low values\nof the hypersonic similarity parameter\nnumber to body fineness ratio) and that\nsecond-order theory appreciably\nextends the range of accurate application .\nthe second-order theory gives\ngood results on ogives when the ratio of\nthe tangent of maximum surface\nangle to the tangent of the mach angle\nis less than 0.9 . tangent-cone\nmethod cannot be widely applied with\ngood accuracy . in general, the\nconical-shock-expansion theory predicts\npressure and drag within\nengineering accuracy when the hypersonic similarity\nparameter is greater than 1.2 .\nalthough newtonian theory gives good accuracy,\nexcept for cones, at the\nhighest values of the hypersonic similarity\nparameter investigated, it is\nless accurate than the conical-shock-expansion theory ."}, {"doc_id": 233, "text": "the theoretical wave drag of some bodies of revolution .\n this report investigates the wave drag of bodies\nof revolution with pointed or open-nose forebodies\nand pointed or truncated afterbodies . the 'quasi-cylinder'\nand 'slender-body' theories are reviewed, a reversibility\ntheorem is established, and the concept of the interference\neffect of a forebody on an afterbody is introduced .\n the theories are applied to bodies whose profiles are either\nstraight or parabolic arcs, formulae and curves being\ngiven for forebody and afterbody drag, and for the interference\ndrag . the results of the two theories are compared\nand are seen to agree well in the region of geometries where both\ntheories are applicable ."}, {"doc_id": 234, "text": "a second order shock-expansion method applicable to\nbodies of revolution near zero lift .\n a second-order shock-expansion\nmethod applicable to bodies of\nrevolution near zero lift is developed .\nexpressions defining the pressures on\nnoninclined bodies are derived by the\nuse of characteristics theory in\ncombination with properties of the flow\npredicted by the generalized\nshock-expansion method . this result is\nextended to inclined bodies to\nobtain expressions for the normal-force\nand pitching-moment derivatives\nat zero angle of attack . the method is\nintended for application under\nconditions between the ranges of applicability\nof the second-order\npotential theory and the generalized shock-expansion\nmehtod - namely, when the\nratio of free-stream mach number to nose fineness\nratio is in the\nneighborhood of 1 .\n for noninclined bodies, the pressure\ndistributions predicted by the\nsecond-order shock-expansion method are\ncompared with existing experimental\nresults and with predictions of other\ntheories . for inclined bodies, the\nnormal-force derivatives and locations\nof the center of pressure at zero\nangle of attack predicted by the method\nare compared with experimental\nresults for mach numbers from 3.00 to 6.28 .\nfineness ratio 7, 5, and 3\ncones and tangent ogives were tested alone\nand with cylindrical afterbodies\nup to 10 diameters long . in general, the\npredictions of the present method\nare found to be in good agreement with the\nexperimental results . for\nnon-inclined bodies, pressure distributions\npredicted with the method are in\ngood agreement with existing experimental\nresults and with distributions\nobtained with the method of characteristics .\nfor inclined bodies, the\nnormal-force derivatives per radian (for\nnormal-force coefficients\nreferenced to body base area) are predicted\nwithin 0.2 and the locations of\nthe center of pressure are predicted\nwithin 0.2 body diameters . on the\nbasis of these results, the\nsecond-order shock-expansion method appears\napplicable for values of the ratio\nof free-stream mach number to nose\nfineness ratio from 0.4 to 2 ."}, {"doc_id": 235, "text": "on the minimisation and numerical evaluation of wave\ndrag .\n a fourier analysis of the linearised theory expression for the\nzero-lift wave drag of a smooth, slender body in terms of its\ncross-sectional area distribution is used\nto derive the area distribution which\nminimises the expression for given\nlength, volume, nose area, base area\nand n intermediate areas . another\nminimal deduced from this by relaxing\nthe restriction on volume is used to\nevolve a method for the numerical\nevaluation of the original expression .\n two practical applications of these\nresults are discussed . the first\nis in the design of wing-body combinations\nto have small drag rise at\ntransonic speeds . the second is in the\ncalculation of the wave drag of\nwing-body combinations at zero lift,.\nan example is constructed to\nillustrate the method and to give an indication of its accuracy ."}, {"doc_id": 236, "text": "criteria for thermodynamic equilibrium in gas flow .\n when gases flow at high velocity, the rates\nof internal processes may not be fast enough to\nmaintain thermodynamic equilibrium . by defining\nquasi-equilibrium in flow as the condition in which\nthe temperature, pressure, density, and velocity\ndeviate by less than a fixed, small percentage from\nwhat they would be if the flowing gas could actually\nbe in thermodynamic equilibrium, criteria are\nderived for determining whether quasi-equilibrium\nis a stable condition in the flow . by use of\nexcitation of molecular vibration as an example, the\ngeneral properties of criteria curves are discussed and\ninterpreted . a discussion is given of how to use\nthese results to determine definitely whether a flow\nis or is not in thermodynamic equilibrium .\napplications to dissociating gases, to mixtures, and to\nthe phenomenon of /choking/ in a laval nozzle\nare given special consideration . for cases when\napplication of the criteria predict nonequilibrium,\nequations are provided in a form useful for\nnumerical forward integration along streamlines ."}, {"doc_id": 237, "text": "a compressor routine test code .\nthe routine testing of aircraft-type compressors.dash in the main,\naxial-flow, multi-stage compressors.dash requires a compromise between\nresearch accuracy and the practical considerations . this test code\nis the outcome of a survey of compressor testing techniques and\ninstrumentation, initiated and subsequently discussed and endorsed\nby the aerodynamics sub-committee of the gas turbine collaboration\ncommittee .\nthe code aims at defining methods of measurement and weighting whereby\ncompressor performance can be obtained sufficiently accurately\nfor a realistic and direct comparison to be made between one compressor\nand another . the measurement of a quantity at a point in the fluid\nflow, and the averaging and weighting of such measurements have been\ntreated separately as far as is possible .\nthe recommendations are given in the main text, whilst additional\ndiscussion on these is put into the appendices ."}, {"doc_id": 238, "text": "on a determination of the pitot-static tube factor\nat low reynolds numbers, with special reference to\nthe measurement of low air speeds .\n reasons for enquiry--to provide a standard instrument for\nthe calibration of low speed anemometers ."}, {"doc_id": 239, "text": "design and calibration at low speeds of a static tube\nand a pitot-static tube with semi-ellipsoidal nose\nshapes .\n a new static tube and a new pitot-static tube have been designed and\ncalibrated in the no.1 and the no.2 11 ft x 8 ft wind tunnels of the\nr.a.e., using a long static tube, the error of which is believed to be\nvery small, as a standard for comparison .\n the results show that the static pressure measured by these tubes\nis in error due to the supporting strut and to the nose shape of the\ntube by an amount which may be calculated for positions of the static\nslot, or holes, greater than 10 tube diameters ahead of the strut . the\nreadings show no measurable scale effect in the speed range 100-230 ft\nsec . the static tube is insensitive to yaw in the range 1 with a\nsquare-edged slot and is even less sensitive to yaw when the slot edges\nare rounded . the turbulence of the tunnel has an effect on the static\npressure reading ."}, {"doc_id": 240, "text": "a theoretical analysis of heat transfer in regions of separated flow .\n the flow field analyzed consists of a thin, constant pressure\nviscous mixing layer separated from a solid surface by an enclosed\nregion of low-velocity air (/dead air/) . the law of conservation of\nenergy is employed to relate calculated conditions within the\nseparated mixing layer to the rate of heat transfer at the solid\nsurface . this physical speed is app ied to alminar separations in\ncompressible flow for various prandtl numbers, including consideration\nof the case where air is injected into the separated region .\n.A\napplication to turbulent separations is made for a prandtl number of\n.B\nunity in low-speed flow without injection .\nall calculations are for the case of zero boundary-layer thickness at\nthe position of separation .\n for alminar separations the differential equations for viscous flow\nat arbitrary mach number are solved for the enthalpy and velocity\nprofiles within the thin layer where mixing with dead air takes place .\nresults are presented in tabular form for prandtl numbers between 0.1\nand 10 . the rate of heat transfer to a separated laminar region in air\nlaminar boundary layer having the same constant pressure . injection\nof gas into the separated region is calculated to have a powerful effect\nin reducing the rate of heat transfn to the wall . it is calculated\nthat a moderate quantity of gas injection reduces to zero the heat\ntransfer in a laminar separated flow ."}, {"doc_id": 241, "text": "laminar mixing of a non-uniform stream with a fluid\nat rest .\n a theoretical analysis is made of the constant pressure\nlaminar mixing process between a stream having an initial boundary layer\nvelocity profile, and a fluid at rest .\n the present theory follows the methods of w. tollmien and\ns. i. pai with certain modifications .\nthe results apply to incompressible\nflow, but can be extended to the compressible case without difficulty ."}, {"doc_id": 242, "text": "an approximate theory of base pressure in two dimensional\nflow at supersonic speeds .\n an approximate theory of the base pressure in two-dimensional flow\nat supersonic speeds is presented using asimplified representation of\nthe flow and some of the findings of tollmien's work on turbulent mixing\nin incompressible flow . good qualitative predictions of the effects of\na boundary layer, of bleed air and of boat-tailing are obtained ."}, {"doc_id": 243, "text": "investigation with an interferometer of the turbulent\nmixing of a free supersonic jet .\n the free turbulent mixing of a supersonic jet of mach number\nof which a description is given, was used for the investigation .\ndensity and velocity distributions through the mixing zone\nhave been obtained . it was found that there was similarity\nin distribution at the cross sections investigated and that, in\nthe subsonic portion of the mixing zone, the velocity\ndistribution fitted the theoretical distribution for incompressible flow .\nit was found that the rates of spread of the mixing zone both\ninto the jet and into the ambient air were less than those of\nsubsonic jets ."}, {"doc_id": 244, "text": "an improved smoke generator for use in the visualisation\nof airflow, particularly boundary layer flow at high\nreynolds numbers .\nand rapid method by which boundary\nlayer flow was rendered visible has been\npreviously described in the journal of the royal\naeronautical society . it gave promise of\nbeing useful at the highest tunnel speeds provided\na denser smoke could be obtained, which at\nthe same time was free from the troublesome deposits\nassociated with the wood smoke .\nof the aerodynamics division attempts were made\nby the fuel research station to improve the\ndensity of the wood smoke and to reduce the\ndeposits . these they showed were conflicting\nrequirements, and whilst some improvement\nwas effected, it was not sufficient for observation\nin the new tunnels at high speeds .\n the staff of the director-general of scientific\nresearch and development, ministry of supply,\nwas then approached and it was decided to\ndevelop an oil smoke generator from a simple\ngenerator of this type which was demonstrated\nto us . this has been done successfully .\nthe final apparatus in contrast to the wood smoke\ngenerator is light and compact . it takes\nonly a few minutes to start and can be run as long as desired .\nimprovement on the wood smoke both as regards\ndensity and freedom from deposits, which cause\npremature transition . the density and quality\nof the smoke are now under control . smokes\nranging from a light smoke of bluish white colour\nto a heavy smoke dense white in appearance\ncan be obtained . the oil smoke retains the\nadvantages of the wood smoke in that it is\nnon-corrosive and non-irritant, and the smell can be\ntolerated even when it is present in a considerable\nconcentration . a certain amount of condensation\nis inevitable with oil smokes, but with suitable\nprecautions troubles arising from this can be\navoided . a dry solid smoke made by melting a\nhard wax was successfully generated with the\nsame apparatus . unfortunately because of its\nflocculent nature this smoke gave rise to solid\ndeposits when passed through bore tubing,\nleading eventually to complete blockage . this\nseems to be a feature of solid smokes .\n the apparatus has been used to determine\ntransition and laminar separation points on model\nwings in a number of the national physical\nlaboratory tunnels . smoke filaments have been\nmaintained in the laminar state up to wind\nspeeds of 180 ft. sec. in the new tunnels .\n there is much to be said for making a standard\npractice of visualising boundary layer flow on\nmodels, particularly as the technique is simple and\nrapid . it would greatly assist the\ninterpretation of force measurements and the more detailed\nexplorations of the boundary layer by total\nhead tubes and hot wires .\n the use of oil smoke is not limited to\nboundary layer flow visualisation . the apparatus\ndescribed in this report would seem to be\nparticularly suited for educational work in small\ndemonstration tunnels ."}, {"doc_id": 245, "text": "the ground effect on the jet flap in two dimensions .\n this paper presents the results of the first part of an\nexperimental investigation of the ground effect on simple jet flap\naerofoils . in this part of the work an aerofoil having a 58.1 deg jet\nflap was tested under two-dimensional conditions .\n the pressure lift on the aerofoil was measured, with the ground\nat fixed positions, for varying jet momentum coefficients . it was\nfound that the effect of the ground on the pressure lift was very small\nup to a certain critical jet coefficient . on increasing the jet\ncoefficient beyond the critical value a marked loss of pressure lift was\nobserved . this critical value referred to is approximately the same as\nthe jet coefficient at which the jet first hits the ground .\n some significant, though highly tentative comments, are made\nregarding the practical application of this work to the take-off\ncharacteristics of a jet flapped aircraft ."}, {"doc_id": 246, "text": "the design of minimum drag tip fins . with an appendix\n- on the conformal transformation of a wing with a\nfin .\n the report describes an investigation into\nthe design of minimum drag tip fins by lifting line theory . the\nwork is based on an exact solution of the conformal\ntransformation which is applicable to this problem following the\nmethod of trefitz . three types of solution are treated,\ncorresponding to symmetrical upper and lower fins, single\nupper or lower fins, and unequal upper and lower fins .\na representative range of solutions for circulation distribution\nalong wing and fins has been calculated for each of the\nthree cases by the use of elliptic and theta functions .\n a detailed account is given, with examples, of the\nprocedure for calculating the plan of wing and fins, the lift and\ninduced drag, and the setting of the fins ."}, {"doc_id": 247, "text": "the calculation of the pressure distribution on thick\nwings of small aspect ratio at zero lift in subsonic\nflow .\n the method of expressing the velocity increment\nover aerofoils directly in terms of the section ordinates\nwings of finite aspect ratio . the wings considered are\nuntapered in plan-form but may be tapered in thickness .\nthe section can be of any given shape so that in this sense\nthe analysis is more general than that of refs. 3 to 6 which\ndeal with wings of biconvex section .\n the coefficients required in the calculation are tabulated\nfor the centre-section of straight and swept-back wings\nof aspect ratios 0.5,. 1,. 2,. and 4, the wing of infinite\naspect ratio having been\ntreated in ref. 1 . the remaining calculations can be made\nvery quickly .\n since wings of very small aspect ratio can be treated also by\nthe method of slender-body theory, the relations between\nlinear theory, slender-body theory, and linearised slender-body\ntheory are discussed . for the special case of ellipsoids,\nthe results obtained from the various methods are compared\nwith the exact solution ."}, {"doc_id": 248, "text": "the application of lighthill formula for numerical\ncalculation of pressure distributions on bodies of\nrevolution at supersonic speed and zero angle of attack .\nan integral expression, given by lighthill and based\non linearized theory, for the external\nsupersonic flow over the surface of slender pointed\nor ducted bodies of revolution at zero\nangle of attack is shown to give a good approximation\nof the exact flow for a much wider mach\nnumber and thickness range than could be expected from\nlinearized theory . a numerical method,\nbased on this expression, is developed and applied for\ndigital computing . some results from\napplying the digital computing procedure for determining\nthe pressure distribution and wave\ndrag for various bodies of revolution are given ."}, {"doc_id": 249, "text": "formulae for the computation of the functions employed\nfor calculating the velocity distribution about a given\naerofoil .\n in order to determine the velocity distribution\nabout an arbitrary aerofoil, it is necessary to evaluate\nthe functions and (in the notation of aerofoil theory)\nwhen is given numerically . if the values of are specified\nat 2n points equally spaced about the circle into which the\naerofoil is transformed, the formulae obtained here may be\nused to calculate these functions at the same points .\nformulae are also given for calculating the integrals of or,\nsince these have application to the design of aerofoils by\nthwaites's numerical method .\n the simplicity of the formulae for and enables\nthe effect on the velocity distribution of a local change of shape\nreadily to be determined by making n large . this is\ndiscussed in 3 .\n the formulae are collected in the appendix, and a table\nof the coefficients for the case n = 20 is given ."}, {"doc_id": 250, "text": "pressure distributions at zero lift for delta wings\nwith rhombic cross sections .\n the linearised theory of thin wings is used to calculate pressure\ndistributions over delta wings with rhombic cross sections . a deuce\nprogramme has been written for the calculation and some of the results\nare compared with those of slender thin wing theory ."}, {"doc_id": 251, "text": "a collection of longitudinal stability derivatives\nof wings at supersonic speeds .\n a collection has been made of\ntheoretical data, for wings alone, on\nthose stability derivatives that govern\nthe short-period oscillation of\naircraft travelling at supersonic speeds .\nall the derivatives available\nhave been obtained by means of the linear\ntheory, and so the information\ngiven is subject to the usual limitations .\nthe information has been\npresented in what is hoped is the most\nconvenient form to show its extent,\nand to expose the parts of the field\nwhere experimental investigation is\nmost needed ."}, {"doc_id": 252, "text": "an investigation of interference effects on similar models of\ndifferent size in various transonic tunnels in the u.k. .\ndetails are given of a programme of tests being made on similar\nswept-wing models in transonic tunnels of different types . force measurement\nresults at subsonic speeds in the r.a.e. 3 ft. by 3 ft. slotted tunnel\nshow only small interference effects for models of moderate blockage\nat low incidence., at higher incidences, the interference effect on\nlift becomes appreciably greater than estimated by theory, and\nsignificant pitching moment differences occur, apparently due to wall\ninterference on the wing flow field . comparable but smaller effects\nare evident in the results from the a.r.a. 9 ft. by 8 ft. perforated\ntunnel . at speeds just above m = 1, the force fluctuates as speed\nis increased, because of wave reflection interference . the magnitude\nof the fluctuations diminishes as speed is further increased and this\nreduction is more marked in the perforated tunnel . pressure\nmeasurements along the top of the body at zero incidence show delay in\nshock movements at high subsonic speeds indicating a blockage effect\non speed., the effect is larger in the perforated tunnel though\nsmaller than predicted by theory . above m = 1, both expansion and\nshock waves are strongly reflected in the slotted tunnel but\nconsiderable alleviation, particularly of shock waves, is achieved\nin the perforated tunnel, for which an analysis of the effects is\ngiven, showing for example, the effect of the open-area distribution of\nthe walls ."}, {"doc_id": 253, "text": "on the ground level disturbance from large aircraft\nflying at supersonic speeds .\n the whitham-walkden theory for the estimation of the strength\nof shock waves at ground level from aircraft flying at supersonic\nspeeds is applied to the case of a typical projected supersonic civil\ntransport aeroplane .\n if a figure of 2 lb sq.ft. (including a factor of 2 for ground\nreflection) is taken as an upper limit for the acceptable strength of\nthe bow wave from such an aircraft it is shown that restrictions on\nthe climb and flight plan will be involved . the advantage of the\nemployment of larger engines with or without afterburning is discussed,\nwith reference also to the penalties involved owing to the increase in\nweight of the aircraft and its direct operating costs .\n finally it is suggested that an aircraft of given volume could be\ndesigned, by suitable choice of thickness and lift distribution, to\nminimise the strength of the shock waves in the far field ."}, {"doc_id": 254, "text": "boundary layers with suction and injection . a review\nof published work on skin friction .\n available data on the effects of suction and injection on skin\nfriction are summarised and compared .\n it is shown that injection into a turbulent boundary layer can\nproduce a skin friction coefficient lower than the laminar value at the\nsame reynolds number on an impermeable plate ."}, {"doc_id": 255, "text": "an approximate solution of the turbulent boundary layer\nequations in incompressible and compressible .\n if over the 'outer region' of the boundary layer, where the mean\nvelocity varies but little from its value outside the shear layer, a\nvirtual eddy viscosity is defined, which is constant over the outer\nregion but varies in the direction of the mainstream, a solution of the\nturbulent boundary layer equations can be found which satisfies the\nappropriate boundary conditions . the solution leads to a compatibility\ncondition for the virtual eddy viscosity in terms of the wall shear\nstress, the boundary layer momentum thickness and the mainstream\nvelocity, at least for the case of a constant external velocity . this\ncompatibility condition, which can be expressed as\nfor moderate to high reynolds numbers, where is the shear velocity,\nis the boundary layer thickness and is the virtual eddy (kinematic)\nviscosity, is just the condition townsend (1956) found for the\nequilibrium of the large eddies . the numerical value of the constant\nderived by townsend agrees with ours for reynolds numbers (based on x)\nof about . with this relation for an equation, analoguous to the\nmomentum integral equation solution, can be found for as a function of\nlocal freestream velocity, with one disposable parameter ."}, {"doc_id": 256, "text": "an experimental study of the glancing interaction between\na shock wave and a turbulent boundary layer .\n an experimental study has been made at mach numbers from 1.6 to 2.0 of\nthe interaction between the turbulent\nboundary layer on a side wall of a wind\ntunnel and the shock wave produced by\na plate mounted on the wall . under\nthese conditions the shock wave boundary\nlayer interaction was three\ndimensional at least over the region\ninvestigated (up to 10 boundary layer\nthicknesses from the plate) . it was\nfound that the boundary layer was\nseparated by a shock wave of strength\ntype occur on the sides of fuselages at\nthe wing fuselage junction and may\ntherefore be important with regard to the\ndesign of waisted shapes ."}, {"doc_id": 257, "text": "on turbulen flow between parallel plates .\n the reynolds equations of motion of turbulent flow of\nincompressible fluid have been studied for turbulent\nflow between parallel plates . the number of these\nequations is finally reduced to two . one of these consists of\nmean velocity and correlation between transverse and\nlongitudinal turbulent-velocity fluctuations only .\nthe other consists of the mean pressure and transverse\nturbulent-velocity intensity . some conclusions about\nthe mean pressure distribution and turbulent fluctuations\nare drawn . these equations are applied to two special\ncases .. one is poiseuille flow in which both plates are\nat rest and the other is couette flow in which one plate is at\nrest and the other is moving with constant velocity . the\nmean velocity distribution and the correlation can\nbe expressed in a form of polynomial of the co-ordinate in\nthe direction perpendicular to the plates, with the ratio\nof shearing stress on the plate to that of the corresponding\nlaminar flow of the same maximum velocity as a\nparameter . these expressions hold true all the way across the\nplates, i.e., both the turbulent region and viscous layer\nincluding the laminar sublayer . these expressions for\npoiseuille flow have been checked with experimental data\nof laufer fairly well . it also shows that the logarithmic\nmean velocity distribution is not a rigorous solution of\nreynolds equations ."}, {"doc_id": 258, "text": "the effect of turbulence on slider bearing lubrication .\nbased on prandtl's mixing-length mechanism, the pressure\nequation for turbulent flow in\nslider-bearing lubrication is derived . an analytical\nsolution is given and compared with\nthe one for laminar flow . it is found that the turbulent\neffect increases the pressure and\nconsequently, the load-carrying capacity . however, the\npower loss also increases ."}, {"doc_id": 259, "text": "second order theory for unsteady supersonic flow\npast slender pointed bodies of revolution .\n the thermodynamic properties (z = pv rt, e rt, h rt, s r,\nand pressure) are given for equilibrium mixtures of dissociated and\nionized molecules and atoms of the elements nitrogen and oxygen\nhaving the low temperature composition of .78847 n and .21153 o .\nthe tabulated properties of this mixture (a close approximation to\nthe properties of air) are given at close intervals from 2000 to\nand 10 times the normal density . the results are based on\nchemical equilibria between the species o, o, n, n, no, no, no,\nno, o, o, o, o, n, n, n and electrons . the method of\npresentation permits later corrections for the effect of argon and co\nand the contribution of intermolecular forces . the calculations are\nbased on 9.758 e.v. as the dissociation energy of molecular nitrogen\nand 1.45 e.v. as the electron affinity of atomic oxygen ."}, {"doc_id": 260, "text": "a critical review of skin friction and heat transfer\nsolutions of the laminar boundary layer of a flat plate .\n a review is made of existing literature concerned with\nthe analytical investigation of the velocity and\ntemperature distributions in the boundary layers of a heated (or\ncooled) flat plate . the plate is postulated infinitely thin\nand is parallel to a uniform fluid stream . the more\nrecent solutions include the combined effects of frictional\ndissipation and variable fluid properties . only the results\npertaining to the transfer phenomena occurring at the\nplate surface are included, i.e., skin drag and over-all\nheat transfer,. the individual temperature and velocity\ndistributions leading to these results are omitted ."}, {"doc_id": 261, "text": "experiments on axi-symmetric boundary layers along\na long cylinder in incompressible flow .\n experiments on axi-symmetric boundary\nlayers along a long cylinder were made\nespecially to investigate the effect of transverse\ncurvature on the velocity profile . laminar\nvelocity profiles were measured and compared\nwith theoretical ones with good accuracy .\na representative profile was plotted to see the\neffect of transverse curvature, which showed\nsmall, but obvious effect accompanied by\nincreasing skin friction .\n the transition of the flow from laminar to\nturbulent was observed, and its reynolds\nnumber was estimated to occur at 1.2 1.8x10\nin the present experiment . the turbulent\nprofile was also measured and plotted by using\nthe coordinates to express the wall law\ndeduced by richmond, from which it was\nestimated that, as the ratio of the momentum\nthickness to body radius increases, the profile\nnear the outer layer tends to bend down\nrelative to the line of logarithmic wall law ."}, {"doc_id": 262, "text": "the formation of a blast wave by a very intense explosion .\nthis paper was written early in 1941\nand circulated to the civil defence research\ncommittee of the ministry of home security\nin june of that year . the present writer\nhad been told that it might be possible\nto produce a bomb in which a very large\namount of energy would be released by\nnuclear fission--the name atomic bomb had\nnot then been used--and the work here\ndescribed represents his first attempt to form\nan idea of what mechanical effects might\nbe expected if such an explosion could occur .\nin the then common explosive bomb mechanical\neffects were produced by the sudden\ngeneration of a large amount of gas at a high\ntemperature in a confined space . the\npractical question which required an answer\nwas .. would similar effects be produced\nif energy could be released in a highly\nconcentrated form unaccompanied by the\ngeneration of gas .qm this paper has now\nbeen declassified, and though it has been\nsuperseded by more complete calculations,\nit seems appropriate to publish it as it was\nfirst written, without alteration, except for\nthe omission of a few lines, the addition of\nthis summary, and a comparison with some\nmore recent experimental work, so that\nthe writings of later workers in this field may be appreciated .\n an ideal problem is here discussed . a finite\namount of energy is suddenly released\nin an infinitely concentrated form . the motion\nand pressure of the surrounding air is\ncalculated . it is found that a spherical shock\nwave is propagated outwards whose\nradius r is related to the time t since the explosion\nstarted by the equation\nwhere is the atmospheric density, e is\nthe energy released and s a calculated\nfunction of, the ratio of the specific heats of air .\n the effect of the explosion is to force most\nof the air within the shock front into a\nthin shell just inside that front . as the front\nexpands, the maximum pressure\ndecreases till, at about 10 atm., the analysis ceases\nto be accurate . at 20 atm. 45 of\nthe energy has been degraded into heat which is\nnot available for doing work and used\nup in expanding against atmospheric pressure .\nthis leads to the prediction that an\natomic bomb would be only half as efficient, as\na blast-producer, as a high explosive\nreleasing the same amount of energy .\n in the ideal problem the maximum pressure is\nproportional to r, and comparison\nwith the measured pressures near high explosives,\nin the range of radii where the two\nmight be expected to be comparable, shows that\nthese conclusions are borne out by\nexperiment ."}, {"doc_id": 263, "text": "cylindrical shock waves produced by instantaneous energy\nrelease .\n taylor's analysis of the intense spherical explosion\nhas been extended to the cylindrical case . it is found\nthat the radius r of a strong cylindrical shock wave\nproduced by a sudden release of energy e per unit length\ngrows with time t according to the equation\nwhere is the atmospheric density and\nis a calculated function of the specific\nheat ratio . for is found to be approximately\nunity . for this case, the pressure behind the\nshock wave decays with radius r according to the relation .\napplying the results of this analysis\nto the case of hypersonic flight, it can be shown that\nthe shock envelope behind a meteor or a high-speed\nmissile is approximately a paraboloid given by\nwhere d and v denote the total\ndrag and the velocity of the missile, respectively,\nand x is the distance behind the missile ."}, {"doc_id": 264, "text": "asymptotic solution of the two dimensional oscillating\naerofoil problem for high subsonic mach numbers .\n a new method has been given, for obtaining asymptotic solutions of a\nboundary value problem for the wave equation . the method is simpler\nthan the method previously given by burger, and leads to a result\nidentical with burger's result ."}, {"doc_id": 265, "text": "some instabilities arising from the interaction between\nshock waves and boundary layer .\n a brief review is made of the available information concerning\nthe flow fluctuations and instabilities arising from shock-induced\nseparation in the flow over aerofoils and wings . the influence this\nphenomenon has on the oscillatory behaviour of aerofoils and control\nsurfaces is also briefly discussed .\n a more detailed consideration is devoted to a recent investigation\nat the n.p.l. into the part played by shock-induced separation in the\ninstability of a control surface ."}, {"doc_id": 266, "text": "exact solution of the neumann problem . calculation\nfor non- circulatory plane and axially symmetric flows\nabout or within arbitrary boundaries .\n an exact general method of solving\nthe neumann or second boundary-value\nproblem has been developed and has been\napplied to the calculation of\nlow-speed flows about or within bodies of\nalmost any shape, provided the flow is\neither plane or has axial symmetry .\nsolid-body, inlet, and purely internal\nflow problems can be solved . the\nmethod is capable of dealing with several\nbodies at once in the presence of\none another, and consequently interference\nproblems can be treated with ease .\nboundaries need not be solid, that is,\nflows involving area suction can be\ncalculated . velocities can be computed\nnot only for points on the surface of\nthe body but for the entire flow field .\n a surface source distribution is\nused as a basis for solution . this\nleads to a fredholm integral equation\nof the second kind, which is solved as\na set of linear algebraic equations,\nusually by a modified seidel method .\nat the present time the solution is\nprogramed on the ibm 704 edpm to solve\nthe flow about any body that has the\npreviously mentioned characteristics\nand whose profile can be defined\nsatisfactorily by no more than 300\ncoordinate points . a number of solutions\nare presented, to show both the scope\nof the method and its accuracy .\ncomputations require from three minutes\nto two hours, depending upon the\nshape of the body and the number of points\nused to define it ."}, {"doc_id": 267, "text": "steady and transient free convection of an electrically\nconducting fluid from a vertical plate in the presence\nof a magnetic field .\n an analysis is made for the laminar\nfree convection and heat transfer of\na viscous electrically conducting fluid\nfrom a hot vertical plate in the case\nwhen the induced field is negligible\ncompared to the imposed magnetic field .\nit is found that similar solutions for\nvelocity and temperature exist when\nthe imposed magnetic field (acting\nperpendicular to the plate) varies inversely\nas the fourth root of the distance from\nthe lowest end of the plate . explicit\nexpressions for velocity, temperature,\nboundary layer thickness and nusselt\nnumber are obtained and the effect\nof a magnetic field on them is studied .\nit is found that the effect of the\nmagnetic field is to decrease the rate of\nheat transfer from the wall . in the\nsecond part, the method of characteristics\nis employed to obtain solutions of\nthe time-dependent hydromagnetic free\nconvection equations (hyperbolic) of\nmomentum and energy put into integral\nform . the results yield the time required\nfor the steady flow to be established,\nand the effect of the magnetic field on this time is studied ."}, {"doc_id": 268, "text": "several magnetohydrodynamic free-convection solutions .\nthe influence of transverse magnetic fields on\nthe laminar free-convection flow of liquid\nmetals over a vertical flat plate and between\nvertical parallel plates is examined for\nspecific wall temperature variations and\nprandtl numbers . the extent of influence on\nthe flow and temperature fields is determined\nby the magnitude of a nondimensional\ninfluence parameter which is the ratio of the\nmagnetic force to the buoyant force . in\ngeneral, increasing the magnetic field strength\ndecreases the magnitude of the velocity, wall\nshear, and surfaces heat transfer and\nincreases the temperature throughout the fluid .\nanalytical results demonstrate that magnetic\nfields of practical strengths exert\nconsiderable influence on liquid metal free-convection flow fields ."}, {"doc_id": 269, "text": "on a laminar free-convection flow and heat transfer\nof electrically conducting fluid on a vertical flat\nplate in the presence of a transverse magnetic field .\n the free-convection flow and heat transfer of an\nelectrically conducting fluid on a\nvertical plate in the presence of a transverse magnetic\nfield is analysed for a magnetic field\nfixed to the electrically non-conducting wall . the\nboundary layer equations for\nself-preserving flows are integrated numerically for the\nprandtl number of unity, and the effect\nof the transverse magnetic field on the velocity\nprofile, temperature profile and rate of\nheat transfer is discussed . it is concluded that\nthe heat transfer rate is reduced as the\nmagnetic field intensity is increased ."}, {"doc_id": 270, "text": "on combined free and forced convection laminar magnetohydrodynamic\nflow and heat transfer in channels with transverse\nmagnetic field .\n combined free and forced convective heat\ntransfer in vertical channels has been studied by many\nresearchers . due to the need for engineering design\ninformation there have been many papers concerning\ncases of fully developed flow with varying wall\ntemperature . forced flows in a channel of electrically\nconducting fluid with a transverse magnetic field\nhave been studied and the large effects of a magnetic\nfield on the flow pattern have been established .\n flows of combined free and forced convection in\nelectrically conducting fluids in vertical channels\nwith a transverse magnetic field are expected to\nattract attention in future engineering applications, for\nexample, in a magneto-hydrodynamic generator or in\nplasma studies . however, except for a report by\ngershuni and zhukhovitskii (1) concerning a\nparticular case, no general study has been published .\n this paper is a general treatment of fully\ndeveloped, free and forced convective, laminar,\nmagneto-hydrodynamic flow in a vertical channel with a\ntransverse magnetic field . it includes combined free and\nforced convective flows in channels without a\nmagnetic field reported by ostrach (2), tao (3), etc. as\nspecial cases . hartmann flow (4) is included in the\nother limit ."}, {"doc_id": 271, "text": "an experimental test of compressibility transformation\nfor turbulent boundary layer .\n discussion of various turbulent-boundary-layer theories, in\nthe light of experimental measurements by matting and co-workers .\nthe application of (1) the mager insulated-wall transformation, and\nand illustrated graphically ."}, {"doc_id": 272, "text": "oscillatory aerodynamic coefficients for a unified supersonic\nhypersonic strip theory .\n the shock tube is shown to be a feasible research tool for\nconducting boundary-layer transition experiments . the use of the\nshock tube permits the study of transition with highly cooled\nboundary layers, as may be encountered on hypersonic vehicles .\n boundary-layer transition investigations have been made on\noptically polished pyrex hemisphere-cylinder and ellipse-cylinder\nmodels with stagnation-to-wall enthalpy ratios between 4.5 and\nroughness estimated to be less than 1 microinch (rms) .\ntransition was detected by measurements of the heat-transfer rates on\nthe model surface .\n the shock tube experiments indicated that a characteristic\nfeature of transition of a highly cooled boundary layer on a\nhemisphere was the simultaneous occurrence of transition over the\nentire supersonic portion of the hemisphere . this implies that\ntransition first occurred in the sonic region . the transition\nreynolds number (based on local fluid properties at the outer\nedge of the boundary layer and the momentum thickness) in the\nsonic region increased from about 225 to 325 as the stagnation-\nto-wall enthalpy ratio increased from about 9.5 to 29.5 . transition\noccurred along the cylindrical portion of the hemisphere-cylinder\nmodel at a nearly constant momentum thickness reynolds\nnumber, increasing from about 400 to 625 as the stagnation-\nto-wall enthalpy ratio increased from about 9.5 to 29.5 .\n the highly cooled boundary layers obtained on the cylindrical\nportion of the shock tube hemisphere-cylinder model provided an\nextension of nasa transition results obtained on a cooled\nhemisphere-cone-cylinder model in a wind tunnel . the transition\nreynolds numbers obtained from these shock tube data were of\nthe same order of magnitude as the minimum transition\nreynolds numbers obtained in the wind-tunnel experiments . the\nresults indicate that, for practical purposes, boundary-layer\ncooling is not a critical transition parameter for blunt bodies with\na highly cooled boundary layer resulting from a stagnation-\nto-wall enthalpy ratio of about 3 to 30 . that is, the transition\nreynolds number did not vary significantly with boundary-\nlayer cooling in this cooling range, but transition always occurred\nat a low reynolds number (between about 350,000 and 750,000\nbased on local external properties and a distance along the body\nsurface from the stagnation point) .\n the boundary-layer history (body shape history) appeared to\nbe an important parameter affecting the magnitude of the\nreynolds number for transition and the amount of increase in the\ntransition reynolds number with increased boundary-layer\ncooling . that is, transition occurred at a lower reynolds\nnumber on the ellipse-cylinder configuration than on the\nhemisphere-cylinder . also, the increase in transition reynolds number with\nan increase in boundary-layer cooling was even less significant\nfor the ellipse-cylinder than the hemisphere-cylinder ."}, {"doc_id": 273, "text": "flow past slender blunt bodies - a review and extension .\n a numerical solution of the inviscid flow field about slender blunt\nbodies of revolution has been developed through a combination of two\nmethods .. the van dyke solution in the subsonic flow\nregion at the nose, and the method of\ncharacteristics in the supersonic region .\nthe results are compared with\nsecond-order blast wave theory and with experimental\ndata,. and the respective merits and\ndeficiencies of the two theoretical methods\nare pointed out . the results of the\nnumerical solution are further used in a\ndiscussion of the entropy layer, to\npropose a possible criterion of entropy layer thickness ."}, {"doc_id": 274, "text": "analysis of quartz and teflon shields for a particular\nre-entry mission .\n the transient performance of\nablation type heat protection shields is\ntreated herein for the surface of\na vehicle returning from outer space to the\nearth . the vehicle weighs 8640 kg,\nhas a ballistic factor of 500 lb ft,\nre-enters with a speed of 11 km sec at\nratio of 0.5, and is subjected to a\nmaximum deceleration of 7.7 times the\ngravity constant .\n by use of well known equations\nfor the heat transfer and the mass\ntransfer at a heated surface, a numerical\ncalculation method is derived which, for\nthe investigated ablation processes,\nyields exact transient solutions of the\nfundamental system of partial differential\nequations . the method is applied\nto various quartz shields and to one\nteflon shield, which all evaporate so\nreadily under the conditions of the\nproblem at hand that practically no flow\nof molten shield material exists .\nthe solutions also show comparatively small\ntemperature changes parallel to the surface .\n the results show that the nose\nof the vehicle is cooled predominantly by\nthe evaporation of the quartz or the\nteflon,. the rest of the vehicle's surface\nis cooled by radiation of the quartz\nor evaporation of the teflon . the large\nmass transfer effects on the nose of\nthe vehicle are detrimental since the\nresulting low surface temperatures prevent\nthe radiative heat transfer out of\nthe shield, which does not involve any\nmass loss, from being the desirable\ngoverning cooling factor ."}, {"doc_id": 275, "text": "the effect of lift on entry corridor depth and guidance\nrequirements for the return lunar flight .\n corridors for manned vehicles are\ndefined consistent with requirements\nfor avoiding radiation exposure and for\nlimiting values of peak\ndeceleration . use of lift increases the depth\nof the entry corridor . mid-course\nguidance requirements appear to be critical\nonly for the flight-path angle .\nincreasing the energy of the transfer orbit\nincreases the required guidance\naccuracy for the flight-path angle .\n corrective thrust applied essentially\nparallel to the local horizontal\nproduces the maximum change in perigee\naltitude for a given increment of\nvelocity . energy required to effect a\ngiven change in perigee altitude\nvaries inversely with range measured\nfrom the center of the earth ."}, {"doc_id": 276, "text": "reaction tests of turbine nozzles for supersonic velocities .\n a machine for testing turbine nozzles by the reaction\nmethod, which was described in a previous paper, was\nused to test a series of convergent-divergent turbine\nnozzles . the results of these tests, along with the test\nof a convergent turbine nozzle, are compared with each\nother and with analytical values . two kinds of analytical\nvalues are employed, namely, the usual values obtained\nfrom an assumed isentropic expansion from inlet state to\nexhaust pressure, and the values obtained from the\nassumption that the processes in the nozzle are isentropic\nexcept for a normal shock which takes up a position in the\nnozzle such as to cause the stream to fill the exit area at\nthe exhaust pressure whenever possible . this latter kind\nof analytical value involves no shock when the exit area can\nbe filled at the exhaust pressure by means of isentropic\nprocesses only, or when the exhaust pressure is lowered\nso far that the shock has passed out of the passage . the\nagreement of the test results with the calculated results\nof this latter kind is good, and the disagreement which\nexists can be attributed largely to separation at the shock\nand to transmission of exhaust-pressure effects upstream\nthrough the boundary layer ."}, {"doc_id": 277, "text": "study of flow conditions and deflection angle at exit\nof two-dimensional cascade of turbine rotor blades\nat critical and supercritical pressure ratios .\n an analysis was made of the flow conditions downstream of a\ncascade of turbine rotor blades at critical and supercritical\npressure ratios . the results of five theoretical methods for\ndetermining the deflection angle are compared with those of an experimental\nmethod using the conservation-of-momentum principle and\nstatic-pressure surveys, and also are compared with an analysis of\nschlieren photographs of the flow downstream of the blades . a two-\ndimensional cascade of six blades with an axial width of 1.80 inches\nwas used for the static-pressure surveys and for some of the\nschlieren photographs . in order to determine the flow conditions several\nblade chords downstream of the cascade, schlieren photographs were\ntaken of the flow through a cascade of 18 blades having an axial\nwidth of 0.60 inch .\n for the blade design studied, even at static-to-total pressure\nratios considerably lower than that required to give critical\nvelocity at the throat section, the flow was deflected in the tangential\ndirection as predicted for the incompressible case . as the pressure\nratio was lowered further, the aerodynamic loading of the rear\nportion of the blade reached a maximum value and remained constant .\nafter this condition was attained, the expansion downstream of the\ncascade took place with a constant tangential velocity so that no\nfurther increase in the amount of turning across the blade row and\nno further increase in the loading of the blade was available ."}, {"doc_id": 278, "text": "on source and vortex distributions in the linearised\ntheory of steady supersonic flow .\n the hyperbolic character of the differential\nequation satisfied by the velocity\npotential in linearized supersonic flow entails\nthe presence of fractional infinities\nin the fundamental solutions of the equation .\ndifficulties arising from this fact can\nbe overcome by the introduction of hadamard's\nfinite part of an infinite integral .\ntogether with the definition of certain counterparts\nof the familiar vector operators\nthis leads to a natural development of the analogy\nbetween incompressible flow\nand linearized supersonic flow . in particular, formulae\nare derived for the field of\nflow due to an arbitrary distribution of supersonic\nsources and vortices .\n applications to aerofoil theory, including the\ncalculation of the downwash in the\nwake of an aerofoil, are given in a separate report (ref. 9) ."}, {"doc_id": 279, "text": "supersonic drag calculations for a cylindrical shell\nwing of semicircular cross section combined with a\ncentral body of revolution .\n a semi-circular ring wing with a body of revolution on\nthe axis is studied to find the wave and the vortex drag for\nvarious chordwise lift distributions and for three values of\na parameter describing the wing geometry . using the\nwave drag obtained from the chordwise loading that gives the\nleast drag, together with the vortex and skin friction drags,\nthe maximum lift to drag ratio for each wing geometry is\ncomputed . compared to the estimates made by lomax and\nheaslet, somewhat lower drags are found ."}, {"doc_id": 280, "text": "the surface oil flow technique as used in high speed\nwind tunnels in the united kingdom .\n an examination has been made of the\nvarious versions of the surface oil\nflow technique used in different high speed\nwind tunnels . to provide\nbackground information for this investigation\nsome systematic tests were made on\na simple model in a small supersonic tunnel .\nthe experience gained made it\npossible to explain many of the variations\nin terms of the different operating\nconditions of the tunnels .\n the time taken to form a pattern\non a typical model is, to a first\napproximation, directly proportional to\nthe value of the parameter,\nthe factor being 36,000 12,000 . the\ntime taken appears to be independent\nof the initial thickness of the oil sheet .\n a general procedure for the development\nof oil mixtures for any purpose\nis suggested ."}, {"doc_id": 281, "text": "higher order approximations for relaxation oscillations .\nthe problem of solving asymptotic developments for all quantities\ninvolved in relaxation oscillations has been solved by haag . this\npaper indicates how one can carry out such developments in a case\nwhich is simple enough to be treated explicitly ."}, {"doc_id": 282, "text": "jet effects on base pressure of conical afterbodies\nat mach 1. 91 and 3. 12 .\n data are presented which show the effect of a jet on base pressure\nfor a series of conical afterbody-jet-nozzle combinations having\nboat-tail angles that varied from 0 to 11 and base-to-jet diameter ratios\nthat varied from 1.11 to 2.67 . the jet nozzles had exit angles from 0\nto 20 and were designed for exit mach numbers from 1.0 to 3.2 .\npressure ratios up to 30 were tested for both a cold (air) and a hot\nnumbers of 1.91 and 3.12 .\n in general, base pressure increased for increasing values of\nboat-tail angle, nozzle angle, jet temperature, and jet total pressure and\nfor decreasing values of base-to-jet diameter ratio, jet mach number,\nand free-stream mach number . the addition of tail surfaces produced\nonly small changes in base pressure .\n for all variables, base pressure is governed by the maximum\npressure rise that can be supported by the wake fluid in the region of the\ntrailing shock . the wake pressure ratio is in turn governed by the jet\nand free-stream mach numbers adjacent to the wake region and by the\nstate of the boundary layer on the boattail and on the nozzle .\n values of wake pressure ratio computed using the theory of korst,\npage, and childs were in good agreement with experimental values for\nconvergent nozzles ."}, {"doc_id": 283, "text": "laminar heat transfer around blunt bodies in dissociated\nair .\n a method of predicting laminar heat-transfer rates to blunt,\nhighly cooled bodies with constant wall temperature in dissociated\nair flow is developed . attention is restricted to the case of\naxisymmetric bodies at zero incidence, although two-dimensional\nbodies could be treated the same way . the method is based on\nthe use of the /local similarity/ concept and an extension of the\nideas used by fay and riddell . a simple formula is given for\npredicting the ratio of local heat-transfer rate to stagnation-point\nrate . it depends on wall conditions and pressure distribution,\nbut not on the thermodynamic or transport properties of the hot\nexternal flow, except at the stagnation point .\n experimental heat-transfer rates obtained with correct\nstagnation-point simulation and high wall cooling in shock tubes are\nalso presented and compared with the theoretical predictions .\non the whole, the agreement is good, although in regions of\nrapidly varying pressure there is evidence that the local similarity\nassumption breaks down, and the theory underestimates the\nactual heat-transfer rate by up to 25 per cent ."}, {"doc_id": 284, "text": "the divergence of supersonic wings including chordwise\nbending .\n the static aeroelastic stability or divergence problem is\ninvestigated for thin supersonic wings when not only the spanwise\nbending and twist are taken into account but also the chordwise\nbending . the problem is treated in successive phases of\nincreasing complexity from the two-dimensional curling-up of the\nleading edge to the three-dimensional stability of the cantilever\nwing . several methods of approach are developed including\nthe nonlinear aspects of the structure and the aerodynamics .\nresults indicate a strong dependence of stability on poisson's\nratio and the magnitude of the deformation ."}, {"doc_id": 285, "text": "on the flutter of panels at high mach numbers .\nthere have recently arisen some questions as to the\npossibility of panel flutter at high dynamic pressures and\nmach numbers . in addition, some doubts have been raised\nabout the convergence of the galerkin method when applied to\nsuch problems . this note is intended to shed light on these\nmatters ."}, {"doc_id": 286, "text": "effect of roll on dynamic instability of symmetric\nmissiles .\n this note attempts to extend the discussion by stating a\nslightly neater form of generalized stability conditions and\ndescribing certain experimental results on dynamic instability ."}, {"doc_id": 287, "text": "some theoretical low-speed loading characteristics\nof swept wings in roll and sideslip .\n the weissinger method for determining additional span\nloading for incompressible flow is used to find the damping in\nroll, the lateral center of pressure of the rolling load, and the\nspan loading coefficients caused by rolling for wing plan forms\nof various aspect ratios, taper ratios, and sweep angles . in\naddition, the applicability of the method to the determination\nof certain other aerodynamic derivatives is investigated, and\ncorrections for the first-order effects of compressibility are\nindicated .\n the agreement obtained between experimentally and\ntheoretically determined values for the aerodynamic coefficients\nindicates that the method of weissinger is well suited to the\ncalculation of the additional span loading caused by rolling\nand for the calculation of such resulting aerodynamic\nderivatives of wings as do not involve considerations of tip suction ."}, {"doc_id": 288, "text": "the rolling up of the trailing vortex sheet and its\neffect on the downwash behind wings .\n the motion of the trailing vortices associated with a lifting wing\nis investigated by theoretical and visual-flow methods for the\npurpose of determining the proper vortex distribution to be used\nfor downwash calculations . both subsonic and supersonic speeds\nare considered in the analysis .\n it is found that the degree to which the vortices are rolled up\ndepends upon the distance behind the wing and upon the lift\ncoefficient, span loading, and aspect ratio of the wing . while the\nrolling up of the trailing vortices associated with high\naspect-ratio wings is of little practical importance, it is shown that, with\nlow-aspect-ratio wings, the trailing vortex sheet may become\nessentially rolled up into two trailing vortex cores within a chord\nlength of the trailing edge .\n the downwash fields associated with the two limiting cases of\nthe flat vortex sheet and the fully rolled-up vortices are\ninvestigated in detail for both subsonic and supersonic speeds . the\nintermediate case in which the rolling-up process is only partially\ncompleted at the tail position is also discussed ."}, {"doc_id": 289, "text": "a theoretical study of the aerodynamics of slender\ncruciform-wing arrangements and their wakes .\n a theoretical study is made of some cruciform-wing\narrangements and their wakes by means of slender-body theory . the\nbasic ideas of this theory are reviewed and equations are\ndeveloped for the pressures, loadings, and forces on slender\ncruciform wings and wing-body combinations . the rolling-up of\nthe vortex sheet behind a slender cruciform wing is considered\nat length and a numerical analysis is carried out using 40\nvortices to calculate the wake shape at various distances behind\nan equal-span cruciform wing at 45 bank . analytical\nexpressions are developed for the corresponding positions of\nthe rolled-up vortex sheets using a 4-vortex approximation to\nthe wake, and these positions are compared with the positions\nof the centroids of vorticity resulting from the numerical analysis .\nthe agreement is found to be remarkably good at all distances\nbehind the wing .\n photographs of the wake as observed in a water tank are\npresented for various distances behind a cruciform wing at 0\nand 45 bank . for 45 bank, the distance behind the wing\nat which the upper two vortices pass between the lower two is\nmeasured experimentally and is found to agree well with the\n the calculation of loads on cruciform tails is considered in\nsome detail by the method of reverse flow, and equations are\ndeveloped for the tail loads in terms of the vortex positions\ncalculated in the earlier analyses ."}, {"doc_id": 290, "text": "dynamic stability of a missile in rolling flight .\n the paper sets down the equations of motion for a symmetric\nrolling missile with respect to axes attached to the missile . the\nmissile may be jet (or rocket) propelled or coasting under\naccelerating or decelerating conditions, respectively, wherein the\nvariable rolling velocity is derived from intentionally or\nunintentionally /canted/ fins and or wings .\n the equations contain a force and moment system that\nincludes, in addition to the usual forces and moments, those due to\nmagnus effects, misaligned surfaces, canted surfaces, jet\nmisalignment, and the linear accelerations in the plane normal to the\nmissile axis .\n the results present general stability criteria for a rolling missile\nwhich are summarized in the /discussion of stability ./"}, {"doc_id": 291, "text": "sweepback effects in the turbulent boundary-layer shock-wave\ninteraction .\n experiments are reported on the interaction of turbulent\nboundary layers and shock waves with sweptback configurations .\nthey show that the peak pressure rise at separation, the\nupstream influence ahead of separation, and the pressure rise at\nreattachment for moderate sweep angles can all be understood by\nsimple extensions of available two-dimensional theories ."}, {"doc_id": 292, "text": "rapid laminar boundary layer calculations by piece-wise\napplication of similar solutions .\n a method is presented for the rapid calculation of the\nincompressible laminar boundary layer in an arbitrary flow around\neither a two-dimensional or a rotationally-symmetrical body .\nthe solution is obtained without recourse to von karman's\nmomentum equation by means of a coarse step-by-step procedure\nin which each segment of the velocity distribution is\napproximated by one of the falkner-skan family of similar flows .\n solutions have at least as much accuracy as those of any other\none-parameter approximate method, and in certain cases the\nsolutions become exact . in regions of accelerating velocity, the\naccuracy appears to be very high . in decelerating flows,\nseparation is predicted somewhat early compared with exact solutions\nthat is, the method is conservative in contrast to the von\nkarman-pohlhausen procedure which sometimes fails to predict\nseparation that actually exists .\n the method is the most rapid hand procedure known to the\nauthor, provided the full history of the boundary layer is\nrequired . if only a thickness such as is needed at one point on a\nsurface, then it is about equal in speed to the quadrature method .\nbut, if several values of or other properties along a surface are\nrequired, it is appreciably faster than the quadrature method .\ncharacteristically, only four steps are needed between the forward\nstagnation point and the pressure peak . once the\nvelocity-distribution data are available, each step in a two-dimensional\ncalculation requires about 5 minutes, using a slide rule ."}, {"doc_id": 293, "text": "recent studies on the effect of cooling on boundary\nlayer transition at mach 4.\nthe advent of high-speed flight has necessitated the study of\nboundary-layer transition on highly cooled bodies .\ninvestigations such as those of references 1-4 have concentrated\non this problem and have indicated, contrary to the trends\npredicted by small-disturbance theory, that premature transition\ncan be found with cooling . this phenomenon, commonly called\ndetail in references 2-5 .\n the purpose of this note is to report some recent transition\ndata obtained on a cooled cone in a mach 4 wind tunnel . the\nmodel, a sharp-tip cone (included angle 13.5), was cooled by\nliquid nitrogen to a temperature of -340 f . the cooling\nmethod and the data analysis are similar to that described in\nreference 3 ."}, {"doc_id": 294, "text": "an investigation of laminar transitional and turbulent\nheat transfer on blunt-nosed bodies in hypersonic flow .\n laminar, transitional, and turbulent heating rates have been\nmeasured by means of the shrouded model technique . the\nreynolds number was varied over a ninefold range,. the enthalpy\nratio (stagnation to wall) varied from 2.3 to approximately 1.5 .\ntwo different pressure distributions were imposed on the model\nwhich consisted of a spherically capped cone .\n the experimental data are compared to the laminar hypersonic\nboundary-layer theory and shown to be in good agreement on the\nconical portion of the model . on the spherical portion the data\nare approximately 20 per cent higher than the theoretical\nprediction . some of this discrepancy can be attributed to radiation to\nthe nose of the model .\n the fully developed turbulent heat-transfer data are compared\nto two theories .. (1) a relatively simple turbulent theory which is\nbased on recent theoretical work and which takes into account\nthe upstream history of the boundary layer, and (2) the flat-plate\nreference-enthalpy theory, which depends on only /local/\nconditions . although both theories are in reasonable agreement with\nthe data, the latter method is simpler and somewhat more\naccurate .\n for transitional flow the theory mentioned first can be readily\nmodified in order to permit reasonable estimates of transitional\nheat transfer to be obtained . on this basis it is possible to\nestimate laminar, transitional, and fully developed turbulent heat\ntransfer under hypersonic blunt-body conditions .\n the behavior of transition reynolds number based on\nmomentum thickness is also discussed and shown to be in quantitative\nagreement with recent shock-tube measurements ."}, {"doc_id": 295, "text": "a note on transitional heat transfer under hypersonic conditions .\nin references 1 and 2 there were presented experimental data on\ntransitional heat transfer on a blunt body under hypersonic-flow\nconditions obtained by the shroud technique . the data were compared\nwith a theoretical prediction of transitional heat transfer based\non a suggestion of persh . the agreement between theory and experiment\nin the transitional region was found to be 'qualitatively good and\nquantitatively fair' .\nit is the purpose of this note to present some additional transitional\ndata obtained in conventional wind-tunnel tests and to indicate a\nmeans for improving somewhat the agreement between transitional\ntheory and experiment ."}, {"doc_id": 296, "text": "notes on waves through gases at pressures small compared\nwith the magnetic pressure, with applications to upper\natmosphere aerodynamics .\nmost treatments of magnetohydrodynamic\nwaves have confined physical\ninterpretation to cases when the alfven velocity a\nis small compared with the sound\nvelocity a . here we consider the 'low-beta\nsituation', in which a is much\nlarger than a . then, except for two modes with\nwave velocity a the only possible\nwaves are longitudinal ones, propagated\nunidirectionally along lines of magnetic\nforce with velocity a . these can be\ninterpreted as sound waves, confined to\neffectively rigid magnetic tubes of force .\nhall-current effects do not alter these\nconclusions (in contrast to the high-beta\nsituation), and finite conductivity\nintroduces only small dissipation .\n an application is made to the flow pattern\naround a body moving through the\nf layer of the ionosphere, where, although\nneutral particles have a very large\nmean free path, charged particles interact\nelectrostatically and, it is argued, may\nbe regarded as forming a continuous fluid\nwhose movement is independent of\nthat of the neutral particles . a body moving\nat satellite speed or below would\nthen excite the above-mentioned unidirectional\nsound waves, but no waves at\nmuch faster alfven velocity . these considerations\nsuggest that its movement\nwould be accompanied by a v-shaped pattern of\nelectron density (figure 2),\nwhich might be in part responsible for some\nanomalous radar echoes that have\nbeen reported ."}, {"doc_id": 297, "text": "compressibility effects in magneto-aerodynamic flows\npast thin bodies .\n the effects of compressibility on the steady motion of a highly\nconducting fluid past thin cylindrical bodies in the presence of a\nmagnetic field are studied . procedures are developed for the\nsolution of this class of magnetoaerodynamic problems over the\nentire mach number range and for all ratios of magnetic to\nfluid-dynamic pressure . the results obtained are analogous either to\nthe ackeret theory or the prandtl-glauert rule of conventional\naerodynamics, depending on the relative values of the flow speed\nand the appropriate speed of propagation of magnetoacoustic\ndisturbances . the methods used and the physical interpretation\nof the solutions obtained vary according to the orientation of the\nmagnetic field with respect to the flow direction .\n the results of the theory are explained in terms of the\nanisotropic propagation of magnetoacoustic pulses studied previously\nby several authors ."}, {"doc_id": 298, "text": "incompressible wedge flows of an electrically conducting\nviscous fluid in the presence of a magnetic field .\n the purpose of this note is to discuss the two-dimensional\nflow of an electrically conducting viscous fluid past a wedge\nin the presence of a magnetic field . the governing differential\nequations and boundary conditions are given and analyzed ."}, {"doc_id": 299, "text": "magnetohydrodynamic flow past a semi-infinite plate .\n the flow of viscous electrically conducting fluid\npast a semi-infinite plate is considered . the\napplied constant magnetic field and the constant\non-coming velocity of the fluid are in the direction parallel\nto the plate .\n in addition to reynolds number the flow in the\nboundary layer depends on two parameters\nand . the two simultaneous\nordinary nonlinear differential equations are solved by\nthe asymptotic method for the cases when\nand respectively .\n the main results obtained are as follows . the\nequations can be solved exactly for and .\nthe perturbation effect from infinity when k is large\ndepends on, whereas the perturbation effect from\nzero when k is small depends on . for large k,\nincluding there is no solution for . it is\nassumed that the fluid is incompressible with constant\nphysical properties ."}, {"doc_id": 300, "text": "on a particular class of similar solutions of the equations\nof motion and energy of a viscous fluid .\n by introducing the similarity concept to the two-dimensional,\nincompressible navier-stokes equations and energy equation, a\nparticular class of solutions is found . two general types of flows\nare considered .. (1) laminar free convection--i.e., flows which\ntake place due to a body force--and (2) laminar forced\nconvection .\n for free convection on vertical plates, similar solutions are\nobtained for two different power-law surface temperature\nvariations, and it is shown that one of these solutions constitutes a\nnew type of boundary problem . results of numerical\nintegrations of the equations are compared with solutions of the similar\nboundary-layer equations for free convection, and it is\ndemonstrated that a range of surface temperature variations exists for\nwhich the boundary layer equations are no longer valid .\n for forced convection, it is shown that the use of similarity\ntransformations provides an alternate method of deriving the\nordinary differential equations for some well-known solutions,\nsuch as couette and stagnation point flows . solutions are\nobtained for radial converging or diverging flows between plane\nsurfaces when the temperatures of the surfaces vary as arbitrary\npowers of the distance from the orgin . results of numerical\nintegrations of the ordinary differential equations are presented\nfor prandtl numbers of 0.01 and 1.0 and for linear surface\ntemperature variations . some rather surprising results are obtained\nfor diverging flows when separation occurs and some revealing\ncomparisons with results from boundary-layer theory are made ."}, {"doc_id": 301, "text": "approximate design of sharp-cornered supersonic nozzles .\na modified parabolic curve appears to be in close proximity to that\nobtained by either the method of characteristics or the wave method .\nthus an attempt has been made to use analytic geometry to determine\napproximately the contour of a two-dimensional, sharp-cornered\nsupersonic nozzle in a very short time ."}, {"doc_id": 302, "text": "approximations for the thermodynamic and transport properties of high\ntemperature air .\nthe thermodynamic and transport properties of high-temperature air are\nfound in closed form starting from approximate partition functions for\nthe major components in air and neglecting all minor components . the\ncompressibility, enthalpy, entropy, the specific heats, the speed of\nsound, the coefficients of viscosity and of thermal conductivity, and\nthe prandtl numbers for air are tabulated from 500degree to 15,000degree\n k over a range of pressure from 0.0001 to 100 atmospheres . the energy\nof air and the mol fractions of the major components of air can be found\n from the tabulated values for compressibility and enthalpy . it is\npredicted that the prandtl number for fully ionized air, which is in\ncomplete equilibrium, will become small compared to unity, the order of\ntransparent to heat flux ."}, {"doc_id": 303, "text": "effect of variable heat recombination on stagnation\npoint heat transfer .\n earlier studies assume an average heat of formation of atoms\nbased upon external flow conditions . it is shown that equilibrium\nheat transfer decreases by 35 for a typical mach number 24 case\nwhen allowance is made for the proportions of air components .\nthe variable recombination energy also results in atom mass\nfractions which are realistically less for equilibrium than frozen\nsituations throughout the cold-wall boundary layer ."}, {"doc_id": 304, "text": "first-order approach to a strong interaction problem\nin hypersonic flow over an insulated flat plate .\n the present paper concerns with\nthe strong interaction phenomenon over an\ninsulated semi-infinite flat plate with a sharp\nleading edge . in particular the main interest\nis in the consistent treatment in which the\nboundary-layer solution may be joined\ncontinuously with the inviscid solution regarding\nflow variables including pressure, normal\nvelocity, temperature (or streamwise velocity) and density .\n it is shown that the behavior of the inviscid\nsolution may be consistent with that of the\nboundary-layer solution to at least first-order\napproximation that is correct to the order of,\nwhere m is the mach\nnumber of undisturbed flow, r the reynolds\nnumber based on the distance from leading\nedge and the ratio of specific heats . then\nthe first-order boundary-layer problem is\nformulated under such an external circumstance\nand an attempt is made for arriving at the solution .\n actual calculations are carried out for both\ncases of air and helium . from the solution\nit is found that the region in which the viscous\neffect plays a significant role is ranged over\nfrom 0 to a certain finite value of n, say n, in\nterms of the similarity coordinate n in the\ncorresponding incompressible boundary layer .\nthe numerical results moreover indicate\nthat the induced pressure is considerably smaller\nthan the estimate of lees (7) obtained by\nhis approximate method in which the effect\nof the first-order induced pressure on the\nboundary layer is ignored and no survey of the\nfirst-order boundary-layer equation is made .\nthe present results are also found to be in\nexcellent agreement with experimental data\nrecently obtained in helium flow by erickson (15) ."}, {"doc_id": 305, "text": "hypersonic strong viscous interaction on a flat plate\nwith surface mass transfer .\nthe present report gives an account of\nthe development of an\napproximate theory to the problem of hypersonic\nstrong viscous interaction\non a flat plate with mass-transfer at the\nplate surface . the disturbance\nflow region is divided into inviscid and\nviscous flow regions . the\nhypersonic small perturbation theory is applied\nto the solution of the inviscid\nflow region . the method of similar solutions\nof compressible laminar\nboundary layer equations is applied to the\ntreatment of the viscous flow\nregion . the law of surface mass-transfer\nfor similar solutions is derived .\nthe pressure and the normal velocity are\nmatched between the inviscid and\nviscous flow solutions . formulas for induced\nsurface pressure, boundary\nlayer thickness, skin friction coefficient,\nand heat transfer coefficient\nare obtained . numerical results and their\nsignificance are discussed .\nfuture improvements are indicated ."}, {"doc_id": 306, "text": "second approximation to laminar compressible boundary\nlayer on flat plate in slip flow .\n the first-order solution for the laminar compressible boundary-layer\nflow over a flat plate at constant wall temperature is given . the\neffect of slip at the wall as well as the interaction between the\nboundary-layer flow and the outer stream flow are taken into\nconsideration . the solution is obtained explicitly in terms of the known zero\norder, or continuum, solution . no\nassumptions regarding the prandtl\nnumber or viscosity-temperature law need be made . it is found that the\nfirst-order solution gives a decrease in heat transfer and, for\nsupersonic flow, an increase in skin friction .\nfor subsonic flow there is no\nfirst-order shear effect . the change in heat transfer is due to slip\nand the change in friction is due to the interaction of the zero- and\nfirst-order velocities at the outer edge of the boundary layer ."}, {"doc_id": 307, "text": "an approximate solution of hypersonic laminar boundary\nlayer equations and its application .\n approximate formulae of the displacement thickness and the skin\nfriction of the hypersonic laminar boundary layer are derived by use of\nvon karman's integral method, assuming the heat-insulated wall, the\nprandtl number of unity and chapman and rubesin's formula for the\nvariation of viscosity with temperature .\nthe results obtained are\ncompared with some exact solutions .\nbecause of the good agreement, it\nseems that these formulae are very useful .\n these formulae, together with the tangent-wedge-approximation, are\napplied to the viscous flow over\nslender bodies with a sufficiently sharp\nleading edge . as an example, the\npressure distribution over a flat plate\nis calculated numerically over the\nentire region of the surface .\ncomparison with other author's theoretical\nresults as well as experimental\nvalues is made ."}, {"doc_id": 308, "text": "on the hypersonic viscous flow past a flat plate with\nsuction or injection .\n the hypersonic viscous flow past a flat\nplate with suction or injection\nis dealt with by karman-pohlhausen's\nmethod in special cases when\nsuction or injection velocity proportional\nto, especially\nfor the region of strong interaction between\nthe shock wave and the\nboundary layer, were p is the pressure on\nthe plate and x is the\ndistance measured along the plate from its leading edge .\n several numerical examples are given,\nwhich shows similar effects of\ninjection to those in the case of incompressible\nflow that the injection\nmakes all the height of the shock wave,\nthe thickness of the boundary\nlayer and the pressure on the plate larger\nthan those in the case of no\ninjection . on the contrary, in the case of\nsuction no remarkable change\nboth in the height of the shock wave and\nthe pressure on the plate can\nbe seen and only the velocity profile in\nthe boundary layer is affected\nby the suction ."}, {"doc_id": 309, "text": "on the motion of a flat plate at high speed in a viscous\ncompressible fluid, ii, steady motion .\n the theory of the steady flow of a viscous compressible fluid\npast a flat plate at high mach number due to lees and\nprobstein is extended by a more complete discussion of the flow in\nthe inviscid layer between the shock wave and the boundary layer .\nit is shown that similar solutions exist in this layer, analogously\nto those found by li and nagamatsu in the boundary layer, and\nthat the two may be joined to give, allowing one minor\nassumption, a full account of the flow . it is shown that the\nboundary-layer equations may be reduced to those for an incompressible\nfluid and that the von karman-pohlhausen method describes\nthe flow in it with good accuracy . the tangent wedge\napproximation for the pressure on the plate, used by lees and his\ncollaborators, is found to be in deficit\nby 10 per cent for air . finally,\nit is shown that the theory for weak interaction cannot be\nextended further without a complete knowledge of the flow ."}, {"doc_id": 310, "text": "hypersonic viscous flow over a flat plate .\n in dealing with the steady laminar viscous flow over a\nsemi-infinite flat plate some of the following topics are discussed .\nthe streamline in the boundary layer over a leading edge of given\nthickness . the rate of growth of the boundary layer in the main stream, and\ncauses of pressure variations .\nasymptotic solutions for thn downstream flow region, including the\njoining interaction of shock waves at the leading edge .\npressure variations in the interanl viscous flow layer and in external\ninviscid flow considered as prandtl meyer flow . in cases of streamline\ndeflection, the free stream mach number, zero pressure gradient, and\nsurface pressure distribution . asymptotic solutions for cases of\nfluid injection of a cool gas . prandtl heat transfer . the joining\ninteraction between the external inviscid flow and the internal viscous\nflow layer . steady laminar hpyersonic viscous flow over a flat wedge\nand a cone ."}, {"doc_id": 311, "text": "a method for predicting the onset of buffeting and other separation\neffects from wind tunnel tests on rigid models .\nthe method is based on the observation of the divergence that occurs in\nthe variation of mean static pressure at the trailing edge of an\naircraft wing at the critical stage in the development of boundary-layer\nseparation when its influence first spreads to the trailing edge and\nthereby to the overall flow .\nthe significance of the trailing-edge pressure variations and their\nconnection with the effects that separation has on the mean and unsteady\n loads is discussed for various types of separation . good prediction\ncan be obtained from wind-tunnel tests, or warning provided in flight,\nfor low-speed separations and for shock-induced ones up to the stage at\nwhich the shock wave reaches the trailing edge . related divergences in\nwake width, lift coefficient, or shock position can also be used .\npressure measurements at other isolated points often indicate the type\nof separation .\ncertain special considerations apply for swept wings .\nthe various flow changes that are considered are illustrated by\nschlieren photographs and described in an appendix ."}, {"doc_id": 312, "text": "chordwise pressure distributions over several naca\n16 series airfoils at transonic mach numbers up to\n1.25 .\n a two-dimensional wind-tunnel\ninvestigation of the pressure\ndistributions over several naca 16-series\nairfoils with thicknesses of\nand design lift coefficients of\nthe langley airfoil test apparatus\nat transonic mach numbers from 0.7 to\nnumber from 2.4 x 10 to 2.8 x 10 and\nin angle of attack from -10 to\nand schlieren flow photographs\nare presented without analysis ."}, {"doc_id": 313, "text": "on alternative forms for the basic equations of transonic\nflow theory .\nattention has been called by numerous authors to the\npossibility of certain alternative forms for the equations for\ntransonic flow about thin wings . it is the purpose of this note\nto contribute to this discussion and to indicate some reasons for\nthe selection of one form of these in preference to another more\nwidely used form ."}, {"doc_id": 314, "text": "simplified method for determination of the critical\nheight of distributed roughness particles for boundary\nlayer transition at mach numbers from 0 to 5.\n a simplified method has been devised for determination of the\ncritical height of three-dimensional roughness particles required to\npromote premature transition of a laminar boundary layer on models of\nairplanes or airplane components in a wind tunnel with zero heat\ntransfer . a single equation is derived which relates the roughness height\nto a reynolds number based on the roughness height and on local flow\nconditions at the height of the roughness, and charts are presented\nfrom which the critical roughness height can be easily obtained for\nmach numbers from 0 to 5 . a discussion of the use of these charts is\npresented with consideration of various model configurations .\n the method has been applied to various types of configurations in\nseveral wind-tunnel investigations conducted by the national advisory\ncommittee for aeronautics at mach numbers up to 4, and in all cases\nthe calculated roughness height caused premature boundary-layer\ntransition for the range of test conditions ."}, {"doc_id": 315, "text": "scale effects at high subsonic and transonic speeds\nand methods for fixing transition in model experiments .\n the major scale effects at high subsonic and transonic\nspeeds arise from differences between the conditions\nunder which laminar and turbulent boundary layers separate, and in\nhow they behave after separation . for turbulent\nboundary layers, these conditions and behaviour do not vary greatly\nas the reynolds number is changed and in many\nexamples, it has been shown that they are similar for the turbulent\nlayers that occur naturally at high reynolds number\nand for boundary layers in which transition to turbulent flow is fixed\nartificially . the scale effects arising in wind-tunnel\ntests made at low reynolds number may, therefore, often be\nminimised by fixing transition to turbulent flow by\nintroducing an artificial disturbance such as that produced by\nexcrescences attached to the surface . the fact that the\neffects of separation are often less severe for laminar layers than\nfor the turbulent layers that are likely to be encountered\nat full scale, makes it all the more important to do this whenever\npossible .\n several methods which can be used to fix transition are described,\nand the results obtained by using them are compared .\nin general, in experiments in two-dimensional flow, good agreement\nis found, and explanations can be advanced for\ncases in which discrepancies occur . several uncertainties and\ndifficulties that arise in fixing transition are discussed\nand illustrated by examples . in particular, special care is needed\nin interpreting the results obtained with transition\nfixed at very low reynolds numbers (say, less than about r = 1 x 10\nbased on local chord for wings of about 0.1\nthickness chord ratio and possibly higher reynolds numbers for thinner\nwings) .\n the difficulties of fixing transition satisfactorily are increased\nfor three-dimensional wings, particularly if they are\nswept-back or highly tapered (i.e., small chord and reynolds\nnumber near the tip) and if the tests cover a large range\nof incidence including high incidences for which the flow may\nseparate from very close to the leading edge . under\nthese circumstances, it is frequently necessary to place the\nexcrescences at different chordwise positions for low and\nhigh angles of incidence, and this is inconvenient in practice .\nmore research is needed before sound recommendations\ncan be made as to how and where transition should be fixed\non such models, particularly since in routine testing, it is\noften not possible to check the effects of transition-fixing fully .\n in the sections dealing with three-dimensional tests, examples\nare given of the spurious results that have been avoided\nsuccessfully by fixing transition, of the conditions where even\nat low reynolds numbers artificial fixing of transition\nmay not be necessary to give a turbulent boundary layer ahead\nof the shock, and of the conditions under which there\nare some doubts whether the methods used for fixing transition\nhave been satisfactory ."}, {"doc_id": 316, "text": "the occurrence and development of boundary layer separations at high\nincidences and high speeds .\nthis note describes the manner in which the onset of the effects of\nboundary-layer separation varies with mach number for two-dimensional\naerofoils, and discusses the influence of section shape as far as it is\nknown . a brief qualitative description is given of the mechanism\nunderlying the development of the separated flow and its effects,\nfollowed by a discussion of some of the ways in which this is likely to\ndiffer for swept-back wings at high speeds . finally, the need is\nemphasized for continued work in a broadening field ."}, {"doc_id": 317, "text": "non-equilibrium flow of an ideal dissociating gas .\nthe theory of an'ideal dissociating'gas developed by lighthill/1957/for\nconditions of thermodynamic equilibrium is extended to non-equilibrium\nconditions by postulating a simple rate equation for the dissociation\nprocess/including the effects of recombination/ . this equation contains\n the'equilibrium'parameters of the lighthill theory plus a further\ndissociation phenomena .\nthe behaviour of this gas is investigated in flow through a strong\nnormal shock wave and past a bluff body . the assumption is made that\nthe gas receives complete excitation of its rotational and vibrational\ndegrees of freedom in an infinitesimally thin region according to the\nfamiliar rankine-hugoniot shock wave relations before dissociation\nbegins . the variation of the relevant thermodynamic variables\ndown-stream of this region is then computed in a few particular cases . the\nmethod used in the latter case is an extension of the'newtonian'theory\nof hypersonic inviscid flow . in particular, the case of a sphere is\ntreated in some detail . the variation of the shock shape and the\nsphere diameter to the length scale of the dissociation process, is\nexhibited for conditions extending from completely undissociated flow\nto dissociated flow in thermal equilibrium . results would indicate\nthat significant and observable changes from the undissociated values\noccur, although values for the non-equilibrium parameter are not, at\npresent, available ."}, {"doc_id": 318, "text": "inviscid hypersonic flow past blunt bodies .\n two methods are shown for the calculation of the flow field\nbetween a blunt body and the shock associated with it for the\ncase of hypersonic flow . real gas effects are included . the\nsolutions consider only symmetric flows--that is, symmetric\nbodies at zero incidence .\n one method consists in tracing successive stream tubes around\nthe body and leads to iterations on the initially assumed position\nof the shock . the second is an integral method closely analogous\nto the karman-pohlhausen procedure for boundary layers . a\ndistinction is made between round-nosed and flat-nosed bodies,\nand both cases are discussed .\n a specific example corresponding to a re-entry missile situation\nis calculated,. the two methods agree within a few per cent .\ncomparison is also made with other known solutions in the\nstagnation region ."}, {"doc_id": 319, "text": "propagation of weak disturbances in a gas subject to\nrelaxation effects .\n a generalized wave equation is derived for sound disturbances\nin a gas when relaxation effects connected with, for example,\nmolecular vibration or dissociation are important . solutions\ninvolving discontinuous wave fronts are presented, and it is shown\nthat, under certain assumptions, the complete wave equation\nreduces to a variant of the telegraph equation . detailed solutions\nare presented for disturbance fields produced by a wavy wall in\nsubsonic and supersonic flow and a simple wedge in supersonic\nflow . this study is viewed as a step in the development of a\ntheory of small disturbances of a high-temperature gas, as is found\nbehind the shock in hypersonic flight ."}, {"doc_id": 320, "text": "comment on improved numerical solution of the blasius problem with\nthree-point boundary conditions .\nattention is drawn to a previous accurate solution to the problem ."}, {"doc_id": 321, "text": "improved numerical solution of the blasius problem with three-point\nboundary conditions .\nthe blasius equation describes the velocity distribution resulting from\nlaminar, constant-pressure mixing of a stationary fluid layer and a\nmoving stream . in connection with a numerical procedure for the univac\nbased on analytic continuation of the function f' . high-speed computers\n now make it feasible to use analytic continuation for numerical\nintegration of single-point boundary-value problems such that, within\nthe limits of taylor's expansion, truncation error may be made\narbitrarily small . a brief description of the application of the\nroutine is given ."}, {"doc_id": 322, "text": "on the numerical solution of the blasius problem with three-point\nboundary conditions .\nrelates to a technique for approximate determination of the initial\nparameters . the technique is an application of the asymptotic\nintegration method introduced by meksyn and has been applied to the computation\n of the skin friction for shock-generated boundary-layer flow ."}, {"doc_id": 323, "text": "vorticity interaction at an axisymmetric stagnation\npoint in a viscous incompressible fluid .\n the purpose of the present note is to give an exact solution of\nthe incompressible navier-stokes equations at an axisymmetric\nstagnation point with vorticity in the oncoming flow which varies\nlinearly with distance from the axis . this solution has application\nto the hypersonic axisymmetric blunt body problem, for which\nlighthill has shown the vorticity in the inviscid shock layer is\nvery nearly of this form ."}, {"doc_id": 324, "text": "vorticity effect on the stagnation point flow of a viscous\nincompressible fluid .\nthe effect of vorticity on axisymmetric stagnation point boundary layer\ncalculations is investigated by calculating a perturbation to the\nstagnation point flow . the shear caused by the vorticity effect is\nfound to be surprisingly large,.the slope of the shear curve /at zero\nvorticity/ as calculated by kemp agrees perfectly with the value deduced\n in this note ."}, {"doc_id": 325, "text": "heat transfer to constant property laminar boundary\nlayer flows with power function free stream velocity\nand wall temperature variation .\n numerical computations have been performed for the\nboundary-layer form of the energy equation for incompressible flows\nwith power-function variation of free-stream velocity (u =\ncx) and of wall temperature (t = ax), the pertinent solutions\nof the momentum equation in this case being those of hartree .\nthe numerical computations given herein are to some extent a\nrepetition of those given by schuh and by chapman and rubesin,\nthe object of the present computations being the resolution of\ndiscrepancies appearing in the previous solutions and an extension of\ntheir range . ibm machine calculations were employed in the\nfinite difference calculation presently utilized, the results thereof\ncovering a range of wall-temperature function exponents from\nvalues of m(4, 1, 0, -0.0904) . the accuracy of the numerical\ncomputations is examined in detail, and the accuracy of the\ncomputed functions at the wall, which determine the heat-transfer\nrate, is estimated to be within 2 per cent .\n examination of the results reveals that the results of schuh\nfor the flat plate are in error . for the range of the calculations,\nit was found that the local heat-transfer coefficient can, with the\nexception of large negative values, be expressed within 5\nper cent as\nwhere the exponent of the prandtl number varies from 0.254\nto 0.367 for -0.0904 and where the function\ncan be approximated by the equation"}, {"doc_id": 326, "text": "forst-order slip effects on the compressible laminar\nboundary layer over a slender body of revolution in\naxial flow .\nanalysis of the\ncompressible boundary layer with transverse curvature in first\norder slip flow . no boundary-layer interaction effects are considered\nand only the zero pressure-gradient case is examined ."}, {"doc_id": 327, "text": "on local flat plate similarity in the hypersonic boundary\nlayer .\n a study is made of lees' /local flat-plate similarity/ rule for\nthe hypersonic laminar boundary layer . it is shown that this\nrule is exact under assumptions commonly invoked in the\ninviscid theory of hypersonic flow .\n beginning from this theoretical basis, a modified local\nflat-plate similarity scheme is derived, involving separate rules for\nvelocity and enthalpy profiles, and is compared with exact\nsimilarity solutions and with the existing theory of hypersonic\nleading-edge interaction ."}, {"doc_id": 328, "text": "the boundary layer near the stagnation point in hypersonic\nflow past a sphere .\n flow properties behind shock waves caused by bluff bodies\ntraveling at supersonic speeds are of major importance in missile\nand high-speed aircraft design . paper presents a mathematical\nsolution for the laminar boundary layer near the stagnation point of a\nsphere . surface temperature is free-stream static and shock is\nstrong . air is assumed calorically and thermally perfect with a\nprandtl number of 0.72 and a dynamic viscosity directly\nproportional to temperature .\n based on work of homann (zamm 16, p. 153, 1936) and lighthill\nsimultaneous differential equations for the velocity and\ntemperature profiles . these are solved by numerical integration along a\nnormal to the surface using a digital computer . results are\npresented as functions of free-stream mach number, reynolds\nnumber, and specific heat ratio . as increases,\nboundary-layer thickness is shown to decrease while shock stand-off\ndistance increases . stand-off distance also decreases with increasing\nand decreasing specific heat . for constant and specific\nheat ratio, the product of skin-friction coefficient and the square\nroot of decreases with increasing only approaching a\nconstant value at greater than 10,000 .\n reviewer's comment is concerned with the perfect gas\nassumption for air . author suggests that the effects of dissociation on\nflow properties are accounted for by a proper choice of specific\nheat ratio . a consideration of the kinetics of chemical reaction in\nthe cooled boundary layer emphasizes the oversimplification of\nthis approach . the effect on transport properties could have been\napproximated in present analysis by changing the prandtl number\nto one more representative of the existing pressures and\ntemperatures ."}, {"doc_id": 329, "text": "various aerodynamic characteristics in hypersonic rarefied\ngas flow .\n this paper considers the problem of calculating viscous\naerodynamic characteristics of blunt bodies at hypersonic speeds and\nat sufficiently high altitudes where the appropriate mean free\npath becomes too large for the use of familiar boundary-layer\ntheory but not so large that free molecule concepts apply .\n results of an order-of-magnitude analysis are presented to\ndefine the regimes of rarefied gas flow and the limits of\ncontinuum theory . based on theoretical and experimental\nevidence, the complete navier-stokes equations are used as a\nmodel, except /very close/ to the free molecule condition . this\nmodel may not necessarily give the shock wave structure in\ndetail but satisfies overall conservation laws and should give a\nreasonably accurate picture of all mean aerodynamic quantities .\n in this /intermediate/ regime there are two fundamental classes\nof problems .. a /viscous layer/ class and a /merged layer/\nclass, the latter corresponding to a larger degree of rarefaction .\nfor the viscous layer class there is a thin shock wave, but the\nshock layer region between the shock and the body is fully\nviscous, although the viscous stresses and conductive heat transfer\nare small at the shock wave boundary . here, the use of the\nnavier-stokes equations with outer boundary conditions given\nby the hugoniot relations is justified . for the merged layer\nclass, the shock wave is no longer thin, and the navier-stokes\nequations can be used to give a solution which includes the shock\nstructure and has free-stream conditions as outer boundary\nconditions . a simpler procedure is presented for /incipient merged/\nconditions where the shock may no longer be considered an\ninfinitesimally thin discontinuity but where it has not thickened\nsufficiently to entail the /fully merged layer/ analysis . in this\ncase we approximate the shock by a discontinuity obeying\nconservation laws which include curvature effects, viscous stresses,\nand heat conduction .\n for a sphere and cylinder it is shown that the navier-stokes\nequations can be reduced to ordinary differential equations for\nboth the viscous and merged layer class of problems . solutions\nof these equations, when used in connection with hypersonic flow\nproblems, are in general only valid in the stagnation region . to\nillustrate the viscous layer solutions, numerical calculations\nhave been performed for a sphere and cylinder with the\nassumption of constant density in the shock layer, which is a useful\napproximation at hypersonic speeds . to illustrate the merged\nlayer solution, calculations have been carried out for a sphere\nusing the incipient merged layer approximation .\n results are presented for detachment distance, surface shear,\nand heat-transfer rate in the stagnation region of a highly cooled\nsphere flying at hypersonic speed . with decreasing reynolds\nnumber, the shear and heat transfer are shown to increase above\nthe extrapolated boundary-layer values in the viscous layer\nregime and then to begin falling in the incipient merged regime .\nas the reynolds number decreases in the incipient merged\nregime, the density in the shock layer increases, and the static\nand stagnation enthalpy behind the shock decrease .\n calculations performed for an insulated sphere show that, with\ndecreasing reynolds number in the incipient merged regime,\nthe density in the shock layer decreases,. the total enthalpy\nbehind the shock and at the stagnation point increase so that they\nare higher than the free-stream total enthalpy,. and the\nstagnation-point pressure behaves like the total enthalpy .\n for the highly cooled cylinder in the viscous layer regime, the\nsame quantities are presented as for the sphere . the increase\nfound in shear and heat transfer above extrapolated\nboundary-layer theory is small, in agreement with vorticity interaction\ntheory .\n a discussion is given of the behavior of available experimental\ndata for viscous flow quantities in the intermediate regime and\nthe behavior predicted by the results of the present calculations .\nqualitative agreement is indicated ."}, {"doc_id": 330, "text": "taylor instability of finite surface waves .\nthe instability of the accelerated interface\nbetween a liquid (methanol or carbon\ntetrachloride) and air has been investigated\nexperimentally for approximate\nsinusoidal disturbances of wave-number range\nfrom well below to well above the\ncut-off . the growth rates are measured and\ncompared with theoretical results .\na third-order theory shows the phenomena\nof overstability which is found in the\nexperimental results . some measurements\nof later stages of growth agree\nmoderately well with the available theory\nand disclose some additional\nphenomena of bubble competition, helmholtz\ninstability with transition to turbulence,\nand jet instability with production of drops ."}, {"doc_id": 331, "text": "effects of surface tension and viscosity on taylor\ninstability .\n the model used is that of two\nfluids of infinite depth, with the interface\ninitially in the form of a sine wave with\namplitude small compared to wave length .\nthe fluids are considered incompressible,\nand only the linear terms in the equations of\nhydrodynamics are used . the first four\nsections discuss the effects of surface tension\nand viscosity . the fifth gives a few numerical\nresults to illustrate the main points of\nthe preceding sections ."}, {"doc_id": 332, "text": "similitude of hypersonic real-gas flows over slender\nbodies with blunted noses .\n on the basis of the hypersonic small-perturbation theory, the\nlaws of similitude for hypersonic inviscid flow fields over thin or\nslender bodies are examined, and the restrictions to ideal gases\nwith constant specific heats and to bodies with pointed noses are\nremoved . only steady plane or axisymmetric flows are\nconsidered .\n inspection of the governing system of equations shows that a\nsimilitude law exists for flow fields, under local thermal\nequilibrium, having the same free-stream atmosphere . for flows of\nideal gas with constant specific heats, the requirement of the same\nfree-stream atmosphere--i.e., the same composition, pressure, and\ndensity--can be replaced by the requirement of the same ratio of\nspecific heats .\n for flows over blunted wedges or cones, special laws of\nsimilitude can be obtained .\n application of the similarity rules is examined for the case of\nhypersonic flows of an ideal gas with over flat plates\nwith blunt leading edges, and for the case of equilibrium air\nflows over wedges . the possibility of simulating nonequilibrium\nflows over slender or thin bodies is also pointed out ."}, {"doc_id": 333, "text": "boundary-layer interaction on a yawed infinite wing in hypersonic\nflow .\nthe equations are given for the laminar boundary-layer\nequations on a yawed infinite wing for constant\nwall temperature, under the combined howorth and\nmangler transformation . diagrams show the relatively\nsmall influence of yaw, the increase of boundary-layer\nsecondary flow, and the variation of the local heat\ntransfer rate with yaw ."}, {"doc_id": 334, "text": "influence of the leading-edge shock wave on the laminar boundary layer\nat hypersonic speeds .\nin order to bring out the importance of the leading-edge region at\nhypersonic speeds, the influence of the leading-edge shock wave on\nthe laminar boundary layer is investigated in two simple cases of\nsteady flow over a semi-infinite, insulated flat plate.. (1) sharp\nleading edge., (2) blunt leading edge, as approximated by a normal\nshock wave . the streamlines that enter the boundary layer over a large\nregion of the plate surface has previously crossed the shock wave\nvery near the leading-edge, where the shock is strong and highly\ncurved . consequently, the temperature at the outer edge of the\nboundary layer is appreciably higher than free-stream temperature,\nand the vorticity there is not zero . the effects of this shock-wave\nlarger than the usual /errors/ made in the boundary-layer theory,\nand an estimate of these effects can therefore be obtained within the\nframework of that theory . the numerical magnitude of the shock-wave\ninfluence is found to be appreciable . for the case of the blunt\nleading edge the slope of the curve of induced pressures plotted against\nthe hypersonic interaction parameter closely approaches the experimental\ndata of hammitt and bogdonoff obtained in helium at large values of this\nparameter . these approximate results show that the influence of the\nleading-edge region at hypersonic speeds requires careful theoretical\nand experimental study ."}, {"doc_id": 335, "text": "the interaction between boundary layer and shock waves in transonic\nflow .\nexperiments of transonic flow past a circular arc profile show that the\nshock-wave pattern and the pressure distribution are strongly dependent\nupon the state of the boundary layer . a change from laminar to\nturbulent boundary layer at a given mach number changes the flow pattern\n considerably .\nshock waves can interact with the boundary layer in a manner similar to\na reflection from a free jet boundary . these shock waves are not\ndistinctly discernible from pressure distribution measurements ."}, {"doc_id": 336, "text": "simplified laminar boundary layer calculations for\nbodies of revolution and for yawed wings .\n since the introduction of momentum methods in\nboundary-layer calculations by von karman and pohlhausen, many\nimprovements have been proposed . an especially simple solution\nreduces the problem to a quadrature . here, it is proposed to\nextend these methods to elementary three-dimensional cases and to\ncompressible laminar boundary-layer calculations . for\ncomparison, the corresponding problems for the turbulent boundary\nlayer are also discussed briefly ."}, {"doc_id": 337, "text": "boundary layer transition with gas injection .\nthe mass-injection process has been proposed as a method\nof cooling aerodynamic surfaces, and, since the amount of\ncoolant required to maintain practical wall temperatures is\nconsiderably larger for turbulent than for laminar boundary layers,\nknowledge of the effect of the cooling method on the transition\nprocess is certainly important . exploratory studies reported\nhere were conducted at mach number 3.7 to ascertain the\neffects of gas injection on the stability of the laminar boundary\nlayer on a conical surface ."}, {"doc_id": 338, "text": "mass transfer cooling at mach number 4. 8.\nmass-transfer experiments on a 5 mil wire porous cone\nof 20 total angle have been conducted at using\nair and helium injection . details of the experimental technique\nare described in references 1 and 2 . in the laminar boundary\nlayer the recovery factors and heat-transfer coefficients measured\nwith zero injection agreed within per cent with theory .\ntransition reynolds numbers observed on the porous cone with\nzero injection were half as large as observed on a smooth,\nimpermeable model of identical geometry in the same channel, but\ninjection of large amounts of air or helium did not cause\ntransition to move forward from its zero-injection position on the\nporous cone . distributed roughness of this type apparently does\nnot disturb impermeable wall theory, but it masks whatever\neffective roughness may be caused by discrete pore injection ."}, {"doc_id": 339, "text": "experimental evaluation of heat transfer with transpiration\ncooling in a turbulent boundary layer at m=3 .2.\n it is found that for prescribed velocity field, electrical field and\nconductivity, the current can be calculated by integration . work is\nrelated to analytic investigation of the boundary layer in a\nphysically reasonable accelerator ."}, {"doc_id": 340, "text": "analysis of effects of diffusion of a foreign gas into\nthe laminar boundary layer of a supersonic flow of\nair in a tube .\n adiabatic wall temperatures and recovery factors are calculated\nfor pipe flows with an entrance mach number of 5 and with uniform\ninjection of helium . predicted values of the recovery factor\nincrease slowly with increasing injection rate and with increasing\ndistance from the tube entrance ."}, {"doc_id": 341, "text": "the analytical design of an axially symmetric laval\nnozzle for a parallel and uniform jet .\n the equations for the nozzle's contours are derived by\nintegration of the characteristic equations of the axially symmetric flow .\nsince it is not possible to integrate these equations\nmathematically in an exact form, it was necessary to find a way to\napproximate the calculations . the approximation offers itself by\nconsidering and comparing the conditions of the flow in a cone with\nthose in a nozzle, as a linearization of the characteristic equations .\n the first part of the report deals with equations for the\ntransition curve by which the conical source flow is converted into a\nparallel stream of uniform velocity . the equations are derived\nby integration along a mach line of the flow in the region where\nthe conversion takes place . a factor f is introduced expressing a\nrelation between the direction and the velocity of the flow along\na certain mach line . f remains undetermined and is not involved\nin the final equations .\n in the second part of the report, the spherical sonic flow\nsection is converted into a plane circular section of the throat .\nthe nozzle's contour adjacent to the throat is formed by the arc\nof a circle connected with the transition curve by a straight line .\nthe gas dynamic properties of the boundary mach line are\ncalculated in table 1, the use of which shortens the calculations\nconsiderably ."}, {"doc_id": 342, "text": "effect of diffusion fields on the laminar boundary\nlayer .\n a theory is developed which describes the effect of a general\ndiffusion field on the dynamic and thermal characteristics of a\nlaminar boundary layer on a flat plate in steady compressible\nflow . fluid properties are considered as functions of\ntemperature and local concentration of the foreign gas . the diffusion\nfield is described by a differential equation that relates\nconvective and diffusion transfer and which considers diffusion currents\narising from gradients of concentration and temperature . by\nmeans of the usual transformations the system is reduced to a set\nof ordinary differential equations, which in turn are transformed\ninto a set of integral equations . the latter is amenable to\nsolution by the method of successive approximations .\n the theory and results have bearing on the problem of control\nand reduction of aerodynamic heating at hypersonic speeds .\nthe special feature of this approach lies in the utilization of\ndiffusion fields for the purpose of reducing the detrimental effects\nof viscous dissipation . although the theory is adapted to a\nfuller investigation of this problem, the numerical examples\nconsidered involve mainly diffusion fields of helium, with which\ngood results have been achieved at mach numbers 8 and 12 .\nwhereas at the higher mach number the influx of heat was\npractically eliminated, a reversal in the direction of heat flow has\nbeen effected at the lower mach number ."}, {"doc_id": 343, "text": "transpiration cooling experiments in a turbulent boundary\nlayer at m=3 .\n turbulent recovery factor and heat-transfer measurements have been\nmade on a porous flat wall section at a nominal mach number of 3.0 and a\nreynolds number of approximately 4 x 10 using both air and helium as the\ntranspired gas . measured heat-transfer\ncoefficients correlate well with the\ncompressible theory of rubesin for air\nand qualitatively with simple film\ntheory for either coolant, indicating that\nthe heat transfer from a turbulent\nboundary layer can be reduced by transpiration\ncooling to well below that of\nthe uncooled boundary layer at the same reynolds number ."}, {"doc_id": 344, "text": "some experimental techniques in mass transfer cooling .\n author introduces his survey by a brief review of the history of\ninvestigations dealing with boundary layers on impermeable solid\nsurfaces, and notes that no true theory exists for turbulent\nboundary layers, the success of studies in this area having been due to\nthe introduction of artificial, if ingenious, assumptions which\npermitted empirical correlations fd data . the terminology introduced\nby the author for distinguishing the different situations involving\nmass transfer from the wall to the stream may give rise to some\nobjections . for instance, /film cooling/ need not refer only to\nthe injection of a liquid, since applications involving gas film\ncooling exist . also, his restriction of the term /transpiration\ncooling/ to refer to the injection through a porous surface of a gas\nonly of the same composition as the exterior stream does not enjoy\nuniversal usage . the influence of mass transfer on heat transfer\nthrough laminar boundary layers and on the transition from laminar\nto turbulent flow is described, with consideration given to the\nquestion of the net effect of the stabilizing influence of surface\ncooling and the destabilizing influence of injection .\n reviewer suggests that author's inaccurate statement to the\neffect that /thus far the higher energy conditions do not threaten\nto involve turbulent injection, so turbulent boundary-layer research\nenjoys a fairly academic serenity broken only by its own\nfrustrations/ be excused on grounds of poetic license, although it\nignores the efforts being devoted to the pressing practical problems\nof erosive burning of solid propellants (possibly the most common\nexample of a complete /aerothermochemical/ problem involving\ndistributed surface heat and mass transfer with chemical reaction\nin a flow system) and of effusion cooling of rocket nozzles, both\nof which involve turbulent boundary-layer conditions . author\nemphasizes the tedious experimental problems involved in research\non boundary layers with blowing, and notes the desirability of\nvelocity distribution measurements, especially in turbulent injection\nlayers . the observation that no good data on concentration\nprofiles in the case of the diffusion boundary layer have been\npublished may be an overstatement, since author's bibliography\noverlooks the work of j. berger (/contribution a l'etude de l'injection\nparietale,/ doctor's thesis, university of paris, memorial des\npoudres 38 (annex), p. 1,. paris, imprimerie nationale, 1956) ."}, {"doc_id": 345, "text": "the interaction of shock waves with boundary layer\non a flat surface .\n the development of supersonic compressors, supersonic\ndiffusers, and high-speed aircraft points to the increasing\nimportance of the interaction between shock waves and boundary\nlayers .\n the experimental work reported here is intended to (1)\nprovide a better understanding of the nature of the shock\nboundary-layer interaction, (2) serve as a guide and stimulus to theoretical\nwork, and (3) develop an empirical method for predicting the\neffects of the interaction .\n experiments were performed on the reflection of an oblique\nshock from a boundary layer on a flat surface at a mach number\nof 2.05 . the effects of shock strength and boundary-layer regime\nwere explored .\n the results are in the form of schlieren photographs,\nconstant-density contours found from interferometer photographs, and\nstatic pressure distributions at the plate surface ."}, {"doc_id": 346, "text": "measurements of turbulent friction on a smooth flat plate in supersonic .\n direct measurements of supersonic local skin friction, using the\nfloating-element technique, are presented for mach numbers from\nbulent flow and transition are emphasized, although some\nmeasurements in the laminar regime are included . the observed effect\nof compressibility is to reduce the magnitude of turbulent skin\nfriction by a factor of two at a mach number of 4.5 and a\nreynolds number of about 10 .\n the boundary-layer momentum-integral equation for constant\npressure is verified within a few per cent by two experimental\nmethods . typical static pressure measurements are presented to\nshow that transition can be detected by observing disturbances\nin pressure associated with changes in displacement thickness\nof the boundary layer .\n it is found that the turbulent boundary layer cannot be defined\nexperimentally for values of less than about 2,000, where\nis the momentum thickness . for larger values of there is a\nunique relationship between local friction coefficient and\nmomentum-thickness reynolds number at a fixed mach number . the\nappendix compares the present measurements at m = 2.5 with\nexperimental data from other sources ."}, {"doc_id": 347, "text": "boundary layer measurements in hypersonic flow .\n experimental data are presented on boundary-layer formation,\nheat transfer, and skin-friction coefficient at mach numbers of\nthe wall of a conical nozzle in the presence of a favorable pressure\ngradient and several rates of heat transfer . the reynolds\nnumber based on momentum thickness varied from 1,500 to 3,500 .\ncomparison is made with data at lower mach numbers and with\nthe semiempirical theory of von karman . the existing data up\nto mach numbers of nine indicate agreement to within 5 per\ncent when compared with a form of the wilson theory, but it is\nclear that the effects of heat transfer and pressure gradients\npresent problems which require extensive study and experiment in\nthe future ."}, {"doc_id": 348, "text": "turbulent boundary layer in compressible fluids .\n the continuity, momentum, and energy differential equations\nfor turbulent flow of a compressible fluid are derived, and the\napparent turbulent stresses and dissipation function are\nidentified . a general formula for skin friction, including heat\ntransfer to a flat plate, is developed for a thin turbulent boundary\nlayer in compressible fluids with zero pressure gradient . curves\nare presented giving skin-friction coefficients and heat-transfer\ncoefficients for air for various wall-to-free-stream temperature\nratios and free-stream mach numbers .\n in the special case when the boundary layer is insulated, this\ngeneral formula yields skin-friction coefficients higher than those\ngiven by the von karman wall-property compressible-fluid\nformula but lower than those given by the von karman\nincompressible-fluid formula . heat transfer from the boundary layer\nto the plate generally increases the friction and heat-transfer\ncoefficients ."}, {"doc_id": 349, "text": "numerical solution of the boundary layer equations\nwithout similarity assumptions .\n the crocco transformation combined with a mangler\ntransformation is used to carry the boundary-layer problem for axially\nsymmetric blunt bodies into a form suitable for direct numerical\ncomputation without introduction of similarity assumptions .\nconditions which in the original problem appear at infinity now\nare brought to a finite straight line, and the body is transformed\nto a parallel line . data can be generated on the stagnation line\nthe equations are a parabolic system of two second-order\nequations, the boundary-value problem is analogous to the slab\nproblem for the heat equation . an implicit difference equation is\nused to reduce stability difficulties . special techniques in\nforming the difference equation result in a linear system of algebraic\nequations to be solved on any given line of integration, and these\nsolutions are computed from recursion relations generated by\nback substitution . for bluntnosed bodies with approach flow\nmach numbers greater than 8 (approximately), large\ntemperature gradients occur across a thin boundary layer of dissociated\ngas, and it is necessary to use real-gas effects, approximated here\nby certain fits to the gas tables . a case is computed, however,\nfor a lower mach number approach flow using perfect-gas theory\nto provide a standard against which similarity solutions may be\ntested ."}, {"doc_id": 350, "text": "laminar jet mixing of two compressible fluids with heat release .\nthe laminar jet mixing problems with heat release have been formulated .\na general discussion of the solution of these problems is also given .\nthe important parameters of these problems are brought out . some\nspecific cases of the jet mixing problem, such as jet mixing of one\ncompressible fluid, isothermal jet mixing of two compressible fluids,\nand isovel jet mixing of two compressible fluids with heat release, are\ndiscussed in detail."}, {"doc_id": 351, "text": "thermal distributions in jeffrey-hamel flows between nonparallel plane\nwalls .\nthe authors give the exact solution for the thermal distributions for\nthe steady laminar flow of a viscous incompressible fluid between\nnon-parallel plane walls held at a constant temperature . the velocity\nprofiles are determined with the aid of jacobian elliptic functions by\nusing the jeffery-hamel solution of the hydrodynamic problem . it is\nshown that in this special case the energy equation giving the\ntemperature profiles can be reduced to an ordinary linear differential\nequation with variable coefficients . after the introduction of\ndimensionless parameters, numerical solutions are given for diverging and\nconverging channels with total openings of 10degree for the possible\ncombinations of three reynolds numbers and five prandtl numbers ."}, {"doc_id": 352, "text": "on heat transfer over a sweat-cooled surface in laminar\ncompressible flow with a pressure gradient .\n a simple expression is derived for the normal injection velocity\ndistribution theoretically required to maintain a given uniform\ntemperature along a porous surface in the laminar\nboundary-layer region of a compressible flow with a given velocity\ndistribution outside of the boundary layer . this expression is valid for\nany given free-stream mach number but is based on a prandtl\nnumber of unity and on the assumption that the viscosity\ncoefficient varies linearly with the temperature . by using the\ndorodnitsyn type of transformation, the variation of fluid\nproperties even in the case of zero mach number is taken into\naccount . this study is of particular practical interest in\nconnection with the sweat-cooling of turbine blades and of airfoil surfaces\nin high speed flow . the method of analysis consists of applying\nthe karman-pohlhausen method to both the momentum and\nenergy boundary-layer equations and of using an additional heat\nbalance equation, involving the coolant temperature . a\nclosed-form approximate solution of the equations is then derived .\nnumerical examples for flow in the immediate vicinity of a\nstagnation point and for a typical type of flow over a turbine blade are\ngiven ."}, {"doc_id": 353, "text": "the effect of helium injection at an axially symmetric stagnation\npoint .\nan effective means of protecting the surface of a hypersonic re-entry\nvehicle is to inject small quantities of a lightweight gas into the\nboundary layer through a porous wall . this process, which is known\nas mass-transfer cooling, protects the surface in two ways . first\nof all, as the injected gas or coolant passes from the reservoir through\nthe wall to the surface, a considerable quantity of heat is absorbed as\nits temperature is raised from the reservoir temperature to the wall\nsurface temperature . characteristically, lightweight gases have\nrelatively high specific heats .\nsecondly, the transfer of mass and enthalpy by convection and diffusion\nnormal to the surface alters the characteristics of the boundary\nlayer in such a manner as to reduce the temperature gradient at the\nwall, and, hence, the conductive heat transfer at the wall . this is\nsometimes referred to as the blowing effect ."}, {"doc_id": 354, "text": "laminar heat-transfer and pressure measurements over blunt-nosed\ncones at large angle of attack .\ntests have been conducted at a mach number of 6, in the pibal hypersonic\nfacility, in order to determine the heat-transfer and pressure\ndistributions over a slender blunted cone at angles of attack of\nerature ratio, stagnation to wall, was approximately 2.3 . the model\ntested has a sperical nose diameter of 1.0 in., a base diameter of 3.75\nin., and a cone half-angle of 20 degrees . the measurements were made\nat 5 peripheral stations on the model .\nin this note the experimental results at a 15 degree angle of attack\nare presented . a more detailed analysis of the results for all\nangles of attack is presented in reference 1 ."}, {"doc_id": 355, "text": "the injection of air into the dissociated hypersonic laminar boundary\nlayer .\nin first approximation, dissociated air may be treated as a binary\nmixture of air atoms and air molecules . in order to include the\neffects of mass transfer into the boundary layer, it becomes necessary\nto introduce a third chemical species and hence a second diffusion\nequation . we have avoided this complexity by considering the injection\nof air molecules into the boundary layer, and hence the theoretical\ntreatment is accomplished within the framework of a binary mixture gas ."}, {"doc_id": 356, "text": "on optimum nose curves for missiles in the super-aerodynamic\nregime .\n author shows that the differential equations defining the\nminimum drag body shapes for free molecule flow that were developed\nand numerically integrated by w. j. carter (amr 11 (1958), rev.\nrealized, however, that numerical or analytical integration of the\nsecond-order differential equation is unnecessary since, for the\nflow conditions considered, the first integral to the euler equation\ncan be written prior to the substitution of the expression defining\nthe pressure coefficient ."}, {"doc_id": 357, "text": "optimum nose shapes for missiles in the super-aerodynamic\nregion .\n the mechanics of the kinetic theory of gases is employed to\ndescribe the drag force on the nose of a missile moving in the\nsuper-aerodynamic region of the atmosphere . three separate cases are\nconsidered--ideal specular reflection, specular-type reflection\nfrom a slightly rough surface, and surface absorption followed by\nrandom emission of the striking molecules . the calculus of\nvariations is employed to obtain the differential equation of the nose\nshape which minimizes the drag force for each of the three cases .\nthe resulting differential equations are then solved by a numerical\nprocedure . the drag coefficients for the optimum nose shapes are\nlikewise determined and these are compared with the drag\ncoefficients given by other nose shapes . it is further shown that\nthe drag coefficients arising when specular-type reflections occur\nare significantly dependent on the nose shape . when surface\nabsorption followed by random emission occurs, the drag\ncoefficient is not strongly dependent on either the missile nose shape\nor the fineness ratio of the nose ."}, {"doc_id": 358, "text": "on the model of the free shock separation, turbulent\nboundary layer .\n by free shock-separated boundary layers, one means that type of\nseparation where the flow downstream of the separation region is free to\nadjust to any direction that may result from the shock-boundary-layer\ninteraction process . a detailed model of the free shock-separated\nturbulent boundary layer is postulated, and the pressure rise following\nfrom this model is estimated and compared with experiments . the\nresults are applied to the prediction of separation in an overexpanded\nnozzle ."}, {"doc_id": 359, "text": "note on the hypersonic similarity law for an unyawed\ncone .\n it is now known that the hypersonic similarity law derived for\nslender cones and ogival bodies under the assumption, is\napplicable for mach numbers as low as 3 . this note makes use of\na series development to infer the hypersonic similarity law for\nunyawed cones from the taylor-maccoll differential equations and\nassociated boundary conditions . a simple approximate formula\nfor the function of the similarity law is obtained,\nand the drag function computed with this formula is compared\nwith kopal's numerical results and, for very slender cones, with\nvon karman's linearized formula ."}, {"doc_id": 360, "text": "lift on inclined bodies of revolution in hypersonic flow .\nthe importance of body lift lies in the fact that at moderate angles of\nattack and high mach number it can constitute an appreciable part of\nthe total lift of a winged missile . in this paper an attempt has been\nmade to analyze body lift in hypersonic flow by an approximate method\nand, together with a correlation of existing experimental data, to\nindicate the probable variation of body lift over a wide range of mach\nnumbers extending from low supersonic to hypersonic . the method of\nanalysis of hypersonic flow over inclined bodies of revolution employed\nherein has been denoted as the hypersonic approximation . it is an\nimprovement on the newtonian corpuscular theory of aerodynamics, since it\nconsiders the centrifugal forces resulting from the curved paths of the\nair particles in addition to the impact /newtonian/ forces ."}, {"doc_id": 361, "text": "the flow of a viscous liquid past a flat plate at small\nreynolds number .\n the authors repeat the earlier calculations of piercy\nand winny (proc. roy. soc. london. ser. a. 140 (1933),\nearlier works were known to be different from each other .\nthe careful analysis of the present authors shows that the\nskin-friction coefficient up to the second approximation\nagrees perfectly with that of piercy and winny ."}, {"doc_id": 362, "text": "three-dimensional effect of flutter in a real fluid .\nin ref. 1, an alternative semi-empirical formulation for flutter in a\nreal fluid is given . for more accurate determination of the empirical\ncoefficients, the three-dimensional effect of finite span should be\ntaken into account . following reissner's approximation for\nlarge-aspect-ratio rectangular wings, the boundary-value problem governing the\ndownwash w and the vorticity distribution ."}, {"doc_id": 363, "text": "an alternative formulation of the problem of flutter\nin real fluids .\nit is well known, in steady flow, that the actual lift curve\nslope is somewhat less than that predicted by inviscid flow\ntheory, even at small angles of attack . as the stall angle is\napproached, the lift curve slope continually decreases and thus\ndeviates even more from the theoretical value . pinkerton\nemployed the measured circulation to determine the pressure\ndistribution and found that the resulting prediction of the moment\nis considerably improved over that given by the classical theory .\nthis amounts to replacing the conventional kutta-joukowski\ncondition with the condition that the total lift should agree with\nthe measured value, and this, in turn, completely determines the\nflow pattern . practically, this is accomplished by giving a\nfictitious camber to the profile . since potential flow theory is\nvalid outside of the boundary layer, once the boundary-layer\nthickness is known, the potential flow may be corrected for the\ndisplacement thickness and the viscous wake by appropriate\nsource distributions . the boundary layer cannot be evaluated,\nof course, until the potential flow is known and the circulation is\napplied . a criterion to determine the circulation, by\ngeneralizing the kutta-joukowski condition, was proposed by preston\nand spence by assuming that the pressure at the trailing edge\nshall have the same value when determined from the\npotential-flow values above and below the airfoil . this procedure gives\nqualitative information concerning viscous effects in steady\nflow ."}, {"doc_id": 364, "text": "a method for analysing the insulating properties of\nthe laminar compressible boundary layer .\n in some cooling problems associated with high energy flows\nit may be convenient to localize strongly the cooling, as for\nexample by injecting a coolant through an upstream porous strip,\nand to depend on the insulating properties of the boundary layer\nto reduce, or to eliminate completely the need for further cooling\non the surface downstream of the highly cooled section . this\nupstream cooling technique may be of interest in connection with\noptical windows in hypersonic wind tunnels, and on radomes,\nwings, and bodies of high-speed aircraft and missiles .\n in this paper a method for investigating the insulating\nproperties of a laminar compressible boundary layer on a two-\ndimensional surface with zero heat transfer is presented . the physical\nsituation considered thus corresponds to the case in which the\nheat transfer downstream of the strongly cooled section is\ncompletely eliminated . of practical concern is how the\ntemperature of the uncooled surface varies in the downstream direction\nfrom its low initial value and thus how the low energy layer\nestablished by the upstream cooling insulates the downstream\nsurface .\n the karman integral method extended to both the momentum\nand energy partial differential equations of the boundary layer\nhas been used . the station, at which cooling and or injection\nceases, corresponds to a discontinuity in boundary conditions\nand thus in solutions . at this point the flux of mass, momentum,\nand energy within the boundary layer has been made continuous\nby the introduction of three additional parameters in the velocity\nand stagnation enthalpy profiles . thus the velocity and\nstagnation enthalpy profiles have both been taken as sixth degree\npolynomials . the resulting two integral-differential equations\nare then solved for two unknown functions of the distance along\nthe wall . these two functions are related to the boundary-layer\nthickness and to the wall temperature . initial conditions\ncorresponding to a given initial wall temperature and an initial\nboundary-layer thickness are prescribed . exact closed-form solutions\nfor the case of zero axial pressure gradient are obtained . for\nflows with significant pressure gradients, numerical solutions\nare required in general . several numerical examples of practical\ninterest are presented ."}, {"doc_id": 365, "text": "the homogeneous boundary layer at an axisymmetric stagnation\npoint with large rates of injection .\n this report presents a theoretical analysis of the boundary\nlayer at an axisymmetric stagnation point with large rates of\nair injection . the results of a previous investigation indicated\nthat for localized mass transfer in the stagnation region, the\nrates of injection are considerably greater than those usually\ntreated . the exact stagnation-point boundary-layer equations\nare integrated numerically for an approximate representation\nof the gas properties . the two-point boundary conditions are\ntreated in a new manner which is useful for various\nboundary-layer and mixing problems . the exact solutions indicate that\nfor large rates of injection the boundary layer is closely\nrepresented by an inner isothermal shear flow and by and exterior,\nrelatively thin region, in which the flow variables change to their\nfree-stream values . an integral method based on profiles\nsuggested by the exact solutions is developed and shown to lead\nto accurate predictions of the integral thicknesses which are\nof interest for a study of the downstream influence of the\nstagnation-point mass transfer ."}, {"doc_id": 366, "text": "helium injection into the boundary layer at an axisymmetric\nstagnation point .\n this report presents a theoretical analysis of the boundary\nlayer at an axisymmetric stagnation point with large rates of\nhelium injection . the exact stagnation-point boundary-layer\nequations are integrated numerically with approximate\nrepresentations of the gas properties . the treatment of the\ntwo-point boundary-value problem employed herein is shown to be\nuseful for various boundary-layer and mixing problems . the\nexact solutions indicate that for large rates of injection the\nboundary layer can be represented by a thick, inner layer of\nconstant shear, temperature, and composition and by a relatively\nthin outer region in which the flow variables adjust to their\nfree-stream values . an inviscid-flow model is shown to lead to\naccurate predictions of this shear layer and will thus provide\nsufficiently accurate profiles for use in the study of the downstream\ninfluence of stagnation-point mass transfer . the heat transfer\nto the stagnation point is also considered . tabulations of the\neigenvalues for a variety of wall conditions and injection rates\nare given ."}, {"doc_id": 367, "text": "control system and analysis and design via the second method of\nlyapunov .\nthe/second method/of lyapunov is the most general approach currently in\nthe theory of stability of dynamic systems . after a rigorous exposition\n of the fundamental concepts of this theory, applications are made to/a/\nstability of linear stationary, linear nonslationary, and nonlinear\nsystems,./b/estimation of transient behavior,./c/control-system\noptimization,./d/design of relay servos . the discussion is essentially\nself-contained, with emphasis on the thorough development of the\nprincipal ideas and mathematical tools . only systems governed by\ndifferential equations are treated here . systems governed by difference\nequations are the subject of a companion paper ."}, {"doc_id": 368, "text": "some problems of polar missile control .\n a polar-controlled missile is one in which manoeuvre\nis carried out by rotations about roll and pitch axes,\nthat is, in the manner of a conventional aeroplane . this\npaper discusses some problems in the application of this\nform of control to homing missiles .\n in comparison with the alternative cartesian\nconfiguration, this method presents some special design\nproblems . in the former case, it is often possible to\nresolve the motion into two planes and consider the\npitch and yaw control systems as independent\ntwo-dimensional problems . this simplification is not\npossible in the case of polar control and it is usually\nnecessary to consider the whole three-dimensional\nsystem . the equations of motion which result are, in\ngeneral, not susceptible to analysis . because of this,\nthe design of control systems requires extensive use of\nsimulators ."}, {"doc_id": 369, "text": "an approximate solution of the supersonic blunt body\nproblem for prescribed arbitrary axisymmetric shapes .\n the integral method of belotserkovskii has been carried out to\nthe first approximation for arbitrary blunt axisymmetric bodies\nin supersonic or hypersonic flight . this method is direct, in\nthat it gives the surface-pressure distribution and shock shape for\na prescribed body . results obtained by numerical integration\nfor several body shapes at several mach numbers are compared\nto experimental results with good agreement . it is also shown\nthat the method can be successfully applied to pointed bodies\nwith attached shock . in the stagnation region, simple\nrelationships are found from the equations of the first approximation\nwhich connect the surface-velocity gradient, shock curvature,\nshock-detachment distance, and body curvature . these\nrelations are also correlated with experiment for a variety of shapes\nas a function of mach number . the correlations permit a rapid\nestimate of the stagnation-point velocity gradient, important for\nheat-transfer calculations, for any blunt body from the shock\nstand-off distance . a method for a higher approximation is\ndescribed, for which, in contrast to the higher approximations of\nbelotserkovskii, a large number of simultaneous total differential\nequations with unknown parameters does not occur . one form\nof this method has been studied numerically . results are given\nwhich, though only partially successful, indicate the amount of\nimprovement to be expected from a higher approximation ."}, {"doc_id": 370, "text": "theoretical pressure distribution on a hemisphere-cylinder\ncombination .\nin recent years great use has been made of approximate methods for\nthe determination of the pressure distribution on blunt-nosed bodies\nand afterbodies at high mach numbers . for quasi-spherical bodies\nit has been suggested that modified newtonian theory in combination\nwith a prandtl-meyer expansion be used on the nose portion, the two\nlaws being matched at the point where the pressure gradients are equal .\nno simple approximation, however, has been found for flat-nosed bodies .\nas for the pressure distribution on the afterbody, the blast-wave\nanalogy has been suggested for general nose shapes but particular\nafterbody profiles .\nthe purpose of the present note is to compare these approximate\nestimates with a more accurate determination of the flow field about\na hemisphere-cylinder in an ideal gas flow . it was felt that since\nexperimental investigations in air at this mach number are scarce\nand very difficult to obtain, the comparison would be of interest . the\nbasis of comparison is the flow field as it results from a numerical\nintegration of the exact equations governing the motion of the ideal\nfluid ."}, {"doc_id": 371, "text": "note on tip-bluntness effects in the supersonic and\nhypersonic regimes .\nin a recent letter, m. h. bertram presents some data on\nflows at m = 6.85 around 10 half-angle cones with blunted\ntips . since the demarcation between the supersonic and\nhypersonic regimes is not sharp and since one expects hypersonic flows\nto be generally similar to those at lower mach numbers--\nespecially where viscous effects do not predominate throughout the\nentire field of interest--it is of some value to compare bertram's\nresults with those obtained by giese and bergdolt for 15\nhalf-angle cones at m = 2.45 . following the observation by charters\nand stein that drag coefficient measurements on blunted cones\nimply a reynolds number effect, giese and bergdolt study the\nconvergence to conical flow of the perturbed flow about a cone\nwith truncated tip . they employ the mach-zehnder\ninterferometer and the conical flow criterion as analytical tools ."}, {"doc_id": 372, "text": "an experimental investigation of flow about simple\nblunt bodies at a nominal mach number of 5. 8.\n an experimental investigation was\nconducted in the galcit hypersonic\nwind tunnel to determine flow characteristics\nfor a series of blunt bodies at a\nnominal mach number of 5.8 and free-stream\nreynolds numbers per in. of\nmeasured values for the pressure\ncoefficient distributions are compared with\na modified newtonian\nexpression . the agreement is very good for the\nthree-dimensional bodies and is\nfair for the circular cylinder transverse to the\nfree-stream flow direction . a\ncomplete report of the investigation is given in\na galcit hypersonic wind\ntunnel memorandum ."}, {"doc_id": 373, "text": "the generalized expansion method and its application\nto bodies travelling at high supersonic airspeeds .\n it is demonstrated that the shock-expansion method can be\ngeneralized to treat a large class of hypersonic flows, only one of\nwhich is flow about airfoils . this generalized method predicts\nthe whole flow field, including shock-wave curvatures and\nresulting vorticity, providing that (1) disturbances originating on\nthe surface of an object are largely absorbed in shock waves with\nwhich they interact and (2) disturbances associated with the\ndivergence of stream lines in tangent planes to the surface are of\nsecondary importance compared to those associated with the\ncurvature of stream lines in planes normal to the surface . it is\nshown that these conditions may be met in three-dimensional as\nwell as two-dimensional hypersonic flows . when they are met,\nsurface streamlines may be taken as geodesics, which, in turn,\nmay be related to the geometry of the surface .\n the validity of the generalized shock-expansion method for\nthree-dimensional hypersonic flows is checked by comparing\npredictions of theory with experiment for the surface pressures and\nbow shock waves of bodies of revolution . the bodies treated\nare two ogives having fineness ratios of 3 and 5 . tests were\nconducted at mach numbers from 2.7 to 6.3 and angles of attack up\nto 15 degrees in the 10- by 14-in. supersonic wind tunnel of the\names aeronautical laboratory . at the lower angles of attack,\ntheory and experiment approach agreement when the ratio of\nmach number to fineness ratio--that is, the hypersonic\nsimilarity parameter--exceeds 1 . at the larger angles of attack, theory\ntends to break down, as would be expected, on the leeward sides\nof the bodies .\n as a final point, it is inquired if the two-dimensionality of\ninviscid hypersonic flows has any counterpart in hypersonic\nboundary-layer flows . the question is answered in the\naffirmative, and results of experiment are employed to provide a partial\ncheck of this conclusion ."}, {"doc_id": 374, "text": "an investigation of optimum zoom climb techniques .\n the problem of optimal zoom climb maneuvering of a turbojet\naircraft has been investigated using the mayer formulation of the\ncalculus of variations . the euler-lagrange equations governing\noptimum symmetric flight have been integrated numerically by\ndigital computation .\n discontinuities in thrust arising from turbojet afterburner\nblowout have been treated, and conditions which must be\nsatisfied across the interface generated by the discontinuity have been\nderived .\n arbitrary control techniques have been compared with the\noptimum, and it has been found that performance is relatively\ninsensitive to piloting technique unless a time limitation is\nimposed which requires high maneuvering load factors ."}, {"doc_id": 375, "text": "steady flow in the laminar boundary layer of a gas .\nif the boundary-layer equations for a gas are\ntransformed by mises's transformation, as\nwas done by karman tsion for the flow\nalong a flat plate of a gas with unit prandtl\nnumber, the computation of solutions is\nsimplified, and use may be made of previously\ncomputed solutions for an incompressible fluid .\nfor any value of the prandtl number, and\nany variation of the viscosity with the temperature\nt, after the method has been applied\nto flow along a flat plate (a problem otherwise treated\nby crocco), the flow near the forward\nstagnation point of a cylinder is calculated with\ndissipation neglected, both with the effect of\ngravity on the flow neglected and with this effect\nretained for vertical flow past a horizontal\ncylinder . the approximations involved by the neglect\nof gravity are considered generally,\nand the cross-drift is calculated when a horizontal\nstream flows past a vertical surface .\nwhen, and the boundary is heat-insulated,\nit is shown that the boundary-layer\nequations for a gas may be made identical, whatever be\nthe main stream, with the\nboundary-layer equations for an incompressible fluid with a certain,\ndeterminable, main stream . the\nmethod is also applied to free convection at a flat plate\nvariation with altitude of the state of the surrounding\nfluid neglected) and to laminar flow in\nplane wakes, but for plane jets the conditions,\npreviously imposed by howarth,\nare also imposed here in order to obtain simple solutions ."}, {"doc_id": 376, "text": "transformation between compressible and incompressible\nboundary layer equations .\nit is proposed to show that the boundary-layer equation of\ncompressible flow can be reduced to that of incompressible\nflow . such work was initiated by stewartson and by rott and\ncrabtree . in the following some of the restrictions imposed by\nreferences 1 and 2 will be removed, and it will be shown that the\ntransformation from compressible boundary layer to\nincompressible boundary layer can be applied to the laminar, as well as\nturbulent, case . a direct method will be used for this purpose ."}, {"doc_id": 377, "text": "a turbulent analog of the stewartson-illingworth transformation .\n the stewartson-illingworth transformation is applied to the\nintegral momentum equation for compressible boundary-layer\nflow, leaving the x-coordinate transformation unspecified,\nhowever . it is shown that the transformed equation is the integral\nmomentum equation for incompressible flow if (a) the effect of\ncompressibility on the boundary-layer shape parameter h can be\nrepresented by\nand (b) the x-coordinate transformation is chosen to be suitably\nrelated to the ratio of skin-friction coefficients in compressible\nand incompressible flows .\n experimental evidence is presented which shows that\ncondition (a) is satisfied for turbulent boundary layers up to m = 5 .\nan x-transformation is chosen according to (b) and an equation is\npresented which gives the turbulent boundary-layer growth in\ncompressible flow in terms of a simple quadrature . the\npredictions of this equation are then compared with some\nmeasurements on wind-tunnel nozzles ."}, {"doc_id": 378, "text": "engineering relations for friction and heat transfer to surfaces in high\n velocity flow .\nin calculations of thermodynamic heating for high speed missiles\nparameters have been used based on relationships which hold for\nconstant-property fluids . the validity of this procedure has been verified\nrecently in a survey of heat transfer in which a relationship for the\nreference temperature was developed . a calculation procedure for\nlaminar and turbulent boundary layers, based on this relationship, is\ngiven ."}, {"doc_id": 379, "text": "reverse flow and variational theorems for lifting surfaces\nin nonstationary compressible flow .\n a reverse-flow theorem for compressible nonsteady flow, valid\nwithin the limits of linearized theory, is derived . this theorem\ngives a general class of relations between linearized solutions for\nlifting surfaces in direct and reverse flow . based on the same\nconsiderations used to establish the theorem, an adjoint variational\nprinciple, which may be useful in approximate solutions of\nnon-steady lifting surface problems, is obtained . to illustrate the\nuses of the reverse-flow theorem, it is applied to the determination\nof relations between aerodynamic coefficients in direct and\nreverse flow and to the obtaining of influence functions for total\nlift, pitching moment, and rolling moment for a wing oscillating\nwith arbitrary motion and surface deformation, in terms of the\npressure distributions for simpler cases in reverse flow ."}, {"doc_id": 380, "text": "effect of quasi-steady air forces on incompressible\nbending-torsion flutter .\n explicit solutions are obtained for the bending-torsion flutter\nof a two-dimensional airfoil in incompressible flow under the\nassumptions that the theodorsen function, c(k) is set equal to a\nreal constant, and the diagonal virtual mass terms are negligible .\nfor the case of small bending to torsion frequency ratio, a\ncomparison is made of these quasi-steady solutions with an\nearlier empirical expression suggested by theodorsen and garrick\nfor the nonsteady case, and the effect of the c(k) function is\nindicated . the importance of the c.g. location for these small\ncases is re-emphasized, and the possibility of flutter at zero\nair speed is indicated ."}, {"doc_id": 381, "text": "the axisymmetric boundary layer on a long thin cylinder .\nthe laminar boundary layer in axial flow about\na long thin cylinder is investigated by two\nmethods . one (2) is a pohlhausen method,\nbased on a velocity profile chosen to represent\nconditions near the surface as accurately as\npossible . the other (3) is an asymptotic series\nsolution, valid far enough downstream from\nthe nose for the boundary-layer thickness to\nhave become large compared with the cylinder\nradius . another series solution (due to seban,\nbond and kelly) is known, valid near enough\nto the nose for the boundary layer to be thin\ncompared with the cylinder radius . the\npohlhausen solution shows good agreement with\nboth series, near and far from the nose, and\nenables an interpolation to be made (4) between\nthem in the extensive range of distances from\nthe nose for which neither is applicable . the\nfinal recommended curves, for the variation\nalong the cylinder of skin friction,\nboundary-layer displacement area and momentum defect\narea, are displayed in graphical and tabular\nform (figure 1 and table 1) and are expected to\nbe correct to within about 2 .\n the velocity near the wall is closely proportional\nto the logarithm of the distance from the\naxis,. this is the profile used in the pohlhausen\nmethod . the analogy with the distribution\nof mean velocity in turbulent flow over a flat\nplate is discussed at the end of 2 ."}, {"doc_id": 382, "text": "a note on the laminar boundary layer on a circular cylinder in\naxial incompressible flow .\na correction is made for the equation to compute the ratio\nof the displacement thickness on a cylinder to the corresponding\nthickness on a flat plate ."}, {"doc_id": 383, "text": "integration of the boundary layer equations for a plane in compressible\nflow with heat transfer .\nthe equations of motion of compressible viscous flow with vanishing\npressure gradient past a plane are integrated in semi-convergent\nexpressions, for the case when the physical constants depend on\ntemperature and the prandtl number is close to unity .\nsimple expressions are obtained for the temperature and velocity\ndistributions in the boundary layer, the drag coefficient, and their\ndependence on the physical constants,.they contain the well-known results\nand several new ones .\nfor the case when the temperature of the boundary is either above, or\nnot much below, the temperature of the main flow, the results obtained\nclosely agree with crocco's numerical computations ."}, {"doc_id": 384, "text": "application of second-order shock-expansion theory\nto several types of bodies of revolution .\n second-order shock-expansion theory is utilized to obtain equations\nfor the initial normal force curve slope, initial pitching moment curve\nslope, and zero-lift wave drag for several type bodies of revolution .\nbodies considered are the cone-cylinder, cone-cylinder-frustum,\ncone-cylinder-frustum-booster, cone-frustum, and cone-frustum booster ."}, {"doc_id": 385, "text": "on a generalised porous-wall ?couette type? flow .\n in a recent paper, the problem of a /couette-type/ flow in\nwhich the fixed wall is porous has been considered . the\nresults quoted in the above reference can be obtained rigorously\nby the method stated below in which a different interpretation to\none of the parameters is made ."}, {"doc_id": 386, "text": "a generalised porous-wall ?couette type? flow .\n recently, it was observed that the two existing\nboundary-layer texts (references 1 and 2) did not contain a solution\nfor the case of couette flow with a constant, uniformly\ndistributed suction or blowing . thus, the following analysis\nconsiders a /couette-type/ flow between a stationary flat surface and\na slightly inclined flat plate moving at a constant velocity . in\naddition, the flow is subjected to a constant, uniformly distributed\nsuction or blowing at the fixed surface ."}, {"doc_id": 387, "text": "heat transfer for laminar flow in an annulus with porous\nwall .\n temperature profiles and heat-transfer rates of established\nincompressible flow through an annulus channel with porous walls\nof constant temperatures are determined at different injection rates .\naxial conduction and viscous dissipation are, as usual, neglected .\ninjecting fluid is tacitly assumed to have the same temperature as\nthe porous wall ."}, {"doc_id": 388, "text": "the pressure gradient induced by shear flow past a\nflat plate .\n article is a continuation of an earlier note on papers by li\non a semiinfinite plate in a uniform shear flow . li had deduced\nfrom the form of his equations that stream vorticity caused an\ninduced pressure gradient in the flow . later papers by li and\nmurray (amr 15(1962), rev. 7157) support the induced pressure\ngradient theory . the author notes, however, that the mathematics used\nby li and murray are not acceptable and the problem thus not\nresolved . the present note sets up simple models of complete flows\nexaminable by elementary means . author holds that analyses\ndemonstrate conclusively that no pressure gradient is induced in\nthe boundary layer on a flat plate in a limited region of shear flow .\nhe notes that the original question in the case of unbounded shear\nremains obscure--and anyway an unlimited shear layer is not of\ngreat practical importance ."}, {"doc_id": 389, "text": "simple shear flow past a flat plate in a compressible\nviscous fluid .\n by transformation of variables, the problem of a simple shear flow of\na compressible fluid over a flat plate is reduced to the corresponding\nproblem for an incompressible fluid . the prandtl number of the\ncompressible fluid is assumed to be unity and its viscosity to be a linear\nfunction of temperature ."}, {"doc_id": 390, "text": "some panel-flutter studies using piston theory .\n the use of piston theory was recently advocated for\nsupersonic aeroelastic analyses, including the problem of panel flutter,\nand this has stimulated the investigation reported here .\n linear piston theory is mainly considered, but some effects of\nintroducing higher order terms are discussed .\n flutter of rectangular simply supported panels and of\nelliptically shaped clamped-edge panels is considered, and some\njustification is provided for the use of /static/ aerodynamic forces\nand the neglect of aerodynamic damping . hence, it is concluded\nthat ackeret loading gives more exact results than piston theory .\n solution of the flutter equations is made by applying galerkin's\nmethod to a rayleigh-type analysis using assumed modes of\ndeformation ."}, {"doc_id": 391, "text": "flutter of rectangular simply supported panels at high\nsupersonic speeds .\n the problem of panel flutter of rectangular simply supported\nplates subjected to supersonic flow over one surface is treated\ntheoretically . the assumption is made, and subsequently\nverified, that the /static/ approximation to the aerodynamic flutter\nforces yields flutter boundaries with satisfactory accuracy for\nmach numbers greater than about 2 . two panel flutter analyses\nare performed using this static approximation in conjunction with\nthin-plate theory--one employs aerodynamic strip theory, the\nother aerodynamic surface theory . the influence of mach\nnumber, dynamic pressure, panel aspect ratio, and midplane\nstress on the panel thickness required to prevent flutter is\ndetermined for extensive ranges of these parameters ."}, {"doc_id": 392, "text": "natural frequencies of rectangular plates with edges\nelastically restrained against rotation .\n plates with attachments to heavier members along the\nedges can be described as having edges elastically restrained\nagainst rotation, in many cases uniformly along each edge . at\nthe edges, setting slope, when is the edge bending\nmoment with always positive, the elastic restraint can be\nanalytically defined with describing respectively,\nclamped and simply supported edges . in this note natural\nfrequencies of such plates are calculated mainly following the\nnomenclature of dana young ."}, {"doc_id": 393, "text": "the shear flow along a flat plate with uniform suction .\n recently, several authors have investigated the boundary\nlayer in a shear flow . in this note, an exact solution of the\nnavier-stokes equations will be presented, which represents the\nboundary layer along an infinite flat plate with uniform suction\nsituated in a shear flow ."}, {"doc_id": 394, "text": "the viscous flow near a stagnation point when the external flow has\nuniform vorticity .\nin view of the recent controversy between li and glauert on the nature\nof the solution of the boundary-layer equations when the external\nflow is rotational, it seems worthwhile to draw attention to a certain\nexact solution of the navier-stokes equations which lends support to\nglauert's point of view ."}, {"doc_id": 395, "text": "new methods in heat flow analysis with application\nto flight structures .\n new methods are presented for the analysis of transient heat\nflow in complex structures, leading to drastic simplifications in\nthe calculation and the possibility of including nonlinear and\nsurface effects . these methods are in part a direct application of\nsome general variational principles developed earlier for linear\nthermodynamics . they are further developed in the\nparticular case of purely thermal problems to include surface and\nboundary-layer heat transfer, nonlinear systems with\ntemperature-dependent parameters, and radiation . the concepts of\nthermal potential, dissipation function, and generalized thermal\nforce are introduced, leading to ordinary differential equations\nof the lagrangian type for the thermal flow field . because of the\nparticular nature of heat flow phenomena, compared with\ndynamics, suitable procedures must be developed in order to formulate\neach problem in the simplest way . this is done by treating a\nnumber of examples . the concepts of penetration depth and\ntransit time are introduced and discussed in connection with\none-dimensional flow . application of the general method to the\nheating of a slab, with temperature-dependent heat capacity,\nshows a substantial difference between the heating and cooling\nprocesses . an example of heat flow analysis of a supersonic wing\nstructure by the present method is also given and requires only\nextremely simple calculations . the results are found to be in\ngood agreement with those obtained by the classical and much\nmore elaborate procedures ."}, {"doc_id": 396, "text": "variational and lagrangian thermodynamics of thermal\nconvection-fundamental shortcomings of the heat transfer\ncoefficient .\n extension of previous analyses, indicating the possibility of\nextending the thermodynamics of irreversible processes to systems\nwhich are not in the vicinity of an equilibrium state and for which\nonsager's relations are not verified . this involves generalizations\nbeyond the narrow field of heat transfer and to principles of wider\nrange than those of current nonequilibrium thermodynamics ."}, {"doc_id": 397, "text": "a sublayer for fluid injection into the incompressible\nturbulent boundary layer .\n a sublayer region is introduced in which the intensity of\nturbulence grows at a prescribed rate . the decrease in wall shear\nstress due to fluid injection into the boundary layer is found under\nthe hypothesis that the effect of injection is restricted to the\nsublayer region . experimental measurements of the velocity\nprofiles with fluid injection substantiate this hypothesis . the\ntheoretical decrease in wall shear stress is in good agreement\nwith experiment,. the solution is particularly simple and for small\nvalues of the injection parameter it contains no arbitrary\nparameters . the theory provides a similarity parameter which differs\nfrom the one in general use ."}, {"doc_id": 398, "text": "heat transfer in turbulent shear flow .\n the problems of heat transfer in turbulent shear flow along a\nsmooth wall are discussed from the point of view of von karman's\nwell-known 1939 paper on the analogy between fluid friction and\nheat transfer . methods for extending the analysis to higher\nprandtl numbers are suggested ."}, {"doc_id": 399, "text": "conduction of heat in composite slabs .\na method of calculating the total quantity of heat that passes through a\n unit area from zero time to time t is developed . allowance is made for\n surface resistance by regarding each contact resistance as an\nadditional layer of the appropriate thermal resistance and zero heat\ncapacity"}, {"doc_id": 400, "text": "buckling stress of clamped rectangular plates in shear .\n by consideration of antisymmetrical, as well as symmetrical,\nbuckling configurations, the theoretical shear buckling stresses of\nclamped rectangular flat plates are evaluated more correctly than in\nprevious work . the results given, which represent the average of upper\nand lower-limit solutions obtained by the lagrangian multiplier method,\nare within percent of the true buckling stresses ."}, {"doc_id": 401, "text": "inviscid hypersonic airflows with coupled non-equilibrium\nprocesses .\n analyses have been made of the effects of coupled chemical rate\nprocesses in external inviscid hypersonic airflows at high enthalpy\nlevels . exact (numerical) solutions have been obtained by the\ninverse method for inviscid airflow over a near-spherical nose\nunder flight conditions where substantial nonequilibrium prevails\nthrough the nose region . typical conditions considered include\nnose radii of the order of 1 ft at an altitude of 250,000 ft and\nvelocities of 15,000 and 23,000 ft per sec .\n the results illustrate the general importance of the coupling\namong the reactions considered . these included\ndissociation-recombination, bimolecular-exchange, and ionization reactions .\nthe exact solutions show the bimolecular, no exchange reactions\nto be important in blunt-nose flow for the kinetics of no and n,\nas they are in the case of a plane shock wave . an important\ndifference between blunt-nose flow and plane shock flow,\nhowever, is the gasdynamic expansion in the curved shock layer of the\nformer . this expansion reduces post-shock reaction rates . as a\nconsequence, in the regime studied the oxygen and nitrogen-atom\nconcentrations tend to freeze in the nose region at levels below\nthose for infinite-rate equilibrium . the reduction below the\nequilibrium dissociation level can be large, particularly for\nnitrogen dissociation at higher velocities .\n in the regime considered, the chemical kinetics are dominated\nby two-body collision processes . the inviscid nose flow,\nincluding coupled nonequilibrium phenomena, is thus amenable to\nbinary scaling for a given velocity . the binary scaling is\ndemonstrated for a range of altitude and scale by correlation of the\nexact solutions for given velocity and a constant product of\nambient density and nose radius . this similitude, which can\nalso scale viscous nonequilibrium and radiation phenomena in the\nshock layer, provides a useful flexibility for hypersonic testing\nwhere it is applicable .\n the afterbody inviscid-flow problem is briefly discussed in the\nlight of the results for the nose flow ."}, {"doc_id": 402, "text": "magnetohydrodynamics shocks .\n a mathematical treatment of the coupled motion of\nhydrodynamic flow and electromagnetic fields is\ngiven . two simplifying assumptions are introduced .. first,\nthe conductivity of the medium is infinite, and\nsecond, the motion is described by a plane shock wave .\nvarious orientations of the plane of the shock and\nthe magnetic field are discussed separately, and the\nextreme relativistic and unrelativistic behavior is\nexamined . special consideration is given to the behavior\nof weak shocks, that is, of sound waves . it is\ninteresting to note that the waves degenerate into common\nsound waves and into common electromagnetic\nwaves in the extreme cases of very weak and very strong\nmagnetic fields ."}, {"doc_id": 403, "text": "magnetohydrodynamic shock waves .\n an interpretation of the de hoffman-teller shock-wave\nequations for an infinitely conducting\nmedium is given analogous to the classical interpretation of\nthe ordinary hydrodynamic shock-wave\nequations of rankine and hugoniot . two cases of interest\nare considered as a consequence of this theory .\nit is shown that weak magnetic fields in interstellar clouds\nwill be amplified, and, if external mechanisms\nare available to reduce the compressional effects of shock\nwaves, the field will reach a value,\nwhere p is the pressure . also, some aspects of the internal\nmotions of prominences are considered ,. it is\nshown that gauss will yield results in accord with\nthe observational material ."}, {"doc_id": 404, "text": "two dimensional transonic flow past airfoils .\n this report concerns the problem of constructing solutions for\ntransonic flows over symmetric airfoils . the aspect of the problem\nemphasized is, of necessity, not how to form a solution for compressible\nflow but how to simplify the initial phase of the problem, namely, the\nmapping of the incompressible flow . in the case of the symmetric\njoukowski airfoil without circulation, the mapping is relatively simple,\nbut the coefficients in the power series are difficult to evaluate . as\na result, the problem requires simplification . instead of the exact\nincompressible flow past the airfoil, an approximate flow is used, which\nis derived from a combination of source and sink . this flow differs\nonly slightly from the exact one when the thickness is small . by the\nsame method, the flow with circulation is also considered .\n after the incompressible-flow functions are approximated in this\nfashion, the numerical calculation of the corresponding compressible\nflow, by the hodograph theory, does not present any\nessential difficulty ."}, {"doc_id": 405, "text": "tables of thermal properties of gases .\ntables of thermodynamic and transport properties\nof air, argon, carbon dioxide, carbon monoxide, hydrogen,\nnitrogen, oxygen, and steam ."}, {"doc_id": 406, "text": "on the behaviour of boundary layers at supersonic speeds .\nthis paper considers the implications of recent advances in knowledge of\n the behaviour of boundary layers in supersonic flow . only the simplest\n case is considered-dashthat of the two-dimensional boundary layer on a\nflat plate, with nominal zero longitudinal pressure and temperature\ngradients .\nit is shown that the empirical/intermediate enthalpy/used with success\nin approximations for skin friction, etc., of laminar boundary layers is\nclosely the same as the mean enthalpy with respect to velocity .\nfurthermore, the mean enthalpics of laminar and turbulent boundary\nlayers may be the same . a nonrigorous approach is made to the problems\nof self-induced pressure gradients, and the indications are that their\neffects on laminar skin friction, etc., may become noticeable at mach\nnumbers greater than 5 and they increase as the surface temperature\nbuilds up towards zero heat-transfer conditions . the effects with\nturbulent boundary layers may not be so severe .\nfinally, the results are applied to give an idea of the magnitude of the\ndrag and aerodynamic heating problems up to m 10, and one result is\nthat, if there is any conflict at the higher mach numbers between\nsurface conditions required for high radiative emissivity and those\nwhich may be thought necessary for preserving a laminar boundary layer,\nthen it may be better to choose the former ."}, {"doc_id": 407, "text": "stationary convection flow of an electrically conducting\nliquid between parallel plates in a magnetic field .\n a study is made of the stationary convection\nof an electrically conducting liquid in the space\nbetween two parallel plates, heated to different\ntemperatures, in the presence of a magnetic\nfield . the distribution of velocity, temperature,\nand induced fields are found, and the convective\nheat flow is calculated ."}, {"doc_id": 408, "text": "on convective motion of a conducting fluid between\nparallel vertical plates in a magnetic field .\n stationary convective motion of a conducting fluid\nbetween vertical parallel plates in a\nmagnetic field is considered . an exact solution of the\nmagnetohydrodynamic equations is\nobtained for the case of a constant vertical temperature\ngradient . the critical value of\ngrasshof's number is determined for the case when the\ntemperature of both plates is the same ."}, {"doc_id": 409, "text": "on the base pressure resulting from the interaction of a supersonic\nexternal stream with a sonic or subsonic jet .\nit is shown that the two-dimensional base pressure problems relating to\nbase bleed into the wake of blunt-trailing-edge airfoils, or the\ninteraction between an external supersonic or sonic slipstream with a\nsonic or subsonic jet stream of a jet engine, can be calculated by\ntheoretical considerations . constant-pressure, isoenergetic, turbulent\nmixing between the streams and the stagnant fluid in the wake is\nassumed . the theoretical calculations are in good agreement with the\nexperimental results ."}, {"doc_id": 410, "text": "the supersonic flow about a blunt body of revolution\nfor gases at chemical equilibrium .\n the supersonic flow about a blunt body of\nrevolution for gases at chemical\nequilibrium . a method to determine the shock\nwave, and its location, about a body\nof revolution moving at supersonic speeds is given .\nthe method provides also the means\nto compute the flow characteristics in the shock layer .\nthe fluid in which the motion\ntakes place is assumed to be in chemical equilibrium\nwithin the shock layer ,. its\nthermochemical properties must be known . the essential\nnew features of the method are ..\na) it solves the direct problem, i. e., the initial data\nare the conditions upstream and\nthe body shape ,. b) the integration of the fundamental\nequations is done in the physical\nplane and the difficulties inherent to other, less direct,\nmathematical formulations\nof the problem are avoided . a physical interpretation of\nthe method is made which\nis in accord with the analytical definition of the problem ."}, {"doc_id": 411, "text": "data on shape and location of detached shock waves\nin cones and sphere .\n accurate experimental data are given on the shape and the location\nof detached shock waves on cones and spheres at mach numbers from 1.17\nto 1.81 . the data are correlated to obtain equations that describe the\nshock waves . this knowledge of the shock waves should be useful in\ncalculations of the pressure distribution and the pressure drag of the\nfore part of cones and spheres . the experimental data on shock waves\nare compared with theory ."}, {"doc_id": 412, "text": "critical combinations of shear and transverse direct\nstress for an infinitely long flat plate with\nedges elastically restrained against rotation .\n an exact solution and a closely concurring approximate\nenergy solution are given for the buckling of an infinitely long\nflat plate under combined shear and transverse direct stress\nwith edges elastically restrained against rotation . it was found\nthat an appreciable fraction of the critical stress in pure shear\nmay be applied to the plate without any reduction in the\ntransverse compressive stress necessary to produce buckling . an\ninteraction formula in general use was shown to be decidedly\nconservative for the range in which it is supposed to apply ."}, {"doc_id": 413, "text": "turbulent skin friction at high mach numbers and reynolds\nnumbers in air and helium . nasa r82, 1960 .\n results are given of local skin-friction measurements in turbulent\nboundary layers over an equivalent air mach number range from 0.2 to 9.9\nand an over-all reynolds number variation of 2x10 to 100x10 . direct\nforce measurements were made by means of a floating element . flows\nwere two-dimensional over a smooth flat surface with essentially zero\npressure gradient and with adiabatic conditions at the wall . air and\nhelium were used as working fluids . an equivalence parameter for\ncomparing boundary layers in different working fluids is derived and\nthe experimental verification of the parameter is demonstrated .\nexperimental results are compared with the results obtained by several\nmethods of calculating skin friction in the turbulent boundary layer ."}, {"doc_id": 414, "text": "the problem of resistance in compressible fluids .\n this report is restricted to the\nresistance of bodies of revolution and\nof cylindrical bodies of infinite length\nmoving with uniform velocity in\na compressible fluid . in the case of bodies\nof revolution it will be assumed\nthat the direction of the movement is\nparallel to the axis of symmetry .\nit will be assumed that the fluid satisfies\nthe equation of state of perfect\ngases, i. e. const., where p denotes\nthe pressure, the density and\nt the absolute temperature . in addition\nto obeying this equation the\nfluid is characterized by the statement\nthat the intrinsic energy of the\nunit mass amounts to where for\nsimplicity's sake the specific heat\nwill be expressed in work rather\nthan heat units . the ratio between\nthe specific heat at constant pressure\nand the specific heat at constant\nvolume will be denoted by . it is\nknown that the value of x depends\nupon the number of degrees of freedom\nof the molecules,. if this number\nis denoted by n . for air\nthe value x = 1.4 will be used .\nthe limiting case x = 1 will\nbe referred to as that of a\nassumed that in the range\nconsidered and are independent of\nthe temperature ."}, {"doc_id": 415, "text": "the aerodynamic design of section shapes for swept wings .\nan extension of work of lock and rogers and the result of cooperation by\nn.p.l., r.a.e. and members of the british aircraft industry to achieve a\n satisfactory design for an aircraft cruising at low supersonic speeds .\n knowledge of shock-wave prediction, onset of wave drag and\nshock-induced separation allows the basic design to be generalized for a wide\nrange of parameters . unpublished work by bagley on the relation of\naerodynamic coefficients and geometry is used . the role of upper\nsurface velocity distribution is noted and methods for predicting pressure\ndistributions with shock waves are reviewed for both subsonic and\ntransonic flows ."}, {"doc_id": 416, "text": "methods of boundary-layer control for postponing and alleviating\nbuffeting and other effects of shock-induced separation .\nthe use of boundary-layer control to increase the separation-free\nmargins of mach number and lift coefficient beyond the cruise point of\nhigh-speed aircraft may often be preferred to design changes that impair\n the cruising performance or the landing and take-off characteristics .\nthe factors that influence the choice of method and details of its\napplication are discussed, emphasising particularly the need to maintain\neffectiveness over most of the chord to cover the wide range of\nseparation positions encountered as the shock moves over the wing with\nchanging flight conditions .\nresearch at the national physical laboratory that has embraced\nhigh-velocity blowing, vane and air-jet vortex generators, and, in a\npreliminary way, distributed suction, is briefly described . the\nrelative merits of the various methods are discussed, and some results\nachieved in their application are given .\nfor vortex generators, the importance is stressed of the vortex paths\ndetermined by the interactions of neighbouring vortices and their\nimages . thus, systems of counter-rotating vortices always leave the\nsurface in pairs and lose their effectiveness . co-rotating systems are\ntherefore preferred for many applications . blowing, which in\nwind-tunnel tests gives results as good as or better than vortex generators\nand does not have the disadvantage of a drag penalty at cruise, has not\nyet been assessed in flight . air-jet vortex generators, which would\nalso avoid the drag penalty, show promise of producing significant\neffects with relatively small blowing pressures and quantities ."}, {"doc_id": 417, "text": "on the stability of two dimensional parallel flows .\n this is the last part of the author's theory of the stability\nof plane laminar motion . (for parts 1 and 2, cf. the same\nquart. 3, 117-142, 218-234 (1945),. these rev. 7,225,226 .)\nthe stability character of a viscous fluid is considered in\ndetail . the author proceeds first to give a proof of a criterion\nof stability due to heisenberg .. if a velocity profile has an\nnumber and phase velocity, the disturbance with the same\nwave number is unstable in the real fluid when the reynolds\nnumber is sufficiently large . this destabilizing effect of\nviscosity is one of the most interesting phenomena in the\ngeneral stability theory,. its physical and mathematical\nsignificance is carefully discussed .\n the author then discusses the behavior of the so-called\nneutral curve for the two characteristic types of\nvelocity distribution, the boundary layer type profile and\nthe symmetrical profile . the asymptotic behavior of the\nneutral curve is discussed first . the main difference between\nprofiles with and without a point of inflection is that the two\nbranches of the neutral curve approach and for\nprofiles with a flex, but both converge to for the profile\nwithout a flex . the most important results are as follows .\nfor sufficiently large reynolds number r . (2) there always\nexists a minimum r below which the motion is stable . a\nsimilar result was obtained by synge from energy\nconsiderations . synge found a limiting curve below which the\nmotion is necessarily stable . the author's discussion of the\nasymptotic behavior of the curves shows further\nthat there always exists a maximum value of a beyond\nwhich the motion is stable for all reynolds numbers . hence\nthe qualitative shape of the curve is determined .\n the author proceeds to show that simple approximate\nexpressions for the stability limit can be obtained from his\ngeneral analysis for a given velocity profile . these\napproximate stability limits for plane poiseuille flow and blasius\nflow are found to be r=5906 and r=502 . the reynolds\nnumbers are based on the width of the channel and the\ndisplacement thickness, respectively . finally, the method\nfor computing the complete instability curve is presented\nand the plane poiseuille case and the blasius problem worked\nout in detail . the stability limit for blasius flow had been\ngiven before by tollmien and schlichting . the present more\nexact computations agree well with tollmien's result as far\nas the minimum critical reynolds number is concerned .\nthe value found here is r=420 . the neutral curve for\npoiseuille motion had not been obtained before . the\nminimum critical number here is found to be r=5314 . the\nagreement with the estimate from the simple criterion\nmentioned above is thus very good .\n a discussion of the physical significance of the viscous\neffects and of future developments concludes the paper ."}, {"doc_id": 418, "text": "transition form laminar to turbulent shear flow .\n recent experimental studies of transition from laminar to\nturbulent shear flows are reviewed . certain common features\nare emphasized and related to the stability theories of viscous\nshear layers . the three-dimensional character, the\nunsteadiness, and the nonlinear and random behavior of the latter stages\nof the transition process are also examined ."}, {"doc_id": 419, "text": "the design of intermediate vertical stiffeners on web\nplates subjected to shear .\n the correct design of intermediate vertical stiffeners on web plates\nsubjected to shear becomes very important when\nthe web plates are designed\nto operate at loads close to their buckling loads .\nthis paper presents details\nof an extensive series of tests conducted on\nstiffened web plates subjected to\nshear . from the analysis of the results obtained\nfrom these tests, new empirical\nrelationships between the flexural rigidity and\nspacing of the intermediate\nstiffeners and the buckling stress of the stiffened\nweb plate have been obtained .\n one interesting and important feature of\nthese new relationships is that\nthey define more clearly than hitherto the difference\nin the behaviour of\nsingle-and double-sided stiffeners ."}, {"doc_id": 420, "text": "an experimental study of the flow field about swept and delta wings\nwith sharp leading edges .\na series of experiments was performed to define the flow field on the\nupper surface of high aspect ratio swept wings and narrow delta wings at\n high angles of attack .\nit was found that near the root section of either type of wing the flow\nis conical . the edge of the vortex sheet which originates at the\nleading edge is a straight line whose position relative to the leading edge\ndepends only on incidence . on swept wings, the vortex edge turns\ndown-stream as soon as the vortex sheet covers the front half of the wing\nchord, and the flow under the vortex sheet outboard of that turning\npoint is uniform and parallel to the leading edge of the wing . on\nnarrow delta wings, the conical symmetry persists almost to the trailing\nedge ."}, {"doc_id": 421, "text": "analytic study of induced pressure on long bodies of\nrevolution with varying nose bluntness at hypersonic\nspeeds .\n a systematic study of induced pressures on a series\nof bodies of revolution with varying nose bluntness\nhas been made by using the method of characteristics\nfor a perfect gas . the fluid mediums investigated\nwere air and helium and the mach number range\nwas from 5 to 40 . a study of representative shock\nshapes was also made . flow parameters obtained\nfrom the blast-wave analogy gave good correlations of\ninduced pressures and shock shapes . the\ninduced-pressure correlations yielded empirical equations for\nair and helium which cover the complete range of\nnose bluntness considered . (nose fineness ratios\nvaried from 0.4 to 4.) available experimental\nresults were in good agreement with the characteristics\nsolutions . properties connected with the concept of\nhypersonic similitude enabled correlations of the\ncalculations to be made with respect to nose shape,\nmach number, and ratio of specific heats ."}, {"doc_id": 422, "text": "bending of a square plate with two adjacent edges free\nand the others clamped or simply supported .\n the title problems were solved for the two cases .. (1) uniform\ntransverse loading, (2) a concentrated force at the free corner . a\nfunction is chosen to exactly satisfy the biharmonic equation\nwhile the boundary conditions are enforced at a number of points\nplied at discrete points around the boundary for each of the four\nproblems and the resulting 35 simultaneous equations were solved\non an ibm 704 . tables listing the values of deflection and\nbending moments are presented . this paper provides useful information\non the solution of these problems which are intractable by\nanalytical methods ."}, {"doc_id": 423, "text": "an experimental investigation of the flow over blunt-nosed\ncones at a mach number of 5. 8.\n shock shapes were observed and static pressures were measured\non spherically-blunted cones at a nominal mach number of 5.8 over a\nrange of reynolds numbers per inch from 97,000 to 238,000, for angles\nof yaw from 0 to 8 . six combinations of the bluntness ratios 0.4, 0.8,\nand 1.064 with the cone half angles 10, 20, and 40 were used in\ndetermining the significant parameters governing pressure distribution .\n the pressure distribution on the spherical nose for both yawed\nand unyawed bodies is predicted quite accurately by the modified\nnewtonian theory given by, where is the angle between the\nnormal to a surface element and the flow direction ahead of the bow\nshock . cone half angle was found to be the significant parameter in\ndetermining the pressure distribution near the nose-cone junction and\nover the conical afterbody . on the 40 spherical nosed cone models\nthe flow overexpanded with respect to the taylor-maccoll pressure in\nthe region of the spherical-conical juncture, after which the pressure\nreturned rapidly to the taylor-maccoll value . for models with smaller\ncone angles the region of minimum pressure occurred farther back on\nthe conical portion of the model, and the taylor-maccoll pressure was\napproached more gradually . the shape of the pressure distributions\nas described in nondimensional coordinates was independent of the\nradius of the spherical nose and of the reynolds number over the range\nof reynolds number per inch between .97 x 10 and 2.38 x 10 .\n integrated results for the pressure foredrag of the models at zero\nyaw compared very closely with the predictions of the modified newtonian\napproximation, except for models with large cone angles and small nose\nradii, where the drag approaches the value given by the taylor-maccoll\ntheory for sharp cones ."}, {"doc_id": 424, "text": "cantilever plate with concentrated edge load .\n the author gives, by the method of finite differences, an\napproximate solution of the problem of a finite length\nof a cantilever plate which bears a concentrated load at\nthe longitudinal free edge . all the boundary conditions\nare taken into account, and the plate action is\ndetermined approximately at all points of the plate . the\nauthor points out that a secondary maximum transverse\nstress occurs at the clamped edge nearest the loading\npoint, and that the longitudinal stress is greatest directly\nunder the loading point ."}, {"doc_id": 425, "text": "the solution of elastic plate problems by electrical analogies .\na dynamic-analogy method for the solution of elastic plate problems is\ndescribed in this paper . the electrical circuits developed here can be\nset-up and studied on an electric-analog computer . problems involving\ndeflections under constant load, transient vibrations, or normal\nmodes can be solved in this way . the method of applying boundary\nconditions to plates with irregular edges is given, together with\na detailed description of the representation of the boundary conditions\nfor a rectangular variable-thickness plate . solutions that have been\nobtained on the cal tech electric-analog computer are presented for\nthe static deflections and normal modes of a rectangular cantilever\nplate ."}, {"doc_id": 426, "text": "preliminary analysis of axial flow compressors having\nsupersonic velocity at the entrance of the stator .\n a supersonic compressor design having supersonic velocity at the\nentrance of the stator is analyzed on the assumption of two-dimensional\nflow . the rotor and stator losses assumed in the analysis are based on\nthe results of preliminary supersonic cascade tests . the results of\nthe analysis show that compression ratios per stage of 6 to 10 can be\nobtained with adiabatic efficiency between 70 and 80 percent .\n consideration is also given in the analysis to the starting,\nstability, and range of efficient performance of this type of\ncompressor . the desirability of employing variable-geometry stators\nand adjustable inlet guide vanes is indicated . although either\nsupersonic or subsonic axial component of velocity at the stator\nentrance can be used, the cascade test results suggest that higher\npressure recovery can be obtained if the axial component is supersonic ."}, {"doc_id": 427, "text": "flow of gas through turbine lattices .\n paper is a translation of chap. 7 of the book /technical\ngas-dynamics/ (see amr 9, rev 1869) . the topics treated are best\nshown by the list of paragraph headings . they are .. 7-1 .\ngeometrical and gasdynamical parameters of the lattices,.\nfundamentals of flow through lattices,. 7-2 . theoretical methods of\ninvestigation or plane potential flow of incompressible fluid through a\nlattice,. 7-3 . electro-hydrodynamic analogy,. 7-4 . forces acting\non an airfoil in a lattice,. theorem of joukowsky for lattices,. 7-5 .\nfundamental characteristics of lattices,. 7-6 . friction losses in\nplane lattice at subsonic velocities,. 7-7 . edge losses in plane\nlattice at subsonic velocities,. 7-8 . several results of\nexperimental investigations of plane lattices at small subsonic\nvelocities,. 7-9 . flow of gas through lattice at large subsonic\nvelocities,. critical mach number for lattice,. 7-10 . profile losses in\nlattices at large subsonic velocities,. 7-11 . flow of a gas through\nreaction lattices at supersonic pressure drops,. 7-12 . impulse\nlattices in supersonic flow,. 7-13 . losses in lattices at near sonic\nand supersonic velocities,. 7-14 . computation of angle of\ndeflection of flow in overhang section of a reaction lattice at supersonic\npressure drops,. 7-15 . characteristic features of three-dimensional\nflow in lattices ."}, {"doc_id": 428, "text": "the quasi-cylinder of specified thickness and shell\nloading in supersonic flow .\n the methods of the operational\ncalculus are used to obtain a linear\napproximation to the shape of the mean camber\nsurface of a quasi-cylinder in a\nsupersonic flow in terms of its shell thickness\nand loading distributions . the\nanalysis deals with a generalised quasi-cylinder ,.\nthat is one which, although lying\nclose to a mean cylinder, need not possess\naxial symmetry . the quasi-cylinder\nis also permitted to be within the small\ndisturbance field of other separate\ncomponents, e.g. a centre-body . because\nthe linearised theory is inadmissable\nfor internal duct flows close to and beyond\nthe first reflected characteristic cone,\nthe present solution is likewise invalid close\nto and beyond the position where\nthis characteristic meets the mean cylinder .\nthe work given here enables the\ncamber shapes of /ring-wings/, which have\nbeen used theoretically to reduce or\neven nullify the wave-drag of a central slender-body,\nto be found . an example\nillustrates the general method ."}, {"doc_id": 429, "text": "a description of the r. a. e. high speed supersonic\ntunnel .\n an account is given of the high supersonic speed tunnel now nearing\ncompletion . the design philosophy is reviewed, the principal features\nare described and some of the more interesting development problems\nare noted ."}, {"doc_id": 430, "text": "calibration of the flow in the mach 4 working section\nof the 4ft . x 3ft . high supersonic speed wind tunnel\nat rae bedford .\n mach number and flow angle distributions in the working section of\nthe mach 4 nozzle of the 4 ft x 3 ft high-supersonic-speed wind tunnel\nare presented for a range of total pressure and humidity ."}, {"doc_id": 431, "text": "free-flight measurements of the zero-lift drag and\nbase pressure on a wind tunnel interference model (m=0 .\n8 - 1. 5) .\n five free-flight models were flown to measure the zero-lift drag and\nbody base pressure on a standard wind tunnel interference model over a\nmach number range of 0.84 to 1.48 .\n roughness bands on the wings and body of the model are shown to\nproduce a small but definite increase in the zero-lift drag at all mach\nnumbers .\n the measured drag is in fair agreement with corresponding measurements\nmade in various transonic tunnels with differences that could plausibly\nbe explained as the effects of tunnel interference .\n the effect of a simulated wind tunnel support sting is shown to\nincrease the base pressure . the discrepancy between models with and\nwithout a sting is greatest at subsonic speeds and progressively\ndecreases with increasing mach number until at m = 1.4 the sting has no\neffect on base pressure ."}, {"doc_id": 432, "text": "theoretical damping in roll and rolling moment due\nto differential wing incidence for slender cruciform\nwings and wing-body combinations .\n a method of analysis based on slender-wing theory is developed\nto investigate the characteristics in roll of slender cruciform wings\nand wing-body combinations . the method makes use of the\nconformal mapping processes of classical hydrodynamics which\ntransform the region outside a circle and the region outside\nan arbitrary arrangement of line segments intersecting at the\norigin . the method of analysis may be utilized to solve other\nslender cruciform wing-body problems involving arbitrarily\nassigned boundary conditions .\n in the present report, the application of the method has\nshown ..\ndifferential incidence of both pairs of opposite surfaces of the\ncruciform wing-body combinations are practically independent\nof the body-diameter-maximum-span ratio up to a value of this\nratio of 0.3 .\narrangement is only 62 percent greater than that for a\ncorresponding planar wing-body combination .\ndence of both pairs of the opposing surfaces of the cruciform\nwing-body arrangement, is only 52 percent greater than that\nfor a corresponding planar wing-body combination .\nunit surface deflection) of the cruciform wing-body arrangement\nhaving four equally deflected panels is therefore 94 percent of\nthe corresponding planar wing-body combination ."}, {"doc_id": 433, "text": "application of two dimensional vortex theory to the\nprediction of flow fields behind wings of wing-body\ncombinations at subsonic and supersonic speeds .\n a theoretical investigation has been made of a general method for\npredicting the flow field behind the wings of plane and cruciform wing\nand body combinations at transonic or supersonic speeds and slender\nconfigurations at subsonic speeds . the wing trailing-vortex wake is\nrepresented initially by line vortices distributed to approximate the\nspanwise distribution of circulation along the trailing edge of the\nexposed wing panels . the afterbody is represented by corresponding\nimage vortices within the body . two-dimensional line-vortex theory is\nthen used to compute the induced velocities at each vortex and the\nresulting displacement of each vortex is determined by means of a\nnumerical stepwise integration procedure . the method was applied to the\ncalculation of the position of the vortex wake and the estimation of\ndownwash at chosen tail locations behind triangular-wing and\ncylindrical-body combinations at supersonic speeds . the effects of\nsuch geometric parameters as aspect ratio, angle of attack and\nincidence, ratio of body radius to wing semi-span, and angle of bank on\nthe vortex wake behind wings of wing-body combinations were studied .\nthe relative importance of wing vortices, the corresponding image\nvortices within the body, and body crossflow indetermining the the total\ndownwash was assessed at a possible tail location .\n it was found that the line-vortex method of this report permitted\nthe calculation of vortex paths behind wings of wing-body combinations\nwith reasonable facility and accuracy . a calculated sample wake shape\nagreed qualitatively with one observed experimentally, and sample\nresults of the line-vortex method compared well with an available exact\ncrossflow-plane solution . an empirical formula was derived to estimate\nthe number of vortices required per wing panel for a satisfactory\ncomputation of downwash at tail locations . it was found that the shape\nof the vortex wake and the ultimate number of rolled-up vortices behind\na wing depend on the circulation distribution along the wing trailing\nedge . for the low-aspect-ratio plane wing and body combinations\nconsidered, it appeared that downwash at horizontal tail locations is\nlargely determined except near the tail-body juncture by the wing\nvortices alone for small ratios of body radius to wing semispan, and by\nthe body upwash alone for large values of that ratio ."}, {"doc_id": 434, "text": "contributions of the wing panels to the forces and\nmoments of supersonic wing-body combinations at combined\nangles .\n a wind-tunnel investigation was\nconducted at a mach number of 1.96\nand at reynolds numbers (based on the\nmean aerodynamic chord of the\nexposed wing) of 0.36 and 1.03 million\nto determine the normal forces,\npitching moments, and rolling moments\ncontributed by each wing panel of\na cruciform-wing and body combination\nover a wide range of combined\nangles of pitch and roll . the wings\nwere triangular of aspect ratio 2,\nand the body was an ogive-cylinder\ncombination . the effects of forebody\nlength and roughness and of the\npresence of the adjacent panels on these\npanel contributions were determined .\n the results of the investigation\nshow that large changes in the panel\nforces and moments can occur as the\nresult of combined angles . a general\ntheoretical method based on slender-body\nand strip theories was found to\nyield results in good agreement with the\nwind-tunnel measurements . these\ncomparisons indicate that the changes in\nthe panel characteristics due to\ncombined angles are caused primarily by\na cross coupling between the\nside-wash velocities due to angle of attack\nand sideslip and by the presence\nof forebody vortices due to crossflow\nseparation . it was found that an\nincrease in forebody length increases\nthe effect of the forebody vortices\nbecause of the dependence of the strength\nof these vortices on the forebody\nlength ."}, {"doc_id": 435, "text": "application of similar solutions to calculations of\nlaminar heat transfer on bodies with yaw and large\npressure gradients in high speed flow .\n an integral method for the rapid calculation of heat-transfer\ndistributions on yawed cylinders of arbitrary cross-sectional shape\nand on bodies of revolution in high-speed flows is developed for\nlaminar boundary layers . the method involves the quadrature of a\nfunction of the pressure distribution (assumed given) and satisfies\nthe integral energy equation with the assumption of local similarity,\nwherein the actual boundary-layer profiles at every station are\nreplaced by corresponding profiles from a family of similar solutions .\n the method is compared with other local similarity methods and\nwith experimental heat-transfer data on a circular cylinder and on a\nbody of revolution designed for large axial pressure gradients . good\nagreement between theory and data is obtained and it is shown that the\npresent integral method, in both its complete and simplified form, gives\ngenerally better agreement with the data than certain other local\nsimilarity methods .\n numerical examples are presented showing that the effect of sweep\nand gas properties on heat-transfer distribution is small ."}, {"doc_id": 436, "text": "heat transfer in planetary atmospheres at super-satellite speeds .\nthe main purpose of this investigation is to examine the dependence of\nheat transfer in planetary atmospheres on the total enthalpy up to\nflight velocities of 50,000 ft/sec where a large proportion of the atoms\n are ionized . the /total thermodynamic and transport property/ concept\ndiscussed by hirshfelder /j.chem.phys.,26/2/,feb.,1957/ is used ."}, {"doc_id": 437, "text": "hypervelocity stagnation point heat transfer .\nthis analysis includes the specific contributions of atoms, molecules,\ntions are .. /i/ partially ionized air can be approximated as a\nfour-component gas including n2, n, n and e,. /ii/ the gas is in local\nthermochemical equilibrium,. /iii/ there is no charge separation,. /iv/\nthermal diffusion is neglected,. /v/ no electrical or magnetic fields,.\n low re effects are neglected ."}, {"doc_id": 438, "text": "stagnation point heat transfer measurements at super\nsatellite speeds .\n brief description of experiments performed by using shock tube\ntechniques for measurement of the stagnation point heating of a blunt\nbody over a stagnation enthalpy range of 650 to 900,\ncorresponding to velocities between 32,000 ft. per sec. and 39,000\nft per sec., respectively . data thus provided are used for\ncomparison with theory ."}, {"doc_id": 439, "text": "a factor affecting transonic leading edge flow separation .\n a change in flow pattern that was observed as the free-stream mach\nnumber was increased in the vicinity of 0.8 was described in naca\ntechnical note 1211 by lindsey, daley, and humphreys . the flow on the\nupper surface behind the leading edge of an airfoil at an angle of\nattack changed abruptly from detached flow with an extensive region of\nseparation to attached supersonic flow terminated by a shock wave . in\nthe present paper, the consequences of shock-wave--boundary-layer\ninteraction are proposed as a factor that may be important in determining the\nconditions under which the change in flow pattern occurs . when the\nmach number is high enough, the attached-flow pattern exists because\nthen the shock wave is far enough behind the leading edge to keep the\ninfluence of the high pressure behind the shock wave from extending\nthrough the boundary layer to the immediate vicinity of the leading edge\nand affecting the flow there . some experimental evidence in support of\nthe importance of shock-wave--boundary-layer interaction is presented ."}, {"doc_id": 440, "text": "compilation of information on the transonic attachment\nof flows at the leading edge of airfoils .\n schlieren photographs have been compiled of the two-dimensional flow\nat transonic speeds past 37 airfoils having variously shaped profiles,\nsome of which are related and vary in thickness and camber . the data\nfor these airfoils were analyzed to provide basic information on the\nflow changes involved and to determine factors affecting transonic-flow\nattachment, which is a transition from separated to unseparated flow at\nthe leading edges of two-dimensional airfoils at fixed angles of attack\nas the subsonic mach number is increased ."}, {"doc_id": 441, "text": "evaluation of high angle-of-attack aerodynamic derivative\ndata and stall-flutter prediction techniques .\n the problem of stall flutter is approached in two ways . first,\nusing the m.i.t.-naca airfoil oscillator, the aerodynamic reactions on\nwings oscillating harmonically in pitch and translation in the stall\nrange have been measured, evaluated, and correlated where possible with\navailable published data, with the purpose of providing empirical\ninformation where no aerodynamic theory exists . the major effects of\nreynolds number, airfoil shape, and reduced frequency on the aerodynamic\nreactions have been reaffirmed . no instances of negative damping were\nobserved in pure translatory motion and the ranges of negative damping\noccurring in pure pitch had the same general trends noted by other\nexperimenters . data on the time-average values in the stall range of\nboth lift and moment are presented for the first time .\n second, the results of numerous experimental observations of stall\nflutter have been reviewed and the various known attempts at its\nprediction have been examined, compared, and extended . the sharp drop in\ncritical speed and change to a predominantly torsional oscillation\nusually associated with the transition from classical to stall flutter\nis apparently primarily but not entirely caused by the marked changes\nin moment due to pitch . fairly good stall-flutter predictions have\nbeen reported only when adequate empirical data for this aerodynamic\nreaction happened to be available for the desired airfoil shape,\nreynolds number range, and reduced-frequency range . a semiempirical\nmethod of predicting the variations of moment in pitch with airfoil\nshape, reduced frequency, initial angle of attack, and amplitude of\noscillation has been presented ."}, {"doc_id": 442, "text": "some effects of variations in several parameters including\nfluid density on the flutter speed of light uniform\ncantilever wings .\n an experimental investigation has been made of some effects of\nvariations in several parameters, including fluid density, on the\nflutter characteristics of light uniform cantilever wings . the\nassortment of wings tested covered a variety of positions of the elastic axis\nand center of gravity and values of the aspect ratio of 8, 6, and 4 .\nthe relative-density parameter (where k is representative of the\nratio of fluid density to wing mass) was varied over a range of values\nfrom 1.2 to nearly 14 . special emphasis has been placed on the lower\nvalues .\n the experimental investigation has been supplemented by an\nanalytical investigation based on the two-dimensional aerodynamic theory for\nincompressible flow . in a few instances corrections for the effects of\nfinite span have been made . in general, the theoretical results\nfollowed the trends indicated by experiment except at very low values of\nthe relative-density parameter . for these low values\nthe analytical considerations employed indicated a freedom from flutter\nnot found experimentally . at higher values of the flutter-speed\ncoefficient is shown to decrease with decreasing values of and\nto be nearly proportional to the inverse of the square root of the air\ndensity ."}, {"doc_id": 443, "text": "calculated and measured pressure distributions over the midspan section\nof the naca 4412 airfoil .\npressures were simultaneously measured in the variable-density tunnel\nat 54 orifices distributed over the midspan section of a 5 by 30 inch\nrectangular model of the n.a.c.a. 4412 airfoil at 17 angles of attack\nranging from -dash 20degree to 30degree at a reynolds number of\napproximately 3,000,000 . accurate data were thus obtained for studying the\ndeviations of the results of potential-flow theory from measured results\ntechnique are presented .\nit is shown that theoretical calculations made either at the effective\nangle of attack or at a given actual lift do not accurately describe the\n observed pressure distribution over an airfoil section . there is\ntherefore developed a modified theoretical calculation that agrees\nreasonably well with the measured results of the tests of the n.a.c.a. 4412\n section and that consists of making the calculations and evaluating the\n circulation by means of the experimentally obtained lift at the\neffective angle of attack,. i.e., the angle that the chord of the model makes\n with the direction of the flow in the region of the section under\nconsideration . in the course of the computations the shape parameter\nis modified, thus leading to a modified or an effective profile shape\nthat differs slightly from the specified shape ."}, {"doc_id": 444, "text": "an approach to the flutter problem in real fluids .\n an approximate theory of airfoils in unsteady motion in a viscous\nfluid is proposed, in which viscous effects are accounted for by\nrelaxing the kutta condition and replacing it by a relation derived from\nexperiments in steady flow . applications here, are limited to moderate\nviscous effects below the stall . the possibility of one-degree-\nof-freedom flutter is discussed under this assumption . the discussion is\npartly extrapolated to the domain of stall flutter . some possibilities\nof further development of this theory for the stalled case are\nindicated ."}, {"doc_id": 445, "text": "on the application of mathieu functions in the theory\nof subsonic compressible flow past oscillating airfoils .\n an account is given of explicit solutions in terms of mathieu function\nfunctions of the problem of two-dimensional subsonic compressible\nflow past oscillating airfoils . the results are applied to the\ncalculation of three-dimensional corrections for the two-dimensional\ntheory and the effect of the incorporation of the three-dimensional\neffects on the mathieu function solution of the two-dimensional\nproblem is shown . the developments are formal and must be\nsupplemented by an appreciable amount of numerical calculations before the\ntheory can be applied to specific problems ."}, {"doc_id": 446, "text": "wake of a satellite traversing the ionosphere .\n the particle treatment is applied to a study of the\nstructure of the wake behind a charged body\nmoving supersonically through a low-density plasma .\nfor the case of a body whose dimensions are\nconsiderably smaller than a debye length, a solution is obtained\nwhich is very similar in structure to the\nsolution obtained by using the linearized fluid dynamics equation .\nfor the case of a disk whose radial\ndimensions are much larger than a debye length, two\nconical regions are found in the wake . at the\nsurface of each of these cones, over thicknesses of\nthe order of a debye length, the ion and electron\ndensities are increased over their ambient values .\nformulae for the electrohydrodynamic drag on a\nwire, and on a large disk are obtained ."}, {"doc_id": 447, "text": "motion of thin bodies in a highly rarefied plasma .\n magnetic effects are considered negligible,\nand the velocity of the body is in a range between the\nelectron and positive ion thermal speeds .\nthe self-consistent field approach is used in which the\nelectron distribution is assumed to be maxwellian,\nwhile the positive ion distribution function is given\nby the /collision-free/ boltzmann equation .\nit is assumed that the ion reflection at the body surface\nis specular, and the body is sufficiently thin so\nthat the ion distribution function is a small perturbation\nof a maxwellian distribution . the solution for\nthe simple case of a dielectric body with a given surface\ncharge, as well as some general properties to\nbe expected for a conducting body are given ."}, {"doc_id": 448, "text": "induction drag on a large negatively charged satellite\nmoving in a magnetic-field-free ionosphere .\n an induction drag, experienced by a\ncharged satellite during its traversal of the\nionosphere, has been theoretically postulated by\nseveral authors . previous 'exact' treatments\nof the problem are inapplicable to large systems, and\nthe semiempirical approach of jastrow\nand pearse may yield somewhat questionable results .\nthe present description initially\nconsiders the satellite as a completely permeable spherical\nshell of charge, thus avoiding the\ndifficult boundary conditions introduced by the 'exact'\nlinearized treatment . the effects of\npermeability are then shown to be approximately removable\nby means of an iterative process . a\nfinal result, apparently valid to within an order of\nmagnitude, is obtained for the drag force\narising solely from electrical effects . its magnitude\nis considerably less than that obtained by\njastrow and pearse ."}, {"doc_id": 449, "text": "interaction of a charged satellite with the ionosphere .\n the problem of the ion density distribution around a\ncharged satellite has been treated by a numerical method\nwhich does not require linearization of the equations or\nrestriction to infinitesimal objects . however, magnetic field\neffects were not considered, and a number of other\nsimplifying assumptions were required . some sample calculations\nfor spherical satellites are presented, illustrating the\ngeneral character of the satellite wake . calculations of the\nso-called /charge drag/ were also made, yielding results\nqualitatively similar to those previously obtained by jastrow and pearse ."}, {"doc_id": 450, "text": "some physical interpretations of magnetohydrodynamic duct flows .\nthis note presents some physical interpretations of magnetohydrodynamic\nduct flows with various boundary conditions viewed in the light of the\neffects of conducting walls on the pattern of electric current, taking\nexamples from published results on rectangular ducts . the current\npatterns are illustrated in fig. 1 for rectangular ducts having\nvarious combinations of conducting and nonconducting walls, a uniform\nmagnetic field being applied in the horizontal direction ."}, {"doc_id": 451, "text": "liapunov's methods in automatic control theory .\nthe work of a. m. liapunov and his theory of stability is discussed .\nthe second method of liapunov is shown to have applications for linear\nequations with real constant coefficients, for a proof of the\nrouth-hurwitz criterion, and linear equations with periodic coefficients .\npractical examples include non-linear stability problems of control, and\n the functions have uses in other areas of control systems ."}, {"doc_id": 452, "text": "symmetric joukowsky airfoils in shear flow .\n the velocity components of the fluid far from the airfoil\nare given by where c is the chord of\nthe airfoil, and k are constants, u and v are velocity\ncomponents in the directions of the coordinates x and y .\nthe solution is sought in the form of the stream function\nand satisfies laplace's equation . a general expression for\nfor vanishing disturbance velocities at points far from\nthe origin is written, and the flows due to a source, a vortex\nand a solid circular cylinder in shear flow are considered\nas examples . typical streamline patterns are shown for\nthese cases . from the eulerian equations of motion the\nauthor obtains the expression for in terms of the\nparameter and derivatives of . the general form\nof is introduced and the appropriate solution for the\npressure p is obtained . by integration around a contour\nenclosing the body, expressions are obtained, analogous to\nthe blasius formulae, for the force and couple on any\ncylinder in this type of flow . these formulae are applied to\nthe case of a symmetrical joukowsky airfoil . the method of\nconformal transformation is employed in the determination\nof . the boundary condition of tangential flow at the\nairfoil surface must be satisfied by the total flow in the airfoil\nplane, but this condition leads to a boundary condition for\nin the transformed plane . the kutta-joukowsky\ncondition of finite velocity at the trailing edge also leads to a\ncondition on in this plane . from these conditions and the\ngeneral expression for the circulation and the strengths\nof the doublets and quadruplets required for the force and\nmoment are determined . hence, the formulae for lift and\nmoment coefficient are obtained . these involve, in addition\nto the usual (potential-flow) terms, terms proportional to .\n the ten functions that appear in the expressions for the\nlift and moment coefficients are tabulated for values of the\nthickness ratio between 0 and 1 . the aerodynamic-center\nposition and the coefficient of the moment about the\naerodynamic center are also calculated and are presented\ngraphically as functions of ."}, {"doc_id": 453, "text": "the influence of two-dimensional stream shear on airfoil maximum lift .\nthe cornell aeronautical laboratory is conducting a program of\ntheoretical and experimental research on low-speed aerodynamics as\napplied to stol and vtol aircraft . the objective of this program is to\nre-examine certain aspects of classical aerodynamic information, in the\nlight of low-speed flight requirements, with the aim of seeking\naerodynamic processes which might be exploited to enhance law-speed\nperformance .\none aspect of propeller-driven aircraft which has recently received\nincreasing attention is the existence of strong gradients of\nlongitudinal velocity, or shear, in the propeller slipstream . this\nslipstream shear interacts with a wing surface and can alter the wing\ncharacteristics . in theoretical treatments of a wing interacting with\na propeller slipstream, the first important simplification is the\nreplacement of the slipstream with an ideal uniform\njet, free of all velocity\ngradients . the application of these theories requires that one equate\nthe actual slipstream to an effective uniform jet . one method\nemployed is to assume the uniform jet has a momentum flux equal to the\naverage in the propeller slipstream . these and similar procedures\nare well founded on momentum considerations., however, the implicit\nassumption is that the flow nonuniformity, the shear, does not influence\nthe wing characteristics ."}, {"doc_id": 454, "text": "several approximate analyses of the bending of a rectangular\ncantilever plate by uniform normal pressure .\n three methods of approximating the deflections and\nmoments occurring in a rectangular cantilever plate\nsubjected to uniform normal pressure over its entire surface\nare presented in this paper . the first is the application of\nthe well-known finite-difference procedure . the second\nand third are collocation methods, one based upon\npolynomial solutions of the lagrange equation, the other\nemploying /mixed/ hyperbolic-trigonometric terms\nsatisfying this equation . in the last two methods the boundary\nconditions are satisfied exactly along the clamped edge and\nat a finite number of points along the free edges of the plate .\nthe results obtained for the particular case of a cantilever\nplate with uniform normal load indicate that the use of a\nrelatively small number of points in the collocation\nmethod yields values of deflections and moments that are\nin substantial agreement with those given by the\nfinite-difference procedure . it cannot be concluded from these\nresults that the collocation method using the assumed\nfunctions will give satisfactory results with fewer points\nthan the finite-difference method for cantilever plates with\nloading different from the one investigated ."}, {"doc_id": 455, "text": "modified cross-lees mixing theory for supersonic separated\nand reattaching flows .\n re-examination of the crocco-lees method has shown that the\nprevious quantitative disagreement between theory and\nexperiment in the region of flow up to separation was caused primarily\nby the improper c(k) relation assumed . a new c(k) correlation,\nbased on low-speed theoretical and experimental data and on\nsupersonic experimental results has been developed and found to\nbe satisfactory for accurate calculation of two-dimensional,\nlaminar, supersonic flows up to separation .\na physical model which incorporates the concept of the /dividing/\nstreamline and the results of experiment . according to this\nphysical model, viscous momentum transport is the essential\nmechanism in the zone between separation and the beginning of\nreattachment, while the reattachment process is, on the contrary,\nan essentially inviscid process . this physical model has been\ntranslated into crocco-lees languages using a semiempirical\napproach, and approximate c(k) and f(k) relations have been\ndetermined for the separated and reattaching regions . the\nresults of this analysis have been applied to the problem of\nshockwave, laminar-boundary-layer interaction, and satisfactory\n a study of separated and reattaching regions of flow has led to\nquantitative agreement with experiment has been achieved ."}, {"doc_id": 456, "text": "a study of flow fields about some typical blunt-nosed\nslender bodies .\n complete inviscid flow fields about three model axisymmetric\nconfigurations have been determined numerically . configurations\ndecreasing bluntness) and flight conditions have been selected so\nas to indicate separately effects of nose shape, drag coefficient,\nflight mach number, and thermodynamic behavior of the gas (either\nideal calorically perfect gas or air in equilibrium dissociation) .\nresults are presented for thirteen cases . particular attention is\ndevoted to interpretation and, when possible, correlation of\npressure distributions on, and shock shapes about, the cylindrical\nafterbodies . it is found that .. (a) the correlation of pressure\ndistributions on bodies having nonspherical noses involves interpretive\nmodifications of the law suggested by blast wave analogy . also\nshocks about these bodies are not described by parabolae,. (b) for\nall configurations there is substantial influence of gas behavior\non shock shape,. this, however, can be correlated in terms of the\ngas conditions along a generally defined streamline,. (c) the shock\nlayer can generally be divided into two regions (the first bound by\nthe body and the aforementioned streamline, the second delimited\nby this streamline and the shock) wherein flow properties can\neither be approximated by simple laws or correlated .. (d) for each\nconfiguration knowledge of the complete flow field in one flight\ncondition (even pertaining to ideal gas flow) can be used to\nestimate features of flows under general flight conditions including\nthose where equilibrium dissociation is encountered ."}, {"doc_id": 457, "text": "on laminar boundary-layer flow near a position of separation .\n singularities are considered in the solution of\nthe laminar boundary-layer\nequations at a position of separation . a singularity of\nthe type here considered occurred\nin a careful numerical computation by hartree\nfor a linearly decreasing velocity\ndistribution outside the boundary layer ,. it may\noccur generally . whenever it does\noccur, the boundary-layer equations cease to be\nvalid at and near separation on the\nupstream side, and also downstream of separation .\nthe work suggests that\nsingularities may arise in the solution of non-linear\nparabolic equations due to their\nnon-linearity . the formulae found may help\ncomputers of laminar boundary layers,\nwho desire more than a rough solution, to have\nan end-point at which to aim ."}, {"doc_id": 458, "text": "a new series for calculation of steady laminar boundary\nlayer flows .\n a new and general method for solving\nproblems of plane and steady laminar\nboundary layer flows in incompressible\nfluids with arbitrary outer pressure\ndistribution is developed . this method\nis based on the introduction of the\ndimensionless quantities\nas new independent spatial variables .\nordinates, u(x) the given outer velocity\ndistribution, v the kinematic viscosity .)\nthe solution of the boundary layer problem\nis then given as a power series in e\nwith coefficient functions depending on n .\nthis series is a formally exact solution\nof the boundary layer problem .\n the new series solution has the following qualities ..\n have the significance only of cartesian\n coordinates, the influence of wall\n curvature being neglected in boundary\n layer theory, the new coordinates\n are adjusted to the data of the special\n problem in any case of application .\n the new variables represent a logical\n development of former efforts in\n the field of boundary-layer flow calculation .\n with other series solutions known for\n some special cases is that the leading\n term of the new series satisfies\n exactly the outer boundary condition\n at all cross-sections along the wall .\n therefore, the succeeding terms give\n corrections only in the inner part of\n the boundary layer . accordingly,\n taking also no. 1 into account, the zero\n order term by itself gives a good\n approximation for the boundary layer flow ."}, {"doc_id": 459, "text": "on the solution of the laminar boundary layer equations .\n the theory of the laminar boundary layer\noffers a means of determining the skin friction\nunder the assumption of a given velocity\ndistribution outside the boundary layer . owing to the\nmathematical difficulties, however, exact solutions\nare possible only when the velocity distribution\nis expressed as a simple function of the distance\nalong the surface . more complicated velocity\ndistributions necessitate recourse to the method of\nexpansion in series or that of step-by-step\ncalculations, but the labor involved is too great for the\nmethods to be of practical use . approximate\nmethod due to pohlhausen (1921), which had long\nbeen recommended for general use, gives a\nreasonably accurate solution in a region of accelerated\nflow, but recently its adequacy in a region of\nretarded flow has been questioned . separation of\nflow may actually occur where the solution of\npohlhausen fails to give it . more recently howarth\nsolution, which gives fairly reasonable results in\na region of retarded flow .\n howarth's solution essentially consists in\nsolving the boundary layer equations for the particular\ncase in which the velocity u outside the boundary\nlayer decreases linearly with the distance x\nmeasured along the surface, and utilizing the solution\nby replacing the actual distribution of u by a\ncircumscribing polygon of infinitesimal sides .\ntherefore, it is assumed that the velocity\ndistribution at any section depends on the velocity\ngradient du/dx at that section only, being affected\nby the conditions upstream only in so far as this\naffects the momentum thickness 0 . in other words,\nthe velocity distribution across the boundary layer\nis determined by a parameter ."}, {"doc_id": 460, "text": "correlated incompressible and compressible boundary\nlayers .\n the boundary-layer equations for a compressible\nfluid are transformed into those for an\nincompressible fluid, assuming that the boundary\nis thermally insulating, that the viscosity is\nproportional to the absolute temperature, and\nthat the prandtl number is unity . various\nresults in the theory of incompressible boundary\nlayers are then taken over into the\ncompressible theory . in particular, the existence of\nmethod for retarded flows is applied to determine\nthe point of separation for a uniformly\nretarded main stream velocity . a comparison with\nan exact solution is used to show that this\nmethod gives a closer approximation than does pohlhausen's ."}, {"doc_id": 461, "text": "approximate methods fore predicting separation properties\nof laminar boundary layers .\n some new solutions for steady incompressible laminar boundary\nlayer flow, obtained by gortler, have been used to test the accuracy of\ntwo methods which are commonly used to predict separation . a\nmodification of stratford's criterion for separation is given in this\npaper and is probably the most accurate and the simplest of all methods\nat present in use . modified numerical functions are also given for\nthwaites's method of predicting the main characteristics of the boundary\nlayer over the whole surface, which improve the accuracy of the method ."}, {"doc_id": 462, "text": "photo-thermoelasticity .\n this paper summarizes the optical and physical\nproperties of the photoelastic model material paraplex p-43 over\nthe temperature range from room temperature to -40 f .\ndescriptions are presented of techniques and equipment\ndeveloped to obtain the modulus of elasticity, the material\nfringe value, and the thermal-expansion coefficient as a\nfunction of temperature . experimental investigations\nwere conducted into the plane-stress problems of a disk\ncontracting upon an elastic inclusion and the transient\nthermal-stress field produced by a temperature differential\nsuddenly applied to the upper edge of a long beam . the\ndata are correlated with theory using the material\nproperties obtained in the calibration phase . also included are\nphotographic results of an exploratory investigation of the\nthermal-shock phenomenon produced by the sudden\napplication of a temperature differential upon plastic beams\nof various length-depth ratios ."}, {"doc_id": 463, "text": "physical properties of plastics for photo-thermoelastic\ninvestigation .\n the optical and physical properties of\nparaplex p43, castolite, and epoxy resin\nhysol 6000-op, which are potentially of\ninterest in photothermoelastic investigations,\nwere investigated over a temperature range\nfrom +100 to -60 f . results on the\nthermal-expansion coefficient, the material\nfringe value, and the modulus of elasticity\nas functions of temperature are presented .\nalso evaluated were thermal properties of\nimportance in heat conduction . photothermoelastic\nfigures of merit, which rate the\noptical sensitivity of materials in photothermoelastic\napplications, as well as a new\nmethod to determine this figure in a relative manner are presented ."}, {"doc_id": 464, "text": "flow studies on flat plate delta wings at supersonic\nspeeds .\n an experimental study has been made to investigate some aspects\nof the nature of the flow around delta wings . vapor-screen,\npressure-distribution, and ink-flow studies were made at a mach number of 1.9 on\na series of semispan delta-wing models with slender wedge airfoil\nsections and very sharp leading edges . the models had semiapex angles\nranging from 5 to 31.75 .\n separated regions of vorticity existed along the chords of all\nthe wings in the series tested . concentrated vortex cores were found\nonly on wings of very small semiapex angles . for wings with medium\nand large semiapex angles, the separated vorticity was concentrated in\na region extending over the outboard part of the span and lying close\nto the wing upper surface .\n the results show that theoretical aerodynamic calculations, such\nas those in naca tn 3430, utilizing a single, separated vortex pair\nabove the wing upper surface to represent the separated vorticity can\nbe applied at supersonic speeds for very slender wings ."}, {"doc_id": 465, "text": "slender delta wings with sharp edges at zero lift .\n several slender wings of delta planform with sharp edges have been\ninvestigated theoretically at zero lift at subsonic and at supersonic\nspeeds . most of the wings have diamond-shaped cross sections and are\nintended to lead to a type of flow with leading-edge separation in the\nlifting condition . the pressure distributions and overall\nnormal-pressure drags resulting from various theoretical methods are compared\nwith one another and some discussion is included concerning the\npossibility of achieving the results, calculated for an inviscid stream,\nin a real flow in the presence of a viscous layer around the body ."}, {"doc_id": 466, "text": "development of the vapour screen method of flow\nvisualization in the 3ft tunnel at rae bedford.\n the vapour screen method of flow visualisation in supersonic wind\ntunnels is outlined, and the development of a suitable technique for use\nin the 3 ft tunnel described, together with the associated optical and\nphotographic equipment .\n the results of tests to determine the humidity required to produce an\noptimum density of fog in the working section over the mach number range\ntemperature discussed . numerous vapour screen photographs of the flow\nover and behind delta wings are included and some comparisons made with\nthe corresponding surface oil-flow patterns .\n the process of condensation, the physical and optical properties of\nthe resulting fog, and the formation of the vapour screen picture are\nall considered in some detail .\n the effects of humidity on the mach number and static pressure in the\nworking section were investigated and the results are compared with\ntheoretical estimates at a nominal mach number of 2.0 . it is shown\nthat the adverse effects of condensation on the flow at high mach\nnumbers may be alleviated by the use of liquids with a lower latent heat\nof evaporation than water, and some results obtained at a mach number of\n the possibility of extending the vapour screen technique to transonic\nand subsonic speeds is also considered, and some results obtained at a\nmach number of 0.85 are included ."}, {"doc_id": 467, "text": "thin airfoil theory based on approximate solution of the transonic flow\nequation .\nthe present paper describes a method for the approximate solution of the\n nonlinear equations of transonic small disturbance theory . although\nthe solutions are nonlinear, the analysis is sufficiently simple that\nresults are obtained in closed analytic form for a large and significant\n class of nonlifting airfoils . application to two-dimensional flows\nwith free-stream mach number near 1 leads, for instance, to general\nexpressions for the determination of the pressure distribution on an\nairfoil of specified geometry and for the shape of an airfoil having a\nprescribed pressure distribution and gives, furthermore, the correct\nvariation of pressure with mach number at mach number 1 . for flows that\n are subsonic everywhere, the method yields a pressure-correction\nformula that is more accurate than the prandtl-glauert rule and compares\nfavorably with existing higher approximations . for flows that are\nsupersonic everywhere, the method yields the equivalent, in transonic\napproximation, of simple wave theory . results obtained by application\nof these general expressions are shown to correspond closely to existing\n solutions and to experimental data for a wide variety of airfoils ."}, {"doc_id": 468, "text": "a refinement of the linearised transonic flow theory .\n a new method is proposed to calculate the velocity and pressure\ndistributions around a thin symmetrical aerofoil or a slender body of\nrevolution flying at transonic speed . it is essentially a refinement\nof the linearized transonic flow theory due to oswatitsch and maeder,\nsuch that a correction term is introduced to take account of the\nnonlinear character of the transonic flow . as examples of application,\na symmetrical circular-arc aerofoil and a circular-arc body of\nrevolution in the sonic flow are dealt with, and the results are found\nto be in good agreement with experiments, except for the rear portion in\nthe latter case ."}, {"doc_id": 469, "text": "linearised transonic flow about slender bodies at zero\nangle of attack .\n the simple linearized transonic flow theory\nas originally proposed by oswatitsch and\nkeune(1) and by the present authors (2)\nis improved by considering and partially\ncorrecting its error . in this manner a theory\nwhich is easy to apply and which should\nbe valid for a great number of smooth bodies\nis obtained . this improved theory\npredicts shock waves in the lower transonic regions .\nit is applied to a number of significant\nbody and airfoil shapes and its predictions are\ncompared with experiments and results\nof other theoretical investigations ."}, {"doc_id": 470, "text": "some notes for the small disturbance linear theory\nof the method of local linearisation of the flow over\nan airfoil at mach number of unity .\n in this paper, the pressure\ndistribution at the surface of a symmetrical\nnon-lifting aerofoil with free stream\nmach number of unity has been\ninvestigated by means of the small-disturbance\nlinear theory or the method of local\nlinearization . and by comparing with\nthe calculated results based on an\nhodograph method, the accuracy of these\napproximate methods has been\nevaluated . moreover, when these approximate\nmethods are used for the calculation\nof the pressure coefficient, some notes\nnecessary to obtain more correct\nresults have been discussed ."}, {"doc_id": 471, "text": ""}, {"doc_id": 472, "text": "waves in supersonic flow .\nin this chapter we shall mainly consider problems of steady, two-\ndimensional (plane) supersonic flow . using the fact that in this case\nthere is a steady wave system, we shall find solutions by an indirect\napproach . that is, we shall first study the conditions under which\nsimple stationary waves may exist in the flow, and then find the flow\nboundaries to which they correspond or which may be fitted to\nthem . in this procedure the limited upstream influence in a supersonic\nfield is very helpful, for it allows flows to be analyzed or\nconstructed step by step, which is a method that is not possible in\nthe subsonic case ."}, {"doc_id": 473, "text": "freeman method .\nthe freeman method (ref. 26) is similar to\nchester's method in that the newtonian-plus-centrifugal solution (eq.\nwith the von mises transformation . a method of successive\napproximations is applied to both plane and axially symmetric blunt-nosed bodies\nfor small and infinite free-stream mach number .\nformulas for the streamlines, shock shape, and pressure distribution are\ndetermined to this approximation . a number of special shapes are\ntreated in ref. 26, and in certain cases the theory has a singular point\nwhere the first approximation to the pressure vanishes., that is,\nfor a sphere (see eq. 7-113) . as in chester's method, the theory is\nnot applicable where the pressure becomes too small ."}, {"doc_id": 474, "text": "laminar mixing of a compressible fluid .\na theoretical investigation of the velocity profiles for laminar\nmixing of a high-velocity stream with a region of fluid at rest\nhas been made assuming that the prandtl number is unity . a method\nwhich involves only quadratures is presented for calculating the\nvelocity profile in the mixing layer for an arbitrary value of the\nfree-stream mach number .\ndetailed velocity profiles have been calculated for free-stream mach\nnumbers of 0, 1, 2, 3, and 5 . for each mach number, velocity profiles\nare presented for both a linear and a 0.76-power variation of viscosity\nwith absolute temperature . the calculations for a linear variation are\nmuch simpler than those for a 0.76-power variation . it is shown that\nby selecting the constant of proportionality in the linear approximation\nsuch that it gives the correct value for the viscosity in the\nhigh-temperature part of the mixing layer, the resulting velocity profiles\nare in excellent agreement with those calculated by a 0.76-power\nvariation ."}, {"doc_id": 475, "text": "the velocity distribution in the laminar boundary layer\nbetween parallel streams .\n a method is given for obtaining the solution of the laminar boundary\nlayer equations for the steady flow of a stream of viscous\nincompressible fluid over a parallel stream of different density and\nviscosity . an approximate solution is also obtained by means of the\nmomentum equation . it is shown that the solutions depend only on the\nratio of the velocities of the two streams and on the product of the\ncorresponding density and viscosity ratios . numerical results are\ngiven, in the case where the lower fluid is at rest, for four values of\nand also when for one non-zero value of the velocity ratio ."}, {"doc_id": 476, "text": "the blasius equation with three-point boundary conditions .\nthe blasius equation subject to three-point boundary conditions,\ndescribing the interaction between two parallel streams, is solved by way\nof a series in terms of ascending powers of the ratio equals /u1 -dash\nu2//u1, where the u1's are the outer streams' velocities .\nthe first three terms of the series are analytically expressed in terms\nof the repeated integrals of the complementary error function /im erfc /\nand of the repeated integrals of the square of the successive integrals\nof the complementary error function /jmin erfc n/ . these functions\noften appear in problems leading to extended heat-conduction type of\nequations . a recurrence formula for jmin erfc n is established and\nformulae relating the functions in erfc /-dashn/ and jmjn erfc to\navailable tabulated values of the functions in erfc /n/ are derived .\nthe first three approximations to the blasius function and to its first\ntwo derivatives are also presented in tabulated form with four\nsignificant figures . test on the convergence of the series has been made by\ncomparison with some exact solutions obtained by high speed computing\nmachine . the comparison, extended to the physically essential\nquantities, shows that ..\nsecond and first derivatives .\nyield extremely accurate results . the errors in the first two\nderivatives of the blasius functions are always contained within less than one\n per cent ."}, {"doc_id": 477, "text": "laminar boundary layers at the interface of co-current\nparallel streams .\n the approximate solution of keulegan(1) for the steady flow of a\nstream of viscous incompressible fluid over another at rest is extended\nto the case where both fluids are moving co-current but at different\nvelocities . this solution utilizes a sextic polynomial for the\nvelocity distribution in the boundary layers . the solutions depend\nonly on the ratio of the velocities of the two streams and on the\nproduct of the corresponding viscosity and density ratios . numerical\nresults are given for seven values of at one value of . lock(2) has\npublished an exact solution with a numerical result for and the sextic\npolynomial solution is evaluated f40umerical result for and the sextic\nindicates that in general the sextic polynomial is more accurate than\nthe quartic polynomial but that the advantage is not great ."}, {"doc_id": 478, "text": "tabulation of the blasius function with blowing and\nsuction .\n authors tabulate solutions of f''' + ff'' = 0 for the velocity\ndistribution in a boundary layer . for each solution f'(0) = 0,\nthe third boundary condition is the specification\nof f(0) . f(n) and its first three derivatives are tabulated to 5d\nin gaps of 0.1 in n for f(0) = -1.23849, -1.2(0.05) 0.5 (0.1) 1.5,\nintroduction gives method of solution and\nphysical meaning of boundary conditions, etc . lock's (amr\ncussed ."}, {"doc_id": 479, "text": "on an equation occurring in falkner and skan's approximate\ntreatment of the equation of the boundary layer .\n the differential analyser\nhas been used to evaluate solutions of the equation y''' = -yy'' +\nwith boundary conditions y = y' = 0 at x = 0, as\nwhich occurs in falkner and skan's approximate treatment of the\nlaminar boundary layer (see abstract 1081 (1932)) . a numerical\niterative method has been used to improve the accuracy of the solutions,\nand the results show that the accuracy of the machine solutions is about\ninsufficient to specify a unique solution for negative values of,.\na discussion of this situation is given, and it is shown that for the\napplication to be made of the solution the appropriate condition is that\nfrom below, and as rapidly as possible, as . the condition that\nfrom below can be satisfied only for values of greater than a limiting\nvalue whose value is approximately -0.199, and which is related to the\npoint at which the laminar boundary layer breaks away from the\nboundary ."}, {"doc_id": 480, "text": "adiabatic wall temperature due to mass transfer cooling with a\ncombustible gas .\na recent technical note by sutton (1), with the above title, discusses\nthe influence of the burning of a transpiration coolant on the quantity\nof coolant necessary to maintain a given wall temperature . the present\nnote discusses the same problem in a way which has been found useful\nin calculating the burning rates of solid and liquid fuels (2) .\nconsider the transpiration cooling of a porous surface in a gas stream .\nthen a simple modification of the general mass ."}, {"doc_id": 481, "text": "mass transfer cooling of a laminary boundary layer\nby injection of a light weight foreign gas .\n analytical predictions are given for the development of\nthe velocity, temperature and concentration fields in a\nlaminar air boundary layer on a flat plate in high-speed\ndissipative flow, the plate being considered porous and\ncooled by injection of hydrogen from its surface . the\nadmixture of hydrogen, having a low density and high\nthermal capacity relative to air, is shown to greatly\ndiminish the skin friction and to markedly relieve the\nadverse thermal effects of intense aerodynamic heating under\nconditions of hypersonic flow ."}, {"doc_id": 482, "text": "a re-examination of the use of the simple concepts\nfor prediction the shape and location of detached shock\nwaves .\n a reexamination has been made of the use of simple concepts for\npredicting the shape and location of detached shock waves . the results\nshow that simple concepts and modifications of existing methods can\nyield good predictions for many nose shapes and for a wide range of mach\nnumbers ."}, {"doc_id": 483, "text": "stagnation point shock detachment distance for flow\naround spheres and cylinder .\n development of an analytical relation between shock detachment\ndistance and free-stream mach numbers . results are presented\ngraphically for shock detachment distance of cylinders and spheres\nin air ."}, {"doc_id": 484, "text": "the influence of two-dimensional stream shear for airfoil\nmaximum lift .\n the effects of stream velocity gradients on airfoil maximum\nlift are defined with experimental data obtained in a simulated\ntwo-dimensional slipstream . the experimental results show\nthat when positioned near the slipstream plane of symmetry, the\nairfoil maximum lift varies markedly with location in the\nslipstream . in moving the airfoil from above to below the\nslipstream plane of symmetry through a total distance corresponding\nto the airfoil thickness, force data and boundary-layer\nobservations show that boundary-layer separation is delayed to higher\nangles of attack, and the airfoil maximum lift is doubled .\n it is concluded that the destalling effect observed in the\nnon-uniform slipstream is not associated with slipstream boundary\ninterference, but stems from the influence of the large local\nslipstream shear on airfoil characteristics . the effects of uniform\nand nonuniform shear on airfoil lift and pressure distribution are\ndiscussed, within the framework of existing first-order,\nsmall-shear theory, to show that these effects of shear tend to promote\nstall . a pohlhausen calculation of the laminar boundary layer\nin a stream with shear is used to identify and to assess the effects\nof stream shear on boundary-layer separation criteria . it is\ndemonstrated that these effects are negligibly small, and that the\nuniform-flow criterion applies . it is concluded on the basis of\nthe experimental data that the observed destalling phenomenon\nstems from a shear effect of higher order than those treated in the\ninviscid theories . it is hypothesized that it is a second-order\neffect, fixed by the product of the stream shear and the derivative\nof the shear, which was large in the present experiments ."}, {"doc_id": 485, "text": "linear heat flow in a composite slab .\n the temperature is determined as a function of position and\ntime in the case of linear heat conduction in a composite slab of\nture throughout, and the two external surface temperatures are\nconsidered to be prescribed functions ."}, {"doc_id": 486, "text": "similarity laws for aerothermoelastic testing .\n the similarity laws for aerothermoelastic testing are presented\nin the range . these are obtained by\nmaking nondimensional the appropriate governing equations of\nthe individual external aerodynamic flow, heat conduction to\nthe interior, and stress-deflection problems which make up the\ncombined aerothermoelastic problem .\n for the general aerothermoelastic model, where the model is\nplaced in a high-stagnation-temperature wind tunnel, similitude\nis shown to be very difficult to achieve for a scale ratio other\nthan unity . the primary conflict occurs between the\nfree-stream mach number reynolds number aeroelastic\nparameter heat conduction parameter and\nthermal expansion parameter .\n means of dealing with this basic conflict are presented . these\ninclude (1) looking at more specialized situations, such as the\nbehavior of wing structures and of thin solid plate lifting surfaces,\nand panel flutter, where the aerothermoelastic similarity\nparameters assume less restrictive forms, (2) the use of /incomplete\naerothermoelastic/ testing in which the pressure and/or heating\nrates are estimated in advance and applied artificially to the\nmodel, and (3) the use of /restricted purpose/ models\ninvestigating separately one or another facet of the complete\naerothermoelastic problem .\n some numerical examples of modeling for the general\naerothermoelastic case as well as for the specialized situations\nmentioned in (1) above are given .\n finally, extension of the aerothermoelastic similarity laws to\nhigher speeds and temperatures is discussed ."}, {"doc_id": 487, "text": "theory for supersonic two-dimensional, laminar, base-type\nflows using the crocco-lees mixing concepts .\n a separated flow field, in which the incoming boundary layer\nis undisturbed up to the separation point, is defined as a /\nbase-type/ flow . examples are the flows over a blunt base and over\na backward-facing step . the crocco-lees theory is applied to\nthe supersonic, two-dimensional, laminar, base-type flows\ndefined above . the separated flow is divided into a mixing region\nand a recompression (or reattachment) region . calculations of\nbase pressure show its dependence on the mach number and on\ntwo reynolds-number-dependent variables, and .\n it is shown that existing base-pressure data can be explained\nby these results ."}, {"doc_id": 488, "text": "a reaction-rate parameter for gasdynamics of a chemically\nreacting gas mixture .\n presented note proposes a linearized reaction rate parameter\nwhich is applicable to any reacting gas mixture provided all the\npertinent reactions and their rate constants are known at the\nthermodynamic conditions under consideration . linearizing is\nachieved by expanding equation of rate of chemical reaction in a\ntaylor series and neglecting higher-order terms . author\nannounces that tables of linearized reaction rate parameters for\ndissociated and slightly ionized air are now in preparation at the\nspace sciences laboratory, general electric co., msvo .\n comparison of preliminary results with exact calculations\npublished by hall, i. g., et.al., /inviscid hypersonic air-flows with\ncoupled non-equilibrium processes/ (ias paper 62-67, 30th\nannual meeting, new york, jan. 1962) indicates good agreement ."}, {"doc_id": 489, "text": "on calculation of the laminar separation point and\nresults of certain flows .\n paper studies compressible laminar boundary layer in adverse\npressure gradient . after mentioning mathematical instabilities in\nhowarth's and like solutions, authors quote equation from one of\nthe references, based on the assumptions that zero\nheat transfer and y = 1.4 . thence authors compute nondimensional\ndistances to separation, comparing with solutions by other\nworkers .\n results are interesting, though reviewer feels rather unhappy\nabout approximations leading to eq. (4),. more detailed\njustifications should have been given . thus we have the statement\nber, as ./ surely a fuller discussion of effects\nof letting is warranted .\n typography in eqs. (2) and (3) is rather confusing and there is\na typographical error in heading to table 2 ."}, {"doc_id": 490, "text": "normal-shock relations in magnetohydrodynamics .\n the magnetic-field vector is perpendicular to the flow direction,.\nthus for normal shocks there is no change of flow direction through\nthe shock front . this class of shocks is included in\ninvestigations by several authors (five are referred to here), but the\npresentation here is thought to be especially convenient . all\ndownstream quantities are given in terms of upstream flow conditions,\nincluding the upstream ratio of alfven speed to sound speed, and\nthe shock strength (density ratio) ."}, {"doc_id": 491, "text": "on the close relationship between turbulent plane-couette\nand pressure flows .\n author studies the velocity profiles measured by others in plane\nand turbulent couette flow, such as is induced in parallel\nchannels of which one of the walls moves in its own plane . he finds\nthese profiles to be satisfactorily describable in terms of the\nseventh-power law, which was originally set up for plane and\nturbulent pressure flow in channels where both walls are stationary .\nfurther, he finds the shear law for pressure flow,\nto be applicable also to the couette flow, in a similar range of\nreynolds number, r . no attempt is made in this concise\ncontribution to put these findings on a firmer basis through a theoretical\nexplanation ."}, {"doc_id": 492, "text": "prediction of ogive-forebody pressures at angles of attack .\nvarious approximations are being suggested for obtaining surface\npressures on arbitrary bodies at angle of attack . this not presents\na method for obtaining an approximate pressure distribution over\nthe lower surface of an ogive forebody at angle of attack by utilizing\nthe calculated pressures for zero angle of attack ."}, {"doc_id": 493, "text": "real-gas laminar boundary layer skin friction and heat\ntransfer .\n the laminar-boundary-layer equations have been integrated\nfor the case of a flat plate over a wide range of free-stream\nenthalpies and velocities and over a wide range of enthalpies of\nthe gas at the wall . the range of free-stream velocities extended\nup to 25,000 ft sec at low free-stream enthalpies, corresponding\nto local conditions on a slender body traveling at high speeds .\nat low free-stream velocities, the range of free-stream enthalpies\nextended up to 400,000 btu slug, corresponding to the local\nconditions on a blunt body traveling at speeds up to 25,000 ft sec .\nthe gas was assumed to be in thermodynamic equilibrium at each\npoint in the boundary layer and diffusion effects were neglected .\nthe solutions to the boundary-layer equations were carried out\non a high-speed digital computing machine, both skin-friction and\nheat-transfer coefficients being obtained from the computations .\n before presenting the results, the t' method of rubesin and\njohnson for computing skin-friction coefficients for the\nperfect-gas case is reviewed . for the real-gas case, the average\ntemperature, t', is replaced by the average enthalpy, h', and the h'\nmethod is then used to compute skin-friction coefficients . these\nvalues are in excellent agreement with the computing-machine\nresults . it was found that the recovery factor for the real-gas\ncase can be approximated by, the best results for the\ncases considered being obtained if a value of pr corresponding to\nthe enthalpy, h', is used . using this recovery factor and\nreynolds analogy, heat-transfer rates can be computed which,\nwith a few exceptions, are within 5 percent of values obtained\nfrom computing-machine results ."}, {"doc_id": 494, "text": "axisymmetric viscous flow plast very slender bodies\nof revolution .\n axisymmetric viscous flow past unyawed very slender bodies\nof revolution is treated within the category of the perfect gas .\nattention is paid especially to the effect of transverse curvature\nof the body . from the transformed equations, the similarity\nconditions are deduced, and the parameter characterizing the\neffect of transverse curvature is obtained . several numerical\nsolutions of similarity equations for hypersonic flows are\npresented, and upon the basis of these results, the effect of the\ntransverse-curvature parameter is discussed . a method of\napplying the local-similarity approximation to obtain the\napproximate solution for nonsimilar cases is described, as are\npractical applications to incompressible flow past a long cylinder and\nto hypersonic flow past a very slender cone . comparison with\nexperimental results shows fair agreement with calculations using\nthe local-similarity approximation in the present range of\nexperimental flow conditions ."}, {"doc_id": 495, "text": "on similar solutions for strong blast waves and their\napplication to steady hypersonic flow .\n the general solution of the strong blast wave is found in the\nnewtonian approximation--i.e., neglecting terms of order\nthe expressions obtained for the pressure, temperature, density,\nand velocity profiles are simple . the results are applied to\npower-law bodies in hypersonic flow using the equivalence\nprinciple .\n higher-order approximations for strong blast waves are\ninvestigated for the cases in which the shock layer is thin . a\nsimple pressure formula is found, which constitutes an\nimprovement upon the newton-busemann formula, and some of its\napplications are shown ."}, {"doc_id": 496, "text": "a theory of transonic aileron buzz, neglecting viscous\neffects .\n usaf-sponsored analysis of the unsteady perturbations of\ntwo-dimensional transonic flow around an airfoil, where local supersonic\nregions terminated by shock waves are present in the vicinity of the\nairfoil . viscous effects are neglected, and a linearized theory of\nthe perturbations due to harmonic oscillations of an aileron is\ndeveloped . a series solution for the pressure distribution is obtained,\nand numerical results for the nonsteady hinge moment, from the\nfirst approximation to the solution, are presented . as a result of\nflutter analysis a stability boundary for transonic aileron buzz is\nobtained . comparison of the theoretical results with experimental\nobservations shows satisfactory agreement ."}, {"doc_id": 497, "text": "theoretical and experimental investigation of thermal\nstresses in hypersonic aircraft wing structures .\n a simple and relatively accurate analytic approximation is\ndeveloped to determine the temperature and thermal-stress\ndistribution in aircraft wing structures . theoretical investigations\nshow that the results of the existing thermal-stress theories\nwhich neglect the temperature gradient through the skin\nthickness may exceed, in the range of higher biot numbers, the true\nvalues by more than 30 percent .\n refined photothermoelastic experiments verify these results\nand add another significant conclusion . they indicate that\nthermal stresses in wing structures generated by a variable\nheat-transfer coefficient coincide with the theoretical predictions\nwhich are based on a constant heat-transfer coefficient, as long\nas the latter represents the arithmetic average over the heating\ncycle and the variation is in the order of 10 percent .\nhowever, even much greater variations in the order of 100 percent\nproduce only relatively small differences ."}, {"doc_id": 498, "text": "calculation of potential flow about bodies of revolution\nhaving axes perpendicular to the free-stream direction .\n a general method is described for calculating, with the aid of\nan electronic computer, the potential flow about arbitrary bodies\nof revolution whose axes are perpendicular to the free-stream\ndirection . when combined with the solution for the\naxisymmetric flow about these bodies, this method makes it possible to\ncalculate the pressure distribution on any body of revolution at\nangle of attack forward of any separated region of the flow, and\nalso to calculate the flow at points off the body surface . after\nthe basic equations of the method have been derived, its accuracy\nis exhibited by comparison with analytic solutions for ellipsoids\nof revolution . calculated pressure distributions are then\ncompared with experimental data for a variety of bodies . the\nagreement is quite satisfactory in all cases . the calculated\nvelocities for other selected bodies are presented to exhibit\ncertain properties of this type of flow ."}, {"doc_id": 499, "text": "a closed-form solution for the oscillations of a vehicle\nentering a planetary atmosphere .\n author considers the equation of the yawing motion of a missile,\nderived with a series of customary assumptions and with the\ndistance traveled as the independent variable . his assumptions\ninclude the linearity of the aerodynamic forces, the constancy of the\naerodynamic coefficients with respect to mach number, the\nabsence of spin, and the absence of gravity . if to these assumptions\none could add the common ballistic assumption of a constant air\ndensity, the coefficients of this equation would have been\ncon-damped sinusoids . in ballistics any slow variation of these\ncoefstant, and the solution would have been simply the\nexponentially-ficients is usually treated by adding an approximate correction\nterm to the damping rate (which is spoken of as the wkb\nperturbation) . however, with a body entering the planetary atmosphere the\nvariation of the air density is apparently of greater essence (this\nis a point not stated explicitly in this brief communication), and\nthe equation is of the type .\nthe author shows that with a series of further transformations\nthe equation can be reduced to the form\nthe solutions of which are confluent\nhypergeometric functions . these functions are defined as series\ninvolving gamma functions, and with a series of further assumptions\ncan be reduced to laguerre polynomials and bessel functions .\n it is certainly nice to have an exact solution to a problem which\nhas heretofore been extensively treated by approximations and by\nthe numerical approach . this reviewer is puzzled, however, as to\nthe practical significance of the proposed approach . an\nidealization is of value in that it facilitates our understanding,. and the\nnumerical approach, in that it allows refinements of the problem,\nfreeing us from the necessity of idealizing . but the proposed\nsolution is certainly more difficult to refine than the original\nproblem,. and it is certainly not simple (the solution of the original\nequation is not the value of z, but the various /reverse/\ntransformations of z) . an evaluation of a series in practice must compete\nwith the numerical approach,. and the equation suggested is of the\nzero) . viewing the problem /afresh/ (in the light of the /\ncomputer revolution/ and without the constraints imposed by the prior\nart), it seems at least equally easy to /standardize/ the\nsolutions of the original equation ."}, {"doc_id": 500, "text": "joule heating in magnetohydrodynamic free-convection\nflows .\n the steady, fully developed, laminar, free-convection flow of an\nelectrically conducting fluid between two fully submerged\nopen-ended, constant-temperature vertical plates located in a constant,\nuniformly distributed, transverse magnetic field has been analyzed\nwith the joule heating term retained in the energy equation .\nanalytic results are obtained . such analytic results are useful in\nestimating the actual magnitude of the influence of joule heating as\nwell as a qualitative description of the manner in which it alters\nthe temperature and flow fields . the present result confirms the\nusual practice that the influence of joule heating is negligibly\nsmall ."}, {"doc_id": 501, "text": "stagnation-point shock detachment of blunt bodies in\nsupersonic flow .\n presentation of stagnation-point shock-detachment distances\ndetermined by the exact numerical method of gravalos, edelfelt,\nand emmons . the results are compared with those from the\npreviously published methods of van dyke and gordon, li and geiger,\nand serbin, and with experimental data ."}, {"doc_id": 502, "text": "on squire's test of the compressibility transformation .\n discussion of a previous application, by squire, of the author's\ncompressibility transformation to the correlation of high-speed\nboundary-layer data for air and helium . squire's suggestion that\nthe compressibility transformation is invalid is shown to be\nincorrect ."}, {"doc_id": 503, "text": "theoretical prediction of the transonic characteristics\nof airfoils .\n it is shown that the author's transonic-flow airfoil theory\ncan be used to estimate transonic drag-rise and onset-of-\nseparation-effects mach numbers without reference to experimental\nresults . a simple comparative method is applied to a series of\nairfoils, and the results are analyzed to determine some of the\ndesign features of importance in transonic flow . an\nimprovement to this scheme is shown to give results in good agreement\nwith experiment for both the first appearance of shock waves\nand the onset of separation effects . application to finite swept\nwings is briefly considered and illustrated ."}, {"doc_id": 504, "text": "stability of compressible boundary layers induced by\na moving wave .\n the problem of determining the stability of compressible\nviscous flows with nonzero surface velocities is formulated and is\nshown to be identical to that for conventional boundary layers,\nwith only a redefinition of the mach and reynolds numbers\nrequired . specific consideration is given to the wall boundary\nlayer behind a moving shock wave, and the minimum critical\nreynolds numbers are obtained for various shock velocities .\nthe entire stability map is determined for the limiting case of a\nweak wave, which is analogous to the rayleigh problem .\n the minimum critical reynolds number is found to increase\nmonotonically with shock velocity--i.e., with increasing surface\ncooling and stream mach number combined . for the ratio of\nwall to stream velocity of 2.92 with (shock mach number\nof 2.18) the flow is found to be infinitely stable to two-dimensional\ndisturbances .\n experimental transition data do not follow the trends predicted\nby the theory . in fact, the transition reynolds numbers are\norders of magnitude below the computed minimum critical\nreynolds numbers . the lack of correlation between theory and\nexperiment is attributed to disturbances which are external to\nthe boundary layer ."}, {"doc_id": 505, "text": "transition measurements on cones in free flight ballistics\nrange tests .\n navy-sponsored experimental investigation of the location of\nboundary-layer transition on sharp-nosed cones having 10 total\nangles . the ambient temperature in a portion of the aeroballistics\nrange is varied so as to obtain different adiabatic recovery\ntemperatures at a constant nominal mach number of 3.1 . the location\nof transition is expressed as a transition reynolds number, and\nresults are presented graphically as a function of the ratio between\nthe wall temperature and the adiabatic recovery temperature ."}, {"doc_id": 506, "text": "a note on havelock's shallow-water wave-resistance\ncurves .\nin the continuous quest for improved means of\ntransportation, attention is currently focused on the ground-effect\nmachine . as there is no physical contact between the vehicle\nand the terrain over which it operates, its performance should\nbe similar over land and water . however, over water there is\nan additional resistance to motion due to the gravity-wave\nsystem generated by the supporting or /cushion/ pressure acting\non the water surface . estimates of this component can be made\nusing the analysis of t. h. havelock . it is the purpose of this\nnote to present an ibm 650 digital-computer solution of his\nequations . as shown below, these results differ from havelock's\noriginal results ."}, {"doc_id": 507, "text": "energy equation approximations in fluid mechanics .\n discussion of several forms of the energy equation and of their\nuse for the study of the flow of nearly incompressible fluids ."}, {"doc_id": 508, "text": "a correlation of nose-bluntness induced pressures on\ncylindrical and conical after-bodies at hypersonic\nspeeds .\nvan hise, in his detailed study of the nose-bluntness-induced\npressures on cylindrical afterbodies, shows that, starting\na few nose diameters aft of the nose-afterbody junction, these\npressures are correlated with the parameter\nas predicted by the blast-wave analogy . chernyi developed a\nmodified form of the blast-wave analogy which takes into account\nthe addition of energy to the flow by a thin afterbody . he\nshowed that for thin afterbodies and hypersonic speeds, the\npressure distribution, plotted as should correlate with\nthe parameter . the purpose of this note\nis to show that the above correlation techniques may be\ncombined into a form such that pressures on cylindrical and conical\nafterbodies are correlated by one parameter ."}, {"doc_id": 509, "text": "a graphical approximation for temperatures and sublimation rates at\nsurfaces subjected to small net and large gross heat transfer rates .\nconsiders a material, acted upon by heat of conduction, which changes\nits state by sublimation at the heated surface . the derived method is\nmost suitable under conditions of severe heating such as space vehicle\nre-entry ."}, {"doc_id": 510, "text": "manoeuvring technique for changing the plane of circular\norbits with minimum fuel expenditure .\n usaf-supported discussion of the use of an intermediate\nelliptic orbit for changing the plane of a circular orbit . values of the\nperigee and apogee velocities are calculated for the following cases ..\nthe braking impulse supplied by grazing of the atmosphere,. and (3)\nre-orbit with 90 of the braking impulse supplied in this manner ."}, {"doc_id": 511, "text": "tunnel tests on a double cascade to determine the interaction\nbetween the rotor and the nozzles of a supersonic turbine .\n experimental confirmation has been required that in a supersonic\nturbine the leading edges of the rotor governs the rotor incidence and,\nhence, the gas exit angle from the nozzles . evidence has also been\nrequired that, once the rotor incidence has been allowed for, there is\nno adverse effect of the rotors on the nozzle flow, even when the rotors\nhave a large turning angle .\n the present test cascade represented the stationary configuration\nof a turbine of 2.5 nozzle mach number and 74 swirl angle, the rotors\nbeing designed to operate at 1.9 relative mach number and to provide a\nturning angle of 140 . in the tests, fully supersonic flow could be\nestablished through the system, but the losses were fairly high and an\nincrease in loss of about 25 per cent would have caused choking in the\nrotor ."}, {"doc_id": 512, "text": "quasi-cylindrical surfaces with prescribed thickness\ndistributions .\n a formula for the supersonic velocity field in terms of a given\nsurface distribution of sources is applied to points lying in the\nsurface . an equation giving the camber shape of a quasi\ncircular-cylindrical surface in terms of a prescribed thickness distribution\nis derived and the half ring wing with prescribed thickness distribution\nis discussed as an example ."}, {"doc_id": 513, "text": "pressure measurements at supersonic speeds on three\nuncambered conical wings of unit aspect ratio .\n pressure measurements were made at mach numbers between 1.3 and 2.8\nover a range of incidences on three simple models representing thick\nconical uncambered wings with sharp leading edges . these tests form\npart of an investigation into the effects of thickness and camber on\nslender wings .\n the aspect ratio of the models was unity in each case, and the\nspanwise cross sections were bounded\nby .. the measured pressure distributions are presented, along with overall\nlift and drag (excluding skin friction and base drag) obtained by\nintegration ."}, {"doc_id": 514, "text": "pressure distributions and flow patterns on some conical\nshapes with sharp edges and symmetrical cross-sections\nat m=4 .0.\n results are given of a wind tunnel programme made to study the\npressure distributions and flow patterns over a series of simple,\nconical shapes at a mach number of 4.0 . the results have been compared\nwith various approximate theories and the limitations of these theories\nare discussed .\n it is found that at this mach number leading edge separations still\nhave an influence on the suction surface pressure, and that this surface\nstill makes a significant contribution to the overall forces ."}, {"doc_id": 515, "text": "self sustained oscillations of a system with non-linear\ndamping of a particular type .\n the paper deals with self-sustained\noscillations of a dynamic system\nof single degree of freedom, with linear\nrestoring force and non-linear\ndamping force . the latter is supposed\nto be a function of velocity\nrepresentable by a simple /polygonal/\ngraph, such that the damping is\nnegative at small velocities but becomes\npositive at velocities above a\ncertain value . on these assumptions,\na rigorous solution is presented,\nincluding the equations of motion,\namplitude, maximum velocity and period .\na very simple solution is obtained\nfor the limiting case of vanishingly\nsmall damping . an approximate solution\nby series in powers of damping\nratio is worked out which\ngives a satisfactory accuracy for\nquite large values of ."}, {"doc_id": 516, "text": "free-flight measurements of the dynamic longitudinal\nstability characteristics of a wind tunnel interference\nmodel (m=0 .92 to 1. 35) .\n the dynamic longitudinal-stability characteristics of a standard\nwind tunnel interference model have been investigated in free flight\nover a mach number range of 0.92 to 1.35 .\n measurements of lift-curve slope and manoeuvre margin were\nobtained, and are compared with results from transonic-tunnel tests\nunder low blockage conditions .\n the analysis was extended to obtain damping derivatives to allow\ncomparison to be made with possible future dynamic tests in wind tunnels\non the standard shape ."}, {"doc_id": 517, "text": "reaction-resisted shock fronts .\n it is shown that shock waves whose\nstructure is determined solely by the effects\nof chemical reactions (reaction-resisted\nshock fronts) are possible and completely\nanalogous to relaxation - resisted waves .\na single dissociation reaction is considered\nand numerical results indicate that such\nwaves could be observed experimentally .\nbulk viscosities equivalent to reaction\neffects are possibly 10 or more times shear\nviscosity values . (examples are based on\nlighthill's ideal dissociating gas) ."}, {"doc_id": 518, "text": "heat conduction through a polyatomic gas .\n a heat conduction problem is set up\nwhich, in essence, simulates the conditions\narising when a plane shock wave reflects\nfrom a co-planar solid boundary . the gas\nis assumed to be polyatomic, with one\n the quantity of primary interest is\nthe temperature of the solid at the interface,\nsince this can be observed experimentally\nwithout much difficulty . solutions are\nobtained for this quantity which cover a\nrange of practically plausible relaxation times\nand 'wall effect' parameters . it is essential\nto include proper temperature jump\nboundary conditions for both active and\nrelaxing (or inert) energy modes . thus it is\nnecessary to know accommodation coefficients\nfor these modes of energy storage .\nthe temperature jump effects are found to\ndominate the (interface) solid's temperature\ntime history, with relaxation effects playing\na very secondary role .\n the theoretical results are compared\nwith some experimental observations and\nencouraging agreement is found . as a\nresult of this agreement it proves possible to\nestimate the accommodation coefficient\nfor the active modes (in this case for the\ncombination platinum air), the pressure\nbeing about 15 atmospheres . the pressure\nsensitivity of accommodation effects is commented on ."}, {"doc_id": 519, "text": "base pressure at supersonic speeds in the presence\nof a supersonic jet .\n the effects on base pressure of jet mach number, free stream\nreynolds number and jet to base diameter ratio have been investigated\nexperimentally .\n it was found that, for jet stagnation pressures greater than that\nrequired for the nozzle to reach its design mach number, an increase\nof jet mach number reduced the base pressure . similarly the base\npressure increased with increase of the ratio of jet diameter to base\ndiameter and, at high jet stagnation pressures, base pressures higher\nthan free stream static pressure were found . the base pressure was\nindependent of free stream reynolds numbers greater than 2 x 10 per\nfoot but increased with reduction of reynolds number below 2 x 10 per\nfoot .\n unsteady wave patterns were found when the jet mach number did\nnot differ markedly from the free stream mach number and the jet had\njust reached its design conditions ."}, {"doc_id": 520, "text": "wing-tail interference as a cause of 'magnus' effects\non a finned missile .\n wing-tail interference is shown to cause large /magnus/ effects\non a finned missile whose wings are deflected into an aileron\nsetting . a simple experimental method with water as the\nworking medium is used to obtain low-speed magnus data on a rolling\nmissile . the missile is a slender cruciform configuration with\nall-movable wings and fixed tail fins . magnus data are\npresented for angles of attack up to 15 and for the one (high) roll\nrate which accompanies a 30 aileron deflection angle of the\nwings . tests conducted at zero roll rate but with the wing\ndeflection maintained, revealed large forces in the magnus direction,\nthereby providing the basis for understanding magnus effects due\nto wing-tail interference .\n a semiempirical theory is proposed to explain the experimental\ndata . a simplified model of the wake behind the wings is\nintroduced to predict tail-interference factors . good agreement with\nthe data is obtained .\n this magnus effect is opposite in direction to the classical\nmagnus lift on a spinning cylinder ,. it is much larger than either\nthat effect or the one on a missile with only one set of fins .\nwing-tail interference is the predominant source of the effect ,. roll rate\nonly modifies the basic interference mechanism ."}, {"doc_id": 521, "text": "a note on application of transonic linearization to\nan airfoil with a round leading edge .\nthe profile of a symmetric airfoil of unit length with a round\nleading edge can be expressed, in general, as\nwhere p(x) has a finite slope at x = 0 . it is well known that\nthe conventional sub- and supersonic linear theories of\ncompressible flow break down in the neighborhood of such a round\nleading edge due to the failure of the small-disturbance\nassumption . the linearized transonic flow theory has the same\nshort-coming, but if the determination of the sonic point on the airfoil\nplays an important role in any more advanced theory--e.g.,\nspreiter's local-linearization method or hosokawa's method of\nrefinement--this theoretical barrier will become more serious\nbecause the sonic point is usually located in a flow region near\nthe leading edge that may be greatly affected by the roundness ."}, {"doc_id": 522, "text": "laminar, transitional and turbulent heat transfer to\na cone-cylinder-flare body at mach 8. 0.\n an experimental investigation of the laminar, transitional, and\nturbulent heat transfer rates over a conical cylindrical flared\nbody is presented . regions of favorable, zero, and adverse\npressure gradient on the body are investigated . the experimental\nresults are compared with the theories available in the literature .\n the model chosen for this investigation is a cone-cylinder-flare\nconfiguration consisting of a 20 semivertex conical nose portion\nsmoothly blended by a shoulder radius into a long cylindrical body\nand terminated by a smooth large radius flare .\n the model was tested at a free stream mach number of 8, over\na range of reynolds number from 0.3 x 10 to 1.6 x 10 per inch\nbased on free stream conditions . various stagnation-to-wall\ntemperature ratios were obtained by cooling the model prior to\nthe test with liquid nitrogen . the stagnation-to-wall\ntemperature ratios were 10 and 3.3 .\n the theoretical predictions gave good results for the heat\ntransfer rates in the laminar region, and fair prediction in the\ntransitional and turbulent regimes extending over the shoulder\nand forward portion of the cylindrical body . over the aft portion\nof the cylinder and over the flare the predictions are only\nqualitatively correct, and underestimate the heating rate by a factor as\nhigh as 3 . conversely, the /flat plate reference enthalpy/\nover the aft portion of the body, but to increasingly overestimate\nthe heating rates over the forward portion of the cylinder .\n a modified equation for the heat transfer coefficient in the\ntransitional and fully turbulent region based on the f.p.r.e.\nmethod is then presented . this method gives good agreement\nwith the experimental results presented over the entire range of\ntransitional and turbulent flow .\n from the results the following is concluded .. cooling the wall\ndelayed transition . by expanding the flow rapidly between the\ncone and the cylinder, the transition reynolds number is reached\nvery rapidly . by making a smooth transition between the\ncylinder and the flare, no separation occurred at the cylindrical flare\njunction . the transitional and turbulent heat transfer in the\npresence of an adverse pressure gradient may be predicted with\nsufficient accuracy by the f.p.r.e. method ."}, {"doc_id": 523, "text": "approximate determination of position of the sonic\nline for a blunt body in hypersonic flow .\nthe detached shock in front of a blunt body in hypersonic\nflow tends to acquire the shape of the frontal curvature of the\nbody . thus the curvature of the shock can be assumed to be the\nsame as that of the body, at least up to the sonic point (point a,\nfig. 1) . if the equation of curvature of the body is known, the\nequation of curvature of the shock is also known . in this paper,\nwith this assumption, a method is described to determine the\napproximate position of the sonic line (ao'b, fig. 1) . the\nshock-detachment distance is assumed known .\n the method is, of course, general . this can be applied to\nany detached shock provided its equation of curvature is known\ncorresponding to that of the body . for simplicity the detached\nshock is assumed to be circular in this paper and the procedure is\noutlined below with the assumption that the sonic line ao'b is\nparabolic ."}, {"doc_id": 524, "text": "stagnation point heat transfer in partially ionized\nair .\n comparison of heat-transfer rates, obtained by using transport\nproperties recently reported by peng and pindroh, with rates based\non hansen's thermodynamic and transport properties . it is shown\nthat the heat-transfer rates based on the peng and pindroh data\nare 20 to 30 lower for the velocity range of 25,000 to 40,000\nft sec ."}, {"doc_id": 525, "text": "on hypersonic viscous flow over an insulated flat plate\nwith surface mass transfer .\n hypersonic viscous flow over an insulated flat plate with\nsurface mass transfer is studied . the tangent-wedge approximation\nis used in the inviscid-flow region, and the integral method is\napplied to the treatment of the laminar boundary layer . the law\nof surface mass transfer for the present analysis is derived . a\ncontinuous transition of the pressure variation is achieved from\nthe strong to the weak pressure-interaction region . first-order\nformulas for the induced surface pressure and the skin-friction\ncoefficient are obtained for both the strong and weak\npressure-interaction regions . results are compared with those calculated\nfrom other analyses ."}, {"doc_id": 526, "text": "leading edge attachment in transonic flow with laminar\nor turbulent boundary layers .\n the transonic flow round a two-dimensional airfoil at\nincidence is often determined by the type of flow in the leading-edge\nregion . if the flow separates at the leading edge at low speeds it\nis liable to attach as the speed increases, often quite suddenly .\na review of this change with laminar or with turbulent boundary\nlayers re-emphasizes the importance of fixing transition when\nmaking model tests at transonic speeds in order to obtain flows\nclosest to full-scale conditions .\n it is shown that similar airfoils with attached leading-edge\nflow show transonic similarity upstream of the terminal shock ."}, {"doc_id": 527, "text": "note on the three-point boundary layer problem for\nthe blasius equations .\nin a recent paper a method was presented for obtaining\nhigher accuracy in the numerical solution of the blasius\nequation with three-point boundary conditions . the\nwell-known blasius equation was previously developed in an\ninvestigation of the steady two-dimensional incompressible\nboundary-layer flow over a flat plate, but it has been extensively used in\ninvestigating other fluid flow problems . the three-point\nboundary-value problem is encountered in the theory of laminar\nmixing and in approximate analyses of separated and wake\nflows as noted in ref. 1 ."}, {"doc_id": 528, "text": "first-order slip effects on the laminar boundary layer over a slender\nbody of revolution with zero pressure gradient .\nin reference 1, the analysis given by probstein and elliott for the\nzero-pressure-gradient, constant-wall-temperature, compressible,\nlaminar boundary layer with transverse curvature was extended to\nfirst-order slip flow . this extension was based on a double asymptotic\nexpansion in a transverse-curvature parameter and a slip parameter .\nthe expansion in ref. 1, however, was carried out with the parameter\nheld constant . for and a constant wall temperature, is constant and\ne varies with x due to the dependence of the local body radius on x .\nthus, for arbitrary body shapes, e will not be constant . in the\npresent note, the analysis of ref. 1 is re-examined taking into account\nthe variation of e ."}, {"doc_id": 529, "text": "some effects of injection of foreign gases in a decelerating\nlaminar boundary layer in supersonic flow .\n the purpose of this research program was to investigate the\neffects of a diffusion field on a laminar boundary layer in a\nsupersonic flow . specifically, helium, nitrogen, and argon were\nuniformly injected into the laminar boundary layer of a\nhigh-speed flow in a tube with the objective of determining the effects\nof such injection on the pressure, temperature, and recovery\nfactor distribution along and downstream of the injection region .\n a continuously operating axially-symmetric wind tunnel has\nbeen designed, constructed, and operated . this tunnel consists\nof an air supply system, a flowmeter, an upstream stagnation\ntank, a supersonic nozzle (throat diameter 0.262 and exit\ndiameter 1.400), a test section of variable length (zero to 81 diameters,\ntest section diameter of 1.400), a downstream stagnation tank,\nan exhaust system, a foreign gas supply system, and all necessary\ninstrumentation . the overall performance of this apparatus in\nterms of the design specifications was excellent .\n the tunnel was instrumented with 109 thermocouples . all\ntemperatures except ambient temperatures were automatically\nmeasured and recorded by means of a self-balancing recording\npotentiometer . there was 29 pressure taps distributed along the\ntunnel, 23 along the test section itself . pressures were measured\nby means of an interconnected micromanometer and a vacuum\nreferenced manometer system with overlapping ranges .\n for all of the results reported herein, the overall test section\nwas 41 diameters in length,. composed of a porous test section\napproximately 7.2 diameters in length (leading edge\napproximately 1.8 diameters from the nozzle exit plane) and four nylon\ntest sections of 8 diameters each ."}, {"doc_id": 530, "text": "an aerodynamic analysis for flutter in oseen-type viscous\nflow .\n oseen's equations for unsteady flow are employed to obtain\na linearized solution based on a discontinuous-wake model .\nthe analysis is employed to estimate the viscous correction to\nunsteady lift and moment at large reynolds number . if the\nasymptotic solution is not too slowly convergent, the correction\nis of the order of the ratio of the logarithm of reynolds number\nto the reynolds number . the theory is preliminary in nature\nas it is limited by the accuracy of oseen's equations and is\nrestricted to small angle of attack . however, it also shows that\nthe generalized trailing-edge condition for potential flow is\nreasonable and might predict the essential correction in a real\nfluid ."}, {"doc_id": 531, "text": "the flow about a moving body in the upper ionosphere .\n a particle approach is used to study the flow pattern around a\nbody moving in the upper layers of the ionosphere . the effects\nof distant encounters between charged particles (dynamic\nfriction) and of the earth's magnetic field are taken into account .\nit is shown that, when the magnetic lines of force are parallel\nto the direction of motion of the body, there may be a marked\nconcentration of charged particles in the vicinity of the body\nand a considerable fraction of the reflected or deflected charged\nparticles may reimpinge on the body surface . a numerical\nexample is given for the size and shape of the charged-\nparticle-density contours in the flow field surrounding a circular disc,\nand these are compared with the corresponding neutral-particle\ncontours ."}, {"doc_id": 532, "text": "pitch-yaw stability of a missile oscillating in roll\nvia the second method of lyapunov .\nthe stability theory of a. m. lyapunov, a popular topic in\nthe u.s.s.r., is receiving increasing attention elsewhere .\nthis note describes lyapunov's /second method/ very briefly\nand applies it to an aeronautical stability problem ."}, {"doc_id": 533, "text": "stagnation-point shock-detachment distance for flow\naround spheres and cylinders in air .\n author discusses the problem of deflection of a cantilevered\nbar, initially in the shape of a circular arc, subjected to an\narbitrarily inclined end load ."}, {"doc_id": 534, "text": "consideration of energy separation for laminar slip\nflow in a circular tube .\n the energy separation for laminar low-density-nonunity prandtl\nnumber flow in circular cross-section tubes is the topic of this\nnote . a conclusion is reached as to the effect of prandtl number\non the velocity profiles for these flows . however, in order to\nreach valid quantitative conclusions the reviewer feels that more\ndetailed analysis is in order, and that the analysis as presented\nhere is of qualitative value only ."}, {"doc_id": 535, "text": "shroud design for simulating hypersonic flow over the nose of a\nhemisphere .\nfollowing is an analytical method for designing a shroud which will\ngenerate the hypersonic pressure distribution on a hemisphere . the\nmethod was found to be successful throughout the region of subsonic\nflow . this shroud was designed as part of a low-turbulence wind tunnel\nused for investigating the effects of cooling on boundary-layer\ntransition on a hemisphere .\nthe design of the shroud contour was carried out in two steps . first,\nan approximate solution for the incompressible, irrotational flow\nfield was found in the region, and, second, the resulting contour\nwas corrected for compressibility near the sonic region, assuming\none-dimensional flow ."}, {"doc_id": 536, "text": "transition in the viscous wakes of blunt bodies at\nhypersonic speeds .\n transition from laminar to turbulent flow in the hypersonic\nwakes of spheres was detected in laboratory measurements of the\nradiation from the flow field . a hypervelocity gun facility was\nused to fire models, 0.22-in. in diameter, into a range at velocities\nfrom 10,000 to 17,000 ft sec . experiments were performed by\nchanging .. (a) the material of the projectile ,. (b) the ambient\ngas in the range ,. and (c) the pressure in the range . three\noptical techniques were used to observe the wake radiation ..\nwhich show a turbulent viscous wake as the pressure in the\nrange is decreased from one atmosphere to about 20 cm hg .\nwhich show the luminous flow field at pressures between 30 and\nence of short luminous streaks, which disappear suddenly as the\npressure is decreased below 3 cm hg for air, and below 0.8 cm\nhg for argon .\nboth air and argon, which show the main features of the flow\nfield . above the transition pressure, the intensity of radiation\nfrom the wake is always associated with fluctuations that appear\nto be the same phenomenon as the drum-camera streaks .\n the appearance of the streaks in the drum camera and\nphoto-multiplier data is interpreted as transition from laminar to\nturbulent flow in the viscous wake, because experimental evidence\nshows that their appearance is not controlled by chemical,\nradiative, or ablative processes, but depends on aerodynamic\neffects . this conclusion is supported by other experiments based\non optical and schlieren techniques . the transition in the wake\nat positions very close to the body is given by a local reynolds\nnumber of 10 for air, and 3 x 10 for argon . the results indicate\na possible local-mach-number effect ."}, {"doc_id": 537, "text": "stagnation point viscous hypersonic flow .\nseveral methods have been developed for computing the\nhypersonic, low reynolds number flow in the stagnation\nregion of a blunt body . in general, these methods involve\ncomplicated numerical solutions . simultaneous iterations on several\nparameters are usually required in view of the boundary-value\nnature of the problem .\n the purpose of this note is to present an approximate\nclosed-form solution to axisymmetric stagnation point hypersonic flow\nin the viscous layer regime ."}, {"doc_id": 538, "text": "the conpressibility transformation and the turbulent\nboundary layer equations .\n the compressibility transformation first introduced by\ndorod-nitzyn has been applied in this paper to the equations of the\nturbulent boundary layer on a flat plate, considering heat transfer\nand arbitrary prandtl numbers . assuming the shear\ndistribution to be invariant under the transformation, the stream\nfunction and the momentum equation take the proper form for\nincompressible flow, allowing the use of incompressible velocity\nprofiles in the transformed coordinates . application of crocco's\nmethod to the transformed energy equation permits integration\nof the energy equation resulting in a formulism remarkably\nsimilar to that proposed by eckert . finally, the reference\ncondition was chosen to correspond to the edge of the sublayer from\nconsiderations of the assumptions made regarding the\nshear-stress distribution . with this choice, the reference enthalpy is in\ngood agreement with eckert's formula over the ordinary range of\ntest conditions . in view of these results, the analysis may be\nconsidered to provide a theoretical basis for the\nreference-enthalpy method ."}, {"doc_id": 539, "text": "local heat transfer to a yawed, infite, circular cylinder\nin laminar compressible flow .\n this note presents a simplification of a method for\ncalculating the ratio of local to stagnation-line heat-transfer\ncoefficients on a yawed, infinite, circular cylinder in laminar\ncompressible flow . a brief description of the method of ref. 1 is\npresented, followed by a discussion of the assumptions and\nmathematical procedure which lead to a considerable simplification ."}, {"doc_id": 540, "text": "use of local similarity concepts in hypersonic viscous\ninteraction problems .\n the problem of predicting the characteristics\nof a hypersonic laminar boundary layer that\ninteracts with the external flow field is approached\nusing the tangent wedge formulation for\nthe inviscid flow field and the method of similar\nsolutions for the viscous flow . it is shown\nthat the concept of local similarity which allows\nthe pressure gradient parameter to vary in\nthe streamwise direction leads to an explicit\nrelation between the viscous and inviscid flows\nfor all values of the hypersonic interaction\nparameter . the conditions of /strong/ and\nlimits of the general relations . the present theory\nis compared with three independent experimental\ninvestigations . in each case, the\nagreement is found to be excellent over the range of\ninvestigated . it is shown, using asymptotic\nsolutions to the exact boundary layer equations,\nthat the present theory is applicable to a wide\nvariety of viscous interaction problems .\na large number of solutions to the laminar\nboundary layer similarity equations for a perfect\ngas with cross flow and surface mass transfer are\ngiven . these numerical results, when combined\nwith the solutions of previous authors, are\nsufficient to describe the range of conditions with high precision ."}, {"doc_id": 541, "text": "similitude of hypersonic flows over slender bodies\nin non-equilibrium dissociated gases .\n this paper is concerned with the similitude laws\ngoverning inviscid, nonequilibrium gas flows\naround blunt or sharp-nosed slender bodies at\nzero angle of attack, based on the hypersonic\nsmall disturbance flow theory . some related\nfeatures of the interaction between the effects of\nnose bluntness and nonequilibrium dissociation\nand vibration and the influence of a\ndissociated freestream are also discussed . the\nhypersonic equivalence principle and the related\nsimilitude for affinely related bodies are set\nforth for nonequilibrium flows in either diatomic\ngases or a gas mixture such as air . for a family\nof diatomic gases, as opposed to a given gas\nsuch as air, a generalized ambient gas state\nscaling condition is obtained, whereby the\nambient density and temperature need not be\nsimulated . a detailed discussion is given of\nblunted cylinders and slabs or sharp-nosed\ncones and wedges, including example\nnonequilibrium flow field correlations of numerical\nsolutions available in the literature . low density\nnonequilibrium flows with a negligible shock\nlayer atom recombination rate are also\nexamined ,. as expected, a less restrictive small\ndisturbance similitude law is obtained in this\ncase ."}, {"doc_id": 542, "text": "biot's variational principle in heat conduction .\n biot's variational principle is applied to a number of different\none-dimensional heat conduction problems . these problems\nshow the applicability of the variational principle to problems\ninvolving prescribed heat flux boundary conditions and to those\nwith temperature-dependent material properties .\n a method is introduced for including boundary conditions\nwhen these are expressed as prescribed heat fluxes . the idea\nbehind this is overall energy balance within the body, which is a\nconstraint condition to be satisfied by the time histories of the\ngeneralized coordinates .\n the variational principle is then applied to the well-known\nproblem of constant surface heat flux in order to present the\ntechnique and provide a basis for the remaining sections . the\nequivalence of the result obtained in applying the variational\nprinciple for a prescribed surface temperature history to that\nobtained for a prescribed heat flux is also pointed out . radiation\ncooling due to fourth power radiation from semi-infinite solids\nand finite slabs together with radiation according to newton's\nlaw of cooling is then treated . finally, the introduction of\ntemperature-dependent material properties is discussed and the\ndetermination of the temperature distribution in a semi-infinite\nsolid with variable properties is investigated ."}, {"doc_id": 543, "text": "the stacking of compressor stage characteristics to\ngive an overall compressor performance map .\n a method of calculation is developed to compute the overall\nperformance of a multi-stage axial compressor, from a knowledge of the\nindividual stage characteristics, by a /stacking/ technique .\ncompressor models are designed and their overall performance\ncalculated . these results are compared to show, qualitatively, the\neffect of alterations in design and stage performance on overall\nperformance and to find how compressors should be designed\nfor optimum performance ."}, {"doc_id": 544, "text": "a theoretical and experimental study of oscillating wedge shaped\naerofoils in hypersonic flow .\naerodynamic stiffness and damping derivatives have been measured\nin a /hypersonic gun/ wind tunnel for sharp and blunt-nosed two\ndimensional single wedge shapes oscillating in the pitching mode in\nhypersonic flow . the results, which have been compared with\ntheoretical prediction, modified to account for leading edge bluntness,\nshow that this may increase the damping by up to 50 percent for certain\naxis positions . details of the experimental technique designed to\nmeasure the derivatives in the short running times available are\ndescribed ."}, {"doc_id": 545, "text": "calculation of sideslip derivatives and pressure distribution\nin asymmetric flight conditions on a slender wing-fin\nconfiguration .\n the flow around slender wing-fin\nconfigurations having curved leading\nedges, whose shape is defined by polynomials,\nis considered . a general\nexpression for the pressure distribution\non such a configuration in\nasymmetric flow is derived and the\nderivatives due to the particular case\nof sideslipping motion are also given .\nno numerical results are given for\nwing-fin load distribution, but the\nsideslip derivatives have been\nevaluated in a number of cases for\ngothic and ogee wings ."}, {"doc_id": 546, "text": "measurements of aerodynamic heating on a 15 cone of\ngraded wall thickness at a mach number of 6. 8.\n this note describes transient wall\ntemperature measurements made on a\nin an airstream of mach number 6.8 .\n the skin of the model was\nsufficiently thin to allow it to reach zero\nheat transfer conditions within a\nrunning time of one minute .\n in order to reduce effects\nof longitudinal heat conduction during a\nrun the electroformed-nickel skin\nof the model was made with graded\nthickness, and as a result fairly\nuniform temperature distributions along\nthe surface were obtained at all\ntimes in both the laminar and turbulent\nregions .\n values of heat transfer, calculated from the wall temperature-time\nhistories using the thin-wall\ntemperature are compared to theoretical\nestimates using the intermediate\nenthalpy method 10, 11 ."}, {"doc_id": 547, "text": "boundary layer characteristics of caret wings .\n the theory of laminar boundary\nlayers along flat surfaces has been\nused in conjunction with eckert's\napproximations to the displacement\nthickness, skin friction and temperature\nprofiles on the undersurface of a\ncaret wing configuration . to a first\napproximation it has been assumed\nthat parallel flow exits behind the shock\noutside the boundary layer, and the\ndisplacement of the shock by the boundary\nlayer near the leading edge is neglected .\n conduction of heat within the\nbody and along the surface is neglected\nbut radiation is included, so that\nare found . examples are given for\nvarious altitudes and configurations and\nthe effect of the skin friction on\nthe lift drag ratio calculated, assuming\nthe undersurfaces to be plane ."}, {"doc_id": 548, "text": "the contraction of satellite orbits under the influence\nof air drag . pt .iv with scale height dependent on\naltitude .\n the effect of air drag on satellite\norbits of small eccentricity e\nwas studied in part i (tech. note\ngw 533), on the assumption that\natmospheric density varies exponentially\nwith distance r from the earth's\ncentre, so that the 'density scale height'\nh, defined as, is\nconstant . in practice h varies with height\nin an approximately linear\nmanner, and in the present note the theory\nis developed for an atmosphere\nin which h varies linearly with r . equations\nare derived which show how\nperigee distance and orbital period vary\nwith eccentricity, and how\neccentricity varies with time . expressions\nare also obtained for the\nlife-time and air density at perigee in terms\nof the rate of change of orbital\nperiod . the results are also presented\ngraphically .\n the results are formulated in two\nways . the first is to specify the\nextra terms to be added to the constant-h\nequations of part i . the second\nthe best constant value of h for\nuse with the equations of part i . for\nexample, it is found that the\nconstant-h equations connecting perigee\ndistance (or orbital period) and\neccentricity can be used unchanged without\nloss in accuracy, if h is taken\nas the value of the variable h at a height\nabove the mean perigee height\nduring the time interval being considered,\nwhere, and\ndecreases from to 0 as e decreases\nfrom 0.02 to 0 . similarly the\nconstant-h equations for air density at\nperigee can still be used if h is\nevaluated at a height above perigee,\nwhere, and\ndecreases to zero as e decreases from\nconstant-h equations can still be used\nif h is evaluated at the scale height\nbelow the initial height . variation of\nh with altitude has a small effect\non the lifetime - about 3 - and on the\ne-versus-time curve ."}, {"doc_id": 549, "text": "experimental study of the velocity and temperature\ndistribution in a high-velocity vortex-type flow .\n the vortex tube represents a simple device in which a\nparticular type of vortex motion may be studied in the\nlaboratory in an attempt to obtain a better understanding\nof such flows . such an investigation has been pursued in\nthe heat transfer laboratory of the university of\nminnesota . the present paper summarizes the major results of\nthis vortex-tube investigation ."}, {"doc_id": 550, "text": "laminar heat transfer in tubes under slip-flow conditions .\nthe effects of low-density phenomena on the\nfully developed heat-transfer characteristics\nfor laminar flow in tubes has been studied\nanalytically . consideration is given to the\nslip-flow regime wherein the major rarefaction\neffects are manifested as velocity and\ntemperature jumps at the tube wall . the\nanalysis is carried out for both uniform wall\ntemperature and uniform wall heat flux .\nin both cases, the slip-flow nusselt numbers\nare lower than those for continuum flow\nand decrease with increasing mean free path .\nextension of the results is made to include\nthe effects of shear work at the wall,\ntemperature jump modifications for a moving fluid,\nand thermal creep ."}, {"doc_id": 551, "text": "analysis of a loaded cantilever plate by finite difference\nmethods .\n the various difference patterns necessary for finite difference\nsolution of rectangular plate problems, with various boundary conditions\nand under various transverse loads, are developed . the solution of\none particular problem on deuce is also described ."}, {"doc_id": 552, "text": "chemical kinetics of high temperature air .\n when a hypersonic object enters earth's atmosphere, a shock\nwave is formed in front of it, and the air passing through this\nshock wave is heated to high temperatures . the shock heated\nmolecules equilibrate their translational and rotational\ndegrees of freedom within a distance of a few mean free paths .\nto achieve equilibrium, it is necessary to excite vibration,\ndissociate molecules, produce new molecules and produce ions\nand electrons . the problem is complex, since all these\nphenomena occur simultaneously and because the reaction rates depend\non the temperature, density and composition which are changing\nduring the relaxation toward equilibrium .\n the experimental techniques used to investigate these\nreactions are briefly discussed along with the resulting rate\nexpressions obtained by the various investigators . a compilation\nof the rate expressions for these reactions representing the\nauthor's evaluation of all the available data is presented .\nseveral pertinent problems which are not yet completely\nunderstood and which still require theoretical and experimental\ninvestigation are outlined . computed concentration, temperature\nand density time histories are shown for three different shock\nspeeds in air . the time rate of change of concentration for\neach chemical reaction is also shown and regimes of importance\nfor the various processes are discussed ."}, {"doc_id": 553, "text": "ablation of glassy materials around blunt bodies of\nrevolution .\n the steady-state equations of motion for a\nthin layer of an incompressible glassy material on the\nsurface of an ablating and radiating blunt\nbody are reduced to a first-order ordinary differential\nequation which is integrated numerically .\nthis solution is coupled with the solution of the air\nboundary layer for both laminar and turbulent\nheat transfer with or without mass vaporization of\nthe ablating material . the distribution of the\neffective energy of ablation around the body is thus\nobtained for a cone cylinder with a hemispherical\ncap that re-enters the atmosphere at hypersonic\nflight speeds, and has quartz as the ablating\nmaterial . it is found that the ablation process from\nturbulent heating is more efficient than from\nthe laminar case because of increased vaporization .\nthis solution of the equations of motion at the\nstagnation point has been verified by are wind tunnel\nexperiments . the present state of development\nof the are wind tunnel does not permit its use for\nexperimental investigations of ablation around\nblunt bodies under turbulent heating ."}, {"doc_id": 554, "text": "generalized heat transfer formulas and graphs .\n utilizing the research results of previously\nreported investigations of the laminar, turbulent and\nradiative heat transfer in dissociated air, some\ngeneralized formulas for calculating heat transfer\nare given . graphs for determining the laminar\nheat transfer, momentum thickness reynolds\nnumber, and turbulent heat transfer distributions\naround an axisymmetric body are also given .\nthese heat transfer correlations are valid for velocities\nbetween 6000 and 26,000 fps and for altitudes\nup to 250,000 ft . this range of velocities and\naltitudes covers the important re-entry regime of\npractical re-entry trajectories having interest today .\nin the last section of this report these\ngeneralized results are specialized for icbm nose cone re-entry\napplications . these formulas and graphs\nmay be found useful for making rapid engineering\nestimates and preliminary design evaluations\nof the heating problems associated with re-entry\ninto earth's atmosphere ."}, {"doc_id": 555, "text": "closing reply to comments on generalized heat transfer\nformulas and graphs for nose cone re-entry into the\natmosphere .\nin a recent paper (1), detra and hidalgo have shown\nthat, when the boundary layer is turbulent, the heat\nflux per unit area at the sonic point of a nose cone may exceed\nthe corresponding laminar heat flux per unit area at the\nstagnation point . the ratio of turbulent sonic-point to\nlaminar stagnation-point heat flux per unit area has been\nestimated (2) to vary from about 1.0 to 10 for a hemispherical\nnose as the reynolds number (based on nose diameter)\nincreases from 10 to 10 . since for an axisymmetric body\nthe surface area in the vicinity of the sonic point greatly\nexceeds the area in the vicinity of the stagnation point, the\nratio of turbulent to laminar heat fluxes to the entire body\nwill be much greater than the above quoted ratios of heat\nfluxes per unit area ."}, {"doc_id": 556, "text": "numerical comparison between exact and approximate\ntheories of hypersonic inviscid flow past slender blunt\nnosed bodies .\n this paper presents numerical results of\nexact calculations of the inviscid equilibrium flow about\na long hemisphere-cylinder in motion\nat hypersonic velocity . a comparison is made with blast\nwave as well as free layer theories of hypersonic\nflow . as a result of the comparison, it is concluded\nthat the second-order blast wave theory can\nbe used for the purpose of finding the shock shape and\nthe body pressure distribution . however,\nthis procedure is definitely empirical and cannot be\njustified on rational or theoretical grounds .\nwe show that the presently calculated radial distribution\nof energy is radically different than that\ngiven by blast wave theory . if body shapes other than\nthose considered here are of interest, the\nonly reliable approach at the present time is to carry out\nnumerical calculations . it was found\nthat for certain flight velocities the pressure on the body\ndoes not decay to free stream pressure\nmonotonically but overexpands ."}, {"doc_id": 557, "text": "a numerical comparison between exact and approximate\ntheories of hypersonic inviscid flow past slender blunt\nnosed bodies .\n this note refers to paper of same title by feldman in ars j. 30,\nvalidity of blast wave theory cannot be justified on rational or\ntheoretical grounds because of different values of energy in cross\nflow field as calculated by this theory and by method of\ncharacteristics . present note questions this conclusion, shows reasonably\ngood agreement when energy is calculated for points where shock\nlocation, streamline pattern, and velocity, temperature, and\npressure profiles are adequately defined, and still better agreement\nwhen energy is calculated from flow quantities provided by-\ncharacteristics method . results are checked using data from\nindependent source . conclusion is reached that blast wave theory is\nstill valid ."}, {"doc_id": 558, "text": "experimental measurements of turbulent transition motion,\nstatistics and gross radial growth behind hypervelocity object.\n the laminar-turbulent transition behind 0.500-in.-diameter\nspheres at 8500 ft sec and behind\nmeasured as a function of pressure . schlieren\nmotion-picture techniques were used to analyze the\nturbulent motion and the results are described .\nautocorrelation functions of the density fluctuations\nof the turbulence have been measured . from\nthese values has been calculated and the results\nare given for several positions in the turbulent\ntrail at 30 mm hg downstream air pressure . in addition\nthe authors' previous measurements of the\ngross radial growth of the turbulent wake have been\nextended to pressures of 10 mm hg for the case\nof 0.500-in.-diameter spheres and to the trail behind"}, {"doc_id": 559, "text": "heat transfer at the forward stagnation point of blunt\nbodies .\n relations are presented for the calculation of heat transfer at\nthe forward stagnation point of both two-dimensional and axially\nsymmetric blunt bodies . the relations for the heat transfer, which were\nobtained from exact solutions to the equations of the laminar boundary\nlayer, are presented in terms of the local velocity gradient at the\nstagnation point . these exact solutions include effects of variation\nof fluid properties, prandtl number, and transpiration cooling .\nexamples illustrating the calculation procedure are also included ."}, {"doc_id": 560, "text": "a theoretical study of the effect of upstream\ntranspiration-cooling on the heat transfer and skin friction characteristics\nof a compressible laminar boundary layer .\n an analysis is presented which predicts\nthe skin-friction and\nheat-transfer characteristics of a compressible,\nlaminar boundary layer on a\nsolid flat plate preceded by a porous\nsection that is transpiration cooled .\nthe analysis is restricted to a prandtl\nnumber of unity and linear\nvariation of viscosity with temperature .\n the local skin friction has been\nfound to have a low value in the\nregion of transpiration cooling and then\nto increase until it approaches\nthe value for a completely nonporous surface\nasymptotically . the initial\nincrease in local skin friction is rapid\nas half of the ultimate increase\noccurs in a distance beyond the porous\nregion that is about 20 percent of\nthe length of the porous region for all rates\nof injection . when the\ntotal coolant flow rate is kept constant\nand the porous length is varied,\nit is found that the average skin friction\non a partially porous plate is\nslightly lower than that on a fully porous plate .\n the local heat transfer behaves in\na manner similar to that of the\nlocal skin friction . it is found, in\nan example, that the temperature\nat the end of a partially porous plate\ncould be maintained at about the\nsame temperature as a fully porous plate\nby doubling the total rate of\ncoolant flow ."}, {"doc_id": 561, "text": "a geometric problem related to the optimum distribution\nof lift on a planar wing in supersonic flow .\n the problem studied may be regarded as a problem of\ngeometry . its simplest form (loosely stated) is then as follows .. a\nmountain rises up from the x-y plane . determine the exact\nshape of the mountain knowing only the cross-sectional area of\nevery possible cut which can be made through the mountain with\na vertical plane . in a more complicated version of the problem,\nthe given information might be restricted to the cross-sectional\narea of every cut which can be made by a vertical plane inclined\nless than 45 to the y-axis .\n this latter case has direct applications to certain minimum\ndrag problems in supersonic flow . the shape of the mountain\ncorresponds to the (unknown) shape of the optimum lift\ndistribution on a planar wing . the cross-sectional area of a cut is\nthe integrated value of the lift along a straight line crossing the\nwing plan form . for a restricted range of line inclinations, these\noptimum integrated lift values can sometimes be determined\ndirectly . here it is assumed that they are given .\n the problem in its simplest form was originally solved by\nradon, who found solutions for a large class of such problems .\nthe derivation presented here may perhaps be more readily\nunderstood ."}, {"doc_id": 562, "text": "concerning the effect of compressibility on laminar\nboundary layers and their separation .\n the theory of compressible flow in a laminar\nboundary layer has been developed for the\ncase when the viscosity is assumed to be\nproportional to the absolute temperature and the\nprandtl number is unity . (these assumptions\nmay be compared with the empirical relations\nsuggested by cope .)\nit is shown that a transformation of the ordinate\nnormal to the layer can lead to a simplified\nform of equation of motion very similar to the\nordinary incompressible equation but modified\nby a multiplicative factor g in the pressure\nterm . this factor is greater than unity at the\nboundary and tends to one at the outside of\nthe layer .\n several particular solutions are considered\nincluding accelerated flow with a linearly\nincreasing velocity and retarded flow along a\nflat plate with a linearly decreasing velocity .\n the general implications of the theory are\ndiscussed and qualitative conclusions are drawn\nwhen the mainstream velocity starts from\na stagnation point, rises to a maximum and\nsubsequently falls . it is concluded that for\nsuch a velocity distribution increasing\ncompressibility will reduce the skin friction, increase\nthe boundary layer thickness and cause\nearlier separation as compared with the incompressible\nflow with the same mainstream velocity\ndistribution and the kinematic viscosity corresponding\nto conditions at the stagnation point ."}, {"doc_id": 563, "text": "the law of the wake in the turbulent boundary layer .\n after an extensive survey of mean-velocity profile measurements\nin various two-dimensional incompressible turbulent\nboundary-layer flows, it is proposed to represent the profile by a linear\ncombination of two universal functions . one is the well-known\nlaw of the wall . the other, called the law of the wake, is\ncharacterized by the profile at a point of separation or reattachment .\nthese functions are considered to be established empirically, by\na study of the mean-velocity profile, without reference to any\nhypothetical mechanism of turbulence . using the resulting\ncomplete analytic representation for the mean-velocity field,\nthe shearing-stress field for several flows is computed from the\nboundary-layer equations and compared with experimental data .\n the development of a turbulent boundary layer is ultimately\ninterpreted in terms of an equivalent wake profile, which supposedly\nrepresents the large-eddy structure and is a consequence of the\nconstraint provided by inertia . this equivalent wake profile is\nmodified by the presence of a wall, at which a further constraint is\nprovided by viscosity . the wall constraint, although it penetrates\nthe entire boundary layer, is manifested chiefly in the sublayer flow\nand in the logarithmic profile near the wall .\n finally, it is suggested that yawed or three-dimensional flows\nmay be usefully represented by the same two universal functions,\nconsidered as vector rather than scalar quantities . if the wall\ncomponent is defined to be in the direction of the surface shearing\nstress, then the wake component, at least in the few cases studied,\nis found to be very nearly parallel to the gradient of the pressure ."}, {"doc_id": 564, "text": "local heat transfer and recovery temperature on a yawed\ncylinder at a mach number of 4. 15 and high reynolds\nnumbers .\n local heat transfer, equilibrium temperatures,\nand wall static pressures have been measured on a\ncircular cylinder at yaw angles of 0, 10, 20, 40,\nand 60 . the reynolds number range of the tests\nwas from 1x10 to 4x10 based on cylinder\ndiameter .\n increasing the yaw angle from 0 to 40 increased\nthe stagnation-line heat-transfer coefficients by 100\nto 180 percent . a further increase in yaw angle to\nheat-transfer coefficients .\n at zero yaw angle the boundary layer over the\nentire front half of the cylinder was laminar but at\nyaw angles of 40 and 60 it was evidently completely\nturbulent, including the stagnation line, as\ndetermined by comparison of local heat-transfer coefficients\nwith theoretical predictions . the level of heating\nrates and the nature of the chordwise distribution\nof heat transfer indicated that a flow mechanism\ndifferent from the conventional transitional boundary\nlayer may have existed at the intermediate yaw angles\nof 10 and 20 . at all yaw angles the peak\nheat-transfer coefficient occurred at the stagnation line\nand the chordwise distribution of heat-transfer\ncoefficient decreased monotonically from this peak .\n the average heat-transfer coefficients over the\nfront half of the cylinder are in agreement with\nprevious data for a comparable reynolds number\nrange .\n the theoretical heat-transfer distributions for\nboth laminar and turbulent boundary layers are\ncalculated directly from simple quadrature formulas\nderived in the present report ."}, {"doc_id": 565, "text": "similar solutions for the compressible boundary layer\non a yawed cylinder with transpiration cooling .\n heat-transfer and skin-friction\nparameters obtained from exact\nnumerical solutions to the laminar\ncompressible-boundary-layer equations\nfor the infinite cylinder in yaw are\npresented . the chordwise flow in\nthe transformed plane is of the\nfalkner-skan type . solutions are given\nfor chordwise stagnation flow with\nboth a porous and a nonporous wall .\nthe effect of a linear\nviscosity-temperature relation is compared with\nthe effect of the sutherland\nviscosity-temperature relation at the\nstagnation line of the cylinder for a\nprandtl number of 0.7 . the effects of\npressure gradient, mach number, yaw\nangle, and wall temperature are\ninvestigated for a linear viscosity-temperature\nrelation and a prandtl number\nof 1.0 with a nonporous wall .\n the results indicate that compressibility\neffects become important\nat large mach numbers and yaw angles,\nwith larger percentage effects on\nthe skin friction than on the heat\ntransfer . the use of the two different\nviscosity relations gives about the\nsame results except when large changes\nin temperature occur across the boundary\nlayer, as for a highly cooled\nwall . the present solutions predict that\na larger amount of coolant would\nbe required at a given large mach number\nand yaw angle than would be\npredicted from solutions of the corresponding\nincompressible-boundary-layer\nequations ."}, {"doc_id": 566, "text": "investigation of local heat transfer and pressure drag\ncharacteristics of a yawed circular cylinder at supersonic\nspeeds .\n local heat-transfer coefficients,\ntemperature recovery factors, and\npressure distributions were measured\non a circular cylinder at a nominal\nmach number of 3.9 over a range of\nfree-stream reynolds numbers from\nfrom 0 to 44 .\n it was found that yawing the\ncylinder reduced the local heat-transfer\ncoefficients, the average heat-transfer\ncoefficients, and the pressure\ndrag coefficients over the front side\nof the cylinder . for example, at\nis reduced by 34 percent and the\npressure drag by 60 percent . the\namount of reduction may be predicted by\na theory presented herein . local\ntemperature recovery factors were also\nreduced by yaw, but the amount of\nreduction is small compared to the\nreduction in heat-transfer coefficients .\n a comparison of these data with\nother data obtained under widely\ndifferent conditions of body and stream\ntemperature, mach number, and\nreynolds number indicates that these\nfactors have little effect upon the\ndropoff of heat transfer due to yaw ."}, {"doc_id": 567, "text": "aerodynamic characteristics of a circular cylinder\nat mach number of 6. 86 and angles of attack up to\n90 .\n pressure-distribution and force\ntests of a circular cylinder have\nbeen made in the langley 11-inch\nhypersonic tunnel at a mach number of\nbased on diameter, and angles of\nattack up to 90 . the results are\ncompared with the hypersonic\napproximation of grimminger, williams, and\nyoung and with a simple modification\nof the newtonian flow theory . the\ncomparison of experimental results\nshows that either theory gives adequate\ngeneral aerodynamic\ncharacteristics but that the modified newtonian\ntheory gives a more accurate\nprediction of the pressure distribution .\nthe calculated crossflow drag\ncoefficients plotted as a function\nof crossflow mach number were found\nto be in reasonable agreement with\nsimilar results obtained from other\ninvestigations at lower supersonic\nmach numbers . comparison of the\nresults of this investigation with\ndata obtained at a lower mach number\nindicates that the drag coefficient\nof a cylinder normal to the flow is\nrelatively constant for mach numbers\nabove about 4 ."}, {"doc_id": 568, "text": "shock wave effects on the laminar skin friction of\nan insulated flat plate at hypersonic speeds .\n an approximate theory on the phenomena of interaction\nbetween the shock wave and the laminar boundary layer on an\ninsulated flat plate at hypersonic speeds has been formulated .\nresults on the rate of growth of the boundary-layer thickness and\nthe rate of decay of the shock-wave strength have been found\nthat hold for . a new set of formulas\nfor the average skin-friction coefficient, over an insulated\nflat plate at hypersonic speeds has been obtained . calculations\non the basis of the new formulas yield the data shown in figs.\nsteady decrease in as increases, the present results indicate\nthat may increase with at hypersonic mach\nnumbers ."}, {"doc_id": 569, "text": "an experimental investigation of leading edge shock wave boundary layer\ninteraction at mach 5.8 .\nthe boundary layer on a slender body tends to be very thick at\nhypersonic speeds . it interacts with the external flow by producing larger\nflow deflections near the leading edge than those due to the body alone\nflow around the boundary layer gives rise to an induced pressure with a\nnegative gradient which thins the boundary layer and increases the skin\nfriction with respect to the zero pressure gradient value .\nexperiments on a flat plate with a sharp leading edge have been\nperformed in the galcit 5-dash by 5-dash in. mach 5.8 hypersonic wind\ntunnel . the induced pressure was measured by means of orifices in the\nplate surface . profiles of mach number, velocity, mass flow, pressure,\nand momentum deficiency were calculated from impact pressure surveys\nnormal to the plate surface made at various distances from the leading\nedge .\nthe results are as follows . /1/ the induced pressures are 25 per cent\nhigher than the weak interaction theory . /2/ the boundary layer and the\n external flow are distinctly separate for as low as 6,000 . /3/ the\nshock wave location is in good agreement with that predicted by the\nfriedrichs theory for a body shape equivalent to the observed\nboundary-layer displacement thickness . /4/ expansion waves reflected from the\nshock are weak . /5/ the average skin-friction coefficient tends toward\nand nearly matches the zero pressure gradient value downstream, but\nincreases to approximately twice that value as the leading edge is\napproached ."}, {"doc_id": 570, "text": "on the boundary layer equations in hypersonic flow\nand their approximate solutions .\n analytical solutions of the prandtl boundary-layer equations are\nobtained for the problem of the /strong/ interaction between the\nleading-edge shock and the viscous layer over a flat plate at hypersonic\nvelocities . as the mach number increases and the interaction region\nspreads downstream over the plate, the local skin-friction coefficient\nincreases rapidly over its conventional value . the local heat-transfer\ncoefficient at first remains practically unaffected but then also begins\nto increase with mach number ."}, {"doc_id": 571, "text": "heat transfer to flat plate in high temperature rarefied\nultra-high mach number flow .\n an investigation was conducted in a hypersonic\nshock tunnel to determine the local heat transfer\nrates for a sharp leading edge flat plate . the free\nstream mach number range was 7.95 to 25.1 with\nstagnation temperatures of approximately 2550\nand 6500 r . for these temperature and mach\nnumber conditions, the strong interaction parameter,\nvaried from 2.35 to 826 . the\ncorresponding knudsen numbers, based on the\nratio of the free stream mean free path and the\nleading edge thickness, varied from 0.38 to 85.5 .\nfor free stream mach numbers greater than 10,\nknudsen numbers of approximately unity, and\nperfect gas conditions, the calculated heat transfer\ncoefficients were found to vary as as predicted\nby the noninsulated flat plate theory of li\nand nagamatsu . for the case of,\nthe leading edge slip phenomenon\ndrastically reduced the local heat transfer coefficients\nas compared to the theoretical values predicted\nwith no slip at the surface . for the extreme case of and,\nthe measured local\nheat transfer rate was an order of magnitude\nless than the analytical value . both the knudsen\nnumber and the free stream mach number are\nimportant physical parameters that determine the\nextent of the slip-flow region ."}, {"doc_id": 572, "text": "boundary layer displacement and leading edge bluntness effects in high\ntemperature hypersonic flow .\ntwo important features of hypersonic flow over slender or thin bodies\nare the displacement effect of the boundary layer and the large\ndown-stream influence of leading-edge bluntness . the present paper\ncontributes new theoretical and experimental results on this problem .\nthe interaction of the two effects is treated theoretically by extending\n the basic shock-layer concept . in the outer inviscid flow, a model\nconsisting of a detached shock layer and an entropy layer is introduced\nto account for bluntness . in the boundary layer, the approximate\nsolution is found to be governed by a local flat-plate similarity . under\nthe assumption of a strong bow shock and a specific heat ratio close to\nunity, a theory is developed for an arbitrary thin body . for flat-plate\n afterbodies, the theory yields a solution agreeing with blast-wave\ntheory at one limit and strong-interaction theory at the other . within\nthe framework of the present theory, the problems involving angle of\nattack are also analyzed . complementary to the above study, a\nhypersonic similitude involving strong shocks, but not requiring close to one\n a natural comparison with experimental data correlated on the basis of\nthis similitude .\nflat-plate experiments in air, conducted in the c.a.l. 11 x 15-dashin.\nhypersonic shock tunnel under cold-wall conditions, included measurement\n of surface heat-transfer distributions and schlieren studies for zero\nand nonzero angle of attack . steady laminar heat-transfer rates were\nmeasured by means of thin-film resistance thermometers at air test-flow\nmach numbers around 12, free-stream reynolds numbers from 1.4 x 10 to 1.\nfor most of the experiments, airflow stagnation temperatures ranged from\nratios of about 0.15 . the range of test conditions at this stagnation\ntemperature encompassed the limiting cases of dominant bluntness and\ndominant viscous-interaction effects . heat-transfer distributions were\nalso measured on a sharp plate for air stagnation temperatures ranging\nfrom 2,000degreek up to 4,000degreek .\nthe experimental data are quite well correlated in terms of the\nforegoing theoretical similitude variables characterizing combined effects\nof boundary-layer displacement and bluntness . the correlations obtained\n suggest that for the present experimental conditions, at least, the\nhypersonic viscous similitude is valid even with leading-edge bluntness\n in the paper, is generally fair ."}, {"doc_id": 573, "text": "viscous hypersonic similitude .\n an extension of classical hypersonic similitude is developed\nwhich takes into account the interaction effect of the\ndisplacement thickness of the boundary layer . a basic result of this\nviscous similitude is that the total drag including frictional drag\nobeys the classical similarity law for the pressure drag .\nadditional similarity conditions governing viscous effects must be\nimposed in this similitude .\n underlying the similitude is a new hypersonic boundary-layer\nindependence principle . according to this principle, the\nprincipal part of a hypersonic boundary layer with given pressure\nand wall temperature distributions and free-stream total\nenthalpy is independent of the (high) external mach number\ndistribution outside the boundary layer .\n various features of viscous hypersonic similitudes are\ndiscussed . it is found, for example, that it applies to three-\ndimensional boundary-layer interaction effects on flat bodies, provided\nthe concepts of strip theory may be applied, and provided the\naspect ratio is an invariant ."}, {"doc_id": 574, "text": "inviscid flow with nonequilibrium molecular dissociation for pressure\ndistributions encountered in hypersonic flight .\none-dimensional inviscid nonequilibrium flows of a two-component model\ngas are studied for prescribed pressure variations and an average\nreaction rate based on recent data for oxygen recombination . these flows\nare interpreted in relation to the flow along streamlines around blunt\nhypersonic bodies . assuming equilibrium conditions in the subsonic\nregion, it is estimated that the flow in the initial supersonic\nexpansion region, which is approximately of prandtl-meyer character, will be\nchemically frozen with respect to the molecular dissociation of the\nprimary components under the hypersonic, high-altitude flight conditions\n considered . the flight conditions consist of flight velocities between\nfurthermore, on bodies of small surface inclination beyond the nose, the\n flow will continue to be effectively frozen for at least 20 ft\ndown-stream of the nose . these conclusions may lead to the simplification of\n procedures for theoretical calculation and testing .\nthe problem of distinguishing a dimensionless length-reaction rate\nparameter, which characterizes the extent of departures from equilibrium or\n from frozen behavior in the flow fields of interest here, is discussed"}, {"doc_id": 575, "text": "atomic recombination in a hypersonic wind tunnel nozzle .\nthe flow of an ideal dissociating gas through a nearly conical nozzle is\n considered . the equations of one-dimensional motion are solved\nnumerically assuming a simple rate equation together with a number of\ndifferent values for the rate constant . these calculations suggest that\ndeviations from chemical equilibrium will occur in the nozzle if the\nrate constant lies within a very wide range of values, and that, once\nsuch a deviation has begun, the gas will very rapidly 'freeze' . the\ndissociation fraction will then remain almost constant if the flow is\nexpanded further, or even if it passes through a constant area section .\n an approximate method of solution, making use of this property of\nsudden 'freezing' of the flow, has been developed and applied to the\nproblem of estimating the deviations from equilibrium under a wide range of\n conditions . if all the assumptions made in this paper are accepted,\nthen lack of chemical equilibrium may be expected in the working\nsections of hypersonic wind tunnels and shock tubes . the shape of an\noptimum nozzle is derived in order to minimize this departure from\nequilibrium .\nit is shown that, while the test section conditions are greatly affected\n by 'freezing', the flow behind a normal shock wave is only changed\nslightly . the heat transfer rate and drag of a blunt body are estimated\n to be reduced by only about 25 per cent even if complete freezing\noccurs . however, the shock wave shape is shown to be rather more\nsensitive to departures from equilibrium ."}, {"doc_id": 576, "text": "viscous and inviscid stagnation flow in a dissociated hypervelocity free\n stream .\nhigh reynolds number hypersonic stagnation flow over a blunt-nosed body\nin a nonequilibrium dissociated free stream is analyzed and compared to\na similar flow in an initially undissociated ambient gas . free stream\ndissociation effects on various equilibrium stagnation flow properties\nin air are presented as a function of the ambient atom mass fraction and\n dissociation energy for velocities ranging from 15,000 to 25,000 fps .\nsignificant changes in the bow shock geometry, stagnation gas state, and\n boundary layer behavior are found when the free stream dissociation\ninvolves more than 10( of the total energy . it is observed that for\nlarge amounts of both atomic oxygen and nitrogen ahead of the body, the\nequilibrium shock layer properties converge toward those pertaining to\nchemically and vibrationally-frozen flow across the bow shock .\nmoreover, under certain conditions, the ionization level can be increased by\n an order of magnitude and the usual reduction in frozen boundary layer\nheat transfer due to a highly-cooled noncatalytic surface can increase\nfrom stall of adjacent stages .\nthe effects of compromises of stage matching to favor part-speed\noperation were also considered . this phase of the study indicated that\nsuch compromises would severely reduce the complete-compressor-stall\nmargin . furthermore, the low-speed stage stall problem is transferred\nfrom the inlet stages to the middle stages, which are more susceptible\nto abrupt-stall characteristics .\nthe analysis indicates that inlet stages having continuous performance\ncharacteristics at their stall points are desirable with respect to\npart-speed compressor performance . these characteristics must, however,\n be obtained when the stages are operating in the flow environment of\nthe multistage compressor . alleviation of part-speed operational\nproblems may also be obtained by improvement in either stage flow range or\nstage loading margin .\nthe results of this analysis are only qualitative . the trends obtained,\n however, are in agreement with those obtained from experimental studies\n of high-pressure-ratio multistage axial-flow compressors, and the\nresults are valuable in developing an understanding of the off-design\nproblem . in addition to these stage-matching studies, a general\ndiscussion of variable-geometry features such as air bleed and adjustable\n gas model . numerical solutions of non-equilibrium airflows with fully\ncoupled chemistry provide a preliminary verification of such scaling for\nbenser, w.a.\n.W\nlimit characteristics . the analysis indicated that all these problems\ncould be attributed to discontinuities in the performance\ncharacteristics of the front stages . such discontinuities can be due to the type\n of stage stall or to a deterioration of stage performance resulting\nblades is included ."}, {"doc_id": 577, "text": "on hypersonic similitude .\n tsien in a recent paper (j. math. phys. mass. inst. tech.\nsonic flows around slender bodies and has pointed out that\nthe product of mach number and fineness ratio is a basic\nsimilarity parameter . the author enlarges on this notion,\nindicating that the problem of hypersonic flow about a\nslender body in three dimensions is the same as that of a\ncertain two-dimensional nonsteady flow (with time replacing\nthe lengthwise spatial coordinate) characterized by\nessentially the same similarity parameter ."}, {"doc_id": 578, "text": "dissociation scaling for nonequilibrium blunt nose flows .\nstage-stacking study . the principal problems considered were poor\nlow-speed efficiency, multiple-valued performance characteristics at\nintermediate speeds, and poor intermediate-speed compressor surge or\nstall-naca rm e56b03b, 1956 . chapter xiii\n.W\ncompressor operation with one or more blade rows stalled .\nan analysis of the part-speed operating problems of high-pressure-ratio\n air ."}, {"doc_id": 579, "text": "further developments of new methods in heat flow analysis .\n lagrangian methods in heat-flow problems and transport\nphenomena were introduced by the writer in some previous work .\nthe present paper develops further one particular aspect of the\nmethod,--i.e., the elimination of /ignorable coordinates ./ this\nis accomplished by a special choice of generalized coordinates,\neach of which is constituted by an arbitrary temperature\ndistribution and an /associated flow field ./ the latter is a vector\nfield which is derived from the corresponding scalar field by a\nvariational method . the procedure is valid for a certain class of\nnonlinear problems, provided we replace the temperature by the heat\ncontent as the unknown . it is shown that for normal coordinates\nderivation of the associated flow field is immediate . the use\nof normal coordinates and their associated flow fields is\nillustrated by an example . introduction of dirac functions and\nassociated flow fields yields a procedure which constitutes a\ngeneralization of the classical formulation by green's functions\nand integral equations . this is illustrated by application to\none-dimensional problems of heating of a homogeneous or composite\nslab and directly verified by classical methods in the appendix ."}, {"doc_id": 580, "text": "new thermo-mechanical reciprocity relations with application\nto thermal stress analysis .\n based on the variational formulation of linear\nthermodynamics as developed previously by the writer, thermomechanical\nreciprocity relations are discussed which lead to new methods of\nanalysis of thermal stresses . these reciprocity relations are quite\ndifferent from the usual ones derived from the analogy of thermal\nloading with a combination of surface and body-force distribution .\nthe results are applicable to stationary and transient\ntemperatures in elastic and viscoelastic structures . the methods are\nentirely variational and do not require the evaluation of the\ntemperature field . the stresses at one point are expressed\ndirectly in terms of any arbitrary distribution temperatures applied\nexternally, including the effect of surface heat-transfer layer .\nthe concepts and procedures are illustrated on a simple\nexample . the relation is pointed out between the reciprocity\nproperty and the generalization of castigliano's principle to\nthermomechanics ."}, {"doc_id": 581, "text": "approximate formulas for thermal-stress analysis .\nthe basis of any thermal-stress analysis is the determination of the\ntemperature distributions in the structure . for arbitrary flight\nhistories, the determination of such distributions is rather tedious\nand not completely general . this latter fact handicaps optimization\nstudies in the project design stage when it is desirable to be able to\nexpress the thermal-stress distributions in a general manner .\nin this note, general expressions are derived for the thermal-stress\ndistributions in a typical i-section using similar assumptions to\nthose of biot ."}, {"doc_id": 582, "text": "the melting of finite slabs .\nan approximate method, known as the\nheat-balance integral, is used to determine the\nmelting rate of a finite slab which is initially\nat a uniform temperature below the melting\npoint . the slab is acted upon by a\nconstant heat input at one face and has its other\nface either insulated or kept at its initial\ntemperature . the first three terms of series\nsolutions in an intrinsically small parameter\nare obtained for the time histories of\nmelting and the temperature distribution in the slab ."}, {"doc_id": 583, "text": "influence coefficients for real gases .\nin the analysis of one-dimensional fluid-flow problems, it is often\nassumed that the behavior of the medium is that of a perfect gas .\nthis assumption is justified, provided the pressure and temperature\nrange of interest is small and near atmospheric . at higher pressures\nand temperatures various deviations are introduced thereby causing\ndeviations from the results obtained by using the ideal fluid-flow\nequations .\nin this note, influence coefficients, similar to those developed by\nshapiro, are presented for the case of real gases . this analysis is\nbased upon the use of various functions of the compressibility factor\nemmons . some of the assumptions made were as follows.. (1) the flow\nis one-dimensional and steady, (2) changes in the stream properties\nare continuous, and (3) the flow is comprised of imperfect gases"}, {"doc_id": 584, "text": "conduction of heat in a solid with a power law of heat\ntransfer at its surface .\n the nonlinear boundary value problem, where\nand m are constants, is solved formally by first\nintroducing power series in t for the unknown temperature\nand flux at the surface and then determining the coefficients\nin those series . in this manner the temperature function is\ndetermined as a series of repeated integrals of error\nfunctions . the convergence is rapid only for small values of t .\nthe special cases and generalizations of\nthe condition at the surface for which the same method\napplies, are noted . surface temperatures are also found by\nmethods of difference equations, where t is not limited to\nsmall values . graphs of these temperatures corresponding\nto various laws of heat transfer at the surface are shown ."}, {"doc_id": 585, "text": "nonlinear heat transfer problem .\n a study has been made of the time-dependent heat\nconduction in a semi-infinite medium subject to a\nboundary condition which can involve the temperature\nin a nonlinear manner . a formulation for the\ndetermination of the surface temperature, which is often\nof greatest physical interest, leads to a nonlinear\nvolterra integral equation . a simple iterative solution\nmethod, with an accuracy suitable for many practical\npurposes is presented . as an example, the problem\nof the time-dependent surface temperature of a body\nreceiving heat according to the stefan-boltzmann law\nis treated . the analysis is also applicable to physical\nadsorption or chemisorption processes which occur at\nthe boundary ."}, {"doc_id": 586, "text": "an approximate treatment of unsteady heat conduction\nin semi-infinite solids with variable thermal properties .\n this very short paper presents an approximate procedure for the\ncalculation of unsteady heat conduction in semi-infinite solids\nwith variable thermal properties . it is claimed to be an\nimprovement over previous efforts in this area since it yields physically\nsensible results for cases where thermal properties have a large\ndependence on temperature . instead of using polynomials to\nrepresent an unsteady temperature profile an exponential form is used .\ngood agreement is shown for several cases where the method of\nthe paper is compared with exact solutions ."}, {"doc_id": 587, "text": "variational analysis of ablation .\nthe variational and lagrangian thermodynamics developed in earlier\npublications are directly applicable to problems of heat conduction\nwith melting boundaries . these techniques are used here in treating\nthe problem of a half-space subjected to a constant rate of heat input\nat the melting surface (fig. 1) .\nthe applicability of the lagrangian equations to this case follows\nfrom the fact that the basic variational principle is valid whether the\nboundaries are fixed or move as arbitrary functions of time . this\ncan be seen if we remember that the equations govern only the\ninstantaneous configuration of the flow rates for a given geometry and\ntemperature field ."}, {"doc_id": 588, "text": "compressor operation with one or more blade rows stalled .\nan analysis of the part-speed operating problems of high-pressure-ratio\nratio multistage axial-flow compressors was made by means of a\nsimplified stage-stacking study . the principal problems considered\nwere poor low-speed efficiency, multiple-valued performance\ncharacteristics at intermediate speeds, and poor intermediate-speed compressor\nsurge or stall-limit characteristics . the analysis indicated that all\nthese problems could be attributed to discontinuities in the performance\ncharacteristics of the front stages . such discontinuities can be due\nto the type of stage stall or to a deterioration of stage performance\nresulting from stall of adjacent stages .\n the effects of compromises of stage matching to favor part-speed\noperation were also considered . this phase of the study indicated that such\ncompromises would severly reduce the complete-compressor-stall margin .\nfurthermore, the low-speed stage stall problem is transferred from the\ninlet stages to the middle stages, which are more susceptible to\nabrupt-stall characteristics .\n the analysis indicates that inlet stages having continuous performance\ncharacteristics at their stall points are desirable with respect to\npart-speed compressor performance . these characteristics must, however,\nbe obtained when the stages are operating in the flow environment of the\nmultistage compressor . alleviation of part-speed operation problems may\nalso be obtained by improvement in either stage flow range or stage-\nloading margin .\n the results of this analysis are only qualitative . the trends\nobtained, however, are in agreement with those obtained from experimental\nstudies of high-pressure-ratio multistage axial-flow compressors, and\nthe results are valuable in developing an understanding of the\noff-design problem . in addition to these stage-matching studies, a general\ndiscussion of variable-geometry features such as air bleed and\nadjustable blades is included ."}, {"doc_id": 589, "text": "some stall and surge phenomena in axial flow compressors .\nobservations of rotating stall have shown that a wide variety\nof stall patterns is possible .\n hot-wire anemometer data on a multistage compressor have\nshown a progressive-type stall at low speeds . the amplitude\nof the flow fluctuations increases in magnitude through the first\nfew stages and then diminishes rapidly to a small value in the\nlatter stages . a stage-stacking analysis has shown that rotating\nstall will exist over a large portion of the compressor map at low\nspeeds but will be instigated almost simultaneously with\ncompressor surge at high speeds .\n blades failures attributable to resonant vibrations excited by\nrotating stall have been experienced in single and multistage\ncompressors .\n in the stage-stacking analysis no deterioration of stage\nperformance due to unsteady flow resulting from stall of adjacent stages\nwas considered . in general, the pressure drop at the stall point\nis believed to be much larger than indicated by an analytical\nformulation of compressor performance . compressor surge is\nattributed to a limit cycle operation about the compressor stall\npoint, and, as indicated in a few compressor tests and in\njet-engine tests, a small compressor discharge receiver volume may\nresult simply in stall of the compressor without the cyclic\ncharacteristics of compressor surge . in this event, engine operation\nwill be limited because of the large drop in performance which\naccompanies compressor stall ."}, {"doc_id": 590, "text": "effects of stage characteristics and matching on axial flow compressor\nperformance .\nthe use of stage characteristics obtained from test data in the\nperformance analysis and development of an axial-flow compressor is described\nrelative stage matching as shown by an idealized example and also by\ntest experience . factors governing major performance parameters are\ndiscussed and certain development problems and possible solutions are\nreviewed ."}, {"doc_id": 591, "text": "an approximate equation for the /choke line/ of a compressor .\ndiscussion of a similarity between the pressure-ratio versus\ninlet-mass-flow-coefficient characteristic of a stream or gas turbine and the\nanalogous characteristic of an expansion /laval/ nozzle . this idea is\nextended to a compressor and a compression nozzle, and an approximate\nexpression for the /choke line/ of the compressor is developed ."}, {"doc_id": 592, "text": "design of axial compressors .\nthe main types of axial compressors are described, and the use of\ngeneralized design curves to make performance estimates is advocated . the\ndifferent variables are weight, power, pressure ratio, temperature rise,\n mass flow, rotational speed, stage efficiency, blade bending stresses\ndue to aerodynamic loading, and methods and materials of construction .\nair outlets, flow coefficients and different blade forms are also\nconsidered ."}, {"doc_id": 593, "text": "theoretical considerations of flutter at high mach\nnumber .\n some of the theories for two-dimensional oscillatory air forces\nwhich may be applied in flutter calculations at high mach\nnumbers are discussed . these include linear theory, van dyke's\nsecond-order theory, piston theory, landahl's method,\ntangent-wedge and tangent-cone approximations, newtonian theory, and\na new nonlinear-pressure method . a comparison of the theories\nis made by showing the results of flutter calculations for mach\nnumbers up to 10, and the possibility of flutter at these higher\nmach numbers is pointed out .\n results of flutter calculations are shown to illustrate the\nvarious effects arising from a nonlinear thickness theory . the\npossibility of large flutter speed thickness effects which depend on\nfrequency ratio is shown . the influence of airfoil shape is discussed\nand flutter speed trends with center of gravity and elastic axis\nlocations are presented . some possible refinements of piston\ntheory are discussed for use at very high mach numbers . these\ninclude the use of local flow conditions and the use of newtonian\ntheory over the leading edge of a blunt-nosed airfoil ."}, {"doc_id": 594, "text": "wind tunnel techniques for the measurements of oscillatory\nderivatives .\nthis paper discusses the basic principles employed in techniques for the\n measurement of oscillatory derivatives in wind tunnels, and gives some\naccount of the associated instrumentation . the suitability of the\nvarious techniques for different test conditions is also discussed and\nbrief reference is made to wind tunnel effects on the measurements ."}, {"doc_id": 595, "text": "the equilibrium piston technique for gun tunnel operation .\n a modified technique for the operation of a gun tunnel is\nsuggested based on experimental results . if the piston mass and the\ninitial barrel pressure are chosen correctly, then the peak pressures\nassociated with the gun tunnel may be eliminated . under these\nconditions the piston is brought to rest with no overswing . some\nmeasurements of the piston motion using a microwave technique are\nreported which confirm this idea .\n the wave diagram associated with this mode of operation is\nshown, and some calculations of the stagnation pressure are given which\nshow that during the suggested running time, the stagnation pressure\nmay be considerably greater than the driving pressure if the driving\nchamber cross-sectional area is large compared with that of the driven\nsection . for a uniform shock tube the stagnation pressure will always\nbe less than the driving pressure . the use of air, helium and\nhydrogen as driving gases has been considered .\n experiments in a gun tunnel are reported which show that the\nequilibrium piston technique enables steady stagnation pressures to be\nachieved over a time of approximately 15 ms using air as the driving\ngas . the expansion caused by the piston acceleration is shown to\ninteract with the stationary piston, but this is found to produce only a\nsmall drop in stagnation pressure ."}, {"doc_id": 596, "text": "the properties of crossed flexure pivots, and the influence of the\npoint at which the strips cross .\nit is shown that the rotational stiffness of a crossed flexure pivot\nvaries considerably when subjected to an applied force . the type of\nvariation can be radically changed simply by moving the point at which\nthe strips cross . the relation between torque and rotation for a given\napplied force is not exactly linear and the extent of the non-linearity\nis determined by taking into account the small movements of the centre\nof rotation of the pivot . finally, for design purposes, an analysis of\nthe maximum stresses in the strips is given ."}, {"doc_id": 597, "text": "measurements of pitching moment derivatives for blunt-nose aerofoils\noscillating in two-dimensional supersonic flow .\ndirect pitching moment derivatives have been measured using the method\nof scruton, woodgate et al for two single wedge blunt-nosed aerofoils .\nthese measurements were made at mach numbers of 1.75 and 2.47 and\nfrequency parameters less than 0.02 . in general, nose blunting was found\nto have little effect on the derivatives although changes were observed\nfor the thinner wedge at a mach number of 1.75 ."}, {"doc_id": 598, "text": "new test techniques for a hypervelocity wind tunnel .\nthe measurement of rocket exhaust effects on vehicle stability and the\nmeasurement of aerodynamic damping were made in an arc-discharge type of\n hypervelocity wind tunnel . sample data are given to indicate the\nquality of data obtainable in this tunnel, and samples of self-luminous\nand shadowgraph photographs are also presented ."}, {"doc_id": 599, "text": "aerodynamic forces, moments and stability derivatives\nfor slender bodies of general cross section .\n the problem of determining the total\nforces, moments, and stability\nderivatives for a slender body performing\nslow maneuvers in a compressible\nfluid is treated within the assumptions\nof slender-body theory . general\nexpressions for the total forces (except\ndrag) and moments are developed\nin terms of the geometry and motions of\nthe airplane, and formulas for\nthe stability derivatives are derived in\nterms of the mapping functions\nof the cross sections .\n all components of the motion are\ntreated simultaneously and second\nderivatives as well as first are obtained,\nwith respect to both the\nmotion components and their time rates of\nchange . coupling of the\nlongitudinal and lateral motions is thus\nautomatically included . a number of\ngeneral relationships among the various\nstability derivatives are found\nwhich are independent of the configuration,\nso that, at most, only 35\nof a total of 325 first and second\nderivatives need be calculated\ndirectly . calculations of stability\nderivatives are carried out for two\ntriangular wings with camber and thickness,\none with a blunt trailing\nedge, and for two wing-body combinations, one having a plane wing and\nvertical fin .\n the influence on the stability\nderivatives of the squared terms in\nthe pressure relation is demonstrated,\nand the apparent mass concept as\napplied to slender-body theory is discussed\nat some length in the light\nof the present analysis . it is shown that\nthe stability derivatives can\nbe calculated by apparent mass although the\ngeneral expressions for the\ntotal forces and moments involve additional terms ."}, {"doc_id": 600, "text": "the calculation of lateral stability derivatives of\nslender wings at incidence including fin effectiveness,\nand correlation with experiment .\n comparisons are made between\nlow-speed experimental results and\nestimates based on attached-flow\ntheory for the lateral stability\nderivatives of slender wings at\nincidence, and it is found that the flow\nseparation has little effect on\nthe sideslip derivatives . the reduction\nin due to part-span anhedral\nis evaluated, and a semi-empirical formula\nis derived to account for important\nsecond-order terms . for the rotary\nderivatives, an attempt is made\nto estimate the effect of the leading edge\nvortices, but no satisfactory\nconclusions have been reached .\n the fin contributions to\nthe derivatives are evaluated on the basis\nof treating the wing surface as\na total reflection plate . good agreement\nwith experiment is reached for\nthe sideslip derivatives, and for the\ndamping-in-yaw at moderate incidences .\nsidewash is found to have a large\neffect on the rolling derivatives,\nand further information on the strength\nand position of the leading edge\nvortices in non-symmetric flow is required\nbefore a complete calculation of\nthe sidewash can be given ."}, {"doc_id": 601, "text": "calculation of the flow past slender delta wings with\nleading edge separation .\n the flow past a slender delta\nwing with a sharp leading edge, at\nincidence, usually separates along\nthis edge, i.e. a vortex layer extends\nfrom the edge and rolls up to form\na /core/ (a region of high vorticity) .\na potential flow model of this is\nconstructed in which the layer is\nreplaced by a vortex sheet which\nis rolled up into a spiral in the region\nof the /core/ . this problem\nis reduced to a two-dimensional one by\nassuming a conical field and using\nslender wing theory . the shape and strength\nof the sheet are determined by\nthe two conditions that it is a stream\nsurface and sustains no pressure\ndifference . use is made of results\npreviously obtained for the core\nregion and the remaining finite part of\nthe sheet is dealt with by choosing\ncertain functions for its shape and\nstrength . the parameters in these\nfunctions are found by satisfying the\ntwo conditions stated above at\nisolated points . results are obtained for\nthe pressure distribution, chord\nloading and norman force coefficient as\nfunctions of the ratio of the\nincidence to the apex angle . the lift for a\ngiven incidence is about 15\nbelow that found by brown and michael . flow\npatterns are indicated in two\ntypical cases . the effect of separation on\nthe drag due to lift of a wing\nwith small thickness is discussed ."}, {"doc_id": 602, "text": "the 7 x 7 in . hypersonic wind tunnel at rae farnborough,\npart 1, design, instrumentation and flow visualization\ntechniques .\n this is the first of three parts of\nthe calibration report on the r.a.e.\n some details of the design and lay-out\nof the plant are given, together\nwith the calculated performance figures,\nand the major components of the\nfacility are briefly described .\n the instrumentation provided for\nthe wind-tunnel is described in some\ndetail, including the optical and other\nmethods of flow visualization used\nin the tunnel .\n later parts will describe the\ncalibration of the flow in the\nworking-section, including temperature measurements .\na discussion of the heater\nperformance will also be included as\nwell as the results of tests to determine\nstarting and running pressure ratios,\nblockage effects, model starting loads,\nand humidity of the air flow ."}, {"doc_id": 603, "text": "the 7 in. x 7 in. hypersonic wind tunnel at r.a.e. farnborough\npart ii. heater performance .\ntests on the storage heater, which is cylindrical in form and mounted\nhorizontally, show that its performance is adequate for operation\nat m=6.8 and probably adequate for flows at m=8.2 with the existing\nnozzles . in its present state, the maximum design temperature of 680\ndegrees centigrade for operation at m=9 cannot be realised in the tunnel\nbecause of heat loss to the outlet attachments of the heater and\nquick-acting valve which form, in effect, a large heat sink . because of this\nheat loss there is rather poor response of stagnation temperature\nin the working section at the start of a run . it is hoped to cure this\nby preheating the heater outlet cone and the quick-acting valve .\nat pressures greater than about 100 p.s.i.g. free convection through the\nfibrous thermal insulation surrounding the heated core causes the top\nof the heater shell to become somewhat hotter than the bottom, which\nresults in /hogging/ distortion of the shell . this free convection\ncools the heater core and a vertical temperature gradient is set up\nacross it after only a few minutes at high pressure .\nmodifications to be incorporated in the heater to improve its\nperformance are described ."}, {"doc_id": 604, "text": "the 7 in. x 7 in. hypersonic wind tunnel at r.a.e., farnborough\npart iii - calibration of the flow in the working section .\nthe fused silica nozzle to give m=7 in the 7 in. x 7 in. hypersonic\nwind tunnel produces a flow field with an average mach number of 6.85\nalong the centreline of the working section . the mach number gradually\ndecreases towards the boundary layer, and over a core of approximately\nmach number .\nthe nozzle heats up during a run but this has little effect on the\nmach number distribution . at one station the mach number was one-third\nper cent greater for a run of 1 minute than for a run of 10 seconds .\nthe temperature field in the inviscid flow has an average variation of\nin temperature with time throughout a run ."}, {"doc_id": 605, "text": "pressure measurements on a cone-cylinder-flare configuration at small\nincidences for m 6.8 .\npressure measurements were made on a slender cone-cylinder-flare\nconfiguration, slightly blunted at the nose, for 0, 3 and 6 degrees\nincidence at a free-stream mach number of 6.8 .\nit was found that the surface pressures obtained on the cone agreed with\n extrapolations to m equals 6.8 of theoretical values given in m.i.t.\ntables /kopal/for yawed cones, and that impact theory gave a good\nindication of the pressure level to be expected on all parts of the body\nwhere surface incidence was sufficiently large to merit its use .\nthe semi-angles of the conical and flared parts of the model were both\nthe pressure level on the flare rose in all cases to approximately that\ndeveloped upstream on the cone surface .\nno evidence of a marked over-expansion to pressures below the\nfree-stream value was noticed at the junction between cone and cylinder ."}, {"doc_id": 606, "text": "formulae and approximations for aerodynamic heating rates in high speed\nflight .\nthis note gives formulae and approximations suitable for making\npreliminary estimates of aerodynamic heating rates in high speed flight .\nthe formulae are based on the /intermediate enthalpy/ approximation\nwhich has given good agreement with theoretical and experimental\nevidence . in the general flight case they could be used in conjunction with\n an analogue computer or a step-by-step method of integration to\npredict the variations of heat flow and skin temperature with time .\nin the restricted case of flight at constant altitude and mach number,\nsimple analytical methods and results are given which include the\neffects of radiation and can be applied to /thick/ as well as /thin/ skins\nwhere h is the aerodynamic heat transfer factor, and g, d and k are the\nheat capacity, thickness and thermal conductivity of the skin . if 0.1\nthe skin is approximately /thin/, i.e. temperature gradients across its\nthickness may be neglected ."}, {"doc_id": 607, "text": "duct flow in magnetohydrodynamics .\n this paper is an extension of the work of hartmann (2) and shercliff\ntransverse magnetic fields -- the simplest class of magnetohydrodynamic\nproblems . we are concerned here mainly with the boundary value\nproblems associated with flow in ducts with conducting walls ."}, {"doc_id": 608, "text": "aerodynamic noise in supersonic wind tunnels .\nhot-wire measurements in the free stream of a supersonic wind tunnel\nwere made in the mach number range of 1.6 to 5.0 . it is shown that the\nmass-flow fluctuations increase very rapidly with increasing mach\nnumber . if the fluctuation field is assumed to consist of sound waves-dash\nan assumption that is consistent with the measurements-dashthe sound\nintensity is approximately proportional to m, within the range of the\nexperiments . furthermore, the orientation of the field is found to be\ndifferent from the mach line direction,. it corresponds to a\nsound-source velocity of approximately one-half the free-stream velocity for\nthe higher mach numbers . it is shown that the turbulent boundary layer\nalong the nozzle and the tunnel walls is responsible for this sound\nfield ."}, {"doc_id": 609, "text": "on three dimensional bodies of delta planform which\ncan support plane attached shock waves .\n this note collects together in one report available theoretical work\non bodies which can support attached plane shock waves, discusses some\nof the possible merits of such shapes, and includes some calculations\nillustrating their properties . also, some preliminary results from\nwind tunnel tests are given, together with details of proposed future\ntests ."}, {"doc_id": 610, "text": "corner interference effects .\n the three-dimensional incompressible flow of fluid along the corner of\ntwo semi-infinite plates intersecting at right angles, especially the\ninterference of the boundary layers of the two plates, is discussed .\nmainly, the more important case of turbulent boundary layer is treated\nby means of experimental studies carried out at the technical university\nof braunschweig . some theoretical results for laminar flow are also\ntaken into account .\n in order to describe the interference effects in the boundary layer,\nan interference displacement thickness and an interference skin friction\nhave been introduced . it is shown from experiments and also from\ntheoretical considerations how these two quantities depend on reynolds\nnumber . furthermore, the influence of interference on the transition\nfrom laminar to turbulent flow is investigated . in addition, some\npreliminary results are given about the effect of the pressure gradient\non the interference effects ."}, {"doc_id": 611, "text": "an approximate solution of the compressible laminar\nboundary layer on a flat plate .\n following a major assumption that enthalpy and velocity are dependent\nonly on local conditions, an enthalpy-velocity relation\nis obtained for the laminar boundary layer on a flat plate where\nsubscripts p refer to the plate, 1 to the free stream and e to the\nequilibrium temperature condition at the plate . when compared with\ngeneral results, this relation (exact for prandtl number o = 1)\ngives a close approximation to crocco's numerical results for o = 0.725\nand 1.25, up to .\n using the above relation in conjunction with the approximate\nviscosity-temperature relation suggested by chapman and rubesin, and\nwith young's suggested first approximation for shearing stress it is\nshown that close approximations to displacement thickness and velocity\ndistribution are given by and where and which serves to define c .\n these have the advantage of being algebraic in form whereas previous\nresults have involved complex numerical integrations for individual\ncases ."}, {"doc_id": 612, "text": "pressure distributions and flow patterns at m=4 . on\nsome delta wings of inverted 'v' cross section .\n wind tunnel tests have been made\nto measure pressure distributions\nand to study flow patterns on a series\nof delta wings of inverted 'v'\ncross-section . each of these wings\nwas designed to have a plane shock\nwave in the plane of the leading edges\nat a chosen mach number and incidence .\n it was found that for a wide\nincidence range about the design point\nthe shock wave remained virtually\nattached to the leading edges and at\neach incidence the pressure was\napproximately constant over the lower\nsurface ."}, {"doc_id": 613, "text": "the contraction of satellite orbits under the influence of air drag\npart i . with spherically symmetrical atmosphere .\nthe effect of air drag on satellite orbits of small eccentricity e/0.2/\nis studied analytically by a perturbation method, on the assumption that\n the atmosphere is spherically symmetrical . equations are derived which\n show/1/how orbital period and perigee distance vary with eccentricity\nas the orbit contracts, and/2/how each of these quantities varies with\ntime . the equations of type/1/are nearly independent of the oblateness\nof the atmosphere . in all the equations, terms of order e and higher\nare usually neglected . the results are also presented graphically, in a\n manner designed for practical use .\nthe theory is to be extended to an oblate atmosphere in part ii, and\nwill later be compared with observation ."}, {"doc_id": 614, "text": "the contraction of satellite orbits under the influence of air drag .\npart ii . with oblate atmosphere .\nthe effect of air drag on satellite orbits of small eccentricity e/0.2/\nwas studied in part i/technical note no.g.w.533/on the assumption that\nthe atmosphere was spherically symmetrical . here the theory is extended\n to an atmosphere in which the surfaces of constant density are\nspheroids of arbitrary small ellipticity . equations are derived which\nshow how perigee distance and orbital period vary with eccentricity, and\n how eccentricity is related to time . expressions are also obtained\nwhich give lifetime and air density at perigee in terms of the rate of\nchange of period . in most of the equations, terms of order e and higher\n are neglected . the results take different forms according as the\neccentricity is greater or less than about 0.025, while circular orbits\nare dealt with in a separate section . the results are also presented\ngraphically in a manner designed for practical application, and examples\n of the theory in use are given .\nthe influence of atmospheric oblateness is difficult to summarize fairly\nsimultaneously assume their'worst'values, some of the\nspherical-atmosphere results can be altered by up to 30( as a result of oblateness\nand 5-10( would be a more representative figure ."}, {"doc_id": 615, "text": "the contraction of satellite orbits under the influence of air drag .\npart iii . high eccentricity orbits . /0.2 e 1/ .\nthe effect of air drag on satellite orbits of eccentricity e less than\nbetween 0.2 and 1 is presented . equations are derived which show how\nperigee distance and orbital period vary with eccentricity during the\nsatellite's life, and how eccentricity is related to time,.and formulae\nare obtained for the lifetime and the air density at perigee, in terms\nof the rate of change of period . the results are also presented\ngraphically and their implications and limitations are discussed ."}, {"doc_id": 616, "text": "determination of upper-atmosphere air density and scale height from\nsatellite observations .\na solution is obtained for the rate of change of semi-major axis and\nperigee distance of a satellite orbit with time due to the resistance of\n the atmosphere . the logarithm of air density is assumed to vary\nquadratically with height, and the oblateness of the atmosphere is taken\ninto account .\nthe calculation of perigee air density in terms of the rate of change\nof satellite period is dealt with,. and the method is applied to data\nat present available on six different satellites . the variation of air\ndensity with height is obtained as\nin p-28.59/0.15/-h-200//46/5/0.028/0.013//h-200///46/\nfor h in the range of approximately 170 to 700 km, where p is in grams/c\nm, h is in kilometres and standard deviations are given in brackets ."}, {"doc_id": 617, "text": "determination of upper-atmosphere air density profile from satellite\nobservations .\nthe theory previously developed for the changes in the perigee distance\nand semi-major axis of a satellite orbit due to air drag is extended to\nenable the air-density profile/i.e.its relative variation with height/to\n be derived from the motion of the orbit's perigee . the solution is\nfirst obtained in terms of the change in perigee distance and then in\nterms of the change in the radius of the earth at the sub-perigee point\n the scale height in the 180 and 220 km altitude regions ."}, {"doc_id": 618, "text": "orbit decay and prediction of the motion of artificial satellites .\nthe rate of decay of elliptic satellite orbits, due to atmospheric drag,\n is investigated through variation of parameters and through use of an\natmospheric model involving a power function between density and\naltitude . this model is shown to fit actual conditions better than an\nexponential function .\nthe effects of the equatorial belt and the rotation of the earth are\ninvestigated . the conclusion is reached that through these anomalies\natmospheric drag substantially affects the orbit elements, especially\nthose defining the orbit plane .\nan alternate approach of variation of parameters is presented, by which\na direct relation between period decay and instantaneous density\nconditions is established . this approach, by itself specifically adequate\nfor prediction work, also opens an avenue for systematic and unified\nevaluation of observed decay ."}, {"doc_id": 619, "text": "density of the upper atmosphere from analysis of satellite orbits ..\nfurther results .\nthe method previously described has been refined by taking into account\natmospheric rotation . further results are given from satellites of\nlatitude and season and day-to-night changes are reported ."}, {"doc_id": 620, "text": "earth satellite observations and the upper atmosphere .\natmospheric densities have been derived from artificial satellites in\naltitudes 200-700 km. and from rockets up to about 200 km. to\nconsolidate the two sets of data, h.k. kallmann suggested a model with a\nexact form of this curve has now been derived . corrections for the\n is excellent .\nvery close correlation between atmospheric density variations/h180 km./\nand the solar 20-cm. radiation implies that the origin of the'solar\neffect'may lie in the absorption of solar ultra-violet radiation .\nthe atmospheric density curve between 180 and 200 km. shows a\ntemperature inversion in the fl-layer . it is not yet possible to decide\n whether solar ultra-violet radiation as well as the solar he line and\nsolar x-ray radiation contribute to the heating of the fl-layer .\ndiurnal and seasonal density variations at altitudes 210, 562 and 660\nkm. have been derived from variations in acceleration of three\nsatellites/sputnik 3, vanguard 1 and 2/ . group averages of diurnal\nvariations are taken from different dates within the period\nmay 15, 1958-october 1, 1959 . physcal conditions in the upper\natmosphere are briefly summarized ..the'solar effect'originates in the\nfl-layer as a result of heating by the solar he line at 304 a. diurnal\ndensity variation at 210 km. is only a few per cent . absorption of\nsolar electromagnetic radiation in the f2-layer, and large heat\nconductivity cause intense diurnal density and temperature variations above"}, {"doc_id": 621, "text": "latitude and diurnal variations of air densities from 190 to 280 km.\nas derived from the orbits of discoverer satellites .\nvariations in air density between day and night in the region 190 to 280\n km are found to be small/less than about 25(/ . the presence of a\npossible region of local heating at about 220 km which disappears at\nnight . the night-time density profile conforms with a constant scale\nheight of 35/2/km.no definite variation of air density with latitude is\nevident apart from a possible increase of about 60(, which is indicated\nby rather limited polar-region data . for other latitudes and seasons a\nvariation of less than about 20( is indicated ."}, {"doc_id": 622, "text": "scale height in the upper atmosphere, derived from changes in satellite\norbits .\nthe'density scale height'h in the upper atmosphere is a measure of the\nrate at which air density p varies with height y, being given by\nh-p//dp/dy/ . the value of h, although important because/with the\nmolecular weight of the air/it determines the air temperature, has not\nas yet been well determined at heights above 200 km .\nthis note develops methods for finding h from the decrease in a\nsatellite's perigee height and from the decrease in the orbital period\nof a satellite in a small-eccentricity orbit . these methods are then\napplied to all the 14 satellites found suitable for the purpose . the 44\n values of h obtained, for heights of 200-450 km, represent an average\nover day and night and probably have errors/s.d./of 5-10( . it is found\nthat, as solar activity declined between 1957 and 1961, h decreased\ngreatly ..e.g.at height 275 km, h decreased from 60 km in early 1958 to\nheight becomes much less rapid above 350 km, and are consistent with the\n supposition that h had low values, near 35 km, at heights near 250 km,\nfor 1959-61 . the results could be greatly extended in scope and\nimproved in accuracy if more accurate orbits were available for\nshort-lifetime satellites ."}, {"doc_id": 623, "text": "on the coupling between heat and mass transfer .\nin mixtures of two different gases or liquids, one constituent\nwill migrate spontaneously toward the warmer parts, and\nthe other toward the colder parts . this phenomenon, known\nas the soret effect, and its converse the dufour effect, were\ndiscovered as early as 1856 and 1873 respectively . the two\neffects can also be considered as a simultaneous transport of\nmass and heat, or as a coupling between heat and mass transfer .\nthe effects of this coupling have been neglected in all\ninvestigations of heat transfer in multicomponent flow systems so far,\non the a priori assumption that they are small . in a recent\npublication however, it was shown that they can be large in\nlaminar-boundary-layer-type flows with helium injection .\nturbulent-boundary-layer measurements and an analysis conducted\nat the heat transfer laboratory clearly showed significant\neffects of the coupling on heat transfer and adiabatic wall\ntemperature . from additional measurements, the results of which\nare presented below, it is possible to separate the heat flux at the\nmodel wall into one part depending on the temperature gradient\nand a second part caused by the coupling . it is shown that\nthe latter exceeds the former, and hence the coupling may not\nbe neglected a priori without careful consideration ."}, {"doc_id": 624, "text": "cruise performance of channel-flow ground effect machines .\n the performance theory for high-speed air-cushion vehicles\noperating in close proximity to the ground is developed . the\nanalysis is restricted to cruise flight of vehicles of rectangular\nplanform employing an air pressure seal between the ground and\nthe vehicle along the two streamwise sides . the variation of\nthe optimum rearward deflection angle of the side jet pressure\nseal with speed for minimum overall power expenditure and\nmaximum range is found . it is concluded that a mixed\npropulsion system (jet deflection plus propeller(s)) is required .\nvolume flow and the corresponding fan pressure rise needed are\nalso calculated . the maximum lift drag ratio is determined .\n the maximum thickness ratios of the vehicles are considered\nto be large compared with the ground-height vehicle-length\nratio . two-dimensional airfoil theory is employed to show that\nclose to stagnation conditions exist below the vehicles . the\nlower-surface lift, pitching moment, and aerodynamic-center\nlocation are determined .\n the flow over the upper surface is identified with flow over\nmounds . upper-surface lift coefficients are determined for\ntypical mound shapes .\n it is shown that high total lift coefficients are theoretically\nobtainable with almost zero induced drag . the conventional\ninduced-drag power penalty is replaced by a sealing-air power\nexpenditure, which is shown not to be excessive ."}, {"doc_id": 625, "text": "viscous and inviscid nonequilibrium gas flows .\n the condition of immediate freezing of the mass fraction of\ndissociated species of air at the equilibrium value behind the\nshock envelope prevails over a major portion of the flight\nspectrum associated with lifting re-entry vehicles . this is observed\nby means of order-of-magnitude considerations within the limits\nof the present knowledge of chemical reaction rates for the\nconstituents of air . accordingly, investigations of the viscous and\ninviscid hypersonic flow about blunt and sharp leading edge\nslender bodies are made . the investigations are generalized to\nconsider an arbitrary degree of dissociation in the ambient free\nstream . this condition is included in order to allow comparison\nwith the flow field about a model in the test section of a\nhypersonic facility with dissociated air species present in the free\nstream .\n inviscid frozen flow investigations are made for blunt and\nsharp leading edge slender body power-law geometries . the\nresults indicate that the influence of a finite leading edge, in\ninducing a pressure field far downstream (/blast-wave/ analogy),\nis considerably diminished for this model . this conclusion is\nverified numerically by a characteristics solution for the\nhypersonic flow about a /sonic-wedge/ slab .\n the viscous investigations consider the boundary-layer\ninteraction problem with a frozen degree of dissociation . in\nthis case, as in the inviscid analysis, the governing parameter is\nobserved to be the ratio of the\ndissociation energy to the free-stream kinetic energy . the\ninfluence of this parameter on the boundary-layer interaction\nmechanism for a highly cooled, noncatalytic wall is presented .\nthe influence of a frozen flow field on skin friction and heat\ntransfer is also discussed .\n finally, since higher mach number gas flows may be generated\nin wind tunnel nozzles where dissociation nonequilibrium effects\nare present, the possibility of employing expansions with a\ncontrolled degree of dissociation as a technique for aerodynamic\nsimulation is presented ."}, {"doc_id": 626, "text": "some features of supersonic and hypersonic flow about\nblunted cones .\n for a family of cones of various semiapex angles blunted by\nspherical caps, shock shapes and surface pressure distributions\nhave been obtained from both the belotserkovskii method and\nexperiment . these results are used to study convergence to\nconical flow . conditions leading to both overexpansion and\nunderexpansion on the surface with respect to the asymptotic\nconical pressures are described as well as conditions leading to\nbow shock inflection points . conditions also exist for which a\nsecond shock may occur, or for which the sonic line cannot touch\nthe body surface . the implications of these conditions for\nvarious blunt-body methods are discussed . for cones blunted\nin such a manner as to keep the flow entirely supersonic, the flow\nfield is found to exhibit certain similarities with that for genuine\nblunting . this is related to the fact that the surface entropy\nlayer for blunt bodies can be most influential, in determining\nsurface pressure, in the interior of the flow field rather than near\nthe surface ."}, {"doc_id": 627, "text": "flutter analysis of circular panels .\n the flutter problem of flat circular panels with edges elastically\nrestrained against rotation has been formulated in terms of\nsmall-deflection plate theory . the panel is subjected to uniform\nall-round tension or compression in its middle plane, in addition to\nthe supersonic compressible flow passing over its upper surface\nwith still air below . linear piston theory is employed to predict\nthe aerodynamic load on the vibrating panel .\n the problem is investigated by a rayleigh-type analysis\ninvolving chosen modes of the panel as degrees of freedom .\n in order to investigate the convergence of the solution, the\nflutter-mode shape of the clamped-edge panel has been expressed\nin a series form in powers of r cos o . the results of three-, four-,\nand five-term approximations have displayed oscillatory\nbehavior with apparently rapid convergence of the solution ."}, {"doc_id": 628, "text": "thermal effects on a transpiration cooled hemisphere .\n an approximate method is used to obtain the\ninjection distribution which would exist on an isothermal,\ntranspiration-cooled hemisphere in a supersonic stream .\nthis distribution is the same for both air and helium\ninjection, and is independent of the blowing level . a\nmodel having this distribution was tested in the naval\nsupersonic laboratory wind tunnel at a mach number\nof 3.53 . it is concluded that the design technique is\nreasonably accurate . data taken near the nose are\ncompared with the theories for air and helium\ninjection . the agreement in the case of the reduction in\nheat-transfer coefficient is good . the values of\ninsulated wall temperature obtained near the nose with\nhelium injection are 8 percent above the local\nstagnation temperature, and largely independent of injection\nrate . it is believed that this phenomenon may be\nattributed to the thermal diffusion of the helium within\nthe boundary layer . air injection causes a slight\nreduction in the insulated wall temperature . it is shown\nthat injection of either air or helium at the hemisphere\nnose considerably reduces the heat flux at the surface .\nthe additional reduction in heat flux resulting from\nhelium injection as opposed to air injection, and\npredicted by existing theory, is largely absent ."}, {"doc_id": 629, "text": "second-order effects in laminar boundary layers .\n second-order boundary layer disturbances are\ndue to the displacement of the main flow by\nthe boundary layer, surface curvature, freestream\nvorticity, and slip . a procedure for finding\nthese is given for compressible flow of a perfect gas\nhaving a classically similar boundary layer .\nsolutions are given for the flat plate and circular\ncylinder and for the hypersonic axisymmetric\nstagnation point . for the latter flow, the dominant\neffect is that of vorticity, which increases\nboth shear and heat flux . for the plate or cylinder,\nthe same conclusion tends to hold for high\nspeed flow . the vorticity effect is governed by the\nentire outer flow--not just the wall vorticity ."}, {"doc_id": 630, "text": "stagnation region in rarefied high mach number flow .\n paper describes results of numerical solution of the viscous\nshock-layer equations for axisymmetric stagnation region, using\nthe viscosity-temperature law with w=0.65, pr=0.71 and\ny=1.25 . purpose is to establish applicability of the simple\napproximation of w=1 (obtained earlier) to air at low reynolds\nnumbers and low ratios of wall temperature to stagnation\ntemperature . using a reference temperature (closely equal to\neckert's) to interpret the linear results, excellent agreement is found,\nin the limit of, over a wide range of reynolds numbers,\ncovering fully merged shock layers as well as boundary layers\nwith and without vorticity interaction . agreement with recent\nexperiments of ferri et al is as good as to be expected from\nshock-layer approximation . paper provides valuable extension of the\napplicability of the reference temperature concept ."}, {"doc_id": 631, "text": "low speed wind tunnel tests on a two dimensional aerofoil\nwith split flap near the ground .\n pressure distributions have been\nmeasured on a 10 thick two-dimensional\naerofoil of r.a.e.101 section fitted with\nsplit flaps deflected at 15 and 55 .\nmeasurements were made at two distances\nabove a ground plate, and also without\nthe ground plate . the results have been\nintegrated to give the sectional\nlift, drag and pitching-moment coefficients ."}, {"doc_id": 632, "text": "calculated lift distributions in incompressible flow\non some sweptback wings .\n in the course of a larger survey of some aerodynamic characteristics\nof a family of sweptback wings, the low-speed lift distributions were\ncalculated . the 35 planforms considered cover a range of leading-edge\nsweep angles from 55 to 70, and aspect ratios from 2 to 3.9 . the\nresults are given here, together with a comparison with other\ncalculations and with experimental results on one particular wing ."}, {"doc_id": 633, "text": "an extension of the method of generalised conical flows\nfor lifting wings in supersonic flow .\n the method of generalised conical\nflows has previously been developed\nsubject to the condition that the\nupwash divided by the streamwise\nco-ordinate to the power k, where\nk is the order of the conical flow, must\nhave vanishing (k+1)th derivative\nwith respect to the conical co-ordinate .\n in the present note this restriction is removed .\n the results are also used to\ndiscuss the effect of the application of\nthe leading edge attachment condition\non the wing pressure and geometry ."}, {"doc_id": 634, "text": "effects of leading edge bluntness on flutter characteristics\nof some square- planform double-wedge airfoils at a\nmach number of 15 .4.\n results are presented from a wind-tunnel\ninvestigation in helium flow at a\nmach number of 15.4 . the models were\nsquare-planform, double-wedge, shaft-mounted\nairfoils with leading- and trailing-edge\nradii of 0, 1, 3, and 6 percent chord .\nin general, the tests indicate that bluntness\neffects on the model flutter\ncharacteristics are stabilizing as the leading-edge\nradius is increased from 0 to\ndestabilizing with further increase in\nbluntness .\n results of flutter calculations made\nby using newtonian theory aerodynamics\nand a combination of newtonian theory and\npiston theory aerodynamics in\nconjunction with an uncoupled two-mode analysis\nare compared with experimental results .\nthe piston-theory results accurately\npredicted flutter speeds for the models with"}, {"doc_id": 635, "text": "heat transfer and pressure distributions on a hemisphere-cylinder and a\nbluff-afterbody model\nin methane-air combustion products and in air .\nan experimental investigation has been made to indicate the validity of\nusing methane-air combustion products as the test medium for aerodynamic\nheating and loading tests . tests were conducted on a\nhemisphere-cylinder and on a bluff-afterbody model, both in methane-air combustion\nproducts and in air alone, and covered a range of mach numbers from 6 to\nthe data showed that the nondimensional heating-rate distribution\nalong a hemisphere-cylinder as obtained in combustion products was in\ngood agreement with that obtained in air, and the results were in\nreasonable agreement with theory . the stagnation-point heating rates\nin air and in combustion products over the hemisphere-cylinder agreed\nwithin 10 percent of the theoretical values . the pressure\ndistributions around a hemisphere-cylinder obtained from tests in combution\nproducts were in good agreement with those obtained in air and could\nbe predicted by newtonian flow theory . the tests in combustion\nproducts of a bluff-afterbody model produced nondimensional\nheat-transfer coefficients which were in fair agreement with results\nobtained in air ."}, {"doc_id": 636, "text": "pressure distribution induced on a flat plate at a free-stream\nmach number of 1.39 by rockets exhausting upstream and downstream .\nan experimental investigation was made of the pressures induced on\na flat plate at a free-stream mach number of 1.39 by a supersonic\nrocket jet exhausting upstream and downstream . measurements of the\npressure distribution on a flat plate were made at zero angle of\nattack for 11 different locations of the jet exhaust nozzle beneath\nthe wing . measurements were made at ratios of rocket-exit total\npressure to free-stream static pressure from 6 to 60 and at a reynolds\nnumber per foot of approximately 10 times 10 to the power of 6 . the\nrocket when exhausted upstream produced a strong shock that moved\nfurther upstream with increasing rocket-exit total-pressure ratio .\npositive incremental normal-force coefficients were obtained at all test\npositions . data at 11 test positions are tabulated for rocket-on\nand rocket-off pressure coefficients as well as for incremental pressure\ncoefficients for the 48 orifices of the flat plate for the range of\nratio of rocket-exit total pressure to free-stream static pressure\nof the investigation . changing the location of the model with\nrespect to the plate had a negligible effect when the rocket was\nvaried in the chordwise direction, but the pressure coefficients\nwere reduced as the rocket was lowered away from the flat-plate wing ."}, {"doc_id": 637, "text": "an integral equation relating the general time-dependent lift and\ndownwash distributions on finite wings in subsonic flow .\nan integral equation for obtaining the unsteady air forces on finite\nwings in subsonic compressible flow is presented . this equation\nis applicable for any arbitrary time-dependent motion and can be\nutilized for flexible as well as rigid wings . the approach involves\nthe derivation of an integral equation relating the unknown pressure\nthe form of the equation is such that it should lend itself readily to\nmodern high-speed computers for obtaining pressure distributions .\nspecial cases of the integral equation are treated for two-dimensional\nincompressible flow and are presented in an appendix ."}, {"doc_id": 638, "text": "longitudinal aerodynamic characteristics at low subsonic\nspeeds of a highly swept wing utilizing nose deflection\nfor control .\n an investigation has been conducted\nin the langley 7- by 10-foot transonic\ntunnel at low subsonic speeds to determine\nthe longitudinal aerodynamic\ncharacteristics associated with deflection of the\nnose section of a highly swept delta\nwing having an aspect ratio of 1.33 . in order\nto illustrate the effectiveness of\nthis forward control, the longitudinal control\ncharacteristics are also presented\nfor the wing with upper-and lower-surface\nsplit flaps located at the trailing\nedge .\n comparison between the longitudinal\naerodynamic characteristics of the wing\nutilizing the nose control and those of\nthe wing utilizing the upper-surface\nsplit flap located at the trailing edge\nindicated similar control effectiveness\nfor high control deflections (15) and\nsimilar values of trimmed lift-drag ratio\nwith increasing lift coefficient . use\nof the nose control, however, indicated a\nlower value of trimmed angle of attack\nfor a given value of trimmed lift\ncoefficient than that realized from use of\nthe upper-surface split flap . further\nreductions in trimmed angle of attack\nfor a given value of trimmed lift\ncoefficient may be realized from deflection\nof the lower-surface split flap at the\nwing trailing edge in combination with\nthe nose control and would be accompanied\nby large reductions in lift-drag ratio ."}, {"doc_id": 639, "text": "analytical study of the tumbling motions of vehicles\nentering planetary atmospheres .\n the tumbling motion of vehicles\nentering planetary atmospheres is\nanalyzed . a differential equation\ngoverning the tumbling motion, its\narrest, and the subsequent oscillatory\nmotion is obtained and identified\nas the equation for the fifth painleve\ntranscendant . an approximate\nanalytical solution for the transcendant\nis derived . comparisons with\nresults obtained from numerical\nintegration of the exact equations of\nmotion indicate that the solution for the\nangle-of-attack history is\nsufficiently accurate to be of practical use ."}, {"doc_id": 640, "text": "the design of structures to resist jet noise fatigue .\nthe design of structures to resist jet noise fatigue demands a\nknowledge of a wide range of subjects from pure acoustics at one\nhand to metal physics at the other . at the present time the various\naspects of the problem are not sufficiently well know\nquantitatively for a purely theoretical design study to be made . never-\nthe-less a knowledge of the behaviour of typical forms of\nconstruction in noise environments can be used with a limited\namount of theoretical work to indicate tne most efficient types of\nstructure . this approach to the problem is adopted in this\nlecture as it seems to be the most promising one available at the\nmoment . it must be emphasized, however, that although some\nprogress has been made in dicsovering the behaviour of a\nstructure subjected to noise it is not possible to estimate the life\nof any component at the drawing board stage . some prototype\nstrain measurements and proof testing are therefore essential if\none is to prove the integrity of the design .\n within the structural limits of single skin construction set in\nthis lecture the main conclusion to be reached is that no\nreasonable estimate of fatigue life can yet be made in the drawing\nboard stage of a structure . nevertheless, a study of the form of\nbehaviour of typical structures has led to a theoretical\nsimplification of the problem of skin vibration . from this it has been\npossible to suggest an optimum deisgn for a skin stiffened by\nstringers . a suggestion for an optimum design of skin and rib\nfor control surfaces to minimise stresses at the rib-skin\nintersection is put forward but no experience can check this yet .\n the most resonable basis for the future estimation of\nfatigue life of a component appears to be the /random/ s-n\ncurve and consierable effort should be made to obtain the\nnecessary test data .\n the life expectation of a new design will be uncertain and\nsome proof testing is essential if the integrity of structure in high\nnoise levels (150 db) is to be guaranteed ."}, {"doc_id": 641, "text": "reduction of the clamped plate to two membrane problems\nwith an application to uniformly loaded sectors .\n the clamped plate problem in\nthe classical theory for the small\ndeflection bending of flat plates\nis reduced to the solution by variational\nmethods of two successive membrane\nproblems . the first requires the least\nsquare minimisation of the average\ncurvature of the deflected surface while\nthe second problem concerns the\nintegral of the gaussian curvature . there\nis a similar reduction for extensional\nproblems where the boundary tractions\nare specified .\n the method is demonstrated by\ngiving three distinct solutions to the\nproblem of the clamped sector under\na uniformly distributed load . one\nsolution is of special interest because\nit is derived from a single membrane\nproblem . numerical data are given ."}, {"doc_id": 642, "text": "the buckling strength of a uniform circular cylinder\nloaded in axial compression .\n the theoretical estimation of the buckling strength of a cylinder\nloaded in axial compression is improved by the use of a more\nrepresentative deflected form for the buckled cylinder than has\npreviously been used . kempner's buckling strength for dead weight\nloading is reduced by 18 . the presentation of the magnitude and\ndistribution of the constraint system required to maintain the mode is\nnovel and instructive ."}, {"doc_id": 643, "text": "an investigation of wing-aileron flutter using ground\nlaunched rocket models .\n control surface flutter of the\nwing torsion-control rotation type has\nbeen investigated for an unswept wing\nwith an under-massbalanced, half span,\noutboard aileron . thirteen pairs of\nwings were tested, using ground launched\nrocket driven vehicles, and a range of\nvalues of aileron natural frequency\nwas covered . the test results showed\nconsiderable scatter, but enabled\nupper and lower limits of a flutter\nboundary to be determined approximately .\nit was established that aileron flutter\ncould be eliminated on the models\ntested provided the aileron frequency\nexceeded the wing torsional frequency\nby 20 per cent or more . in this\ncondition the models were also free from\nsingle degree of freedom flutter"}, {"doc_id": 644, "text": "a study of the cantilever square plate subjected to\na uniform loading .\n plate problems involving free edges have been historically\ndifficult to solve, particularly when two free edges are adjacent,\nresulting in a free corner . the cantilevered square plate\nsubjected to a transverse loading is one such problem for which an\nexact solution has not been achieved .\n in the present paper results obtained by various approximate\nmethods are presented for this problem for the case of a uniform\nloading . solutions obtained by the authors using the technique\nof point matching and the rayleigh-ritz method are compared\nwith previously published finite-difference and experimental\nresults and with bernoulli-euler beam and plane-strain approaches .\nnumerical results for deflections, slope components, bending and\ntwisting moments, and transverse distributed shears are presented\nfor a relatively fine gridwork of points on the plate boundary\nand within the interior . the antielastic curvature is exhibited by\nall methods except beam theory . all methods present the\ninteresting conclusion that the free edge deflection is greater when\nthe plate is treated as a plate rather than a beam ."}, {"doc_id": 645, "text": "thermodynamic coupling in boundary layers .\n experimental results gathered in recent years for binary\nmixture mass transfer models are shown to yield consistent\nevidence of discrepancies with analytic considerations . specifically,\nmeasured recovery temperatures are appreciably higher than those\npredicted ,. while heat transfer coefficients are satisfactorily\nreproduced . it is shown on the basis of both approximate and exact\nsolutions for plates and stagnation points that the discrepancies in\nprevious results are related to thermal diffusion effects, a major\ninfluence being apparent in application of the surface boundary\ncondition for an adiabatic wall . as a result, some reexamination is\nnecessary of past criteria for mass addition effects as they pertain to\nspecific injected media . a prime example is the /equivalence/ of\nhelium and air as coolants despite the heretofore suggested preference\nfor low density injectants on a perfect gas basis . ref. 16 ."}, {"doc_id": 646, "text": "thermal diffusion effects on energy transfer in a turbulent\nboundary layer with helium injection .\n a circular cylinder with two-inch\ndiameter and with a porous wall\nfabricated out of woven wire material was\naligned with its axis parallel to an air\nstream with approximately 100 ft sec\nvelocity . helium gas was injected into\nthe turbulent boundary layer through\nthe cylinder walls at a uniform rate in\nthe range 1.55 x 10 to 1.08 x 10\nof the free stream mass velocity . the\nlocal energy transfer along the cylinder\nwas measured at various values of\nthe wall temperature level for the\nsituation that the energy flows from the\ncylinder to the boundary layer and\nvice versa . the results showed clearly\nthat the wall temperature for zero\nenergy transfer - the adiabatic wall\ntemperature - was larger than the free\nstream temperature by up to about 40 f,\nalthough viscous dissipation effects\nare negligible . this temperature excess\nincreases with increasing injection\nrate and is independent of reynolds\nnumber .\n an analysis in which the laminar\nsublayer is treated as couette flow\nwith helium injection and which includes\nthermal diffusion in this layer is\nformulated . the results show appreciable\nthermal diffusion effects on\nadiabatic wall temperature, increasing it\nover its value for zero injection\nby amounts of the same order of magnitude\nas found by measurements . thermal\ndiffusion however has negligible effects\non the heat transfer coefficient .\nits effects on the concentration and\ntemperature distribution are discussed\nand are shown to produce appreciable\nmodifications in the latter ."}, {"doc_id": 647, "text": "bending of a uniformly loaded rectangular plate with\ntwo adjacent edges and the others either simply supported\nor free .\n the distribution of deflection and bending moment in a\nuniformly loaded rectangular plate having two adjacent\nedges clamped and the others either simply supported or\nfree, are obtained by a method of superposition .\nnumerical values are given for square plates and, in one case, the\nresults are compared with those obtained by another\nmethod ."}, {"doc_id": 648, "text": "the approximate analysis of certain boundary value\nproblems .\na simple method is given which is suitable\nfor the approximate analysis of certain\nboundary-value problems, including, for\nexample, the small deflections of clamped\nplates and the torsion of prismatic bars .\nthe analysis is particularly simple and lends\nitself well to the use of the digital computer .\nthe method is applied here to four\nproblems, the uniformly loaded, clamped square,\nand equilateral-triangle plates, and the\ntorsion of bars of square and hexagonal cross\nsection . the results agree well with\nthe exact solutions, where these are known ."}, {"doc_id": 649, "text": "the hovercraft - a new concept in maritime transport .\n the hovercraft is the first operational british\nproject in the ground-effect machine field .\nalthough there has, for a number of years, been\na tentative searching after the principles\nunderlying such machines, it is only now that their\npossibilities as commercial transport and\nservice craft are beginning to be developed .\n since the hovercraft is a new vehicle, the appearance\nof the saunders-roe sr-n1, a manned\nexperimental craft, excited considerable public attention\nand there have been a number of\ndescriptive articles in the press . papers of a more\ntechnical type, on ground-effect machines,\nare now beginning to appear and it is to be expected\nthat these will rapidly increase in number,\nespecially since american interest in both the commercial\nand defence fields is expanding fast .\n the authors of the present paper have, therefore,\nconcentrated attention upon features\nabout which they had something personal to say, and\nwhich they consider to be of particular\nsignificance for assessing the possibility of the\nhovercraft becoming important in maritime\ntransport . these features\nare ..- the hovercraft as a fundamentally new\n principle in the transport field .\n the powering requirements and resistance\n characteristics .\n the likely operating costs of hovercraft\n in comparison with other forms of maritime transport .\nin addition, relatively brief descriptions of\nthe history and the current work being undertaken\non the ground-effect machine and of the design,\nconstruction, and testing of the saunders-roe\nsr-n1 are provided . the final section discusses\noutstanding problems and some future\npossibilities ."}, {"doc_id": 650, "text": "some design problems of hovercraft .\nanalysis of the influence various aerodynamic parameters have on\nthe performance of a simple peripheral jet system . power weight\nratio, lift drag ratio, and effect of jet angles and thickness are\neach considered . structural requirements, optimum cushion\npressure, and dynamic stability over waves are examined and then\nrelated to the economics of ground-effect machine operation ."}, {"doc_id": 651, "text": "heat transfer to separated and reattached subsonic\nturbulen flows obtained downstream of a surface step .\n local heat-transfer coefficients and recovery factors are\npresented for separated and reattached turbulent flows as obtained\nby a downward step in an otherwise flat surface in a two-\ndimensional, subsonic, air flow . the region downstream of the step,\nthe focus of this investigation, contained a region of separated\nflow with reattachment at about five step heights downstream,\nfollowed by a section of reattached flow . the salient feature of\nthe results is the maximum in the local heat-transfer coefficient\nat the reattachment point, with values thereof diminishing in the\nseparated region and also in the reattached region, where they\ntend toward values characteristic of turbulent boundary-layer\nflow . it is found that for most of the region the heat-transfer\ncoefficient depends on the velocity to about the 0.8 power, though\na decreased dependence may exist in the separated region .\nrecovery factors have the characteristically low values associated\nwith separated flows, and do not attain values typical of\nturbulent boundary-layer flows within the downstream lengths\navailable ."}, {"doc_id": 652, "text": "pressure distribution on two dimensional wings near\nthe ground .\n a simple method of calculating\nthe pressure distribution in\nincompressible flow on two-dimensional aerofoils\nof arbitrary section at moderate\ndistances from the ground is developed .\ncomparisons with an /exact/ potential\nflow solution, and with measurements\non a 10 thick aerofoil of rae.101\nsection, provide a satisfactory\nverification of the adequacy of the method ,.\nbut it is shown that it is necessary\nto take account of the boundary layer\non the aerofoil in the calculations ."}, {"doc_id": 653, "text": "transient magnetohydrodynamic duct flow .\n parallel flow of an electrically conducting viscous\nincompressible fluid in a rectangular duct with\ntransverse magnetic field is considered . the walls\nof the duct which are parallel and perpendicular\nto the imposed magnetic field are taken to be\nnonconducting and perfectly conducting, respectively .\nassuming the fluid to be at rest at the initial\nmoment, exact solutions for the velocity and magnetic\nfield components are obtained in the form of\nconvolution integrals taking the longitudinal pressure\ngradient as an arbitrary given function of time .\nlater, taking a step function for the pressure gradient,\nthese expressions are integrated . for this case,\nthe effect of the strength of the imposed magnetic\nfield on the development behavior of the flow is\nstudied . it is found that except for very large magnetic\nfields, the flows are over damped ."}, {"doc_id": 654, "text": "on the propagation and structure of the blast wave .\n part 1.\n as a continuation of part 1 (j. phys. soc. japan 8 (1953) 662), the\nsecond approximation for the propagation and structure of a blast\nwave is now discussed . the solution for r=1.4 is obtained by a\nnumerical method, using the results of the first approximation obtained\nin part 1 . by use of this solution, u-r curves, distance-time curves\nand the changing feature of distributions of velocity, pressure and\ndensity behind the shock front are discussed .\n further, the approximate solution of the equation is discussed by\na refinement of the wkb method due to imai ."}, {"doc_id": 655, "text": "effects of boundary layer displacement and leading edge bluntness on\npressure distribution, skin friction, and heat transfer of bodies at\nhypersonic speeds .\nresults are presented of an investigation to determine the effect of\nboundary-layer displacement and leading-edge bluntness on surfaces in\nhypersonic flow . the presence of the boundary layer and the blunt\nleading edge induce pressure gradients which in turn affect the skin\nfriction and heat transfer to the surface . methods for predicting these\n phenomena on two-dimensional surfaces are given and a brief review of\nrecent three-dimensional results is presented ."}, {"doc_id": 656, "text": "departure from dissociation equilibrium in a hypersonic nozzle .\nthe equations of motion for the flow of an ideal dissociating gas\nthrough a nearly conical nozzle have been solved numerically, assuming\na simple equation for the rate of dissociation, and a number of\ndifferent values of the rate constant . the results of these\ncalculations suggest that deviations from dissociation equilibrium will\noccur in the nozzle if the rate constant lies within a very wide range\nof values . they also suggest that once such a deviation has begun the\ngas will very rapidly/freeze/, so that the dissociation fraction will\nremain almost constant if the flow is expanded further, or even if it\npasses through a constant area test section . an approximate method\nof solution, making use of this property of sudden/freezing/of the flow,\n has been developed and applied to the problem of estimating the\ndeviations from equilibrium under a wide range of conditions . if all\nthe assumptions made in this report are accepted, then lack of\ndissociation equilibrium may be expected in the working sections of\nhypersonic wind tunnels and hypersonic shock tubes .\nit is shown, however, that the flow behind a normal shock wave in such a\n wind tunnel will not be greatly affected by any freezing that may take\nplace in the nozzle upstream of the shock wave . even so, the stand-off\ndistance of a shock wave in front of a blunt model may be quite\nsensitive to deviations from equilibrium ."}, {"doc_id": 657, "text": "interferometric studies of supersonic flows about truncated\ncones .\n fringe shifts on interferograms of flows at m=2.45\nabout variously truncated 15 (half-angle) cone\ncylinders in free flight in a pressurized range have been\nexamined for similarity of the flow fields, occurrence of\nscale effects, and convergence to conical flow . it was\nfound that flows over similar objects with equal tip\nreynolds numbers were similar and that convergence\nto conical flow occurred before the disturbance at the\ntip had been reflected the second time along\ncharacteristics to the body . density distributions have been\ndetermined, and a number of comparisons have\nbeen made with theoretical predictions ."}, {"doc_id": 658, "text": "review of panel flutter and effects of aerodynamic noise\npart i.. panel flutter .\nwith the development of high-speed aircraft and missiles, vibration\nof panels has become a problem of practical significance . many\nof the failures of the early german rockets after attaining supersonic\nspeed have been attributed to the development of such panel\noscillations . it appears this\nphenomenon is not of much concern in the subsonic\nspeed range., however, in the supersonic speed range panels may develop\noscillations which cause instability of the structure . this effect has\nbeen exhibited experimentally under controlled laboratory conditions\nmotion is limited and buckling may not be a serious design problem .\nin these cases panel flutter is still of importance because of its\neffect on the fatigue life and the allowable stresses for design of\nthe panel material .\nthe oscillations of panels may be due either to aerodynamic force\ninduced by the motion of the panel, or to aerodynamic noise, or\nbuffeting (irregular motion induced by turbulence in the flow) .\nthe interaction between aerodynamic forces and panel motions, usually\nreferred to as /panel flutter,/ has been investigated by several workers\nin recent years . since the problem is too complex to be dealt with\nin its entirety, simplifying assumptions have been made in these\ninvestigations . the literature is marked by a certain degree of\ncontroversy over the validity of these assumptions and the applicability of\nthe results obtained . a brief review of the literature with reference\nto several of the approximations made and the results obtained follows ."}, {"doc_id": 659, "text": "nonuniform shear flow past cylinders .\n a general method is described whereby\nan approximation of any desired degree\nof accuracy to the stream functions for\ntwo types of variable shear flows past\nfinite cylinders can be obtained . the two\nshear distributions in the free stream can\nbe approximated to the linear shear\ndistribution and the shear present in an\nunretarded incompressible boundary layer\nrespectively . in every case the stagnation\nstreamline is displaced from the position\nopposite the line of symmetry of the\ncylinder, and general expressions are\nobtained for this displacement . the line of\nsymmetry may be in the direction of\nor perpendicular to the direction of flow .\nthe two particular examples cited are\nthose of a general elliptic cylinder and\ncylinders of the form where and being the polar\ncoordinates, and 2p the maximum width\nof the cylinder ."}, {"doc_id": 660, "text": "the fundamental solution for small steady three dimensional\ndisturbances to a two dimensional parallel shear flow .\n after a brief review of methods of calculating the flow\nfields produced by disturbances in rotational basic flows,\nthe author points out a fundamental difficulty in the\ntreated as a perturbation of the disturbance field that\nwould occur if the basic flow were uniform) .. slow\nattenuation of the secondary-flow disturbance with distance\nfrom the obstacle . the author conjectured (same j. 1\nthe trouble was caused by nonuniform validity of the\napproximation sequence in the region far from the\nobstacle . the analogy with /stokes' and whitehead's\nparadoxes/ is mentioned, and a solution analogous to\noseen's is suggested, one in which disturbances, but not\nthe shear, are assumed to be small . in this paper, such a\nsolution is found, and is shown to overlap with the\nsmall-shear, secondary-flow solution . the basic flow is a parallel,\nsteady, inviscid, two-dimensional shear flow . the /\nfundamental solution/ due to a weak source is sought .\n the method of fourier transforms is used . simple\nsolutions are found for a uniformly sheared basic flow (where\nthe result coincides with the secondary-flow solution) and\nfor an exponential basic-flow profile . in the general case\nit is assumed that the parallel basic flow becomes uniform\nat, where the x-axis lies in the flow direction .\nthe character of the solution is determined by studying\nits hankel transform, especially for the class of flows\nwhere the total variation of the basic stream speed v(y)\nis small . an interpretation in terms of images, due to\nm. b. glauert, is given, and finally the relationship of the\npresent work to theories of the displacement of the\nstagnation streamline (displacement effect of pitot\ntubes) is discussed ."}, {"doc_id": 661, "text": "summary of laminar boundary layer solutions for\nwedge-type flow over convection and transpiration cooled\nsurfaces .\n a summary of exact solutions of the\nlaminar-boundary-layer equations\nfor wedge-type flow, useful in estimating\nheat transfer to such\narbitrarily shaped bodies as turbine blades,\nis presented . the solutions are\ndetermined for small mach numbers and\na prandtl number at the wall of 0.7 ,.\nranges of mainstream pressure gradients\nand rates of coolant flow through\na porous wall are considered for the\nfollowing cases .. (1) small\ntemperature changes in the boundary layer\nalong a constant- and along a\nvariable-temperature wall, and (2) large\ntemperature changes in the boundary layer\nalong a constant-temperature wall .\n dimensionless forms of heat-transfer\nand friction parameters and\nboundary-layer thicknesses are tabulated .\nthe results indicate that\ncoolant emission and increased stream-to-wall\ntemperature ratios diminished\nthe friction and heat transfer for a\nconstant wall temperature . for a\nvariable wall temperature with small\ntemperature differences in the\nboundary layer, the friction was unaffected,\nbut the heat transfer was greatly\nincreased for increased wall-temperature\ngradient . heat-transfer results\nin the literature reveal that transpiration\ncooling is much more effective\nfor prandtl numbers of the order of 5.0 than for 0.7 ."}, {"doc_id": 662, "text": "theoretical and experimental investigation of\naerodynamic-heating and isothermal heat transfer parameters on\na hemisphere nose with laminar boundary layer at supersonic\nmach numbers .\n the effect of a strong, negative\npressure gradient upon the local\nrate of heat transfer through a laminar\nboundary layer on the isothermal\nsurface of an electrically heated,\ncylindrical body of revolution with a\nhemispherical nose was determined from\nwind-tunnel tests at a mach number\nof 1.97 . the investigation indicated\nthat the local heat-transfer\nparameter, based on flow conditions\njust outside the boundary layer,\ndecreased from a value of 0.65 0.10 at\nthe stagnation point of the\nhemisphere to a value of 0.43 0.05 at the\njunction with the cylindrical\nafterbody . because measurements of the\nstatic pressure distribution over\nthe hemisphere indicated that the local\nflow pattern tended to become\nstationary as the free-stream mach number\nwas increased to 3.8, this\ndistribution of heat-transfer parameter is\nbelieved representative of all\nmach numbers greater than 1.97 and of\ntemperatures less than that of\ndissociation . the local heat-transfer\nparameter was independent of reynolds\nnumber based on body diameter in the\nrange from 0.6x10 to 2.3x10 .\n the measured distribution of\nheat-transfer parameter agreed within\ntheoretical distribution calculated with\nforeknowledge only of the pressure\ndistribution about the body . this\nmethod, applicable to any body of\nrevolution with an isothermal surface,\ncombines the mangler transformation,\nstewartson transformation, and thermal\nsolutions to the falkner-skan wedge-flow\nproblem, and thus evaluates the\nheat-transfer rate in axisymmetric\ncompressible flow in terms of the known\nheat-transfer rate in an approximately\nequivalent two-dimensional\nincompressible flow .\n measurements of recovery-temperature\ndistributions at mach numbers\nof 1.97 and 3.04 yielded local recovery\nfactors having an average value\nof 0.823 0.012 on the hemisphere which\nincreased abruptly at the shoulder\nto an average value of 0.840 0.012 on\nthe cylindrical afterbody . this\nresult suggests that the usual representation\nof the laminar recovery\nfactor as the square root of the prandtl\nnumber is conservative in the\npresence of a strong, accelerating pressure gradient ."}, {"doc_id": 663, "text": "viscous flow along a flat plate moving at high speeds .\n by the distortion of coordinates, it is shown that, in the case\nof supersonic viscous flow past a flat plate, the boundary-layer\nand simple wave theories can be combined to give a complete\nrepresentation of the velocity and pressure fields . consistent\nfirst-order solutions are considered . an expression for the\ninduced pressure on the plate, correct to the second order, is\nobtained . at high mach numbers the important parameter\nsatisfies the hypersonic similarity law ,. and for arbitrary mach and\nreynolds numbers and for different gases, the theoretical curve\ncorrelates closely the experimental data . asymptotic shock\ncurve and skin-friction coefficient are also deduced, but the\nexperimental verifications are yet to be made ."}, {"doc_id": 664, "text": "the boundary layer on a flat plate in a stream with\nuniform shear .\nthe incompressible laminar boundary layer\non a semi-infinite flat plate is\nconsidered, when the main stream has uniform\nshear . a solution is obtained for\nthe first two terms of an asymptotic solution\nfor small viscosity . it is shown that\none of the principal effects of free-stream\nvorticity is to introduce a modified\npressure field outside the boundary-layer region ."}, {"doc_id": 665, "text": "on the theory of hypersonic gas flow with a power law\nshock wave .\nplane and axisymmetric hypersonic gas flows are considered with shock\nwaves of very great intensity that have a power-law form . on the basis\nof an investigation of the portions of the flow with high entropy\nadjoining the surface of the body (not necessarily for a shock wave of the\ngiven form) it is shown that the use in the flow problem of the exact\nsolution for the corresponding unsteady self-similar gas motion requires\na supplementary refinement of the thickness of the high entropy layer .\na method is shown for introducing such a correction and constructing the\nshape of the body contour, on which is to be applied the pressure\ndistribution obtained on the basis of the theory of small disturbances ."}, {"doc_id": 666, "text": "blunt body heat transfer at hypersonic speed and low reynolds numbers .\nan analytical method for the determination of effect of shock curvature\non heat transfer in the region of the nose has been developed . it is\nshown that for practical body shape the viscous terms in the\nnavier-stokes equations are not important in the region of the flow far from\nthe wall, and the displacement thickness can be neglected . then the\nflow can be approximately represented by an inviscid-flow solution\nhaving as boundary conditions the body shape, which is not affected by\nthe reynolds number, and by a boundary-layer type of flow near the\nwall, having appropriate boundary conditions . this approach permits us\nto determine the heat transfer in the region of the nose even at very\nlow reynolds numbers .\nexperimental results are presented . the experimental results agree\nwith the values given by the analysis ."}, {"doc_id": 667, "text": "hypersonic shock layer theory of the stagnation region at low reynolds\nnumber .\ncheng, h.k.\nhypersonic flow at low reynolds number is studied utilizing the\nshock-layer concept . the present formulation takes into account the salient\nfeatures of the transport processes within the shock layer in a manner\nconsistent with the shock-layer approximation . the rankine-hugoniot\nshock relations are modified to include contributions due to heat\nconduction and viscous effects immediately behind the shock .\nthe specific problem of an axisymmetric stagnation region is treated .\nthe flow regimes for this problem can be classified according to whether\n or not the transport effects are important immediately behind the\nshock . in one regime where the ordinary rankine-hugoniot relations hold\n across the shock, the vorticity-interaction theory based on the\nboundary-layer approximation is shown to be sufficient . in the other\nregime where the rankine-hugoniot relations have to be modified but the\ncontinuum-flow model applies, an approximate, an analytical solution is\nobtained . this solution reveals a substantial reduction of the\ntemperature behind the shock and of the shock stand-off distance in the\npresence of strong surface cooling .\nthe present study is intended to provide a knowledge to bridge the gap\nbetween the free-molecule flow regime and that of the boundary layer via\n the continuum theory . in this respect, the solution obtained appears\nto be satisfactory in that it yields the correct free-molecule limits\nfor the skin friction and surface-heat transfer rate ."}, {"doc_id": 668, "text": "measurements of stagnation point heat transfer at low\nreynolds number .\n measurements of stagnation point heat transfer are presented\nin the reynolds number range between the free molecular flow\nand the range where modified boundary layer theory still applies .\nthe measurements are compared with the analytical methods\nset forth by ferri, zakkay, and ting . the results show smooth\ntransition between the two regions and indicate that the\npredicted reynolds number for which the modified boundary layer\ntheory can be used is in agreement with experiments . in the\nlower range of reynolds number the ratio of\ndecreases and reaches a value of 1 at a reynolds number of 40 ."}, {"doc_id": 669, "text": "subsonic potential flow past a sphere inside a cylindrical duct .\nthe subsonic potential flow of a compressible fluid past a sphere\nin an infinite medium was first determined by rayleigh . subsequently,\ncaplan and tamada extended the solution to include the fourth power\nof the mach number . to the author's knowledge, no solution for\nsubsonic flow past a sphere in a finite medium has been published . it\nis the purpose of this note to present a solution for subsonic\npotential flow past a sphere inside a circular cylindrical duct ."}, {"doc_id": 670, "text": "on blunt-body heat transfer at hypersonic speed and low reynolds\nnumber .\na discussion of differences arising between experimental and analytical\nresults, in particular those due to inconsistencies introduced in the\npresentation of data and the way the comparison is made ."}, {"doc_id": 671, "text": "pressure and boundary-layer measurements on a two dimensional wing at\nlow speed .\nresults are given of pressure measurements and boundary-layer traverses\non a two-dimensional wing with 10 per cent rae 101 section at reynolds\nnumbers of 1.6x10 and 3.2x10 . these results which have been integrated\nto give lift, drag and aerodynamic-centre characteristics, are used to\ncheck some calculation methods for the growth of the turbulent boundary\nlayer and for the effect of a known boundary layer on the pressure\ndistribution .\nit is concluded that the calculation of the boundary layer still needs a\nlittle refinement before it is accurate enough to predict viscosity\neffects on pressure distribution, lift, drag and aerodynamic center,.but\n that these effects can be calculated if the actual boundary-layer\ncharacteristics are known ."}, {"doc_id": 672, "text": "tunnel interference effects .\nthe problems of solid blockage, wake blockage, lift effect, and the\ninfluence of boundary constraint at high mach number are considered in\ndetail . corrections are given for various open and closed tunnels,\nrectangular, circular and octagonal, and different speeds, two and\nthree dimensional flows, with several aerofoils and wings . other\ninterferences include the wall boundary layer, gradient of static\npressure and problems with the working fluid used ."}, {"doc_id": 673, "text": "investigation of full scale split trailing edge wing\nflaps with various chords and hinge locations .\n an investigation was conducted in the n. a. c. a.\nfull-scale wind tunnel on a small parasol monoplane\nequipped with three different split trailing-edge wing\nflaps . the object of the investigation was to determine\nand correlate data on the characteristics of the airplane\nand flaps as affected by variation in flap chord, flap\ndeflection, and flap location along the wing chord . the\nchords of the flaps were 10, 20, and 30 percent of the\nwing chord and each flap was tested at deflections from 0\nto 75 when located successively at 68, 80, and 88.8\npercent of the wing chord aft of the leading edge . the\ninvestigation included force tests, pressure-distribution\ntests, and downwash surveys . the results give the lift,\nthe drag, and the pitching-moment characteristics of the\nairplane, the flap forces and moments, the pressure\ndistribution over the flaps and wing at one section,\nand the downwash characteristics of the flap and wing\ncombinations .\n an increase in flap chord or distance of the flap from\nthe leading edge of the wing increased the lift of the\nairplane but had an adverse effect on the wing pitching\nmoment . the ld ratio of the airplane decreased with\nincrease in flap deflection or flap chord . flap\nnormal-force coefficients were primarily a function of flap\ndeflection and were relatively independent of flap chord,\nhinge-axis location, and airplane attitude . the location of\nthe flap center of pressure in percentage of flap chord aft of\nthe hinge axis remained practically constant\nirrespective of airplane attitude and of flap deflection, chord, or\nlocation . flap hinge-moment coefficients varied with a\npower of flap chord greater than the square so that with\nregard to hinge moments narrow flaps were the most\nefficient in producing a given increase in lift .\n split trailing-edge flaps materially affected the\nmagnitude and distribution of pressures over the entire wing\nprofile . at low angles of attack the predominant effect\nof the flaps was to increase positively the lower-surface\npressures ,. at high angles of attack, to increase negatively\nthe upper-surface pressures . downwash surveys\nindicated that horizontal tail planes located above the wing\nchord line would be more effective than those below the\nchord in counteracting the increased diving moment of\nthe airplane with flaps deflected ."}, {"doc_id": 674, "text": "the shapes and lift-dependent drags on some sweptback\nwings designed for m= 1. 2.\n the camber and twist distributions\nneeded to produce a constant\nspan-wise -distribution and certain linear\nchordwise load distributions have\nbeen calculated by linearised supersonic\ntheory at for a set of 34\nthin sweptback wings . the wing planforms\ncover a range of aspect ratios\nfrom 2.0 to 3.5 and leading-edge sweep\nangles from 55 to 70 . both leading\nand trailing edges are subsonic at the\ndesign mach number, and the\nslenderness parameter is between 0.19 and 0.40 .\n the lift-dependent vortex and wave\ndrags associated with these loadings\nhave also been calculated, and appear not\nto be excessive in almost all the\ncases considered ."}, {"doc_id": 675, "text": "pressure distribution and surface flow on 5( and 9( thick wings with\ncurved tip and 60degree sweepback .\nextensive tables are given of pressure coefficients measured at reynolds\n numbers from 1.3x10 to 3.9x10 on two half-models of identical planform\nwith 5( rae 101 and 9( rae 101 streamwise sections . the planform of\naspect ratio 3.899 has a straight trailing edge with 60degree of\nsweepback, constant chord over most of the span and a parabolic outer portion\nof the leading edge curving to a pointed tip . the overall wing\ncharacteristics are obtained from integrated normal pressures and are\ncompared with lifting-surface theory .\nthe low-speed experimental pressure distributions and surface oil-flow\npatterns are analysed and discussed in relation to the onset of\nseparation and the distinct vortex flows that develop at high\nincidence . series of contrasting upper-surface isobars illustrate some\nfeatures of the different stalling processes of the two wings . the\ndirect influence of the main vortex on local surface pressures is\nassessed in general terms . a fuller appraisal of secondary surface flow\n is obtained from the oil patterns, observations in water and\nmeasurements of high suction near the trailing edge .\nstudies of the extent of leading-edge stall and location of part-span\nvortices, in particular two simultaneous leading-edge vortices on the\nthinner wing, follow from further analysis of local surface pressures .\nafter a detailed discussion of the effect of reynolds number and the\ndistinct types of separated flow, a few results with leading-edge\nroughness are considered in relation to scale effect on separation and\nthe extensive influence of part-span roughness ."}, {"doc_id": 676, "text": "a simple method for calculating the span and chordwise loading on\nstraight and swept wings of any aspect ratio at subsonic speeds .\nthe methods of the classical aerofoil theory are used to derive a\ngeneral theory for wings of any given planform . the load over the\nwhole surface of a given wing can be calculated at a given subcritical\nmach number, and the procedure is as simple and rapid as that of the\nclassical aerofoil theory . the calculated results are confirmed by\nexperiments ."}, {"doc_id": 677, "text": "methods for calculating the lift distribution of wings /subsonic\nlifting surface theory/ .\nthis report contains some fairly simple and economic methods for\ncalculating the load distribution on wings of any plan form based on\nthe conceptions of lifting surface theory . the computer work required\nis only a small fraction of that of existing methods with comparable\naccuracy . this is achieved by a very careful choice of the positions\nof pivotal points, by plotting once for all those parts of the downwash\nintegral which occur frequently and by a consequent application of\napproximate integration methods similar to those devised by the author\nfor lifting line problems .\nthe basis of the method is to calculate the local lift and pitching\nmoment at a number of chordwise sections from a set of linear equations\nsatisfying the downwash conditions at two pivotal points in each\nsection . interpolation functions of trigonometrical form are used for\nspanwise integration both in setting up the downwash equations and in\ngetting the resultant forces on the wing from the local forces . the\npreliminary chordwise integrations for the downwash are predigested in\na series of charts/figs.1-6/,.it is these which make the method a\npractical computing proposition .\nthe theory is outlined in sections 2-5,.section 6 deals with the\nsolution of the linear equation and section 7 with the resultant forces\non the wing . some examples are worked out in section 8 to compare with\nother methods,. one solution is given in full detail in tables 8-30 as a\n guide for computers . appendices i-vi discuss more carefully some\nsalient points of the mathematical theory, and appendix vii is intended\nto instruct the computer how to carry out the steps of the calculation ."}, {"doc_id": 678, "text": "the effect of end plates on swept wings .\n existing methods of calculating\nthe effect of endplates on straight\nwings are modified so as to apply to\nswept wings . the changes in overall\nlift and drag, and also the spanwise\ndistribution of the additional load,\ncan be calculated .\n the theoretical results are\ncompared with experimental results\nobtained on swept wings, including\nnew measurements of lift, drag and\npitching moment, made on an untapered\n the method of calculation is also\nextended to cover the effect of\nthe tip vortex which is formed on wings\nwithout endplates ."}, {"doc_id": 679, "text": "low speed tests on 45 sweptback wings .\n this report contains the results\nof pressure measurements on three\nand aspect ratio 5, over an\nincidence range up to 10 . chordwise\nand spanwise lift distributions\nare given, mostly near the centre\nwhere, on two of the wings,\nmodifications had been made to the section\nshape . it was found that altering\nthe thickness distribution in the\ncentre did not affect the loading but\nthat approximately straight isobars\ncould be obtained at values of\nbelow about 0.1 . by the incorporation\nof twist and camber in the central\npart the distortion of the lift\ndistribution in the centre could be\navoided at one particular incidence,\nand thus the same chordwise\ndistribution obtained over most of the span .\n twist and camber alone do not improve\nthe isobar pattern and\ntherefore a thickness modification would be\nneeded to give the desired\nlift distribution and isobar pattern at one\nparticular incidence .\n the results of experimental investigations\nof the boundary layer\nand of the effect of aspect ratio will be given\nin a later report ."}, {"doc_id": 680, "text": "generalized conical flow fields in supersonic wing theory .\nlinearized, compressible-flow analysis is applied to the study of\nquasi-conical supersonic wing theory . single-integral equations are\nderived which relate either the loading to the shape of a lifting\nsurface or the thickness of a symmetrical wing to the pressure\ndistribution for triangular wings with subsonic leading edges . the forms of\nthese equations and their inversions are simplified through the\nintroduction of the finite part and the generalized principal part of an\nintegral .\napplications of the theory, in the lifting case, include previously\nknown results . in the nonlifting case, it is shown that for a specified\n pressure distribution the theory does not always predict a unique\nthickness distribution . this is demonstrated for a triangular plan form\n having a constant pressure gradient in the stream direction ."}, {"doc_id": 681, "text": "integrals and integral equations in linearized wing theory .\nthe formulas of subsonic and supersonic wing theory for source, doublet,\n and vortex distributions are reviewed, and a systematic presentation is\n provided which relates these distributions to the pressure and to the\nvertical induced velocity in the plane of the wing . it is shown that\ncare must be used in treating the singularities involved in the analysis\n and that the order of integration is not always reversible . concepts\nsuggested by the irreversibility of order of integration are shown to be\n useful in the inversion of singular integral equations when operational\n techniques are used . a number of examples are given to illustrate the\nmethods presented, attention being directed to supersonic flight\nspeeds ."}, {"doc_id": 682, "text": "the lift of twisted and cambered wings in supersonic flow .\na generalised conical flow theory is used to deduce an integral equation\n relating the velocity potential on a delta wing/with subsonic leading\nedges/to the given downwash distribution over the wing . the complete\nsolution of this integral equation is derived . this complete solution\nis composed of two parts, one being symmetric and the other\nantisymmetric with respect to the spanwise co-ordinate,. each part\nrepresents a velocity potential . for example, if y is the spanwise\nco-ordinate and x is measured in the free stream direction, then a\ndownwash of the form w-a ux/y/is symmetric and will give rise to a\nsymmetric potential, whereas w-a ux/y/sgn y is anti-symmetric and gives\nrise to an anti-symmetric potential . the velocity potentials of such\nflows are given in the form of tables for all downwashes up to and\nincluding homogenous cubics in the spanwise and streamwise\nco-ordinates . table iii gives similar formulae in the limiting case\nwere used over a cycle of the tumbling motion . the analytical\nexpression was in good agreement with numerical solutions of the complete\nnon-linear equations of motion ."}, {"doc_id": 683, "text": "the use of conical camber to produce flow attachment at the leading\nedge of a delta wing and to minimize the lift-dependent drag at sonic\nand supersonic speeds .\nin an attempt to avoid flow separation at the leading edge of a thin\ndelta wing with subsonic leading edges, an attachment line is prescribed\n there . this is done by requiring the load, as predicted by attached\nflow theory, to vanish along the leading edge at the design lift\ncoefficient . for sonic speed, a complete account of this flow is given\nin terms of slender wing theory and the load distributions corresponding\n to arbitrary conical camber are calculated . for supersonic speeds\nload distributions arising in the slender wing theory are considered and\n the corresponding conical camber distributions are found by linearized\ntheory . the lift-dependent drag for a given lift is then minimized with\n respect to the coefficients of a linear combination of these load\ndistributions . it is found that the lift-dependent drag factor for these\nconically cambered wings approaches the value it takes for the attached\nflow/in which leading edge suction occurs/past the uncambered wing at\nthe same mach number, as more terms are included in the linear\ncombination . however, when the leading edge is almost sonic an appreciable\nreduction is predicted . the corresponding load distributions and wing\nshapes are calculated and drawn . the optimum shapes for a fixed number\nof terms resemble flat plates drooped downwards near their edges, so\nthat the localised leading edge suction is replaced by a distributed\nforce on a forward-facing surface, producing an effect of similar\nmagnitude ."}, {"doc_id": 684, "text": "tables of complete elliptic integrals .\nthe present paper contains a set of tables of complete elliptic\nintegrals computed and collected especially for applications to certain\ndynamical problems .\nthe tabulated functions are four in number and are denoted by\nf/a/, g/a/, e/a/, and/a,b/respectively . the definitions of these\nfunctions and their connections with the functions of legendre will be\ndiscussed in the following ."}, {"doc_id": 685, "text": "aerodynamic effects of some configuration variables\non the aeroelastic characteristics of lifting surfaces\nat mach numbers from 0. 7 to 6. 86 .\n results of flutter tests on\nsome simple all-movable-control-type\nmodels are given . one set of models,\nwhich had a square planform with\ndouble-wedge airfoils with four\ndifferent values of leading- and\ntrailing-edge radii from 0 to 6 percent chord\nand airfoil thicknesses of 9, 11,\nat mach numbers from 0.7 to 6.86 .\nthe bending-to-torsion frequency\nratio was about 0.33 . the other set of\nmodels, which had a tapered planform\nwith single-wedge and double-wedge\nairfoils with thicknesses of 3, 6, 9,\nand 12 percent chord, was tested\nat mach numbers from 0.7 to 3.98 and\na frequency ratio of about 0.42 .\n the tests indicate that, in general,\nincreasing thickness has a\ndestabilizing effect at the higher mach\nnumbers but is stabilizing at\nsubsonic and transonic mach numbers .\ndouble-wedge airfoils are more\nprone to flutter than single-wedge\nairfoils at comparable stiffness\nlevels . increasing airfoil bluntness\nhas a stabilizing effect on the\nflutter boundary at supersonic speeds\nbut has a negligible effect at\nsubsonic speeds . however, increasing\nbluntness may also lead to\ndivergence at supersonic speeds .\n results of calculations using\nsecond-order piston-theory aerodynamics\nin conjunction with a coupled-mode\nanalysis and an uncoupled-mode analysis\nare compared with the experimental\nresults for the sharp-edge airfoils at\nsupersonic speeds . the uncoupled-mode\nanalysis more accurately predicted\nthe flutter characteristics of the\ntapered-planform models, whereas the\ncoupled-mode analysis was somewhat\nbetter for the square-planform models .\nfor both the uncoupled- and coupled-mode\nanalyses, agreement with the\nexperimental results improved with\nincreasing mach number . in general,\nboth methods of analysis gave unconservative\nresults with respect to the\nexperimental flutter boundaries ."}, {"doc_id": 686, "text": "flutter tests of some simple models at a mach number\nof 7. 2 in helium flow .\n results of hypersonic flutter\ntests on some simple models are\npresented . the models had rectangular\nplan forms of panel aspect ratio 1.0,\nno sweepback, and bending-to-torsion\nfrequency ratios of about . two\nairfoil sections were included in the\ntests ,. double wedges of 5-, 10-,\nand 15-percent thickness and flat plates\nwith straight, parallel sides\nand beveled leading and trailing edges .\nthe models were supported by a\ncantilevered shaft .\n the double-wedge wings were tested\nin helium at a mach number of 7.2 .\nan effect of airfoil thickness on flutter\nspeed was found, thicker wings\nrequiring more stiffness to avoid flutter .\na few tests in air at a mach\nnumber of 6.9 showed the same thickness\neffect and also indicated that\ntests in helium would predict conservative\nflutter boundaries in air .\nthe data in air and helium seemed to be\ncorrelated by piston-theory\ncalculations . piston-theory calculations\nagreed well with experiment for\nthe thinner models but began to deviate\nas the thickness parameter\napproached and exceeded 1.0 .\n a few tests on flat-plate models\nwith various elastic-axis locations\nwere made . piston-theory calculations\nwould not satisfactorily predict\nthe flutter of these models, probably\nbecause of their blunt leading\nedges ."}, {"doc_id": 687, "text": "oscillating airfoils at high mach number .\na simple formula is given for the pressure distribution on an\noscillating airfoil in two-dimensional flow at high mach number . the\nformula is expected to be reasonably accurate if the pressure on the\nsurface remains within the range 0.2 to 3.5 times the mainstream\npressure . to illustrate the application of the formula, some results\nfor symmetrical airfoils performing pitching oscillations are obtained\nand compared with results obtained from existing theories in the case of\n high mach number ."}, {"doc_id": 688, "text": "tables of aerodynamic coefficients obtained from developed newtonian\nexpressions for complete and partial conic and spheric bodies at\ncombined angles of attack and sideslip with some comparisons with\nhypersonic experimental data .\nclosed-form expressions and tables composed from these expressions are\npresented for complete and partial conic and spheric bodies at combined\nangles of attack and sideslip in newtonian flow . aerodynamic\ncoefficients of these bodies are tabulated for various body segments\nover a range of angles of attack from 1degree to 85degree and angles of\nsideslip from 0degree to 15degree .\nsome comparisons between newtonian predictions and hypersonic\nexperimental aerodynamic characteristics were made for conic bodies\nhaving various surface slopes, nose bluntnesses, and body cross sections\n to indicate the range of validity of the theory . in general, the\ntheory is shown to agree quite well with experimental results for\nsharp-nose complete cones and for configurations having large blunted\nnoses and steep surface slopes . however, agreement between theory and\nexperiment generally is poor for the more slender, slightly blunted\ncomplete or half conic bodies and also for sharp-nose half conic bodies\nwhere real-flow phenomena such as forebody interference, viscous forces,\n leeward surface contributions, or leading-edge pressure reductions may\nhave significant effect . the agreement between theory and experiment\nfor the bodies considered can be improved by using the stagnation\npressure coefficient behind a normal shock rather than 2 as the newtonian\ncoefficient, although for the sharp-nose half conic bodies there is no\ntheoretical justification for this modification ."}, {"doc_id": 689, "text": "investigation of the laminar aerodynamics heat transfer\ncharacteristics of a hemisphere cylinder in the langley\n11-inch hypersonic tunnel at a mach number of 6. 8.\n a program to investigate the aerodynamic heat transfer of a\nnonisothermal hemisphere-cylinder has been conducted in the\nlangley 11-inch hypersonic tunnel at a mach number of 6.8\nand a reynolds number from approximately 0.14x10 to\nexperimental heat-transfer coefficients were slightly less over the\nwhole body than those predicted by the theory of stine and\nwanlass (naca technical note 3344) for an isothermal\nsurface . for stations within 45 of the stagnation point the\nheat-transfer coefficients could be correlated by a single relation\nbetween local stanton number and local reynolds number .\n pitot pressure profiles taken at a mach number of 6.8 on a\nhemisphere-cylinder have verified that the local mach number or\nvelocity outside the boundary layer required in the theories may\nbe computed from the surface pressures by using isentropic flow\nrelations and conditions immediately behind a normal shock .\nthe experimental pressure distribution at a mach number of\nvelocity gradients calculated at the stagnation point by using\nthe modified newtonian theory vary with mach number and\nare in good agreement with those obtained from measured\npressures for mach numbers from 1.2 to 6.8 .\n at the stagnation point the theory of sibulkin, in which the\ndiameter and conditions behind the normal shock were used,\nwas in good agreement with the experiment when the velocity\ngradient at the stagnation point appropriate to the free-stream\nmach number was used ."}, {"doc_id": 690, "text": "investigaion of the flow over a spiked-nose hemisphere\ncylinder at a mach number of 6. 8.\n the shape and nature of the\nflow over a spiked-nose\nhemisphere-cylinder was studied in detail\nat a nominal mach number of 6.8 and in a\nreynolds number range (based on\ndiameter and stream conditions ahead of\nthe model) of 0.12 x 10 to 1.5 x 10 .\nschlieren photographs showed\nthe effect of varying the spike length\nand reynolds number upon the shape\nof the separated boundary and upon the\nlocation of transition . the heat\ntransfer and pressure distribution over\nthe body were then correlated\nwith the location of the start of\nseparation, the location of\nreattachment, and the location of the start of\ntransition ."}, {"doc_id": 691, "text": "calculation procedure for thermodynamic transport, and flow properties\nof the combustion products of a hydrocarbon fuel mixture burned in air\nwith results for ethylene-air and methane-air mixtures .\na procedure is presented whereby the composition, thermodynamic\nproperties, and transport properties of the dissociated combustion\nproducts of a fuel consisting of a mixed hydrocarbon compound burned in\nair may be calculated . equations and procedures for determining\nsupersonic nozzle ordinates and flow properties for the dissociated\ncombustion products are presented in an appendix . results are presented\nfor the respective hydrocarbon fuels, methane and ethylene, at the\nequivalence ratios of 1.0, 0.9, 0.8, and 0.7 for pressures varying\nbetween 10 and 8 x 10 atmospheres and temperatures from 200degree k to"}, {"doc_id": 692, "text": "investigation of the jet effects on a flat surface downstream of the\nexit of a simulated turbojet nacelle at a free-stream mach number of\n2.02 .\nan investigation at a free-stream mach number of 2.02 was made to\ndetermine the effects of a propulsive jet on a wing surface located in\nthe vicinity of a choked convergent nozzle . static-pressure surveys\nwere made on a flat surface that was located in the vicinity of the\npropulsive jet . the nozzle was operated over a range of exit pressure\nratios at different fixed vertical distances from the flat surface .\nwithin the scope of this investigation, it was found that shock waves,\nformed in the external flow because of the presence of the propulsive\njet, impinged on the flat surface and greatly altered the pressure\ndistribution . an integration of this pressure distribution, with the\nlocation of the propulsive jet exit varied from 1.450 propulsive-jet\nexit diameters to 3.392 propulsive-jet exit diameters below the wing,\nresulted in an incremental lift for all jet locations that was equal to\nthe gross thrust at an exit pressure ratio of 2.86 .\nthis incremental lift increased with increase in exit pressure ratio,\nbut not so rapidly as the thrust increased, and was approximately\nconstant at any given exit pressure ratio ."}, {"doc_id": 693, "text": "investigation of jet effects on a flat surface downstream of the exit of\n a simulated turbojet nacelle at a free-stream mach number of 1.39 .\nan investigation at a free-stream mach number of 1.39 utilizing a\nblowdown-type tunnel was made to determine the effects of a propulsive\njet on a zero angle-of-attack wing surface located in the vicinity of\nboth a choked convergent nozzle and a convergent-divergent nozzle .\nstaticpressure surveys were made on a flat surface that was located in\nthe vicinity of the propulsive jet . the nozzles were operated over a\nvaried range of both exit static- and total-pressure ratios at different\nwithin the scope of this investigation, it was found that shock waves,\nformed in the external flow because of the presence of the jet exhaust,\nimpinged on the flat surface and greatly altered the pressure\ndistribution . an integration of this pressure distribution for the choked\nconvergent nozzle, with the location of the propulsive-jet exit varied\nfrom 1.747 jet-exit diameters to 4.981 jet-exit diameters below the wing\n surface, resulted in a positive incremental normal force on the wing at\n all positions ."}, {"doc_id": 694, "text": "pressure distribution induced on a flat plate by a supersonic and sonic\njet exhaust at a free-stream mach number of 1.80 .\nas a continuation of previous research at mach numbers of 2.02 and 1.39,\n an experimental investigation was made of the pressures induced on a\nflat plate by a propulsive jet exhausting from sonic and supersonic\nnozzles at a free-stream mach number of 1.80 . measurements of the\npressure distribution on a flat-plate wing were made at zero angle of\nattack for four different locations of the jet exhaust nozzle beneath\nthe wing . both a choked convergent nozzle and a convergent-divergent\nnozzle on the nacelle were used . the nozzles were operated at\nnacelle-exit total-pressure ratios from 2 to 16 and the reynolds number per foot\n was approximately 13 x 10 .\ntwo distinct shock waves impinged on the wing surface and greatly\naltered the pressure distribution at all nozzle positions . positive\nincremental normal force resulted on the wing at all positions .\ncomparisons are presented for two free-stream mach numbers ."}, {"doc_id": 695, "text": "some experiments relating to the problem of simulation of hot jet\nengines in studies of jet effects on adjacent surfaces at a free-stream\nmach number of 1.80 .\nan investigation at a free-stream mach number of 1.80 in a blowdown type\n tunnel was made to study the effect on the pressure distribution of a\nzero angle of attack wing surface when certain exhaust parameters of a\nhot turbojet engine are varied . static-pressure surveys were made on a\nwing surface that was located in the vicinity of a small-scale\npropulsive jet . this propulsive jet was operated with four types of jet\nexhausts . these jet exhausts were a hot jet /hydrogen burned in air/, a\n cold air jet, a cold helium jet, and a jet composed of a mixture of two\n cold gases /hydrogen and carbon dioxide/ . the hot jet, because of its\nhigh exhaust temperature /3,300degreer/ and because combustion was\nperformed in air, was believed reasonably able to simulate the exhaust\nparameters of an actual afterburning turbojet engine . the cold jets\nused were selected in order that the effects of a variation in the\nexhaust parameters of jet-exit static-pressure ratio, ratio of specific\nheats, density, and velocity, could be obtained by comparing each cold\njet with the hot jet or with another cold jet . the tests were made over\n a range of jet-exit staticpressure ratios from 1 to 9 with values of\nthe ratio of specific heats of 1.27, 1.40, and 1.66 and at variations in\n density and velocity of the order of approximately 8 and 3 times,\nrespectively .\nwithin the scope of this investigation, it was found that jet-exit\nstatic-pressure ratio and the ratio of specific heats affected the\npressure distribution on the wing associated with jet interference while\n a variation in exit velocity and density did not . the jet-exit\nstaticpressure ratio affected the wing pressure distribution in a major\nway while the ratio of specific heats had only a minor effect . the\naddition of temperature in the propulsive jet exhaust at a jet-exit\nstaticpressure ratio of 4 had little or no effect on the pressure\ndistribution associated with jet interference on the wing ."}, {"doc_id": 696, "text": "pressure loads produced on a flat-plate wing by rocket jets exhausting\nin a spanwise direction below the wing and perpendicular to a\nfree-stream flow of mach number 2.0 .\nan investigation at a reynolds number per foot of 14.4 x 10 was made to\ndetermine the pressure loads produced on a flat-plate wing by rocket\njets exhausting in a spanwise direction beneath the wing and\nperpendicular to a free-stream flow of mach number 2.0 . the ranges of the\nvariables involved were /1/ nozzle types - one sonic /jet mach number of\ntwo-dimensional supersonic /jet mach number of 1.71/,. /2/ vertical\nnozzle positions beneath the wing of 4, 8, and 12 nozzle-throat\ndiameters,. and /3/ ratios of rocket-chamber total pressure to\nfree-stream static pressure from 0 to 130 .\nthe incremental normal force due to jet interference on the wing varied\nfrom one to two times the rocket thrust and generally decreased as the\npressure ratio increased . the chordwise coordinate of the\nincremental-normal-force center of pressure remained upstream of the nozzle center\nline for the nozzle positions and pressure ratios of the investigation .\n the chordwise coordinate approached zero as the jet vertical distance\nbeneath the wing increased . in the spanwise direction there was little\nchange due to varying rocket-jet position and pressure ratio . some\nboundary-layer flow separation on the wing was observed for the rocket\njets close to the wing and at the higher pressure ratios . the magnitude\n of the chordwise and spanwise pressure distributions due to jet\ninterference was greatest for rocket jets close to the wing and decreased as\nthe jet was displaced farther from the wing .\nthe design procedure for the rockets used is given in the appendix ."}, {"doc_id": 697, "text": "effects on adjacent surfaces from the firing of rocket jets .\nthis paper is a preliminary and brief account of some research currently\n being conducted to determine the jet effects on adjacent surfaces from\nthe firing of rocket jets . measurements of jet-effect pressures on a\nflat plate as well as shadowgraphs are presented that were obtained when\n a rocket jet at a mach number of 3 was exhausted downstream and\nupstream into free-stream flow at a mach number of 2 located from 2 to 4.7\n rocket-jet-exit diameters from the plate . the jet effects on the flat\nplate with the rocket jet exhausting downstream are of the same order of\n magnitude as those previously obtained from sonic exits with a total\npressure 10 times lower . a maximum pressure coefficient on the plate of\nrocket-jet-exit diameters below the plate, and an integration of the\nmeasured jet-effect pressures at this position resulted in a normal\nforce on the plate equal to 2.3 times the thrust output of the rocket\njet ."}, {"doc_id": 698, "text": "the unsteady lift of a wing of finite aspect ratio .\nunsteady-lift functions for wings of finite aspect ratio have been\ncalculated by correcting the aerodynamic inertia and the angle of attack of\n the infinite wing . the calculations are based on the operational\nmethod .\nthe starting lift of the finite wing is found to be only slightly less\nthan that of the infinite wing,. whereas the final lift may be\nconsiderably less . the theory indicates that the initial distribution of\nlift is similar to the final distribution .\ncurves showing the variation of lift after a sudden unit change in angle\n of attack, during penetration of a sharpedge gust, and during a\ncontinuous oscillation are given . operational equivalents of these\nfunctions have been devised to facilitate the calculation of lift under\nvarious conditions of motion . as an application of these formulas, the\nvertical acceleration of a loaded wing caused by penetrating a gust has\nbeen calculated ."}, {"doc_id": 699, "text": "approximate indical lift functions for several wings of finite span in\nincompressible flow as obtained from oscillatory lift coefficients .\nthe unsteady-lift functions for a wing undergoing a sudden change in\nsinking speed have been presented for delta wings having aspect ratios\nof 0, 2, and 4 and for rectangular and elliptical wings having aspect\nratios of 0, 3, and 6 . for the elliptical and rectangular wings the\nspanwise lift distributions were also presented . these functions were\ncalculated from the lift coefficients associated with a wing oscillating\n harmonically in pure translational motion, as obtained from several\nsources .\nthe results of these calculations indicate that the normalized\nunsteady-lift functions are substantially independent of the shape of\nthe plan form for elliptical, rectangular, or moderately tapered wings,.\n however, for delta wings the increase of lift toward the steady-state\nvalue is much more rapid than that for the aforementioned wings of the\nsame aspect ratio . these results also corroborate the results of other\ninvestigations in that the rate of growth of lift tends to increase with\n a decrease in aspect ratio . the shape of the spanwise distributions of\n the indicial lift seems to be, for all practical purposes, independent\nof time for rectangular and elliptical wings ."}, {"doc_id": 700, "text": "two and three-dimensional unsteady lift problems in high speed flight .\nthe problem of transient lift on two- and three-dimensional wings flying\n at high speeds is discussed as a boundary-value problem for the\nclassical wave equation . kirchhoffs formula is applied so that the\nanalysis is reduced, just as in the steady state, to an investigation of\n sources and doublets . the applications include the evaluation of\nindicial lift and pitchingmoment curves for two-dimensional sinking and\npitching wings flying at mach numbers equal to 0, 0.8, 1.0, 1.2, and\ntriangular wings in both forward and reversed flow are presented and\ncompared with the two-dimensional values ."}, {"doc_id": 701, "text": "numerical determination of indical lift of a two-dimensional sinking\nairfoil at subsonic mach numbers from oscillatory lift coefficients with\n calculations for mach number 0.7 .\nthe reciprocal equations for relating the incompressible circulatory\nindicial lift to the lift due to harmonic oscillations have been\nmodified to include the noncirculatory lift associated with\napparent-mass effects . although the apparent-mass effects are impulsive in\nnature in incompressible flow, the lift due to apparent-mass effects in\ncompressible flow is a time-dependent function . the corresponding\nreciprocal equations for the total compressible lift are given . by use\nof the reciprocal equations for compressible flow, the indicial lift and\n moment functions due to an airfoil's experiencing a sudden acquisition\nof vertical velocity are determined numerically for mach number 0.7 .\nlack of sufficient flutter coefficients prevents the calculation of\nthese functions at other mach numbers .\nalthough the indicial lift and moment functions due to penetration of a\nsharp-edge gust may be obtained from the oscillatory tab or aileron\ncoefficients by a similar analysis, sufficient coefficients are not\navailable at the present . however, an approximate method is shown for\ndetermining a portion of this unsteady-lift function .\nwhen a comparison is made of the indicial lift functions at mach numbers\nappears to be less rapid for the compressible case than for the\nincompressible case . consequently, the calculation of the gust load factor\nat high subsonic mach numbers utilizing the two-dimensional\nincompressible indicial lift functions and an over-all correction for\ncompressibility such as the prandtl-glauert factor might be conservative ."}, {"doc_id": 702, "text": "numerical determination of indical lift and moment functions for a two\ndimensional sinking and pitching airfoil at mach numbers 0.5 and 0.6 .\nthe indicial lift and moment functions are determined approximately for\nsinking and pitching motion at mach numbers m of 0.5 and 0.6 . these\nfunctions are determined from a knowledge of the existing oscillatory\ncoefficients at the low reduced frequencies and from approximate\nexpressions of these coefficients at the high reduced frequencies .\nthe beginning portion of the indicial lift function associated with an\nairfoil penetrating a sharp-edge gust in subsonic flow is evaluated by\nuse of an exact method . by use of an approximate method for determining\n the remaining portion, the complete indicial gust function is\ndetermined for m 0.5, m 0.6, and m 0.7 .\nall the indicial lift and moment functions are approximated by an\nexponential series,. the coefficients which appear in the exponential\napproximations for each indicial function are tabulated for m 0.5,\nm 0.6, and m 0.7 ."}, {"doc_id": 703, "text": "general airfoil theory .\non the assumption of infinitely small disturbances the author develops\na generalized integral equation of airfoil theory which is applicable\nto any motion and compressible fluid . successive specializations yield\nvarious simpler integral equations, such as possio's, birnbaum's, and\nprandtl's integral equations, as well as new ones for the wing of\ninfinite span with periodic downwash distribution and for the oscillating\nwing with high aspect ratio . lastly, several solutions and methods for\nsolving these integral equations are given ."}, {"doc_id": 704, "text": "a systematic kernel function procedure for determining aerodynamic\nforces on oscillating or steady finite wings at subsonic speeds .\na detailed description is given of a method of approximating solutions\nto the integral equation that relates oscillatory or steady lift and\ndownwash distributions on finite wings in subsonic flow . the method of\nsolution is applicable to general plan forms with either curved or\nstraight leading and trailing edges . moreover, it is directly\napplicable to control surfaces such as all-movable tails but modifications\nare needed to apply it to controls in general . applications of the\nmethod involve evaluations of numerous integrals that must be handled by\n numerical procedures but systematic schemes of evaluations have been\nadopted that are well suited to the routines of automatic digital\ncomputing machines . these schemes of evaluation have been incorporated in\na program for an ibm 704 electronic data processing machine . with this\nmachine, a pressure distribution together with such quantities as\nsection or total lift and moment coefficients or generalized forces can be\ndetermined for a given value of frequency and mach number and for\nseveral /four or five/ modes of oscillation in about 4 minutes of\nmachine time . in the case of steady downwash conditions corresponding\nquantities can be obtained in about 2 minutes of machine time .\nin order to illustrate applications of the method, results of several\ncalculations are presented . in these illustrations total forces and\nmoments are compared /1/ with results of analytic procedures for a\ncircular plan form with steady downwash conditions, /2/ with results of\nother theories and with experiment for a rectangular plan form of aspect\n ratio 1 at a uniform angle of attack, and /3/ with some experimental\nresults for a rectangular plan form of aspect ratio 2 undergoing\npitching and flapping oscillations . also included in the illustrations are\nresults of flutter calculations compared with experimental results for\nan allmovable control surface of aspect ratio 3.50 and for a\ncantilevered rectangular plan form of aspect ratio 5.04 ."}, {"doc_id": 705, "text": "on the kernel function of the integral equation relating the lift and\ndownwash distributions of oscillating finite wings in subsonic flow .\nthis report treats the kernel function of an integral equation that\nrelates a known or prescribed downwash distribution to an unknown lift\ndistribution for a harmonically oscillating finite wing in compressible\nsubsonic flow . the kernel function is reduced to a form that can be\naccurately evaluated by separating the kernel function into two parts ..\n a part in which the singularities are isolated and analytically\nexpressed and a nonsingular part which may be tabulated . the form of the\nkernel function for the sonic case /mach number of 1/ is treated\nseparately . in addition, results for the special cases of mach number\nof o /incompressible case/ and frequency of o /steady case/ are given .\nthe derivation of the integral equation which involves this kernel\nfunction, originally performed elsewhere /see, for example, naca\ntechnical memorandum 979/, is reproduced as an appendix . another appendix\ngives the reduction of the form of the kernel function obtained herein\nfor the three-dimensional case to a known result of possio for\ntwo-dimensional flow . a third appendix contains some remarks on the\nevaluation of the kernel function, and a fourth appendix presents an\nalternate form of expression for the kernel function ."}, {"doc_id": 706, "text": "on som reciprocal relations in the theory of nonstationary flows .\nin the theory of nonstationary flows about airfoils, the /indicial lift/\n function k /s/ of wagner and the /alternating lift/ function c /k/ of\ntheodorsen have fundamental significance . this paper reports on some\ninteresting relations of the nature of fourier transforms that exist\nbetween these functions . general problems in transient flows about\nairfoils may be given a unified broad treatment when these functions are\n employed . certain approximate results also are reported which are of\nnotable simplicity, and an analogy with transient electrical flows is\ndrawn ."}, {"doc_id": 707, "text": "thermal analysis of stagnation regions with emphasis on heat-sustaining\nnose shapes at hypersonic speeds .\nthe leading edges and noses of hypersonic vehicles are subjected to\nsevere aerodynamic heating and must be cooled in some manner-dash e.g.,\ninternal convection, transpiration, or radiation . it is this latter\nmode of handling the problem that is discussed in this paper .\nneglecting conduction in the leading-edge region, the maximum temperature for\nlong-range hypersonic gliders is of the same order as the melting point\nof refractory materials, with a corresponding large temperature gradient\n away from the leading edge . inclusion of conduction in the aft\ndirection reduces the maximum temperature and distributes the heat to a\nlocation that will radiate it out from the surface . for either\nsteady-state or transient conditions, the temperature at the leading edge is\nreduced by conduction, while the temperature aft of the leading-edge\nshoulder is increased, thus setting up a heat transmission balance\nbetween the convective influx of heat, the redistribution of heat by\nconduction, and the radiation of heat from the surface . the feasibility of\n such a mechanism can be enhanced by suitably choosing leading-edge\nshapes and materials . the philosophy behind the choice of leading-edge\nshapes is discussed and the effects of varying parameters, such as\nshape, diameter, emissivity, conductivity, thickness, etc., are shown ."}, {"doc_id": 708, "text": "aerodynamic characteristics of two winged reentry vehicles at supersonic\n and hypersonic speeds .\ntests were conducted at the langley research center on two winged\nlifting hypersonic reentry glider configurations . performance, stability,\nand control data are presented at mach numbers of 1.62 and 2.91 for\nangles of attack up to 15degree and at mach numbers of 6.8 and 9.6 for\nangles of attack up to 25degree ."}, {"doc_id": 709, "text": "static longitudinal aerodynamic characteristics at transonic speeds and\nangles of attack up to 99degree of a reentry glider having folding\nwingtip panels .\ndata are presented which were obtained from a transonic wind-tunnel\ninvestigation of a reentry glider having folding wing-tip panels . the\ntests were conducted at angles of attack from -4degrees to 99degrees .\nthe reynolds number based on the mean geometric chord of the fixed\nplanform varied from 2.35 x 10 to 2.99 x 10 .\nthe maximum lift-drag ratio for the model with the folding wing-tip\npanels fully extended decreased from a maximum value of 7.8 at a mach\nnumber of 0.60 to about 3.4 at mach numbers from 1.03 to 1.20 . the\nmodel with the folding wing panels fully extended was stable for values\nof the lift coefficient from 0 up to at least 0.8 . above this lift\ncoefficient pitch-up tendencies were observed, followed by an unstable or\nneutrally stable region which extended up to values of angle of attack\nof 50degrees or 60degrees . deflecting the folding wing panels between\nducing a significant change in the trim angle of attack or in any of the\n force or moment coefficients in the angle-of-attack range from 49degree\nto 99degree ."}, {"doc_id": 710, "text": "the smallest height of roughness capable of affecting boundary-layer\ntransition .\nan investigation was made to determine the smallest size of isolated\nroughness that will affect transition in a laminar-boundary layer .\ncritical heights for three types of roughness were found in a low-speed\nwind tunnel . the types were /1/ two-dimensional spanwise wires, /2/\nthree-dimensional discs, and /3/ a sandpaper type . in addition to type\nof roughness, test variables included the location of roughness,\npressure distribution, degree of tunnel turbulence, and length of natural\nlaminar flow .\nthe most satisfactory correlation parameter was found to be the\nroughness reynolds number, based on the height of roughness and flow\nproperties at this height . the value of this critical reynolds number was\nfound to be substantially independent of all test variables except the\nshape of roughness . this parameter also correlates well other published\n data on critical roughness in low-speed flow . the value of the\nroughness reynolds number necessary to move transition forward to the\nroughness itself was also determined for the three types of roughness and was\n found to be approximately constant for a given type of roughness .\nan investigation of the limited amount of available data on critical\nroughness in supersonic flow indicates that the effects of roughness may\n still be correlated by the roughness reynolds number . the value of\nthis reynolds number depends primarily on the mach number at the top of\nthe roughness . when this mach number is greater than 1.0, the roughness\n reynolds number based on conditions behind a shock is probably the\ncharacteristic parameter ."}, {"doc_id": 711, "text": "an investigation at subsonic speeds of aerodynamic characteristics at\nangles of attack from -dash 4degrees to 100degrees of a delta-wing\nreentry configuration having folding wingtip panels .\nan investigation was made at subsonic speeds in the langley highspeed\nlifting reentry configuration having folding wingtip panels . the\nconfiguration is of the type used in a high angle-of-attack /near 90degree/\n reentry to minimize aerodynamic heating . by unfolding the wingtip\npanels into the airstream, a moderate angle-of-attack glide is used for\na controlled landing . the basic configuration tested utilized a\nwhose area was 25 percent of the total wing area . the effects of\nvarying the plan form and size of the wingtip panels was studied as well\n as the effects of unfolding the wingtip panels in a high angle-\nof-attack attitude . tests were made at mach numbers of 0.40, 0.60, and"}, {"doc_id": 712, "text": "low-speed longitudinal aerodynamic characteristics associated with a\nseries of low-aspect ratio wings having variations in leading-edge\ncontour .\nan investigation has been conducted at various reynolds numbers and low\nsubsonic speeds to determine the longitudinal aerodynamic\ncharacteristics associated with a series of low-aspect-ratio wings having\nvariations in leading-edge contours . the planforms included a highly swept\ntriangular wing, a rectangular wing, and intermediate wings including\nplanforms having elliptic and parabolic leading-edge contours, all\nhaving an aspect ratio of 1.33 . the effects of changing aspect ratio for a\n given leading-edge contour were investigated for two of the wings\npresented,. also included are the longitudinal characteristics associated\nwith various fuselage sizes . an effort has been made to estimate the\nlift variation with angle of attack for the wing planforms of the\npresent investigation .\nimprovements in the lifting capabilities at low subsonic speeds\nassociated with a basic triangular planform of low aspect ratio are possible\nby slight alterations in leading-edge design, which should still conform\n to possible design requirements at hypersonic speeds . these changes in\n planform resulted in increases in lift-curve slope, lift at high angles\n of attack, and in the maximum untrimmed lift-drag ratio, provided the\nfuselage was sufficiently small . the longitudinal stability\ncharacteristics of the majority of planforms indicate more desirable stability\ncharacteristics at high lifts than either a triangular wing or\nrectangular wing of the same aspect ratio . the effects of increasing\nreynolds number for each of the planforms investigated generally resulted\nin slight reductions in the lift at high angles of attack . a method is\npresented for estimating the subsonic-lift variation with angle of\nattack for the low-aspect-ratio wings of the present investigation and\nindicated good agreement with experimental data throughout the\nangle-of-attack range of this investigation ."}, {"doc_id": 713, "text": "static longitudinal stability characteristics of a blunted glider\nre-entry configuration having 79.5degree sweepback and 45degree dihedral at\n a mach number of 6.2 and angles of attack up to 20degree .\nan experimental investigation was conducted at a mach number of 6.2 to\ndetermine the static longitudinal stability characteristics of a model\nof a blunted glider reentry configuration having 79.5degree sweepback\nand 45degree dihedral . the free-stream reynolds number for the\ninvestigation was 3.0 x 10 based on the basic model length of 7.5 inches .\ntests were made through an angle-of-attack range from 0degrees to\ninvestigation showed that incorporating 10degree nose incidence in the\nbasic model resulted in a lower lift-curve slope, a lower lift-drag\nratio, a higher value of trim lift coefficient, and a decrease in static\n longitudinal stability . in comparison, the effect of extending the\nconfiguration length and incorporating 10degrees and 20degrees boattail\nangles resulted in smaller changes in the longitudinal stability\ncharacteristics of the model ."}, {"doc_id": 714, "text": "blockage corrections for three-dimensional flow closed\nthroat wind tunnels, with considerations of the effect\nof compressibility .\n theoretical blockage corrections are presented for a body of\nrevolution and for a three-dimensional unswept wing in a\ncircular or rectangular wind tunnel . the theory takes account of\nthe effects of the wake and of the compressibility of the fluid,\nand is based on the assumption that the dimensions of the model\nare small in comparison with those of the tunnel throat .\nformulas are given for correcting a number of the quantities, such\nas dynamic pressure and mach number, measured in\nwind-tunnel tests . the report presents a summary and unification\nof the existing literature on the subject ."}, {"doc_id": 715, "text": "motion of a ballistic missile angularly misaligned\nwith the flight path upon entering the atmosphere and\nits effect upon aerodynamic heating, aerodynamic loads\nand miss distance .\n an analysis is given of the\noscillating motion of a ballistic missile\nwhich upon entering the atmosphere\nis angularly misaligned with respect\nto the flight path . the history of\nthe motion for some example missiles\nis discussed from the point of view\nof the effect of the motion on the\naerodynamic heating and loading .\nthe miss distance at the target due to\nmisalignment and to small accidental\ntrim angles is treated . the\nstability problem is also discussed for\nthe case where the missile is\ntumbling prior to atmospheric entry ."}, {"doc_id": 716, "text": "study of the oscillatory motion of manned vehicles\nentering the earth's atmosphere .\n an analysis is made of the oscillatory\nmotion of vehicles which\ntraverse arbitrarily prescribed trajectories\nthrough the atmosphere .\nexpressions for the oscillatory motion\nare derived as continuous functions\nof the properties of the trajectory .\n results are applied to a study of\nthe oscillatory behavior of re-entry\nvehicles which have decelerations that\nremain within limits of human\ntolerance . it is found that a deficiency of\naerodynamic damping for such\nvehicles may have more serious consequences\nthan it does for comparable\nballistic missiles ."}, {"doc_id": 717, "text": "motions of a short 10degree blunted cone entering a martian atmosphere\nat arbitrary angles of attack and arbitrary pitching rates .\nthe dynamic behavior of two probe vehicles entering a martian atmosphere\n in a passive manner with arbitrary initial angles of attack and\npitching rates to 12degree per second has been determined . results for an\nentry velocity of 21,700 feet per second and an entry angle of -40degree\n were obtained from machine calculated solutions of the six-degree-\nof-freedom rigid-body equations of motion using experimental aerodynamic\ncharacteristics for the vehicles . one of the vehicles had a flat base\nand was statically stable in two attitudes /nose forward and base\nforward/ . the other vehicle, derived from the first by adding a conical\nafterbody, was statically stable in only one attitude /nose forward/ .\na 10-rpm vehicle spin rate, believed ample for the purpose of\ndistributing solar and aerodynamic heating over the vehicle surface, and\n model atmospheres encompassing the probable extremes for the planet\nwere also considered .\nit was found that while the motion of the flat-based vehicle could be\noscillatory about either the nose-forward or base-forward stable trim\nattitudes when aerodynamic heating rates were high, the range of initial\n angles of attack resulting in base-forward orientation was reduced by\nmore than a factor of 3. when initial pitch rates were increased from\nbody having only nose-forward stability showed that oscillatory angles\nof attack at maximum heating-rate conditions probably would not exceed\nabout 25degrees although angles of attack when heating rates were 50\npercent of maximum could be as high as 40degree . values of these upper\nbound angles of attack were essentially independent of initial pitch\nrates for the range considered . furthermore, the envelope of maximum\nprobable angles of attack was increased only slightly when the vehicle\nwas given a 10-rpm spin rate . the relationship between maximum\namplitudes of oscillation and heating rates through high heating portions of\nthe trajectories was preserved when model atmospheres believed to\nencompass the extreme possibilities for mars were used in the calculations"}, {"doc_id": 718, "text": "means and examples of aeronautical research in france at onera .\ncosmonautics is currently very much to the forefront in the news .\nit embraces and extends aeronautics, and i would like to propose\nincluding both, at least on certain occasions, under a general\ndenomination of /aerocosmonautics/ .\nin your country, the sciences and technology of space are subjects which\nhave been backed by initial advances and abundantly treated .\nsince france has not yet launched any artificial satellite or built\nany circumlunar space vehicle, i propose to confine myself here to the\nfield of aeronautics, where there is still so much progress of manifest\nutility to accomplish .\ni shall accordingly content myself with presenting some examples of\naeronautical research and experiments undertaken in my country by\nonera, a body whose mission is akin to that of the illustrious naca,\nnow nasa, but bearing in mind the considerable difference between the\nscales of the respective resources ."}, {"doc_id": 719, "text": "tumbling bodies entering the atmosphere .\nthe equations of motion of a tumbling flat plate entering an exponential\n atmosphere were linearized and solved analytically to obtain a simple\nexpression for the altitude at which tumbling would cease and libration\nwould commence . the plate had only three degrees of freedom, and\naerodynamic forces were derived from newtonian impact theory . in the\nlinear analysis, mean values of the drag and pitch damping coefficients\nso that flutter occurs in the range of a low-speed wind tunnel .\na particular type of construction for supersonic flutter models is\ndescribed in detail . methods of vibration testing, static testing, and\nflutter testing are discussed . particular emphasis is placed on the\ntechnique of varying flow parameters rather than model parameters to\nprecipitate flutter . the tool for varying flow parameters is the\nvariable mach number supersonic test section of the massachusetts\ninstitute of technology blowdown wind tunnel . the aerodynamic features of\n the supersonic test section are presented ."}, {"doc_id": 720, "text": "a note on the use of sandwich structures in severe acoustic\nenvironments .\nthis paper reviews some of the experience to date of using sandwich type\nstructures in severe acoustic pressure environments . the methods\nused for testing sandwich structures for acoustic fatigue are described\nand their limitations considered . experimental and theoretical work\nrelating to the damping and mode-frequency relationships of certain\nsandwich configurations is also reviewed .\nspecial attention is given to the estimation of the stress in the bond\nof a honeycomb sandwich panel subjected to sudden pressure\nfluctuations . a /uni-modal/ theory is presented, relating the\nmean-square bond-stress to the random exciting pressure and panel dynamic\ncharacteristics . this theory indicates that tensile bond stresses\nmay be encountered of up to six times the local r.m.s. exciting\npressure . these must be combined with bending and shear stresses\nto obtain the principal stresses which precipitate bond fatigue\nfailures .\nfinally, an outline is given of some of the lines of future research\nwhich should lead to the achieving of the maximum possible fatigue\nresistance from sandwich configurations ."}, {"doc_id": 721, "text": "near noise field of a jet engine exhaust .\n aircraft structures located in the near noise field of a jet\nengine are subjected to extremely high fluctuating pressures that\nmay cause structural fatigue . studies of such structures have\nbeen limited by lack of knowledge of the loadings involved .\n the acoustic near field produced by the exhaust of a stationary\nturbojet engine having a high pressure ratio was measured for\na single operating condition without afterburning . the\nmaximum over-all sound pressure without afterburning was found\nto be about 42 pounds per square foot along the jet boundary in\nthe region immediately downstream of the jet-nozzle exit .\nwith afterburning the maximum sound pressure was increased\nby 50 percent . the largest sound pressures without\nafterburning were obtained on a constant percentage band width basis in\nthe frequency range from 350 to 700 cps .\n additional tests were made at a few points to find the effect\nof jet velocity on near-field sound pressures and to determine\nthe difference in value between sound-pressure levels at rigid\nsurfaces and corresponding free-field values . near the jet\nnozzle, over-all sound pressures were found to vary as a low\npower (approx. unity) of the jet velocity . over-all sound-pressure\nlevels considerably greater than the corresponding free-field\nlevels were recorded at the surface of a rigid plate placed along\nthe jet boundary .\n the downstream locations of the maximum sound pressure\nat any given frequency along the jet-engine-exhaust boundary\nand the longitudinal turbulent-velocity maximum of the same\nfrequency along a small cold-air jet at 1 nozzle-exit radius from\nthe jet axis were found to be nearly the same when compared on\na dimensionless basis . also, the strouhal number of the\ncorresponding spectra maximums was found to be nearly equal at\nsimilar distances downstream .\n in addition to the magnitude and frequency distribution of\nthe acoustic pressures, it is necessary to know the cross\ncorrelation of the pressure over the surface area . cross-correlation\nmeasurements with microphones were made for a range of jet\nvelocities at locations along the jet and at a distance from the\njet . free-field correlations of the over-all sound pressure and\nof the sound pressure in frequency bands from 100 to 1000 cps\nwere obtained both longitudinally and laterally . in addition,\ncorrelations were obtained with microphones mounted at the\nsurface of a rigid plate that was large compared with the\ndistance over which a positive correlation existed .\n the region of positive correlation was generally found to\nincrease with distance downstream of the engine to 6.5\nnozzle-exit diameters, but remained nearly constant thereafter . in\ngeneral, little change in the correlation curves was found as a\nfunction of jet velocity or frequency-band width . the distance\nfrom unity correlation to the first zero correlation was greater for\nlateral than for longitudinal correlations for the same\nconditions and locations . the correlation curves obtained in free\nspace and on the surface of the plate were generally similar .\n the results are interpreted in terms of pressure loads on\nsurfaces ."}, {"doc_id": 722, "text": "random excitation of a tailplane section by jet noise .\n the response of a section of tailplane structure to both discrete\nand random noise pressures has been studied in detail . initially the\nspecimen was mounted behind a jet engine and the induced strains were\nanalysed with the object of determining both the resonant frequencies\nand the corresponding modes of vibration . during these tests a survey\nwas made of the spectrum and correlation pattern of the jet noise on\nthe surface of the model . secondly the specimen was mounted in front\nof a loudspeaker in an acoustics laboratory and the structural\nresonances were excited by means of discrete frequency sound . the mode\nshapes were studied in detail with the aid of a stroboscope .\n it is concluded that the tailplane skin on this particular piece\nof structure only responds to any significant degree in one structural\nmode . although reasonable comparison has been obtained between the\nrandom and discrete tests, it was not possible to calculate the induced\nstresses using the observed mode shapes and measured pressure\nexcitation ."}, {"doc_id": 723, "text": "on the fatigue failure of structures due to vibrations excited\nby random pressure fields .\non the assumption that the forced modes of vibration of a structure,\nsubjected to pressure fluctuations random in time and space, can be\napproximated by the composition of the motions of the uncoupled\nnatural modes, a general analysis is made using the ideas of vibration\ntheory and spectrum analysis . the power spectrum, and hence the\nrms value, of any quantity depending linearly upon structural\ndistortions is derived and it involves a quantity (called the /joint\nacceptance/) concerning the spacewise structure of the pressure\nfield and of the geometry of the modes of vibration . it is shown how\nthis result may be used (on assuming /normal/ randomness) to estimate\nthe fatigue life on the hypothesis of cumulative damage ."}, {"doc_id": 724, "text": "structural acoustic proof testing .\nwith the introduction of high-powered\npropulsion systems, and paralleling their\ncontinued development, an\naccompanying increase in acoustical problems has arisen .\n of these acoustical problems, that of\nacoustical fatigue failures has become paramount\nin the eyes of the structural engineer . aircraft\ndesigned to normal strength requirements have\nbeen known literally to fall apart under acoustical\nloading . this problem has required much\nendeavour to produce a solution, and considerable\nstructural research, based upon results of siren or\nother testing, have proved inadequate . this\nfailure to find a satisfactory solution has resulted\nin the conviction that the final proof of a design\ncan be found only in proof testing . proof testing,\nin the acoustic fatigue sense, is the testing of a\ndesign structure in a simulated acoustical\nenvironment for a period of time long enough to assure\nequality with design life ."}, {"doc_id": 725, "text": "the response of a typical aircraft structure to jet\nnoise .\n an analysis is made of experimentally determined mode shapes\nexcited on the rear structure of a modern airliner by jet noise from\na pod-mounted turbojet engine . power spectra of stresses\ndetermined from strain-gage measurements are obtained and cross\ncorrelated . extensive measurements were made on skin panels of the\nfuselage and elevator and limited ones were made on fuselage\nstringers and frames . the skin-panel results are compared with\ntheoretical predictions . reviewer believes that this paper is of\nconsiderable value for those concerned with response of\naircraft-type structures to jet-induced noise ."}, {"doc_id": 726, "text": "on structural fatigue under random loading .\n experience has shown that the fluctuating loads induced by a\njet may cause fatigue failure of aircraft structural components .\nin order to throw some light on this and similar problems, the\nstress spectrum and the /equivalent fatigue stress/ of an elastic\nstructure subjected to random loading are studied . the analysis\nis simplified by assuming the structure to have only a single\ndegree of freedom and by using the concept of cumulative damage,\nthe results being expressed in terms of quantities that can be\ndirectly measured . as an example, a similarity expression for\nthe probable value of the equivalent fatigue stress of a panel\nsubjected to jet buffeting is derived ."}, {"doc_id": 727, "text": "a study of the acoustic fatigue characteristics of\nsome flat and curved aluminium panels exposed to random\nand discrete noise .\n a study was made of the fatigue\nlife of simple 2024-t3\naluminum-alloy panels measuring 11 by 13\ninches and exposed to both\ndiscrete-frequency noise from a siren and\nrandom noise from an air jet . noise\nlevels varied from approximately\npanel variables included thickness,\nedge conditions, curvature, and\nstatic-pressure differential .\n no significant differences were noted\nin the nature of failures\nexperienced for the two types of loadings .\nat a given root-mean-square\nstress level, the failure times were\ngenerally shorter for the random\nloading than for the discrete-frequency\nloading . these differences in\nfailure times were noted to be a function\nof stress level, the larger\ndifferences occurring at the lower stress levels .\n increases in time to failure were\nobtained as a result of increased\npanel thickness, increased panel curvature,\nand particularly for increased\nstatic-pressure differential across curved panels .\n for the discrete-type loading,\nthe location of weak points in these\nsimplified structural designs can be\nsatisfactorily accomplished but\nquantitative predictions of fatigue\nlife are much more difficult ."}, {"doc_id": 728, "text": "free vibrations of continuous skin stringer panels .\nthe determination of the natural frequencies and normal modes of\nvibration for continuous panels, representing more or less typical fuselage\nskin-panel construction for modern airplanes, is discussed in this paper\nare considered . a numerical example is presented, and analytical\nresults for a particular structural configuration agree favorably with\navailable experimental measurements ."}, {"doc_id": 729, "text": "stresses in continuous skin stiffener panels under random loading .\ntheoretical aspects involved in the prediction of stress levels for\ncontinuous skin-stiffener panels subjected to a random pressure field\nare considered in the light of powell's general theory for statistical\nsuperposition of modal response . the choice of structural model is\ndictated by the prevalence of skin-stiffener construction in modern\nflight vehicle design . the present study clearly demonstrates that any\ntruly adequate prediction of stress levels in actual aircraft structures\n requires a much better representation of structural characteristics\nthan can be provided by single panel idealizations . in an example\nconsidering fuselage panels exposed to jet engine noise, essential\nagreement is shown with experimental data, although better correlation is\nshown for rms stress than for power spectrum . it is shown that\nreduction of stress level by increasing damping is effective only in the\nhigher frequency range ."}, {"doc_id": 730, "text": "on the bending of a clamped plate .\n the present paper contains an application\nof a recently developed variational\nmethod to the boundary value problem of the\nbending of a clamped plate of\narbitrary shape . it will be shown that this problem\ncan be linked to the simpler problem\nof the equilibrium of a membrane by a chain\nof intermediate problems, which can be\nsolved explicitly and in finite form in terms\nof the membrane problem . in the\nintermediate problems, the deflection converges\nuniformly in the domain of the plate\nof the clamped plate, and the derivatives\nof all orders of the deflection converge\nuniformly in every domain completely interior\nto the plate . (in the ritz method, not even\nthe convergence of the slopes can be\nguaranteed .) the method yields numerical\nresults for plates of all shapes for which\nthe membrane problem (which we shall call\nthe base problem) admits an explicit\nsolution . as an example we shall consider a\nclamped square plate under a uniform load .\nthis problem has been the object of\nnumerous investigations, some of which are\ntheoretical, while others are purely numerical,\nuse infinite simple and double series,\nand operate with an infinite number of\nlinear equations and an infinite number of\nunknowns . an inspection of the general\nformulae derived in the present paper,\nformulae which become simple in numerical\napplications, would show how some of the\nnumerical methods might be rendered\nrigorous . the convergence of higher\nderivatives is of great practical interest for\nthe approximate computation of the stresses ."}, {"doc_id": 731, "text": "upper and lower bounds for the solution of the first\nbiharmonic boundary value problem .\n let w(x,y) be a solution of the boundary value problem\nwhere r is a plane\ndomain with the boundary c . the authors obtain upper and\nlower bounds for, the value of w at a point in r,\nby a method which is applicable to many other problems .\n if u is a function satisfying the boundary conditions\nand v is a function satisfying the partial differential\nequation, then the authors obtain by applying green's\nclassical identity and schwarz's inequality a pair of inequalities\nof the form where .\n together with the function w the authors consider a\nfunction the solution of the boundary value problem\non c, and in\nanalogy with the functions u and v associated with the\nfunction w a pair of functions and associated with the\nfunction . in the expression for derived from green's\nclassical identity appears an unknown line integral\ncontaining the values of w and on c . but the same line\nintegral appears also in the expressions for\nto which the above inequalities are\napplicable .\n in this way the authors obtain two inequalities of the form\nwhere b and b', respectively, are approximate\nvalues of . in order to improve these bounds\none may add to u a linear set of functions and to v a\nlinear set of functions and then minimize h(u-v) in order\nto determine the coefficients of the best linear combinations .\nif the sequences and are complete in a certain sense\ndefined by the authors the approximations will converge to\nthe value ."}, {"doc_id": 732, "text": "on the analogues relating flexure and extension of\nflat plates .\n the displacement of a flat plate bent\nby transverse loading, and the extensional\nor in 'plane stress', are governed by equations\nof identical form ,. and the boundary\nconditions have identical form when\nedge-displacements are specified in the flexural,\nedge-tractions in the extensional problem,\nso mathematically, in these circumstances,\nonly a single problem is presented . this,\nthe 'first analogue' relating flexure and\nextension, is well known .\n a 'second analogue', relating the flexural\nproblem when edge-tractions with the\nextensional problem when edge-displacements\nare specified, is believed to have been\nfirst propounded in 1941 . by introducing\ntwo quantities u and v, analogous with\nthe components u and v of extensional\ndisplacement, it permits a treatment of the\nflexural problem by any method--e.g.\nwhich yields extensional solutions of this\nsecond type .\n in this paper both analogues are combined\nin an inclusive statement covering the\nperforated (multiply connected) plates which\nwere discussed in 1948 . reasons are\nstated for believing that 'two-diagram technique'\nis preferable in problems governed\nby 'mixed' boundary conditions ."}, {"doc_id": 733, "text": "the bending of a sectorial plate .\n the problem of evaluating the bending moments,\nexisting in a uniformly loaded clamped plate having the form\nof a sector of a ring, is one which arises in connection with\nthe stress analysis of reinforced piston heads and in other\ndesign problems . in this paper, expressions are derived\nfor the bending moments along the edges of such a plate .\nsimilar problems, i.e., those of the clamped rectangular\nplate under uniform pressure, under a central\nconcentrated load, and that of the simply supported sector of a\ndisk under uniform pressure, have been discussed by\nprevious authors . the general approach used in the\nforegoing problems is adopted in the present case ,. a\nconsiderable reduction in the computational work is achieved,\nhowever, by the use of an integral-equation method of\nsolving the boundary-condition equations . numerical\nresults are obtained for plates of various dimensions, and\nthe edge moment distributions are plotted for these cases .\ncurves are also plotted which indicate the relationship\nexisting between the maximum bending moments derived\nfor sectorial plates and those previously obtained for\nclamped rectangular plates of similar size ."}, {"doc_id": 734, "text": "the bending of uniformly loaded clamped plate in the\nform of a circular sector .\n the deflexion of a uniformly loaded\nplate in the form of a semicircle clamped\nalong its boundary is obtained by a\nmethod due to weinstein . this problem\nrequires the solution of the biharmonic\nequation where z is given,\nsubject to the conditions that w = 0 and\non the boundary, n being the\ndirection of the outward normal . the solution\nis expressed in the form\nwhere, writing is found\nby solving (in succession) two harmonic\nequations of the forms where z may\nbe zero, and where f and\nhave to satisfy certain boundary conditions .\nthe constants are then determined\nto satisfy the boundary condition .\n numerical calculations show that five or six\nterms of the series give a\ngood approximation to the accurate value as\njudged by the closeness with which\nthe approximate solution satisfies the boundary\ncondition . the\nprocedure to be adopted in the case of the general\ncircular sector and for non-uniform\nloading is indicated briefly .\n the connexion between the deflexion problem\nand that of plane strain in which\nthe stress function satisfies the equation,\nwhere and have given\nvalues on the boundary, is discussed as a preliminary\nto the further consideration\nof the latter problem by a method of the same type ."}, {"doc_id": 735, "text": "the bending of uniformly loaded sectorial plates with\nclamped edges .\n this paper analyzes the bending of a sectorial plate,\nclamped on all edges and subjected to uniformly\ndistributed load, by using two different methods of superposition\non the elementary solution for a uniformly loaded circular\nplate with a clamped edge ."}, {"doc_id": 736, "text": "the bending of a wedge shaped plate .\n a general method of solution is given in this paper for\nthe problem of bending of a wedge-shaped thin elastic\nplate with arbitrary boundary conditions on the radial edges\nin the case of a single load . the solution is carried out for\na plate with clamped edges and a single load on the bisector\nradius of the plate . stress distribution along the edges\nis shown and the behavior of the solution near the corner\npoint is discussed for several opening angles of the plate ."}, {"doc_id": 737, "text": "on the analysis of elastic plates of variable thickness .\n the extensional and flexural equations\ngoverning the elastic behaviour of a plate\nof variable thickness are expressed in\nterms of the laplacian operator .\ntemperature variations in the plane of the\nplate and across the thickness of the plate\nare taken into account .\n general solutions are given for a rectangular\nplate whose thickness varies\nexponentially along the length, and for a circular,\nor annular, plate whose thickness varies\nas a power of the radius .\n the large-deflexion equations, including\neffects of initial irregularities, are also\ndiscussed ."}, {"doc_id": 738, "text": "finding zero's of arbitrary functions .\n a method for finding real and complex\nroots of polynomial equations, due to\nd. muller, is applied to finding roots of\ngeneral equations of the form f(z) = 0,\nwhere f(z) is analytic in the neighborhood\nof the roots . the procedure does not\ndepend on any prior knowledge of the\nlocation of the roots nor on any special\nstarting process . all that is required is\nthe ability to evaluate f(z) for any\ndesired value of z . multiple roots can also be\nobtained . a general purpose program,\nprepared for the univac scientific 1103\nand 1103a, is described and numerical\nresults are presented for the following\napplications .. finding eigenvalues of\ndifferential operators ,. finding eigenvalues of\narbitrary matrices ,. finding zeros of the\ngeneralized eigenvalue problem ,. finding\nroots of a number of transcendental\nequations ."}, {"doc_id": 739, "text": "the buckling of thin cylindrical shells under axial\ncompression .\nin two previous papers the authors have discussed\nin detail the inadequacy of the classical theory of\nthin shells in explaining the buckling phenomenon of\ncylindrical and spherical shells . it was shown that\nnot only the calculated buckling load is 3 to 5 times\nhigher than that found by experiments, but the\nobserved wave pattern of the buckled shell is also different\nfrom that predicted . furthermore, it was pointed\nout that the different explanations for this discrepancy\nadvanced by l. h. donnell and w. flugge are\nuntenable when certain conclusions drawn from these\nexplanations are compared with the experimental facts .\nby a theoretical investigation on spherical shells the\nauthors were led to the belief that in general the\nbuckling phenomenon of curved shells can only be\nexplained by means of a non-linear large deflection theory .\nthis point of view was substantiated by model\nexperiments on slender columns with non-linear elastic\nsupport . the non-linear characteristics of such structures\ncause the load necessary to keep the shell in\nequilibrium to drop very rapidly with increase in wave\namplitude once the structure started to buckle . thus, first\nof all, a part of the elastic energy stored in the shell is\nreleased once the buckling has started,. this explains\nthe observed rapidity of the buckling process .\nfurthermore, as it was shown in one of the previous papers\nthe buckling load itself can be materially reduced by\nslight imperfections in the test specimen and vibrations\nduring the testing process .\n in this paper, the same ideas are applied to the case\nof a thin uniform cylindrical shell under axial\ncompression . first it is shown by an approximate\ncalculation that again the load sustained by the shell drops\nwith increasing deflection . then the results of this\ncalculation are used for a more detailed discussion of\nthe buckling process as observed in an actual testing\nmachine ."}, {"doc_id": 740, "text": "the behaviour of a cylindrical shell under axial compression\nwhen the buckling load has been exceeded .\n the value of the compressive stress at which\na thin circular cylindrical shell becomes unstable has been\nworked out theoretically by southwell (1914) . subsequent\nexperimental results, however, have indicated that this\nvalue is appreciably too high and that the form of distortion\nwhich occurs in practice differs from that assumed in theory .\n in recent years much work has been done on this problem\nin america . lundquist (1933) and donnell (1934)\nhave concluded that the buckling of a cylindrical shell is greatly\ninfluenced by initial irregularities,. von karman and\ntsien (1941) have indicated that a thin cylindrical shell can be\nmaintained in a buckled state by a compressive load\nconsiderably smaller than that previously predicted by theory .\n the present paper is an extension of the work of von karman\nand tsien . it shows that the smallest load which will\nkeep a thin cylindrical shell in a buckled condition is about one-third\nof that given by southwell, a result in very fair\nagreement with experiment, and that once the cylinder has buckled,\nand so long as the stresses remain within the elastic\nrange of the material, the cylinder has only about one-quarter of its\noriginal stiffness ."}, {"doc_id": 741, "text": "the behaviour of thin cylindrical shells after buckling\nunder axial compression .\n the fundamental investigations of von karman and tsien\non the buckling of cylindrical shells under axial compression\nare continued . the energy expression is simplified and\nminimized with respect to the axial and circumferential wave-length\nparameters . solution of the equations obtained yields curves\nof the reduced average stress and of the wave dimensions plotted\nagainst the reduced average strain . they illustrate the behavior\nof the cylinder during the buckling process . the minimum\nbuckling stress is found to be 0.195e(tr) ."}, {"doc_id": 742, "text": "post-buckling behaviour of axially compressed circular\ncylinder shells .\n the postbuckling characteristics of an axially compressed\nthin-walled circular cylindrical shell loaded either by dead weights\nor by a rigid testing machine are determined . it is shown that\nfor either loading condition the minimum applied stress in the\npostbuckling region is 0.182(er) and that the region of stable\nequilibrium corresponding to loading by the rigid testing machine\nincludes and extends beyond that obtained with dead weight\nloading . the work here described is a continuation of work done\nearlier by von karman and tsien, by michielsen, and by leggett\nand jones ."}, {"doc_id": 743, "text": "new developments in the nonlinear theories of the buckling of thin\ncylindrical shells .\nin the present paper a short survey will be given first of the buckling\nand postbuckling behavior of isotropic cylindrical shells subjected\nto different loading conditions as obtained by the nonlinear theory\nof finite deflections of shells during the last twenty years .\nnext a report will be given on new investigations carried out in the\nstructures department of the dvl concerning the elastic stability of\nisotropic and orthotropic cylindrical shells loaded in axial compression\nand internal pressure . these studies are based on the nonlinear theory\nof finite deformations . the theoretical rsults will be compared with\nnew experimental results obtained with a series of axially loaded\npressurized isotropic and orthotropic cylindrical shells ."}, {"doc_id": 744, "text": "lower buckling load in the non-linear buckling theory\nof thin shells .\n for thin shells the relation between\nthe load p and the deflection beyond the\nclassical buckling load is very often\nnon-linear . for instance, when a uniform thin\ncircular cylinder is loaded in the axial\ndirection, the load p when plotted against the\nend-shortening has the characteristic\nshown in fig. 1 . if the strain energy s and the\ntotal potential are calculated,\ntheir behavior can be represented by the\ncurves shown in figs. 2 and 3 . it can be\ndemonstrated that the branches oc and ab\ncorresponds to stable equilibrium configurations\nand the branch bc to unstable\nequilibrium configurations . the point b is then\nthe point of transition from stable to\nunstable equilibrium configurations ."}, {"doc_id": 745, "text": "an automatic method for finding the greatest or least\nvalue function .\nthe greatest or least value of a function of several\nvariables is to be found when the variables\nare restricted to a given region . a method is\ndeveloped for dealing with this problem and is\ncompared with possible alternatives . the method\ncan be used on a digital computer, and is\nincorporated in a program for mercury ."}, {"doc_id": 746, "text": "aeroelastic problems in connection with high speed\nflight .\n a review is given of developments\nin the field of aeroelasticity during the\npast ten years . the effect of steadily increasing\nmach number has been two-fold .. on\nthe one hand the aerodynamic derivatives have\nchanged, and in some cases brought new\nproblems, and on the other hand the design for\nhigher mach numbers has led to thinner\naerofoils and more slender fuselages for which\nthe required stiffness is more difficult to\nprovide . both these aspects are discussed,\nand various methods of attack on the\nproblems are considered . the relative merits\nof stiffness, damping and massbalance\nfor the prevention of control surface flutter are\ndiscussed . a brief mention is made of\nthe recent problems of damage from jet efflux\nand of the possible aeroelastic effects\nof kinetic heating ."}, {"doc_id": 747, "text": "bodt freedom flutter of ground launched rocket models\nat supersonic and high subsonic speeds .\n a theoretical investigation of symmetric\nbody freedom flutter of a rocket model is described . the results\nconfirm that structural failures of models were caused\nby this type of flutter, and an extension of the investigation\nindicates the parameters that are of importance . a high\nratio of body to wing mass and a well forward position of the\noverall centre of gravity are conditions under which flutter\nmay occur . increase of body pitching radius of gyration\nand tailplane volume are beneficial .\n it is concluded that this type of flutter may be significant\nin some aircraft designs, and that the canard has no\nadvantage in this respect over the conventional lay-out of wing\nand tailplane ."}, {"doc_id": 748, "text": "subsonic aerodynamic flutter derivatives for wings and control surfaces,\n /compressible and incompressible flow/ .\nthis report gives tables of the two-dimensional subsonic flutter\nderivatives,. where possible the values given are based on the published\n work of various authors, but some have been specially calculated for\nthis report . wing derivatives are given for mach numbers 0, 0.5, 0.6\nand 0.7 for the frequency parameter range 0 /0.04/ 0.2 /0.2/ 1.6 and\nmach numbers 0 and 0.7 for frequency parameter 5.0 . control surface\nderivatives are given for mach numbers 0 and 0.7 for control surface/\nwing chord ratios 0.02 /0.02/ 0.10 /0.05/ 0.50 and frequency parameters\nare also given for mach numbers 0, 0.5, 0.6 and 0.7 for frequency\nparameter 0 /0.04/ 0.2 /0.2/ 1.4 . control surface-tab derivatives are\ngiven for some particular values of the variables and methods of\nobtaining approximate values of these derivatives for other values of\nthe variables are suggested . control surface and tab derivatives are in\n all cases for no aerodynamic balance ."}, {"doc_id": 749, "text": "the aerodynamic effects of aspect ratio and sweepback\non wing flutter .\n the report describes tests to obtain direct\nmeasurements of the aerodynamic effects of aspect ratio and\nsweepback on wing flutter . the tests were made on rigid\nwings with root flexibilities .\n it is shown that measured effects of aspect ratio and\nsweepback on the flutter of these wings can be represented\nquite closely in flutter calculations based on two-dimensional\nflow theory by multiplying the two-dimensional\naerodynamic coefficients by appropriate factors . the effect of\nsweepback is represented by multiplying all aerodynamic\ncoefficients by cos, where is the wing leading-edge\nsweepback, and the effect of aspect ratio is represented by\nmultiplying the aerodynamic damping coefficients by 1f(a) and,\nthe stiffness coefficients by 1(f(a)) where a is the\naspect ratio .\n for the wings tested an average value for\nf(a) is f(a) = (1 + (0.8a)) ."}, {"doc_id": 750, "text": "transonic flow in two dimensional and axially symmetrical\nnozzles .\n by means of suitable expansions\nin inverse powers of r, the\nradius of curvature of the nozzle profile\nat the throat measured in throat\nhalf-heights, the velocity components\nin the throat region of a\nconvergent-divergent nozzle can be\ncalculated . the first three terms of\nthe series solution have been obtained\nboth for two-dimensional and for\naxially-symmetric nozzles . the\nnumerical accuracy of the solution is\nconfirmed by comparison with the\nknown exact solution along the branchline ."}, {"doc_id": 751, "text": "a note on the use of end plates to prevent three dimensional\nflow at the ends of bluff cylinders .\n the results are given of\nsome observations of the effects of\nend plates on the three-dimensional\nseparated flow at the ends of\ncylindrical models . while these are\nby no means exhaustive, it is felt\nthat they are of sufficient interest\nto merit putting on record ."}, {"doc_id": 752, "text": "slender not-so-thin wing theory .\n a method for making an approximate thickness correction to slender\nthin-wing theory is presented . the method is tested by applying it to\ncones with rhombic cross-sections and the agreement is found to be good\nif the cones are not too thick . it is then suggested that the\nthickness correction to slender thin-wing theory may be applied\nunchanged to linear thin-wing theory . this suggestion is compared with\nsome experiments on delta wings and it is found that there is\nconsiderable improvement over thin-wing theory near the centre line, but that\nthis improvement is not maintained as the wing tips are approached ."}, {"doc_id": 753, "text": "development of a quasi-steady approach to flutter and\ncorrelation with kernel-function results .\n the quasi-steady approach to flutter utilizes experimental or\ntheoretical steady-state aerodynamic data to arrive at increased\nunderstanding of the flutter mechanism, and also, in many cases,\nacceptably accurate quantitative flutter predictions .\ncirculation lag effects are neglected, but aerodynamic damping is\nincluded in the evaluation of the air forces . situations requiring\nthe inclusion of rate aerodynamics for accurate flutter estimation\nare specified .\n a quasi-unsteady approach is also discussed, in which the\napproximate magnitude of the circulation lag function at flutter\nis included in simple modifications of quasi-steady parameters .\n closed-form solutions are derived for the flutter characteristics\nof a typical section with and without rate aerodynamics .\napplication is then made to the rational flutter analysis of\nthree-dimensional multi-degree-of-freedom lifting surfaces .\n a specific planform is evaluated in the mach-number range\nfrom zero to two . quasi-steady, quasi-unsteady, and\nkernel-function results are compared subsonically . quasi-steady\nresults are utilized supersonically .\n primary applications of the quasi-steady approach are in the\nareas of preliminary design and parameter-variation studies,\nmodification of more sophisticated flutter theories to force\ncompatibility with available steady-state data, and flutter evaluation\nof complex configurations which can be rationally analyzed by\nsteady-state aerodynamic theories, but for which no complete\nunsteady aerodynamic theories are presently available ."}, {"doc_id": 754, "text": "heat transfer through laminar boundary layers on\nsemi-infinite cylinders of arbitrary cross section .\n this paper shows how to calculate the rate of heat transfer\nthrough a laminar boundary layer on a semi-infinite cylinder of\narbitrary cross section . the cylinder is placed in a stream of\nincompressible fluid, the flow at infinity being parallel to the\ngenerators, and is maintained at a uniform temperature . a\nseries solution for small downstream distances and an asymptotic\nformula for large downstream distances are given . to cover\nthe intermediate range an approximate pohlhausen solution is\nobtained,. a correction of the error involved in the pohlhausen\nsolution is suggested which, it is believed, will lead to final errors\nof at most 2 percent . the calculations are applied to elliptic\ncylinders, and illustrate the effect on the local rate of heat transfer\nof varying the ratio of the major and minor axes of cross section,\nthe length of perimeter being held fixed ."}, {"doc_id": 755, "text": "oscillatory derivative measurements on sting-mounted\nwind tunnel models method of test and results for pitch\nand yaw on a cambered ogee wing at mach numbers up\nto 2. 6.\n this report describes a method which has been developed for measuring\noscillatory derivatives on sting-mounted models in the 8 ft by 8 ft\nsupersonic tunnel at r.a.e. bedford . direct and cross derivatives with\nrespect to angular displacements and velocities in pitch and yaw have\nbeen measured satisfactorily, and results are given of tests on a\ncambered ogee wing at six mach numbers from 0.2 to 2.6 . some tests\nwere made on this model in the course of the preliminary development\nwork in the 13 ft by 9 ft low speed wind tunnel, and results of these\nare included ."}, {"doc_id": 756, "text": "further comments on the inversion of large structural matrices .\nin a recent note, klein referred to a paper co-authored by the writer,\nand to ref. 3 . regarding the subject of inversion of large-order\nmatrices, klein stated that he would show 'that the situation is not as\nhopeless as the anove-mentioned authors intimate' .\nthe purpose of this note is not to take exception to klein/s\nconclusions, but rather to disagree with his implication that the\nauthors of ref. 2 were pessimistic with respect to large-matrix\ninversions . two general methods of analysis were treated.. the\nmethod of consistent distortion and the method of transfer matrices .\nthe first method leads directly to a relatively large matrix of\nstructural coefficients of both internal forces and displacements .\nthis matrix must be inverted to solve the problem . the second method\nultimately produces a relatively small matrix requiring inversion.,\nhowever, to arrive at this point one must perform a number of matrix\nmultiplications ."}, {"doc_id": 757, "text": "an investigation of the flow about a plane half-wing\nof cropped delta planform and 6( symmetrical section\nat stream mach numbers between 0. 8 and 1. 41 .\n a study has been made of the flow development\nover the wing as the incidence and stream\nmach number vary and this is illustrated by surface pressure\ndistributions and oil-flow patterns . the growth\nand movement of the two main surface shocks (the rear and\nforward shocks) is discussed, and conditions for\nflow separation through these shocks are considered . for\nthe rear shock, which has little sweep, these\nconditions are similar to those for shock-induced separation\non two-dimensional aerofoils . the forward\nshock is comparatively highly swept and separation seems\nto correspond to two rather different but\nsimultaneously-attained conditions, one related to the\ncomponent mach number normal to the shock front\nand the other to the position of the reattachment line .\n the flow in the region between the leading edge and\nthe forward shock is shown to have certain characteristics\nanalogous to those found upstream of the shock on\ntwo-dimensional aerofoils . to the rear of the forward\nshock, but ahead of the rear shock, the flow at low\nsupersonic speeds resembles in some respects that about\na simple cone .\n the general flow development is related in the\ntext to the wing lift and pitching moment, and the drag .\nthe first two are most affected by the aft movement\nof the rear shock, which also stimulates the transonic\ndrag rise . the lift-dependent drag is shown to be\ninfluenced by the appearance of leading-edge separation\nand possibly also by some stage in the development\nof the forward shock .\n the flow over the cropped-delta planform is\nnoteworthy for the absence of the strong outboard shock\nand this is attributed partly to the cropped tip and\npartly to the unswept trailing edge . a comparison is made\nwith results obtained during preliminary tests in\nwhich the wing planform closely resembled that of a true\ndelta ."}, {"doc_id": 758, "text": "the lower bound of attainable sonic-boom over-pressure\nand design methods of approaching this limit .\n from a study of existing sonic-boom\ntheory it has been possible to establish\nan approximate lower bound of attainable\nsonic-boom overpressure, which depends\nonly on the airplane length, weight, and\nvolume and on the flight conditions .\nthis lower bound may be approached over\na narrow range of flight conditions\nthrough the application of appropriate\ndesign considerations . in general, for\nintermediate values of lift coefficient\nthe major portion of the lift generating\nsurfaces must be located aft of the\nmaximum cross-sectional area, whereas for\nhigher values of lift coefficient\nthe maximum area must be well forward and or\nthe lift-producing surfaces must extend well toward the airplane nose ."}, {"doc_id": 759, "text": "stability investigation of a blunted cone and a blunted\nogive with a flared cylinder afterbody at mach numbers\nfrom 0. 30 to 2. 85 .\n a cone with a blunt nose tip and a\nblunt nose tip and a 20 flared cylinder\nafterbody have been tested in free\nflight over a mach number range from 0.30\nto 2.85 and a reynolds number range\nfrom 1 x 10 to 23 x 10 . time histories,\ncross plots of force and moment\ncoefficients, and plots of the longitudinal-force\ncoefficient, rolling velocity,\naerodynamic center, normal-force-curve slope,\nand dynamic stability are presented .\nwith the center-of-gravity location at about\nmodels were both statically and dynamically\nstable throughout the mach number\nrange . for the cone, the average aerodynamic\ncenter moved slightly forward with\ndecreasing speeds and the normal-force-curve\nslope was fairly constant throughout\nthe speed range . for the ogive, the average\naerodynamic center remained\npractically constant and the normal-force-curve\nslope remained practically constant to\na mach number of approximately 1.6 where\na rising trend was noted . maximum drag\ncoefficient for the cone, with reference\nto the base area, was approximately 0.6,\nand for the ogive, with reference to the\narea of the cylindrical portion, was\napproximately 2.1 ."}, {"doc_id": 760, "text": "inelastic buckling of initially imperfect cylindrical\nshells subject to axial compression .\n an analytical and experimental study is made for inelastic\ninstability of initially imperfect cylindrical shells subject to\naxial compression . donnell's equations and the principle of\nvirtual work are adapted to determine the effects of initial\nimperfections on the buckling modes and the critical buckling\nstresses . the deformation theory and the incremental theory\nof plastic stress-strain relationships are both considered . the\nexperimental results of ten tests on specimens made of aluminum\nalloy 3003-0 are presented . comparison of experimental with\ntheoretical results indicates that the application of the\ndeformation theory provides a fairly accurate prediction of buckling\nstrength, but fails in this case to yield a correct description of\npost-buckling behavior . on the other hand, the application of\nthe incremental theory, which is mathematically and physically\nmore rigorous, leads to an overestimation of buckling strength,\neven though initial imperfections are considered . this paradox\nhas existed for years, and remains to be resolved ."}, {"doc_id": 761, "text": "buckling of sandwich under normal pressure .\n a theoretical study is made of the buckling of a sandwich sphere\ncomprised of a core layer of low-modulus material and two thin\nfacing layers of higher modulus material . the solution for the\nbuckling resistance of the sphere under normal external pressure\nis obtained by linearized theory, and is reducible to the classical\nsolution for monocoque spherical shells . critical buckling\npressures are calculated for various radius-thickness ratios and sphere\nmaterials ."}, {"doc_id": 762, "text": "allowable axial loads and bending moments for inelastic structures\nunder nonuniform temperature distribution .\na strain-analysis method is derived and demonstrated for the\ncalculation of design allowable load-strain curves for the cross section\nof a structure supporting axial loads and bending moments . the\ntemperature effects of thermal stresses and changed material properties\nand all inelastic effects are included in the calculations so that\nthe final curve is a design curve for the applied stresses as calculated\nby room-temperature elastic procedures . the method allows for sequence\napplication and removal of load and temperature, as well as cycling\nof load and/or temperature . applications are shown for a rectangular\nbar under temperature cycling with axial loads and/or bending moments\nand for a box beam with one bending-moment temperature cycle .\ninteraction curves beyween axial load and bending moment with inelastic\neffects included are given, the calculations being done on a digital\ncomputer . a procedure is given for using the method to construct\ndesign curves ."}, {"doc_id": 763, "text": "effects of internal pressure on the buckling of circular-cylindrical\nshells under bending.\n the effect of internal pressure on the small-deflection buckling\nof thin-walled cylinders under bending is investigated by means\nof a modified donnell equation . the results indicate that the\nmaximum critical stress due to bending increases with internal\npressure, unlike the case of pressurized cylinders under\ncompression . these results represent the moment at which\nsignificant deformations appear in the cylinder, rather than the\nmaximum moment able to be carried, but may be a good\napproximation to the latter for metal cylinders ."}, {"doc_id": 764, "text": "breathing vibrations of a circular shell with an internal\nliquid .\n resonant breathing frequencies and mode shapes are\ndetermined experimentally for a thin-walled, circular cylindrical shell\ncontaining a nonviscous incompressible liquid . the resonant\nfrequencies determined for the full shell are in good agreement\nwith those predicted by reissner's shallow-shell vibration theory\nwith the inclusion of an apparent-mass term for the liquid . the\neffect of the internal liquid on the shell mode shapes is significant\nonly for the partially full shell . in this case the circumferential\nnode lines tend to shift toward the bottom or filled portion of the\nshell .\n excitation of low-frequency liquid-sloshing motion by\nhigh-frequency forced oscillation of a partially filled shell occurred in\nmany cases . this low-frequency liquid response is tentatively\nexplained as being excited by a beat frequency in the forced\noscillation . a similar type of response has been reported by\nyarymovych in axially excited rigid tanks ."}, {"doc_id": 765, "text": "clamped short oval cylindrical shells under hydrostatic\npressure .\n the principle of the minimum of the total potential is\nemployed to obtain stresses and displacements for clamped, short,\noval cylindrical shells under hydrostatic pressure . classical\nshell theory, in which buckling effects are not considered, was\nused . a fourier series is assumed for the deflections in the\nclosed circumferential direction so that the partial differential\nequations of equilibrium are replaced by a set of ordinary\ndifferential equations . the energy solution is compared with a\nsimplified approximation which can be considered an equivalent circular\ncylinder solution . graphs of the significant stresses and\ndisplacements are presented for oval cylinders having major to minor\naxis ratios of 1.10, 1.30, and 1.50 . it is shown that the maximum\nstresses and displacements increase significantly as the major to\nminor axis ratio is increased ."}, {"doc_id": 766, "text": "experimental investigation at mach number of 3. 0 of\neffects of thermal stress and buckling on flutter characteristics\nof flat single-bay panels of length-width ratio 0. 96 .\n flat, single-bay, skin stiffener\npanels with length-width ratios of 0.96\nwere tested at a mach number of 3.0,\nat dynamic pressures ranging from 1,500 to\nstagnation temperatures from 300 f to\neffects of thermal stress and buckling on the\nflutter of such panels . the panel\nsupporting structure allowed partial thermal\nexpansion of the skins in both the\nlongitudinal and lateral directions . panel\nskin material and skin thickness were varied .\n a boundary faired through the\nexperimental flutter points consisted of a\nflat-panel portion, a buckled-panel\nportion, and a transition point, at the\nintersection of the two boundaries,\nwhere a panel is most susceptible to flutter .\nthe flutter region consisted of two\nfairly distinct sections, a large-amplitude\nflutter region and a small-amplitude\nflutter region . the results show that an\nincrease in panel skin temperature\nflutter . the flutter trend for buckled\npanels is reversed . use of a modified\ntemperature parameter, which approximately\naccounts for the effects of differential\npressure and variations in panel skin\nmaterial and skin thickness, reduced the\nscatter in the data which resulted when\nthese effects were neglected . the results\nare compared with an exact theory for\nclamped panels for the condition of zero\nmidplane stress . in addition, a\ntwo-mode /transtability/ solution for clamped\npanels is compared with the\nexperimentally determined transition point ."}, {"doc_id": 767, "text": "mathematical techniques applying to the thermal fatigue behaviour\nof high temperature alloys .\nduring thermal fatigue testing\nof a specimen with a thin edge, or\nduring rapid temperature changes in the gas\nflow past turbine blades, the thin\nedges are deformed plastically in compression\nduring heating and subsequently\ncreep in tension as the bulk of the specimen\nor blade heats up . the plastic\ndeformation is determined from temperature\ndistributions, which are calculated\nby biot's variational method . the creep\ndeformation is determined as a function\nof time by a differential equation, which\nexpresses the balance between increasing\nelastic stress and reduction of stress due\nto creep relaxation, and which is solved\nto a riccati equation soluble in\nterms of bessel functions, or (iii) by transformation\nto a second-order differential\nequation with a periodic coefficient .\nusing the thermal stresses obtained from\nthe solution of the differential equation, the theoretical thermal\nfatigue endurance\nis determined from cyclic (mechanical) stress\nendurance data . agreement between\ntheoretical and experimental thermal fatigue\nendurances is obtained, over ranges\nof temperature, strain, and strain rate, or equivalently, over ranges\nof temperature-edge radius and heat transfer coefficient .\nthis agreement supports the use of\nthe theoretical methods in wider contexts .\nthe accuracy of the temperature\ndistributions is better than the accuracy of\nother factors entering into the correlation\nbetween theoretical and experimental endurances .\nimprovement in the\ninterpretation of experimental results requires\nconsideration of the alteration\nof the stress cycles during the course of thermal\nfatigue testing . this requirement\nis catered for partially by the various solutions of the differential\nequation for thermal stress ."}, {"doc_id": 768, "text": "formulae for use with the fatigue load meter in the\nassessment of wing fatigue life .\n this note gives a method for the derivation of suitable constants\nwhich, when multiplied by the readings recorded at each appropriate\nacceleration level on a fatigue load meter and then added together, give\ndirectly the proportion of fatigue life used up in the wing . it is\nsuggested that when the estimated proportion is of order 80, then a more\ndetailed assessment of fatigue life should be made ."}, {"doc_id": 769, "text": "local circumferential buckling of thin circular cylindrical\nshells .\n the problem of circumferential\nbuckling of a thin circular\ncylindrical shell due to compressive\nhoop stresses which vary in the axial\ndirection is examined . for\nextremely localised compressive hoop stress\ndistributions resulting from\nthermal discontinuity effects, or from a\nuniform, radial line loading,\nthe buckle pattern should also be\nlocalised . simplified analyses\ninto these two types of problem are\nconsidered which show that only\na limited number of buckle deflection\nmodes needs to be assumed ."}, {"doc_id": 770, "text": "the flow of a compressible fluid past a sphere .\n the flow of a compressible fluid past a sphere fixed\nin a uniform stream is calculated to the third order of\napproximation by means of the janzen-rayleigh method .\nthe velocity and the pressure distributions over the\nsurface of the sphere are computed and the terms involving\nthe fourth power of the mach number, neglected in rayleigh's\ncalculation, are shown to be of considerable importance as\nthe local velocity of sound is approached on the sphere .\nthe critical mach number, that is, the value of the mach\nnumber at which the maximum velocity of the fluid past the\nsphere is just equal to the local velocity of sound, is\ncalculated for both the second and the third\napproximations and is found to be, respectively, and ."}, {"doc_id": 771, "text": "on the flow of a compressible fluid past a sphere .\n it was shown by raleigh (philos. mag. 32, 1 (1916))\nthat the velocity potential for the subsonic flow of a\ncompressible fluid past a sphere can be expressed as a power\nseries in terms of mach's number m (which is the ratio of\nthe undisturbed velocity u, divided by the velocity of sound\nfor the undisturbed flow) . the equation in question is\nand boundary conditions are prescribed for\nraleigh himself computed the first two terms of this series,.\nthe author finds the third term . he gives some graphs\nshowing numerical differences between raleigh's and his\napproximation ."}, {"doc_id": 772, "text": "an experimental study of jet-flap compressor blades .\nthe results of a preliminary experimental investigation to determine the\n feasibility of using the jet flap to improve the section\ncharacteristics of an axial-flow compressor blade are presented and discussed\n trailing edge . internal design of the blade is described and details\nof the resulting jet flow are given . also included are wind-tunnel\ndesign and test procedures for the two-dimensional cascade used in the\ntest .\ntest results are presented in the form of the measured turning angle,\npressure rise, and lift coefficient . they are examined with particular\nreference to the prevention of rotating stall ."}, {"doc_id": 773, "text": "q . app . math . 7, 1950, 381 . experiments on porous-wall\ncooling and flow separation control in a supersonic\nnozzle .\n control of flow separation by fluid injection at one diverging\nboundary of a two-dimensional, transparent-walled de laval\nnozzle was investigated by spark schlieren photography of dry\nnitrogen flows expanded from two stagnation temperatures\ninjection conditions at the permeable boundary were varied by\nthe use of three grades of porous stainless steel with nominal pore\ndiameters of 10, 20, and 30 microns, through which nitrogen was\nforced by coolant reservoir pressures of 25, 50, and 100 psig, in\naddition to the case of no forced injection . pressure\ndistribution measurements were made along the nonpermeable diverging\nboundary . it was found that flow separation at expansion ratios\napproaching the optimum value for maximum thrust coefficient\ncould be induced at the porous wall by a local injection mass\nvelocity of the order of a few per cent of the local main-stream\nmass velocity . separation at the solid boundary was not\nnoticeably influenced by injection at the opposite wall, and the\nasymmetrical separation thus effected jet deflections of up to 10\ndegrees at the lower stagnation-pressure levels . variation of the\nwall heat-transfer condition by changing the stagnation\ntemperature did not significantly influence separation behavior .\ntemperature measurements at the reservoir face of the porous\nsection, together with use of published correlations and of the\nrube-sin analysis for estimation of stream-side stanton numbers under\nnoninjection and injection conditions, respectively, permitted\nheat-transfer calculations which indicated that the effectiveness\nof the transpiration technique in controlling nozzle wall\ntemperatures derives primarily from intimate fluid-solid contact in a\nporous material of high specific surface ."}, {"doc_id": 774, "text": "general characteristics of the flow through nozzles\nat near critical speeds .\n the characteristics of the position and form of\nthe transition surface through the critical velocity\nare computed for flow through flat and round nozzles\nfrom subsonic to supersonic velocity . corresponding\nconsiderations were carried out for the flow about profiles\nin the vicinity of sonic velocity ."}, {"doc_id": 775, "text": "studies on two dimensional flows of compressible fluid.\n it is well-known that when the flow is everywhere subsonic in a field\nof flow, the nature of the two-dimensional isentropic flow of a\ncompressible perfect fluid differs only slightly from that of the\ncorresponding flow of an incompressible perfect fluid . thus, in such a\ncase, we can calculate the field of flow by any of the well-known\nmethods of approximation . on the other hand, if the flow is supersonic\nthroughout the field, we can determine the flow pattern by the method of\ncharacteristics ."}, {"doc_id": 776, "text": "force measurements on square and dodecagonal sectional\ncylinders at high reynolds numbers .\n results are given of measurements in the compressed air tunnel\nof the forces on two cylinders, one of square cross-section and the\nother dodecagonal . the tests were carried out at various reynolds\nnumbers ranging from approximately 0.1 x 10 to 5.5 x 10, based on\nthe distance between parallel faces ."}, {"doc_id": 777, "text": "a technique for rendering approximate solutions to\nphysical problems uniformly valid .\n a method is described for treating\nsome of the characteristically\nnon-linear problems of physics, in\nparticular those involving a non-linear\npartial differential equation for\nwhich an approximate linearization is\npermissible everywhere except in a\nlimited region, such as the\nneighbourhood of (5) a singular characteristic\nof the approximate solution, or of\napproximation is valueless . the\nmethod involves a transformation of\nan independent variable, which is\ndetermined progressively with successive\napproximations to the solution ..\nonly one step being necessary if a\nfirst approximation valid uniformly\nbe obtained . the method is most\neasily understood in its application\nto simple first order ordinary\ndifferential equations, which are\nstudied in detail in 2 and 3 as a\npreparation for the extension to\nmore complicated problems in 4, 5\nand 6 . physically, the longest\nsection, 6, concerns the /spread/ of\na progressive wave at infinity,\nan important and essentially non-linear\nprocess ."}, {"doc_id": 778, "text": "an integral related to the radiation integrals .\n the author points out the relation of the integral\nto problems in astrophysics and quantum mechanics, and\nbecause of its importance supplies a table of values . the\ntable gives rl(x) to seven places of decimals from x=0 to\nx=6.00 at intervals of 0.01 . second order central differences\nare tabulated to assist in interpolation ."}, {"doc_id": 779, "text": "calculation and compilation of the unsteady lift functions for a rigid\nwing subjected to sinusoidal gusts and to sinusoidal sinking\noscillations .\nthe total lift responses of wings to sinusoidal gusts and to sinusoidal\nvertical oscillations are calculated from the response to gust\npenetration and to a sudden change in sinking velocity through use of the\nwell-established reciprocal relations for unsteady flow . the cases\nconsidered are two-dimensional wings in incompressible, subsonic\ncompressible, sonic, and supersonic flow,. elliptical and rectangular wings\n in incompressible flow,. wide rectangular and delta wings in supersonic\n flow,. and delta wings of vanishingly low aspect ratio in\nincompressible and compressible flow . for most of the cases considered,\nclosed-form expressions are given and the final results are presented in\n the form of plots of the square of the modulus of the lift coefficient\nfor wings in a sinusoidally oscillating gust and in the form of the real\n and imaginary parts of the lift component for wings undergoing\nsinusoidal sinking oscillations . a summary table is presented as a guide to\n the scope and results of this paper,. this table contains the figure\nand equation numbers for the types of flow and plan forms considered ."}, {"doc_id": 780, "text": "the transonic characteristics of 38 cambered rectangular\nwings of varying aspect ratio and thickness as determined\nby transonic-bump technique .\n an investigation to determine\nthe effects of camber on the\naerodynamic characteristics of a series\nof rectangular wings having various\naspect ratios and thickness-to-chord\nratios was conducted in the ames\nthe transonic-bump method .\nthe mach number range of the\ninvestigation was from 0.6 to 1.12, with\na corresponding reynolds number\nrange of 1.7 to 2.2 million . the lift,\ndrag, and pitching-moment data\nare presented for wings having aspect\nratios of 4, 3, 2, 1.5, and 1,\nand naca 63a2xx and 63a4xx sections with\nthickness-to-chord ratios of"}, {"doc_id": 781, "text": "use of subsonic kernel function in an influence-coefficient method of\naeroelastic analysis and some comparisons with experiment .\nthis paper illustrates the development and application of an\ninfluence-coefficient method of analysis for calculating the response\nof a flexible wing in an airstream to an oscillating disturbing force\nand for treating such aeroelastic instabilities as flutter and\ndivergence . aerodynamic coefficients are derived on the basis of\nlifting-surface theory for subsonic compressible flow by use of the method\npresented in nasa technical report r-48 .\napplication of the analysis is made to a uniform cantilever\nwing-tip tank configuration for which responses to a sinusoidal disturbing\nforce and flutter speeds were measured over a range of subsonic mach\nnumbers and densities . calculated responses and flutter speeds based\non flexibility influence coefficients measured at nine stations are in\ngood agreement with experiment, provided the aerodynamic load is\ndistributed over the wing so that local centers of pressure very nearly\ncoincide with these nine influence stations . the use of experimental\nvalues of bending and torsional structural damping coefficients in the\nanalysis generally improved the agreement between calculated and\nexperimental responses . some calculations were made to study the\neffects of density on responses near the flutter conditions, and linear\nresponse trends were obtained over a wide range of densities ."}, {"doc_id": 782, "text": "calculated subsonic span loads and resulting stability derivatives of\nunswept and 45degree sweptback tail surfaces in sideslip and steady roll .\nsubsonic span loads and the resulting stability derivatives have been\ncalculated for a systematic series of vertical- and horizontal-tail\ncombinations in sideslip and in steady roll in order to provide\ninformation embracing a wide range of probable tail configurations . all\n calculations were made by application of the discrete-horseshoe-vortex\nmethod to the problem of estimating loads on intersecting surfaces . the\n investigation covered variations in vertical-tail aspect ratio, the\nratio of horizontal-tail aspect ratio to vertical-tail aspect ratio, the\n effects of horizontal-tail dihedral angle /for the sideslip case/, and\nthe effects of vertical position of the horizontal tail for surfaces\nhaving their quarter-chord lines swept back 0degrees and 45degrees . the\n results of the investigation are presented in charts from which the\nspan loads for the various conditions can be obtained . the resulting\nstability derivatives are presented as vertical- and horizontal-tail\ncontributions as well as total-tail-assembly derivatives .\nthe results of this investigation, which was made for a wider range of\ngeometric variables than previous studies, showed trends which were in\ngeneral agreement with the results of previous investigations . also\npresented in this paper and used in the computations is an extensive\ntable of values of sidewash due to a rectangular vortex ."}, {"doc_id": 783, "text": "a method for calculating the subsonic steady-state loading on an\nairplane with a wing of arbitrary planform and stiffness .\na method for computing the steady-state span load distribution on an\nelastic airplane wing for specified airplane weights and load factors is\n given . the method is based on a modification of the weissinger\nl-method and applies at subcritical mach numbers . it includes the effects\n of external stores and fuselage on the spanwise loading .\nmodifications are outlined for treating tail-boom and tailless airplane\nconfigurations and for calculating the divergence dynamic pressure of a\nswept wing with a large external store . a method is also outlined for\nreducing wind-tunnel data to obtain effective aerodynamic coefficients\nwhich are free of model flexibility effects . the effects of mach number\n can readily be evaluated from the aerodynamic coefficients thus\nobtained ."}, {"doc_id": 784, "text": "heat transfer through the laminar boundary layer on\na circular cylinder in axial incompressible flow .\n this paper presents a method of calculating\nthe distribution of rate of heat transfer\ninto a laminar incompressible boundary layer\nfrom the exterior surface of a long thin\ncircular cylinder, when the surface of the\ncylinder is maintained at a constant\ntemperature and the flow is parallel to the\ncylinder axis,. the temperature difference\nbetween the surface and the main stream\nis taken to be small enough to neglect\nbuoyancy effects . a series solution, valid\nfor small downstream distances from the\nnose, has been obtained already by seban,\nbond, and kelly . this is now extended\nby deriving an asymptotic series solution,\nvalid at large downstream distances, and\nbridging the gap between these two series\nsolutions by an approximate solution,\nbased on the method used recently by davies\nand bourne to calculate heat transfer\nfrom a flat plate . the calculation is used to\ndemonstrate the effect of curvature\nand of prandtl number on the local rate of heat\ntransfer at various downstream\ndistances by comparing with the corresponding flat plate results ."}, {"doc_id": 785, "text": "the flow of fluid along cylinders .\nthe boundary layer equations for uniform flow parallel to the generators\n of any cylinder without corners are put into the form of a series of\nlinear third-order differential equations . the first three of these are\n the same as those obtained by seban and bond /1/ for a circular\ncylinder and solved by kelly /2/ . the rest have additional terms\ndepending on the radius of curvature of the cylinder and its derivatives . the\n problem is also attacked by a pohlhausen method as far as four terms of\n the series . for large distances from the front, rayleigh's method, as\ngiven by hasimoto /3/, gives the first two terms of an asymptotic\nexpansion for the drag . explicit calculations are made of the drag of\nan elliptic cylinder of eccentricity 1/2 3 . there is evidence that the\ndrag is everywhere less than that of a circular cylinder of the same\nperimeter ."}, {"doc_id": 786, "text": "the skin friction on infinite cylinders moving parallell to their length .\nthe frictional force on a cylinder moving steadily parallel to its\nlength through a viscous liquid which is initially at rest is determined\n with reasonable accuracy over the whole range of values of the duration\n of the motion and for a wide variety of shapes of the cylinder\ncross-section . when the time t is small, the first approximation gives a\nforce per unit area which is the same as that for a flat plate of\ninfinite width . the second approximation takes the shape of the cylinder\ninto account and the force on unit length of cylinder is determined in\nterms of the number of corners, and their angles, in the cylinder cross\nlinder is the same, to this approximation, as that on a circular\ncylinder of the same perimeter . for large values of t the determination of\nthe frictional force is reducible to that of a potential problem, the\nsolution of which is known for a number of different shapes . the\napproximations for small and large values of t for any one cylinder do\nnot overlap but can be joined without much ambiguity . for no value of t\n do the forces on cylinders of different shape /excluding those whose\ncurvature is not everywhere inwards/ differ by more than about 25 per\ncent ."}, {"doc_id": 787, "text": "rayleigh's problem for a cylinder of arbitrary shape .\nthe motion of an incompressible viscous fluid generated by a cylinder of\n arbitrary cross-sectional form which is started to move suddenly from\nrest with uniform velocity in the direction of its length is considered\n formulae in powers of are derived for the velocity distribution /valid\nin the vicinity of the cylinder/ and for the frictional drag on the\ncylinder, correct to the order of a, where a is the characteristic length\nof the cross section, v is the kinematic viscosity, and t is the time .\nthese formulae are given in terms of only the analytic function which\nmaps conformally the region outside the cross section of the cylinder\nonto the region outside the unit circle, and of certain integrals e\nwhich are common to any arbitrary cylinder . in particular, when a is\nsufficiently small, the total frictional drag on the cylinder per unit\nlength is expressed as, irrespective of the cross-sectional form, where\nb 2 and y 0.5772.../euler's constant/ ."}, {"doc_id": 788, "text": "an approximate boundary layer theory for semi-infinite cylinders of\narbitrary cross-section .\nan estimate is given of the distribution of skin frictional force per\nunit length, and of displacement area, on the outside of a semi-infinite\n cylinder, of arbitrary cross-section, moving steadily in a direction\nparallel to its generators . a pohlhausen method is employed with a\nvelocity distribution chosen to yield zero viscous retarding force on\nthe boundary layer approximations . /the smallness of the fluid\nacceleration far from the leading edge has been pointed out by batchelor\nreasonable results atlarge distances from the leading edge . however,\nfor a large class of cross-sections, which includes all convex\ncross-sections and locally concave cross-sections with re-entrant angles\ngreater than 1/2, the method yields the expected square root growth of\nthe boundary layer at the leading-edge, with a fairly close\napproximation to the coefficient, and it is supposed that the skin-frictional\nforce and displacement area are given with reasonable accuracy along the\n whole length of the cylinder .\nresults for the elliptic cylinder and the finite flat plate are given in\n closed form, valid for the whole length of the cylinder, and are\nexpected to be in error by at most 20 per cent . in addition, some\nestimate is given of the effect of corners on skin frictional force and\ndisplacement area ."}, {"doc_id": 789, "text": "a further note on the calculation of heat transfer\nthrough the axisymmetrical laminar boundary layer on\na circular cylinder .\n by using a karman-pohlhausen method\nthe distribution of local rate of heat\ntransfer is ovaluated for the case of air flow\nin an axisymmetrical laminar boundary\nlayer on a heated circular cylinder, the temperature\nof the cylinder being independent\nof downstream distance . this calculation\nserves to link the numerical values\nobtained by seban, bond, and kelly\nfor small downstream distances to those\nobtained by bourne and davies for large\ndownstream distances ."}, {"doc_id": 790, "text": "a wind-tunnel test technique for measuring the dynamic rotary\nstability derivatives at subsonic and supersonic speeds .\na method is described for measuring the dynamic stability derivatives\nof a model airplane in a wind tunnel . the characteristic features\nof this system are that single-degree-of-freedom oscillations were\nused to obtain combinations of rolling, yawing and pitching motions.,\nthat the oscillations were excited and controlled by velocity feedback\nwhich permitted operation under conditions unfavorable for more\nconventional types of oscillatory testing., and that data processing was\ngreatly simplified by using analog computer elements in the strain-gage\ncircuitry .\nthe system described is primarily for measurement of the damping\nderivatives damping\nin roll damping in pitch, damping in yaw, and the cross derivatives\nrolling moment due to yawing and yawing moment due to rolling . the\nmethod of testing also permits measurement under oscillatory conditions\nof the static derivatives rolling moment due to sideslip, yawing moment\ndue to sideslip, and pitching moment due to angle of attack . all these\nderivatives are of particular importance in estimating the short-period\noscillatory motions of a rigid airplane .\na small number of experimental data are included to illustrate the\ngeneral scope of results obtainable with this system ."}, {"doc_id": 791, "text": "measurements at mach numbers up to 2. 8 of the longitudinal\ncharacteristics of one plane and three cambered slender\n'ogee' wings .\n measurements have been made of\nthe longitudinal characteristics of one\nplane and three cambered slender ogee\nwings (p = 0.45,) at two\nsubsonic and eight supersonic mach\nnumbers up to 2.8 . the tests also included\nmeasurements of the zero-lift pressure\ndrag and support interference of the\nplane wing . the results have been analysed\nto give data for estimating the\nperformance of supersonic transport aircraft ."}, {"doc_id": 792, "text": "some low speed problems of high speed aircraft .\nthe first part of the paper deals with the low speed aerodynamics of\naircraft shapes suggested by kuchemann, at the second international\ncongress in aeronautical sciences at zurich in 1960, as suitable for\nachieving a required range at supersonic speeds, namely wingbody\narrangements with sweepback angles of 55degrees or 60degrees and\nstreamwise thickness-chord ratio of about 5 per cent suitable for low\nsupersonic speed, and slender near-triangular wings with sharp leading\nedges suitable for mach numbers of about 2 or more .\nno attention is given to /slewed/ wings, powered lift or variable\ngeometry .\nin dealing briefly with swept wings, the need for avoiding separation of\n flow from the leading edge is demonstrated, with the conclusion that it\n is desirable to use leading edge flaps with blowing or suction at the\nknee together with blown trailing edge flaps . wind tunnel tests are\ndescribed on a simplified model with these boundary layer control\nmethods applied . mention is made of the possibility of adverse ground\neffect on maximum lift .\nmore attention is given to the case of slender wings because their use\ninvolves a new type of flow with separation from all edges . this flow\nand its steadiness are therefore discussed from the point of view of\nthe possibility of buffeting,. the effect of plan form on static\nlongitudinal stability and pitch-up is analysed,. and a short summary of\n available results on damping in pitch is given . large rolling moments\ndue to sideslip are shown to give rise to serious problems of control,\nand the present state of knowledge of static lateral and directional\nstability and rolling and yawing rotary derivatives is discussed .\nfinally the effects of proximity to the ground are summarised .\nthe second part of the paper is concerned with work aimed at clarifying\nsome of the requirements for handling qualities of future aircraft . it\nis not so much concerned with forecasts of the dynamic behaviour of\nthese future aircraft as with determining what the pilot wants .\ntwo aspects of control in the vertical plane are discussed in some\ndetail namely speed control and glide path holding . flight tests on an\navro 707a aircraft, with artificially worsened characteristics, are\ndescribed, and it is shown that substantially constant performance in the\npiloting task can be achieved at the expense of increased pilot effort .\n some tentative conclusions on desirable levels of speed stability and\nphugoid damping are, nevertheless, drawn .\na brief review of the present status of lateral/directional handling\nrequirements, using mainly american data, is also included ."}, {"doc_id": 793, "text": "the flow pattern on a tapered sweptback wing at mach numbers between 0.6\n and 1.6 .\nthe development of the flow pattern on a swept wing with incidence and\nstream mach number is described . the wing, of aspect ratio 2 828,\ntaper ratio 0 333 and leading-edge sweep 53 5 deg, was tested at mach\nnumbers between 0 6 and 1 6 at incidences up to about 12 deg . the test\nreynolds number varied with mach number, being typically 2 3 x 10 at m\nleading edge .\nit is shown that the flow pattern at moderate incidences develops\nsmoothly from a subsonic type involving leading-edge separation to a\nsupersonic type where the flow is attached near the leading edge and\nwith shock-induced separation further aft . the formation and movement\nof the shock-wave system and the vortices near the wing surface are\nbriefly discussed ."}, {"doc_id": 794, "text": "experiments with a tapered swept-back wing of warren 12 planform at mach\n numbers between 0.6 and 1.6 .\nthe development of the flow pattern on a wing of aspect ratio 2 828,\ntaper ratio 0 333, leading-edge sweepback 53 5 deg and 6 per cent\nthickness/chord ratio in the streamwise direction has been described in\npart 1, which discussed oil-flow patterns obtained on the surface of the\n wing . the complete programme of tests also included pressure plotting\nat four spanwise stations and force measurements . these are discussed\nin relation to the flow development in this part of the report .\nthe wing was tested at mach numbers between 0 6 and 1 6 for incidences\nup to about 14 deg . the tunnel stagnation pressure was held constant at\na value near atmospheric pressure during the tests, so that the reynolds\n number varied with mach number .. at m 1 0 it was 2 3 x 10 based on the\n mean aerodynamic chord . boundary-layer transition was fixed by a\nroughness band at the leading edge .\na detailed analysis has been made of the pressure distributions on the\nsurface of the wing and the chordwise distributions integrated to\ndetermine the spanwise loading . the overall lift and pitching moment of\n the wing were also obtained from these data, as well as from direct\nmeasurements using a strain-gauge balance, by means of which the wing\ndrag was also determined . these results are considered in some detail\nto illustrate the effects of mach number and incidence on the flow about\n the model . a preliminary analysis is also made of the conditions for\nboundary-layer separation due to shock waves on the wing surface . the\nprincipal factor appears to be the component of mach number normal to\nthe shock front ."}, {"doc_id": 795, "text": "the operation of the npl 18in x 14in. wind tunnel in the transonic speed\n range .\na brief description of the slotted liners used is given together with\nthe power requirements and some flow surveys .\nsome observations are made on wall interference on a half-model of a\nswept wing tested in the wind tunnel ."}, {"doc_id": 796, "text": "an investigation at transonic speeds of the performance of various\ndistributed roughness bands used to cause boundary layer transition\nnear the leading edge of a cropped delta half-wing .\ndistributed roughness bands of no.320 and no.500 carborundum were found\nto be effective in causing boundary-layer transition if they extended\nover the first 5( and 10( respectively of the local chord . use of\nlarger grain sizes, or increases in the band width for a given grain\nsize resulted in a drag penalty . with very large particle sizes /about\nbetween the particles . the drag penalty was constant over the test mach\n number range /0.80 to 1.15/ and decreased slowly with incidence . the\nwing lift and pitching moment were only slightly modified by the\npresence of any of the roughness bands tested, but this result would not\n of course necessarily apply to wings of other planforms or section\nshapes . the test reynolds number was about 2.7 million .\nin the appendix, the structure of the roughness bands is discussed, as\nwell as the details of the materials used and the techniques used to\napply the band ."}, {"doc_id": 797, "text": "a study of the effect of leading-edge modifications on the flow over\na 50degree sweptback wing at transonic speeds .\nsummary . an investigation has been made in the n.p.l. 18 in. x 14 in .\ntunnel of the effects of leading-edge modifications on the flow and\nforces on an untapered wing of 50 deg leading-edge sweep, at stream mach\n numbers between 0 60 and 1 20 . seven leading-edge profiles were\ntested, ranging from a drooped extension of 18 per cent of the chord of\nthe basic sharp-nosed section to a round-nosed section with a\nleading-edge radius of 1 0 per cent of the basic chord .\nleading-edge droop was found to increase the wing drag near zero lift\nbut to reduce appreciably the lift-dependent drag component, except at\nthe highest test mach numbers . droop also increased the lift\ncoefficient at which leading-edge separation occurred on the upper surface\nat moderate subsonic speeds, but in addition reduced the mach number for\n transonic flow attachment . the appearance of the forward shock /but\nnot the rear shock/ is considerably delayed when the leading edge is\ndrooped .\nwith the undrooped sections an increase in leading-edge radius was\naccompanied by successively earlier appearances of the forward shock,\nand hence the outboard shock with its attendant separation . the\nconditions at which the rear shock first appeared changed only slowly as the\nsection was changed .\nthe variations in wing flow pattern as the leading edge is modified are\ndiscussed and related to measured changes in the wing lift and drag .\nan attempt is also made to estimate the local mach numbers on some parts\n of the wing from the oil-flow patterns,. this material is used to\nassess the flow conditions appropriate to shock-induced separation .\nthe main section of the report concludes with a tentative discussion of\nthe significance of the present results to the design of swept wings .\nin an appendix results obtained with the wing in a sweptforward\nconfiguration are briefly considered ."}, {"doc_id": 798, "text": "interaction between shock waves and boundary layers, with a note on the\neffects of the interaction of the performance of supersonic intakes .\nthe interaction between shock waves and boundary layers has important\neffects in many problems of high-speed flow . this paper has been\nwritten as a guide to the literature on the subject, and as a critical\nreview of the present state of knowledge concerning both the underlying\nphysical processes and the practical applications . it will be clear to\nthe reader that, although substantial progress has been made, our\nknowledge is still far from complete and that more work both of a\nfundamental nature and on specific applications is needed before the problem\nis understood sufficiently well for design purposes .\npart i of the paper describes experiments on comparatively simple types\nof flow designed to provide fundamental information and to assist in the\n development of the theory . these experiments show that the interaction\n depends mainly on the mach and reynolds numbers and on the strength of\nthe shock wave . in particular, the interaction of a shock wave with a\nlaminar boundary layer is shown to produce much larger effects than if\nthe boundary layer is turbulent . for most cases where the effects of\nthe interaction are large enough to have serious practical consequences\nit is found that the boundary layer separates from the surface, and the\ndifference between the interaction with laminar and turbulent layers\narises mainly because the laminar layer separates much more readily in\nan adverse pressure gradient . the details of the interaction downstream\n of the separation point thus depend critically on the behaviour of the\nseparated layer, and on the conditions under which it reattaches to the\nsurface .\nmany of the features found in the fundamental experiments appear also in\n practical applications and these are considered in parts ii and iii of\nthe paper . although the emphasis hero is on the performance of\naerfoils and wings moving at high subsonic speeds, the importance of the\ninteraction in other examples such as at supersonic trailing edges and\nin supersonic intakes is also discussed briefly . the differences\nbetween the interaction with laminar and turbulent boundary layers are\noften a source of serious discrepancy between model experiments and\nfull-scale conditions . for small-scale models it is, therefore,\nfrequently essential to make the boundary layer turbulent by artificial\nmeans . some of the difficulties involved in doing this, and certain of\nthe more promising methods are briefly discussed . it is shown that\nexperiments on models with transition fixed can be used to explain a\nnumber of aerodynamic effects encountered in transonic flight, and\nconnected with the occurrence of shock-induced separation of the\nturbulent boundary layers . for both two-dimensional aerofoils and straight\n and sweptback wings, turbulent separation occurs for shocks above a\ncertain strength which applies for both model and full-scale conditions\nfull-scale conditions,. differences in magnitude would be expected if\nthe pressure recovery along the separated layer between the shock and\nthe trailing edge is affected by reynolds number, but little information\n is at present available on this point .\nmost of the repercussions of turbulent separation on the steady-motion\ncharacteristics of aerofoils and wings can be traced to the associated\nreduction in the pressure recovery over the roar of the surface . this\nis because the pressure at the trailing edge controls the inter-relation\n between the two surfaces /so long as the flow at the trailing edge\nremains subsonic/, and in particular the relative movements of the shock\n waves and the extents of the local regions of supersonic flow . certain\n unsteady-flow characteristics such as buffeting and control surface\nseparation .\nsome evidence is presented on the influence of section shape on the\noccurrence and effects of separation, but in this, as in many other\nrespects, information relevant to turbulent boundary layers is scarce .\nsome notes on the further work which is required are given in part iv of\n the paper ."}, {"doc_id": 799, "text": "some effects of wind-tunnel interference observed in tests on\ntwo-dimensional aerofoils at high subsonic and transonic speeds .\nin the high-speed research on two-dimensional aerofoils at the national\nphysical laboratory the need to keep model size above a certain minimum,\n in order to reproduce correctly the boundary layer separation effects\nexperienced at full scale, has been considered paramount even at the\nrisk of incurring significant tunnel interference effects .\nthis report discusses the interference effects for the slotted working\nsections now in use . the magnitudes of the blockage and lift effect\ncorrections are deduced for the ratio of model chord to tunnel height\nnormally used . it is shown that a simple adaptation to reduce the open\narea of the walls would reduce both corrections to insignificant\nproportions simultaneously, but would give a reduced choking mach number\nseparated flows . the observed trends in the variation of the blockage\neffects for other ratios of model chord to tunnel height differ from\nthose predicted theoretically, and so the results cannot be applied more\n generally until these trends have been checked by further\ninvestigations .\nit is suggested that wake interference effects can significantly\ninfluence the manner in which separated flows develop with increasing\nincidence or mach number, particularly for walls of small open area .\nexamples are also given of effects of distortions in the local\nsupersonic flow, which are most noticeable for walls with relatively large\nopen areas ."}, {"doc_id": 800, "text": "wall interference at transonic speeds on a hemisphere cylinder model .\ntests have been made in three n.p.l. wind tunnels on a pressure-plotting\n model consisting of a long cylinder with a hemispherical nose . the\nsurface pressure distributions were measured for stream mach numbers\nbetween 0.7 and 1.1 at zero model incidence, and schlieren photographs\nwere taken . the blockage ratios were 0.211(, 0.117( and 0.120( .\nthe principal feature of the flow is the effect of working section size\non the rate at which the terminal shock wave moves back along the model\nwith increasing stream mach number . this is thought to depend mainly\non the distance from the model to the slotted walls of the tunnel,\nand not necessarily on the blockage ratio . the distance of the solid\nsidewall is important in influencing the local mach number ahead of the\nterminal shock, by reflecting the expansion-wave system originating near\n the model nose ."}, {"doc_id": 801, "text": "experimental study of the equivalence of transonic\nflow about slender cone-cylinders of circular and elliptic\ncross section .\n this report describes an experimental investigation of the equivalence\nrelationship and the related theory for lifting forces proposed by\ntransonic slender-body theory . the models chosen for this study are a\nflat, winglike, elliptic cone-cylinder and its equivalent body of\nrevolution, a circular cone-cylinder . it is determined that the flows\nabout the two models are closely related in the manner predicted by the\ntheory, the relationship persisting over a mach number range of 0.92 to\ncone-cylinder vary linearly only over the small angle-of-attack range of\napproximately 1 and that the aerodynamic loading at sonic speed compares\nfavorably with jones' slender-wing theory .\n the results of the investigation suggest that at transonic speeds and\nat small angles of attack the calculation of all aerodynamic\ncharacteristics of slender, three-dimensional shapes can be made by use\nof transonic slender-body theory when the pressures on the equivalent\nbody of revolution are known, either by experiment, or by an adequate\nnonlinear theory . from transonic slender-body theory it is deduced\nthat the slenderness required for this application is the same as that\nrequired for the successful application of the transonic area rule ."}, {"doc_id": 802, "text": "the behaviour of supersonic flow past a body of revolution\nfar from the axis .\na theory is developed of the supersonic flow past a body of revolution\nat large distances from the axis, where a linearized approximation is\nvalueless owing to the divergence of the characteristics at infinity .\nit is used to find the asymptotic forms of the equations of the shocks\nwhich are formed from the neighbourhoods of the nose and tail . in the\nspecial case of a slender pointed body, the general theory at large\ndistances is used to modify the linearized approximation to give a\ntheory which is uniformly valid at all distances from the axis . the\nresults which are of physical importance are summarized in the\nconclusion (9) and compared with the results of experimental\nobservations ."}, {"doc_id": 803, "text": "the shock pattern of a wing-body combination far from\nthe flight path .\n the position and strength of the front shock wave at large\ndistances from a wing-body combination, are deduced from the linear\ntheory for the combination, using a method developed by whitham . the\ncombination consists of a body of revolution and a wing which has\nthickness and is lifting . the effects of interference between the flow\nover the body and the flow over the wing are included . in any\ndirection the flow far from the wing-body combination is equivalent to\nthe flow past a body of revolution determined from the configuration of\nthe combination . the modified formulae for unsteady flow are given and\nsome results are evaluated for the combination of a body of revolution\nand a delta wing with subsonic leading edges ."}, {"doc_id": 804, "text": "a flight test investigation of the sonic boom .\n the /sonic boom/ as it is now popularly called, has become the\ncenter of considerable interest during the past few years because of\nwidespread public disturbance and possible damage that can result\nfrom it . in the hopes of minimizing this disturbance and to extend\nthe general knowledge of the shock waves which produce the booming\nnoise, the aeronautical research laboratory, wright air development\ncenter, has initiated an extensive research program to study the sonic\nboom phenomenon .\n this report presents the results of flight tests undertaken as one\nphase of this program . the tests had as their objective the\ndetermination and measurement of the shock wave pressure pattern surrounding\nan f-100 aircraft in level supersonic flight .\n the flight tests were conducted at the air force flight test\ncenter, edwards air force base, california, under the authority of air\nresearch and development command test directive no. 5524-f1 ."}, {"doc_id": 805, "text": "ground measurements of the shock wave noise from airplanes\nin level flight at mach numbers to 1. 4 and at altitudes\nto 45,000 feet .\n time histories of noise pressures near ground level were measured\nduring flight tests of fighter-type airplanes over fairly flat, partly\nwooded terrain in the mach number range between 1.13 and 1.4 and at\naltitudes from 25,000 to 45,000 feet . atmospheric soundings and\nradar-tracking studies were made for correlation with the measured noise\ndata .\n the measured and calculated values of the pressure rise across the\nshock wave were generally in good agreement . there is a tendency for\nthe theory to overestimate the pressure at locations remote from the\ntrack and to underestimate the pressures for conditions of high tailwind\nat altitude . the measured values of ground-reflection factor averaged\nabout 1.8 for the surfaces tested as compared to a theoretical value\nof 2.0 . two booms were measured in all cases . the observers also\ngenerally reported two booms,. although, in some cases, only one boom\nwas reported . the shock-wave noise associated with some of the flight\ntests was judged to be objectionable by ground observers, and in one\ncase the cracking of a plate-glass store window was correlated in time\nwith the passage of the airplane at an altitude of 25,000 feet ."}, {"doc_id": 806, "text": "ground measurements of airplane shock wave noise at\nmach numbers to 2, and at altitudes of 60,000 feet .\n the intensity of shock-wave noise at the ground resulting from\nflights at mach numbers to 2.0 and altitudes to 60,000 feet was\nmeasured . measurements near the ground track for flights of a\nsupersonic fighter and one flight of a supersonic bomber are\npresented .\n level cruising flight at an altitude of 60,000 feet and a mach\nnumber of 2.0 produced sonic booms which were considered to be\ntolerable, and it is reasonable to expect that cruising flight at higher\naltitudes will produce booms of tolerable intensity for airplanes of the\nsize and weight of the test airplanes . the measured variation of\nsonic-boom intensity with altitude was in good agreement with the\nvariation calculated by an equation given in nasa technical note d-48 .\n the effect of mach number on the ground overpressure is small between\nmach numbers of 1.4 and 2.0, a result in agreement with the theory . no\namplification of the shock-wave overpressures due to refraction effects\nwas apparent near the cutoff mach number .\n a method for estimating the effect of flight-path angle on cutoff\nmach number is shown . experimental results indicate agreement with the\nmethod, since a climb maneuver produced booms of a much decreased\nintensity as compared with the intensity of those measured in level flight at\nabout the same altitude and mach number .\n comparison of sound pressure levels for the fighter and bomber\nairplanes indicated little effect of either airplane size or weight at an\naltitude of 40,000 feet ."}, {"doc_id": 807, "text": "ground measurements of the shock wave noise from\nsupersonic bomber airplanes in the altitude range from 30,000\nto 50,000 feet .\n shock-wave ground-pressure measurements\nhave been made for\nsupersonic bomber airplanes in the mach number\nrange from 1.24 to 1.52, for\naltitudes from about 30,000 to 50,000 feet,\nand for a gross-weight range\nfrom about 83,000 to 120,000 pounds . the\nmeasured overpressures were\ngenerally higher than would be predicted\nby the theory which accounts\nonly for volume effects . there is thus\na suggestion that lift effects\non sonic-boom intensity may be significant\nfor this type of airplane\nfor the altitude range of the present tests ."}, {"doc_id": 808, "text": "an investigation of some aspects of the sonic boom\nby means of wind tunnel measurements of pressures about\nseveral bodies at a mach number of 2. 01 .\n an investigation of some aspects\nof the sonic boom has been made\nwith the aid of wind-tunnel measurements\nof the pressure distributions\nabout bodies of various shapes . the\ntests were made in the langley\nat a mach number of 2.01 and\nat a reynolds number per foot of 2.5 x 10 .\nmeasurements of the pressure\nfield were made at orifices in the surface\nof a boundary-layer bypass\nplate . the models which represented both\nfuselage and wing types of\nthickness distributions were small enough\nto allow measurements as far\naway as 8 body lengths or 64 chords . the\nresults are compared with\nestimates made using existing theory .\n to the first order, the boom-producing\npressure rise across the bow\nshock is dependent on the longitudinal\ndevelopment of body area and not\non local details . nonaxisymmetrical shapes\nmay be replaced by\nequivalent bodies of revolution to obtain satisfactory\ntheoretical estimates\nof the far-field pressures ."}, {"doc_id": 809, "text": "an investigation of the influence of lift on sonic-boom\nintensity by means of wind tunnel measurements of the\npressure fields of several wing-body combinations at\na mach number of 2. 01 .\n an investigation of the effect\nof lift on sonic-boom intensity has\nbeen performed by means of wind-tunnel\nmeasurements of the pressure fields\nsurrounding small wing-body combinations .\nthe tests were conducted in\nthe langley 4- by 4-foot supersonic\npressure tunnel at a mach number of\nper foot . effects of lift were\nfound to be real and significant .\nmeasured bow-shock intensities agreed\nfairly well with, but were consistently\nless than, shock intensities\nestimated by theoretical methods .\navailable flight data were examined\nfor correlation with wind-tunnel test\nresults ."}, {"doc_id": 810, "text": "the shock wave noise problem of supersonic aircraft\nin steady flight .\n data are presented which provide\nan insight into the nature of the\nshock-wave noise problem, the significant\nvariables involved, and the\nmanner in which airplane operation\nmay be affected . flight-test data\nare also given, and a comparison with\nthe available theory is made . an\nattempt is also made to correlate the\nsubjective reactions of observers\nand some associated physical phenomena\nwith the pressure amplitudes\nduring full-scale flight .\n it is indicated that for the proposed\nsupersonic transport airplanes\nof the future, booms on the ground will\nmost probably be experienced\nduring the major portion of the flight\nplan . the boom pressures will be\nmost severe during the climb and descent\nphases of the flight plan .\nduring the cruise phase of the flight,\nthe boom pressures are of much\nlesser intensity but are spread laterally\nfor many miles . the manner\nin which the airplane is operated appears\nto be significant,. for example,\nthe boom pressures during the climb,\ncruise, and descent phases can be\nminimized by operating the airplane at\nits maximum altitude consistent\nwith its performance capabilities ."}, {"doc_id": 811, "text": "an investigation of lifting effects on the intensity\nof sonic booms .\n this paper is a brief summary of\nan investigation made to check the effect of lift\non the shock noise of aircraft flying at supersonic\nspeeds . the method of hayes has been\ncombined with the theory of whitham to\npredict the asymptotic shock strength of wings\ncarrying lift and of combinations of bodies\nand lifting wings . (a similar, but not quite as\ngeneral, method was derived by walkden in\nref. 6 .) whitham's formula, including only the\nvolume term, has been used extensively to predict\nthe boom intensity of aeroplane type bodies\nand the agreement with experiment has, so far,\nbeen quite reasonable . the test data obtained\nto date extends only up to about 40,000 ft.\naltitude and the calculations of this paper show\nthat under those conditions the shock noise of\nthe aircraft tested so far will, in most cases,\nbe dominated by the volume term . it is shown\nthat at higher altitudes lifting effects will\ndominate for even the small fighter and they will\ndominate over most of the altitude range\nfor large bomber and supersonic transport\naircraft . the boom intensity due to lift decreases\nwith altitude as which compares to\nin the volume case (=pressure at\naltitude h) . it is insensitive to mach number,\nwing loading, wing plan shape and\nlift distribution . a simple rule for calculating\nthe shock noise due to combined volume and\nlifting effects is proposed which is applicable to\nconfigurations with wings located towards the\nrear of the fuselage . the rule states that the shock\nnoise of an aircraft carrying lift is equal\nto the shock noise due to volume (neglecting lift)\nor the shock noise due to lift (neglecting\nvolume), whichever is the greater . a chart is\npresented from which rapid estimates can be\nmade of the shock noise of lifting\nwing-body combinations ."}, {"doc_id": 812, "text": "investigation of two bluff shapes in axial free flight\nover a mach number range from 0. 35 to 2. 15 .\n a fineness-ratio-2.71 right circular cylinder and a fineness-\nratio-been tested in free flight over a mach number range of 0.35 to 2.15 and\na reynolds number range of 1 x 10 to 12 x 10 . time histories, cross\nplots of force coefficients, rolling velocity, and longitudinal-force\ncoefficient are presented for both cylinders . in addition, cross plots\nof moment coefficients and plots of the normal-force curve slope and\nthe aerodynamic center are presented for the fineness-ratio-2.71\ncylinder . the average aerodynamic center of the right circular\ncylinder moved rearward with decreasing speeds until at the subsonic\nmach numbers it remained approximately constant and comparisons of the\ndrag data of this test with wind tunnel and other free-flight data show\ngood agreement . an appreciable decrease in drag was observed when the\ndata of the present test of the rounded nose cylinder were compared with\ndata of a right circular cylinder of a similar configuration ."}, {"doc_id": 813, "text": "the motion of rolling symmetrical missiles referred\nto a body-axis system .\n the linearized equations of motion have been derived for a rolling\nmissile having slight aerodynamic asymmetries . time histories of\nrolling-missile motions referred to a body-axis system have been\nprepared to show the types of missile motions that can be encountered .\nthe motions resulting from a trim change and a pulse-rocket disturbance\nare shown to be determined mainly by the ratio of rolling velocity to\npitching frequency .\n finally, the derived equations are used in establishing a technique\nfor the reduction of rolling-missile oscillation data . it is shown\nthat the aerodynamic derivatives can be obtained from flight data if\nfour accelerations are measured . the method is applied to the results\nobtained from a flight test of a missile configuration ."}, {"doc_id": 814, "text": "stability derivatives of cones at supersonic speeds .\n the aerodynamic stability derivatives due to pitching velocity and\nvertical acceleration are calculated by use of potential theory for\ncircular cones traveling at supersonic speeds . the analysis is based on\ntwo theoretical techniques used successfully previously in application\nto the case of uniform axial and inclined flow . in the first,\npotential solutions for axial flow and crossflow are derived from the\nfirst-order wave equation but in application to calculations for the\nforces no approximations are made either to the tangency condition or\nto the isentropic pressure relation . the second method consists in\ncombining the first-order crossflow potential with an axial-flow\npotential correct to second order . closed-form solutions by both\nmethods are found for a cone, and numerical results for the stability\nderivatives are presented as a function of mach number for cones having\nsemivertex angles of 10 and 20 .\n in addition, expressions for the forces, moments, and stability\nderivatives of arbitrary bodies of revolution are obtained using\nnewtonian impact theory . numerical results for cones compare well\nwith those obtained from the combined first- and second-order potential\ntheory at the highest mach number for which the latter theory is\napplicable ."}, {"doc_id": 815, "text": "investigation of several blunt bodies to determine\ntrans- onic aerodynamic characteristics including effects\nof spinning and of extendible afterbody flaps and some\nmeasurements of unsteady base pressures .\n several blunt bodies having shapes that may be suitable for\natmospheric reentry vehicles were tested to determine the aerodynamic\ncharacteristics of such shapes for angles of attack up to 34 . the tests\nwere conducted through the transonic mach number range and at reynolds\nnumbers from 1.74 x 10 to 2.78 x 10, based on body diameter .\n a full-skirted rather than a short-skirted type of shape developed\nthe greatest amount of static stability and the largest lift-curve\nslopes . the angle of attack for maximum lift for such bodies appears\nto be subject to mach number effects . spinning a full-skirted body\nabout its longitudinal axis generally increased the lift and reduced the\npitching moment at angles of attack and reduced the aerodynamic static\nstability parameter through the transonic mach number range . the\nextension of segmented clamshell-shaped flaps from the afterbody of a\nshort-skirted model served to increase the lift and static stability\nonly if the flaps extended into the airstream .\n some evidence was found of oscillatory base pressures on two\ndissimilar shapes at certain high angles of attack and the highest mach\nnumber in these tests . there is doubt, however, that these pressures\ncan induce any significant oscillatory motion for a reentry vehicle\nbecause of their small amplitude and phasing ."}, {"doc_id": 816, "text": "experimental investigation at a mach number of 3. 11\nof the lift, drag and pitching moment characteristics\nof a number of blunt low-fineness-ratio bodies .\n a number of blunt bodies having shapes that may be suitable for\natmospheric reentry were tested to determine the lift, drag, and\npitching-moment characteristics at a mach number of 3.11 and a reynolds\nnumber of 6 x 10 based on maximum body diameter of 2 inches .\n the results of the tests showed that all the bodies were statically\nstable about a point located one-third of the body length from the\nnose . the results also showed that high-drag bodies which have a large\nportion of their afterbodies negatively sloped (decrease in\ncross-sectional area from nose to base) may have a negative lift-curve slope .\nthis negative slope results from the large negative lift component of\nthe axial force obtained with those bodies and the fact that with\nnegatively sloped afterbodies only small normal forces are developed ."}, {"doc_id": 817, "text": "loading paths and the incremental stress law .\n this paper will be concerned with some properties of the\nstress-strain law for work hardening materials introduced by w. prager\nincremental strain or plastic flow law by which it is meant that the\ndifferentials of strain are expressed as functions of the stresses,\nstrains, and differentials of the stress . we shall also have occasion\nto refer to total strain or plastic deformation laws, in which the\nstrains are given directly as functions of the stress ."}, {"doc_id": 818, "text": "a quantitative comparison of flow and deformation theories\nof plasticity .\n the stresses and displacements in a partly plastic,\ninfinitely long, hollow cylinder are obtained according to the\nflow type of stress-strain law of prandtl-reuss and to the\ndeformation law of hencky . in both cases the mises yield\ncondition is used and the compressibility of the material is\ntaken into account . it is shown that under these\nassumptions the two theories yield substantially the same\nresults for this particular problem, but that one theory or\nthe other may be preferable for computing purposes in\ncertain cases . the results are compared with those of\nother investigations in which different combinations of\nstress-strain law, yield condition, compressibility, and end\nloading were assumed ."}, {"doc_id": 819, "text": "stresses in the plastic range around a normally loaded\ncircular hole in an infinite sheet .\nthe stresses in the plastic range around a normally loaded circular hole\nin an infinite sheet are found numerically on the basis of both\ndeformation and incremental theories . the results of deformation\ntheory are quantitatively assessed in the light of a criterion, recently\ndeveloped by budiansky, for the acceptability of deformation theories .\nthe criterion is completely satisfied . moreover, the results obtained\nby using these two different theories of plasticity do not differ\ngreatly despite the fact that the stress paths are far from being\nradial ."}, {"doc_id": 820, "text": "theories of plastic buckling .\n the theory for the plastic buckling of columns which appears\nfinally to have achieved a satisfactory form, rests upon the\nwell-established uniaxial stress-strain relation . the development of\na correspondingly satisfactory theory for the plastic buckling of\nplates has been hampered by the nonexistence of an established\npolyaxial stress-strain relation in the plastic range .\n present theories for the polyaxial stress-strain relation beyond\nthe elastic range can be divided into two types, often called flow\nand deformation theories . theories of plastic buckling based on\ndeformation theories are in better agreement with experiment\nthan those based on flow theories . on the other hand, tests in\nwhich a material is compressed into the plastic range and then\nsubjected to shear at constant compressive stress are in better\nagreement with flow than with deformation theories . legitimate\ndoubt therefore has existed as to the validity of any theory for\nthe plastic buckling of plates .\n as a result of studying these apparent contradictions, a new\ntheory of plasticity has been developed which is of neither the\nflow nor the deformation type . it is based upon the concept of\nslip, and its formulation was guided more by physical, and less\nby mathematical, considerations than previous theories .\nexperimental evidence of limited scope but of crucial character is in\nbetter agreement with the new theory than with either flow or\ndeformation theories . the new theory accounts for the apparent\ncontradictions previously alluded to and justifies the use of\ndeformation theory in the analysis of the plastic buckling of plates ."}, {"doc_id": 821, "text": "inelastic column theory .\n the action of a column in the plastic range is analyzed on the\nbasis that bending may proceed simultaneously with increasing\naxial load . this leads to a new column formula that includes\nboth the tangent-modulus (engesser) and the reduced-modulus\nthe tangent-modulus load and that the column load increases\nwith increasing lateral deflection, approaching the\nreduced-modulus load as a limit if the tangent modulus is assumed to\nremain constant ."}, {"doc_id": 822, "text": "effects of imperfections on buckling of thin cylinders\nand columns under axial compression .\n von karman and tsien have shown that under elastic\nconditions the resistance of perfect thin cylinders\nsubjected to axial compression drops precipitously after\nbuckling . it is considered that this indicates that this type of\nbuckling is very sensitive to imperfections or disturbances .\nin this paper the effects of certain imperfections of shape\nturbances combined) are studied by the large-deflection\nshell theory developed in a previous paper (2) .\n it is found that two types of buckling failure may occur .\none is of a purely elastic type which occurs when the peak\nof the average stress versus average strain curve is reached,\nwhile the other type is precipitated by yielding, which for\nthicker cylinders or lower-yield material may occur before\nsuch a peak is reached . curves are derived giving the\ndependence of each type of failure upon the dimensions and\nelastic and yield properties of the specimen and also upon\nan /unevenness factor/ u which determines the\nmagnitude of the initial imperfections and is assumed to depend\non the method of fabrication . the relations derived are in\nline with test results, and similar studies of the buckling\nof struts indicate that the magnitude of the initial\nimperfections which have to be assumed to explain test strengths\nare reasonable ."}, {"doc_id": 823, "text": "plastic torsional buckling strength of cylinders including\nthe effects of imperfections .\n the torsional buckling strength of a cylinder in the plastic\nrange has been determined . an energy solution and a more exact\nsolution, both based on a plastic stress-strain relationship given\nby the simple deformation theory, are presented . close\nagreement between the two solutions is found . the effects of large\ndeflections and imperfections on buckling strength are analyzed .\nfor two groups of experimental results used for comparison, the\neffects of geometrical imperfections in the plastic range are\nnegligible . the theoretical results are found to be in good\nagreement with the experimental results ."}, {"doc_id": 824, "text": "on the concept of stability of inelastic systems .\n simple models are employed to bring out the large and\nimportant differences between buckling in the plastic range and\nclassical elastic instability . static and kinetic criteria are\ncompared and their interrelation discussed . nonlinear behavior in\nparticular is often found to be the key to the physically valid\nsolution . the nonconservative nature of plastic deformation in\nitself or in combination with the nonlinearity requires concepts\nnot found in classical approaches . conversely, the classical\nlinearized condition of neutral equilibrium is really not relevant\nin inelastic buckling . plastic buckling loads are not uniquely\ndefined but cover a range of values and are often more properly\nthought of as maximum loads for some reasonable initial\nimperfection in geometry or dynamic disturbance .\n the models indicate that basically the same information is\nobtained from essentially static systems by assuming initial\nimperfection in geometric forms as by assuming dynamic\ndisturbances . one approach complements the other and both are\nhelpful in obtaining an understanding of the physical phenomena ."}, {"doc_id": 825, "text": "inelastic instability and incremental theories of plasticity .\n a most troublesome paradox has existed for a number of years\nwith respect to buckling in the plastic range . theoretical\nconsiderations and all direct experimental evidence show\nconclusively that an incremental or flow type of mathematical theory\nof plasticity is valid . however, the results of plastic buckling\ntests are well correlated by a simple total or deformation theory\nand bear no resemblance to published predictions of incremental\ntheory .\n the suggestion was made that initial imperfections of shape\nor loading might well explain this most peculiar result .\nhowever, subsequent investigations by several authors seem to have\ngiven the impression that excessively large imperfections would\nbe needed and that the answer would be overly sensitive to the\nmagnitude of such imperfections .\n it is the purpose of this paper to demonstrate that extremely\nsmall, and therefore unavoidable, imperfections of shape do\naccount for the paradox in a simple manner . the buckling load is\nshown to be extremely insensitive to the amount of imperfection .\nthe example chosen is a simplified version of the long rectangular\nplate hinged along one edge and free on the other under\nuniform compressive stress at the ends . this is the equivalent of\nthe case of the cruciform column, which has been so disturbing\nin the past because incremental theory applied to a perfect\ncruciform column did lead to an entirely incorrect result ."}, {"doc_id": 826, "text": "small bending and stretching of sandwich type shells .\n a theory has been developed for small bending and stretching of\nsandwich-type shells . this theory is an extension of the known theory\nof homogeneous thin elastic shells . it was found that two effects are\nimportant in the present problem, which have not been considered\npreviously in the theory of curved shells .. (1) the effect of\ntransverse shear deformation and (2) the effect of transverse normal stress\ndeformation . the first of these two effects has been known to be of\nimportance in the theory of plates and beams . the second effect was\nfound to occur in a manner which is typical for shells and has no\ncounterpart in flat-plate theory .\n the general results of this report have been applied to the\nsolution of problems concerning flat plates, circular rings, circular\ncylindrical shells, and spherical shells . in each case numerical\nexamples have been given, illustrating the magnitude of the effects\nof transverse shear and normal stress deformation .\n the results of this investigation indicate the necessity of\ntaking account of transverse shear and normal stress in sandwich-type\nshells, as soon as there is an order-of-magnitude difference between\nthe elastic constants of the core layer and of the face layers of the\ncomposite shell . it was found that the changes due to transverse\nshear and normal stress deformation in the core may be so large as to\nbe no mere corrections to the results of the theory without transverse\ncore flexibility .\n the actual magnitude of the changes is greatly dependent on the\ngeometry and loading condition of the structure under consideration\nso that no general rules may be given which indicate for which elastic\nmodulus ratio the changes begin to be significant .\n solutions of problems in the present theory may in general be\nobtained by mathematical methods which are similar to those employed\nin the theory of plates and shells without the effect of transverse\nshear and normal stress deformation included . the present work does\nnot include consideration of buckling and finite deflection effects ."}, {"doc_id": 827, "text": "a nonlinear theory of bending and buckling of thin\nelastic shallow spherical shells .\n a shallow spherical dome subjected to lateral pressure is a structure\nfor which the deformation departs appreciably from the linear theory at\nrelatively small values of the deflection amplitude . it is also one\nfor which the buckling process is characterized by a rapid decrease in\nthe equilibrium load once the buckling load has been surpassed . for\nstructures having this type of buckling characteristics the question\narises as to whether the proper buckling criterion to apply is the\nclassical criterion, which considers equilibrium with respect to\ninfinitesimal displacements, or the finite-displacement /energy\ncriterion/ proposed by tsien .\n in this paper the problem of the finite displacement and buckling\nof a shallow spherical dome is investigated both theoretically and\nexperimentally . in the theoretical approach the nonlinear equations\nare converted into a sequence of linear equations by expanding all of\nthe variables in powers of the center deflection and then equating the\ncoefficients of equal powers . the basic parameter for the shallow dome\nis proportional to the ratio of the central height of the dome h to its\nthickness t . for small values of this ratio the expansions converge\nrapidly and enough terms are computed to determine the buckling load\naccording to the classical criterion . for higher values of h t,\nconvergence deteriorates rapidly and it was not possible to determine the\nbuckling load with the number of terms which were computed . however\neven for these higher values of h t the deflection shapes are determined\nfor deflection amplitudes below the amplitude at which buckling occurs .\nthese deflection shapes are characterized by their rapid change as h t\nincreases and by the fact that, over most of the range of h t studied,\nthe maximum deflection does not occur at the center of the dome .\n experimental results seem to indicate that the classical criterion\nof buckling is applicable to very shallow spherical domes for which the\ntheoretical calculation was made . a transition to energy criterion for\nhigher domes is also indicated ."}, {"doc_id": 828, "text": "stresses and small displacements of shallow spherical\nshells .\n the purpose of the present paper is to derive a system of\nequations which can be used for the analysis of shallow segments of\nthin, elastic, spherical shells . a segment will be called shallow if\nthe ratio of its height to base diameter is less than, say . the\nresults obtained on the basis of this assumption will often also be\napplicable to shells which are not shallow, namely then, when the loads\nare such that the stresses are effectively restricted to shallow zones .\n the problem of the spherical elastic shell has been the subject of\nnumerous researches . for the rotationally symmetric case the\nfundamental results were obtained in 1912 (1) and have been the starting\npoint of many applications . while it is possible to deduce from these\nresults approximate equations equivalent to part of what follows, it is\nbelieved that the present approach to the problem of the shallow shell\nmay be of some interest even for rotationally symmetric cases .\n a number of investigations have been concerned with the shell loaded\nin a non-rotationally symmetric manner (2,3,4) . in its general form\nthis problem is quite difficult and the results so far obtained are not\neasy to apply . restricting attention to the shallow shell in the\nmanner of the present paper brings with it a very considerable\nsimplification of the analysis ."}, {"doc_id": 829, "text": "stability of thin-walled tubes under torsion .\n in this paper a theoretical solution is developed for the\ntorsion on a round thin-walled tube for which the walls\nbecome unstable . the results of this theory are given by\na few simple formulas and curves which cover all cases .\nthe differential equations of equilibrium are derived in a\nsimpler form than previously found, it being shown that\nmany items can be neglected . the solution obtained is\nlength ratio is zero and infinite, and is a good\napproximation for intermediate cases . the theory is compared\nwith all available experiments, including about 50 tests\nmade by the author . the experimental-failure torque is\nalways smaller than the theoretical-buckling torque,\naveraging about 75 percent of it, with a minimum of 60\npercent . as the form of the deflection checks closely with\nthat predicted by theory and the experiments cover a great\nrange of shapes and materials, this discrepancy can\nreasonably be ascribed largely to initial eccentricities in\nactual tubes ."}, {"doc_id": 830, "text": "nonlinear deflections of shallow spherical shells .\n the equations obtained by chien for the nonlinear deflection\nof shallow spherical shells under uniform external pressure are\nsolved by means of power series expansions, following procedures\nintroduced by friedrichs and stoker in their treatment of\nbuckling of circular plates . these equations depend upon two\nparameters . one of these parameters is related to the external\npressure, while the other depends upon the dimensions of the shell .\nthe equations are solved for several ranges of the parameters\nunder boundary conditions corresponding to a fixed edge .\n the solution, carried out numerically on the aec univac\nat new york university, yields a complete description of the\nstresses and deflections as functions of the polar angle over a\nwide range of values of the loading parameter and the\ndimensional parameter . prediction of the upper buckling load is then\nmade by means of a numerical criterion based on the load vs.\ndeflection curve . for some cases, the postbuckling behavior\nis investigated . the results agree well with existing\nexperimental and theoretical studies and cover a wide range of cases\nnot previously treated ."}, {"doc_id": 831, "text": "buckling of shallow shells under external pressure .\na formula for the initial buckling loads for clamped, shallow spherical\nshells under uniform external pressure is obtained by combining the\nsolutions of two linearized versions of the original nonlinear problem .\none of these versions is a linear eigenvalue problem while the other is\nthe bending problem for a shallow cap in the linear theory of\nelasticity . the formula, which is obtained in a simple manner, yields\nbuckling loads that are in better agreement with experiments than\nprevious approximate solutions to the nonlinear problem ."}, {"doc_id": 832, "text": "accelerating convergence of iteration processes .\n a technique is discussed which, when applied to an iterative procedure\nfor the solution of an equation, accelerates the rate of convergence if\nthe iteration converges and induces convergence if the iteration\ndiverges . an illustrative example is given ."}, {"doc_id": 833, "text": "a simple method of matric structural analysis, part\niv, non-linear problems .\n the method presented in the previous parts is employed to\nsolve various kinds of nonlinear problems, such as problems\nconcerning large deflections or buckling, or thermal creep, or\ninelastic stress redistribution involving thermal gradients, or\ndesign . the procedure used in each case is one of direct\niteration--i. e., after one assumes a starting point all subsequent cycles are\nself-generating . simple numerical examples are worked out ."}, {"doc_id": 834, "text": "limit design for economical missile structures .\na special safety factor alone won't do the trick in the design of\nlightweight, high temperature missile structures . if you really want\nto end up with the most efficient structure you can get, an entirely\nnew design approach is needed ."}, {"doc_id": 835, "text": "the problem of strain accumulation under thermal cycling .\nparkes and sprague and huang have shown that it is possible for strain\ngrowth to occur in a beam structure under temperature-load cycling .\nthe various aspects of this problem as to criteria for convergence and\ndivergence of the strain accumulation can be simply demonstrated by\nthermal cycling one element of a two-element structure ."}, {"doc_id": 836, "text": "analytical and experimental investigation of stress distributions in\nlong flat plates subjected to lingitudinal loads and transverse\ntemperature gradients .\nstress and strain distributions were studied in long flat plates in\norder to develop practical analytical procedures for the design\nanalysis of aircraft structures at elevated temperatures .\nvarious load-temperature conditions are presented . these include ..\nmethods of analysis for calculation of stress distributions under\nand plastic range,.\nture .\nexperimental verification of the analytical procedures is shown with\ncomparisons between the use of constant room temperature or temperature\ndependent values of modulus of elasticity and coefficient of thermal\nexpansion .\nthe test specimen, equipment, instrumentation, and experimental program\nare discussed in detail . experimental data obtained from the specimen\nand associated material control coupon tests are presented ."}, {"doc_id": 837, "text": "inelastic behaviour of structures subjected to cyclic\nthermal and mechanical stressing conditions .\n a general analytical procedure is outlined for structures subjected to\nvarying thermal and mechanical stressing conditions . consideration is\ngiven to the accumulation of time-independent plastic strains and creep\nstrains . stress-strain-temperature-time relations for uniaxial and\nmultiaxial stresses are defined, based on various material behavior\nassumptions . several of the assumptions are compared with a limited\nnumber of time-varying temperature and uniaxial stress tests .\n the procedure is illustrated by its application to uniaxial stress\nproblems in which /planes originally plane remain plane/ and to plane\nstress plate problems . a solution, based on the influence coefficient\napproach to the plane stress plate problem, is obtained which is\napplicable to all plate plan forms, edge boundary conditions, and\ninplane thermal and mechanical loading conditions .\n from the predicted inelastic behavior of a three-bar structure\nsubjected to cyclic thermal and mechanical loading conditions, it is\nshown that eventual failure could result from large permanent\ndeformation accumulations, tensile rupture, or thermal-stress-fatigue .\n a sample plate with a centrally located hole was analyzed for two\ncycles of a time-varying temperature and edge stress condition . both\nplastic strain reversals and plastic strain growths were predicted at\nthe hole . however, a test-theory comparison indicated failure by\ncreep-rupture ."}, {"doc_id": 838, "text": "bending and compression tests of pressurised ring-stiffened\ncylinders .\n the results of tests on pressurized ring-stiffened cylinders\nsubjected to compression and bending are presented and discussed . the\nresults obtained at high values of internal pressure differ from those\nobtained by previous investigators in that the theoretical\nsmall-deflection compressive buckling coefficient of 0.6 was nearly achieved\nin each test . small amounts of internal pressure had a greater\nstabilizing effect in the bending tests than in the compression tests ."}, {"doc_id": 839, "text": "the bending stability of thin-- walled unstiffened\ncircular cylinders including the effects of internal\npressure .\n in a recent paper, the authors presented a statistical,\nsemiempirical design procedure for the determination of the buckling\nstrength of unpressurized and pressurized cylinders under axial\ncompression . this procedure has been extended in the present\npaper to the bending of unpressurized and pressurized cylindrical\nshells and allows the calculation of the critical bending stress with\na knowledge of the cylinder geometry and the internal pressure\nonly .\n because no published data could be found, an extensive series\nof bending tests of pressurized cylinders has been performed .\nthese new data for pressurized cylinders are treated\nsemiempirically together with all of the other known test data for\nunpressurized cylinders . best-fit curves are presented using applicable\ntheoretical parameters . design curves for determining the\ncritical buckling stress for unpressurized and pressurized cylinders\nin bending are then developed as 90 per cent probability curves\nfrom the test data ."}, {"doc_id": 840, "text": "analysis of partly wrinkled membrane .\n a theory is derived to predict the stresses and deformations of\nstretched-membrane structural components for loads under which part of\nthe membrane wrinkles . rather than studying in detail the deformations\nin the wrinkled region, the present theory studies average displacements\nof the wrinkled material . specific solutions of problems in flat and\ncurved membranes are presented . the results of these solutions show\nthat membrane structures retain much of their stiffness at loads\nsubstantially above the load at which wrinkling first occurs ."}, {"doc_id": 841, "text": "on the bending of circular cylindrical shells under\npure bending .\nthe stability of circular cylindrical shells under pure bending is\ninvestigated by means of batdorf's modified donnell's equation and the\ngalerkin method . the results of this investigation have shown that,\ncontrary to the commonly accepted value, the maximum critical bending\nstress is for all practical purposes equal to the critical compressive\nstress ."}, {"doc_id": 842, "text": "an improvement on donnell's approximation for thin-walled\ncircular cylinders .\n donnell's equation for thin-walled circular cylinders is replaced by\nwhere w is a non-dimensional form of the radial displacement and q is\nthe distributed radial loading . this equation retains the essential\nsimplicity of the original but, unlike donnell's equation, the accuracy\ndoes not decrease as the wavelength of circumferential distortion\nincreases ."}, {"doc_id": 843, "text": "a simplified method of elastic stability analysis for\nthin cylindrical shells .\n the equation for the equilibrium of cylindrical\nshells introduced by donnell in naca report no. 479 to\nfind the critical stresses of cylinders in torsion is\napplied to find critical stresses for cylinders with\nsimply supported edges under other loading conditions .\nit is shown that by this method solutions may be obtained\nvery easily and the results in each case may be expressed\nin terms of two nondimensional parameters, one dependent\non the critical stress and the other essentially\ndetermined by the geometry of the cylinder . the influence of\nboundary conditions related to edge displacements in the\nshell median surface is discussed . the accuracy of the\nsolutions found is established by comparing them with\nprevious theoretical solutions and with test results .\n the solutions to a number of problems concerned with\nbuckling of cylinders with simply supported edges on the\nbasis of a unified viewpoint are presented in a convenient\nform for practical use ."}, {"doc_id": 844, "text": "flexural vibrations of the walls of thin cylindrical\nshells having freely supported ends .\nthe paper deals with the general equations for the vibration of thin\ncylinders and a theoretical and experimental investigation is made of\nthe type of vibration usually associated with bells . the cylinders are\nsupported in such a manner that the ends remain circular without\ndirectional restraint being imposed . it is found that the complexity\nof the mode of vibration bears little relation to the natural\nfrequency,. for example, cylinders of very small thickness-diameter\nratio, with length about equal to or less than the diameter, may have\nmany of their higher frequencies associated with the simpler modes of\nvibration . the frequency equation which is derived by the energy\nmethod is based on strain relations given by timoshenko . in this\napproach, displacement equations are evolved which are comparable to\nthose of love and flugge, though differences are evident due to the\nstrain expressions used by each author . results are given for\ncylinders of various lengths, each with the same thickness-diameter\nratio, and also for a very thin cylinder in which the simpler modes of\nvibration occur in the higher frequency range . it is shown that there\nare three possible natural frequencies for a particular nodal pattern,\ntwo of these normally occurring beyond the aural range ."}, {"doc_id": 845, "text": "the flexural vibrations of thin cylinders .\nthe flexural vibrations of the walls of thin cylinders are considered .\nin this type of vibration many forms of nodal pattern may exist owing to\nthe combination of circumferential and axial nodes . theoretical\nexpressions are developed for the natural frequencies of cylinders with\nfreely-supported and fixed ends and a comparison is made with the\nfrequencies obtained experimentally .\n in practice, the ends of cylinders are subjected to a certain degree\nof fixing by end-plates, flanges, etc., and the natural frequencies thus\nlie between the corresponding values for freely-supported and fixed\nends . to make possible the estimation of such frequencies, a method is\ndevised in which an equivalent wavelength factor is used . this factor\nrepresents the wavelength of the freely-supported cylinder that would\nhave the same frequency as the cylinder under consideration when\nvibrating in the same mode . the results of experimental investigations\nwith various end thicknesses and flange dimensions are recorded, and\nfrom these the equivalent factors are derived .\n sets of curves calculated for cylinders with freely-supported ends and\ncovering a range of cylinder thicknesses are given . from these it is\npossible to obtain close approximation to the frequencies of cylinders\nunder other end conditions by the use of an appropriate factor . an\nexample is given of frequency calculations for a large air-receiver for\nwhich two frequencies were identified by experiment ."}, {"doc_id": 846, "text": "on the vibration of thin cylindrical shells under internal\npressure .\n the frequency spectra and vibration modes of thin-walled\ncircular cylinders subjected to internal pressure are considered .\nit is shown that for very thin cylinders the internal pressure\nhas a significant effect on the natural vibration characteristics .\nfor these cylinders, particularly those having smaller length to\ndiameter ratios, the mode associated with the lowest frequency\nis in general not the simplest mode . the exact number of\ncircumferential nodes, n, which occur in the mode associated\nwith the lowest frequency, depends on the internal pressure p .\nif this number n is large, it decreases rapidly with increasing p\nwhen p is small, and the /fundamental/ frequency--the lowest\nfrequency at each p--increases rapidly with increasing internal\npressure . at higher values of internal pressure the frequency\nspectrum tends to be arranged in the regular manner, the\nfrequency increases with the increasing number of circumferential\nnodes, and the lowest frequency rises slowly with the internal\npressure .\n experimental results on the frequency spectra, vibration\nmodes, and structural damping of a series of thin-walled cylinders\nsubjected to internal pressure are briefly described . these\nresults show agreement with the features predicted by reissner's\n the effect of slight deviation of the cylinder from perfect\ncircular symmetry is discussed ."}, {"doc_id": 847, "text": "experimental study of the vibrations of a circular\ncylindrical shell .\n an apparatus is described which permits the mode\nshape of a vibrating circular cylindrical shell to be\nobtained quite easily . these measurements are made\nwithout contacting the cylinder and can be converted\nto actual lineal values . a representative number of\nresults obtained with such a system are shown to\nillustrate the relationship between the nodal pattern and\nfrequency in a cylinder as well as the effect of internal\npressure on these frequencies . finally, comparisons\nare made between these results and timoshenko theory\nand an appropriate shell theory ."}, {"doc_id": 848, "text": "the effect of an internal compressible fluid column\non the breathing vibrations of a thin pressurised cylindrical\nshell .\n the free oscillations of a thin pressurized cylindrical shell\ncontaining a compressible fluid are studied here . the use of an\napproximate set of shell equations (shallow shell theory) leads to\na relatively simple formula for the natural frequencies of the\ncoupled fluid-cylinder system . the results of some\ncomputations are presented ."}, {"doc_id": 849, "text": "a theory of imperfection for the vibrations of elastic bodies of\nrevolution .\nvarious observations and preliminary experiments\nhave shown that the effect of imperfections upon the\nvibrations of bodies of revolution cannot be neglected .\nowing to the possibility of applying the lagrange\nequation, the influence of the imperfections could be\ntraced through the kinetic energy, the potential energy\nand the dissipation function . although the fundamental\ndifficulty of the uncertainty of certain variables\nwas not eliminated, this procedure permitted at least\nthe making of general qualitative statements as to the\nbehaviour of the system if imperfections are present ."}, {"doc_id": 850, "text": "remarks on donnell's equations .\n flugge's set of differential equations of equilibrium for\ncircular cylindrical shells is expressed in a form analogous\nto the donnell equations . the results of solutions of the\ntwo sets of equations for a simply supported cylinder under\na centrally applied, uniformly distributed radial line load\nover a generator segment, as well as under sinusoidally\napplied line loads, are in very good agreement for the\nparticular geometry investigated ."}, {"doc_id": 851, "text": "energy expressions and differential equations for stress\nand displacement analysis of arbitrary cylindrical\nshells .\nenergy expressions and the related equilibrium equations and natural\nboundary conditions for the determination of the stresses in and\ndisplacements of uniform, thin-walled cylinders of arbitrary cross section\nloaded in an arbitrary manner by surface and edge forces and moments are\npresented . the derivations are based upon the kirchhoff-love\nassumptions of the classical theory of shells and are performed to\nwithin a degree of accuracy employed by flugge in his derivation of the\nequilibrium equations applicable to circular cylindrical shells,. hence,\nin terms of stress resultants, the exact, small-deflection equilibrium\nequations are obtained . methods of simplification of the relations\nderived and of solution of the differential equations presented are\nindicated ."}, {"doc_id": 852, "text": "stress and displacement analysis of simply supported\nnon- circular cylindrical shell under lateral pressure .\nthis paper presents an analysis of the deflections of and stresses in a\nshort noncircular cylindrical shell of uniform wall thickness whose\nmedian-surface cross section is described analytically by a simple\nexpression corresponding to a family of doubly symmetric ovals . the\ncylinder is under a uniform lateral load and is simply supported at its\nedges . the small deflection analysis considered is based upon a series\nsolution of appropriate differential equations of shell theory which\nleads ultimately to infinite sets of algebraic equations, truncated\nforms of which are considered . numerical values of the significant\nstresses and displacements for points of the oval cylinder, which are 5\npercent of the axial length and 2.5 percent of the circumferential\nlength apart, have been calculated for an oval cross section with a\nmajor-minor axis ratio of 1.10 ."}, {"doc_id": 853, "text": "the accuracy of donnell's equations .\n solutions of donnell's equations of the small\ndeformations of the perfectly elastic thin-walled circular\ncylindrical shell are compared with those obtainable from flugge's\nequations . the range of the basic parameters is found\nwithin which the two solutions are approximately equal ."}, {"doc_id": 854, "text": "boundary-value problems of the thin-walled circular\ncylinder .\n the homogeneous differential equations of donnell's\ntheory of thin cylindrical shells are integrated .\nexpressions are obtained in closed form for the displacements,\nmembrane stresses, moments, and shear forces ."}, {"doc_id": 855, "text": "simplified formulas for boundary value problems of\nthe thin-- walled circular cylinder .\n n. j. hoff has presented formulas which can be used in\nthe solution of boundary-value problems of circular\ncylinders . the purpose of this note is to express these\nresults in exact simplified form,. a more detailed\ninvestigation appears elsewhere . the notation will be that of\nhoff unless otherwise stated ."}, {"doc_id": 856, "text": "some experimental studies of panel flutter at mach\n1 .3.\n experimental studies of panel flutter were conducted at a mach\nnumber of 1.3 to verify the existence of this phenomenon and to study the\neffects of some structural parameters on the flutter characteristics .\nthin rectangular metal plates were used in these studies and were\nmounted as a section of the tunnel wall . most of the data were obtained by\nusing aluminum-alloy panels, although a few steel, magnesium, and brass\npanels were also used . different materials with various thicknesses\nand lengths were used to determine the effect of these parameters on\npanel flutter . the experimental program consisted of three phases ..\npanels clamped front and rear, and (3) buckled panels clamped on all\nfour edges .\n panel flutter was obtained under controlled laboratory conditions\nand it was found that, at the flow conditions of these tests, increasing\ntensile forces were effective in eliminating flutter, as were\nshortening the panels or increasing the bending stiffness . no apparent\nsystematic trends in the flutter modes or frequencies could be observed,\nand it is significant that the panel flutter sometimes involved higher\nmodes and frequencies . the presence of a pressure differential between\nthe two surfaces of a panel was observed to have a stabilizing effect .\ninitially buckled panels were more susceptible to flutter than panels\nwithout buckling . buckled panels with all four edges clamped were much\nless prone to flutter than buckled panels clamped front and rear ."}, {"doc_id": 857, "text": "experimental studies of flutter of buckled rectangular\npanels at mach numbers from 1. 2 to 3. 0 including\neffects of pressure differential and of panel\nwidth-length ratio .\n experimental panel flutter data have been obtained at mach numbers\nfrom 1.2 to 3.0 for buckled rectangular panels and the effect of a\npressure differential has been determined . increasing the pressure\ndifferential was effective in eliminating flutter on most of the panels\ntested . the effects of the variables in the panel flutter parameter\nsure, e is young's modulus, and t and l are the panel thickness and\nlength, respectively) were investigated for buckled panels clamped on\nthe front and rear edges and a critical value of this parameter of 0.44\nis indicated at zero pressure differential when the panel width-length\nratio is 0.69 . an estimated flutter boundary is presented for buckled\npanels clamped on four edges, with width-length ratios of 0.21 to 4.0 .\nthis boundary shows that the panel width is more significant than the\npanel length when the ratio of width to length is less than\napproximately 0.5 . panels clamped on four edges and buckled in two half waves\nin the direction of flow were found to be particularly susceptible to\nflutter . the results of limited tests on panels with applied damping,\ncurvature, and lengthwise stiffeners are also presented and discussed ."}, {"doc_id": 858, "text": "experimental investigation at mach numbers 3. 0 of\nthe effects of thermal stress and buckling on the flutter\nof four-bay aluminium alloy panels with length-width\nratios of 10 .\n skin-stiffener aluminum alloy panels consisting of four bays, each\nbay having a length-width ratio of 10, were tested at a mach number\nof 3.0 at dynamic pressures ranging from 1,500 psf to 5,000 psf and at\nstagnation temperatures from 300 f to 655 f . the panels were\nrestrained by the supporting structure in such a manner that partial thermal\nexpansion of the skins could occur in both the longitudinal and lateral\ndirections .\n a boundary faired through the experimental flutter points\nconsisted of a flat-panel portion, a buckled-panel portion, and a\ntransition point at the intersection of the two boundaries . in the region\nwhere a panel must be flat when flutter occurs, an increase in panel\nskin temperature (or midplane compressive stress) makes the panel more\nsusceptible to flutter . in the region where a panel must be buckled\nwhen flutter occurs, the flutter trend is reversed . this reversal in\ntrend is attributed to the panel postbuckling behavior ."}, {"doc_id": 859, "text": "flutter of aerodynamically heated aluminium-alloy and\nstainless steel panels with length-width ratio of 10\nat mach 3. 0.\n an investigation of the effects of aerodynamic heating on the\nflutter of multibay external-skin panels has been carried out at a mach\nnumber of 3.0 in the langley 9- by 6-foot thermal structures tunnel . both\naluminum-alloy and 17-7 ph stainless-steel panels with a length-width\nratio of 10 for each bay were tested at dynamic pressures between\naddition, a few tests were made on the lower vertical stabilizer of the\nx-15 airplane which has external-skin panels unsupported for a length\n all panels showed flutter boundaries characterized by an increase\nin panel thickness required to prevent flutter with increasing thermally\ninduced stress prior to buckling . after buckling the panels showed\nflutter boundaries characterized by a decrease in thickness required to\nprevent flutter with further increases in thermal stress . the largest\nthickness required to prevent flutter in the presence of aerodynamic\nheating occurred at the transition between the flat-panel boundary and\nthe buckled-panel boundary . this peak value (for aluminum-alloy panel)\nwas as much as 60 percent greater than the extrapolated value for an\nunheated, unloaded panel .\n values of the modified-thickness-ratio flutter parameter for the\nunstressed panels (obtained by extrapolation) were in fair agreement for\nthe aluminum, steel, and x-15 stabilizer panels . peak values at\ntransition, however, showed large differences due to apparently minor\nchanges in panel-support construction and or changes in panel-skin\nmaterial ."}, {"doc_id": 860, "text": "test of an aerodynamically heated multi-- web wing\nstructure (mw-1) in a free jet at mach number 2.\n a multiweb wing structure, representing an airplane or missile wing,\nwas tested under simulated supersonic flight conditions to determine the\ntransient temperature distribution . the aerodynamic loads played an\nimportant and unanticipated role, however, in that the model experienced\na dynamic failure near the end of the test . the test is discussed and\nthe conclusion reached that the model failed as a result of the combined\naction of aerodynamic heating and loading . the temperature data\ncollected are analyzed and are shown to be in reasonable agreement with\ncalculated values ."}, {"doc_id": 861, "text": "charts adapted from van driest's turbulent flat-plate\ntheory for determining values of turbulent aerodynamic\nfriction and heat transfer coefficients .\n a modified method of van driest's flat-plate theory for turbulent\nboundary layer has been found to simplify the calculation of local\nskin-friction coefficients which, in turn, have made it possible to obtain\nthrough reynolds analogy theoretical turbulent heat-transfer\ncoefficients in the form of stanton number . a general formula is given and\ncharts are presented from which the modified method can be solved for\nmach numbers 1.0 to 12.0, temperature ratios 0.2 to 6.0, and reynolds\nnumbers 0.2 x 10 to 200 x 10 ."}, {"doc_id": 862, "text": "the phenomenon of change in buckle pattern in elastic\nstructures .\n a model is analyzed which exhibits the important properties\nassociated with change in buckle pattern of plates . the analysis includes\na rigorous study of stability in its various modes . a discussion of\nhow the present results may be applied to plates and other elastic\nstructures is given ."}, {"doc_id": 863, "text": "loads and deformations of buckled rectangular plates .\n the nonlinear large deflection equations of von karman for plates\nare converted into a set of linear equations by expanding the\ndisplacements into a power series in terms of an arbitrary parameter . the\npost-buckling behavior of simply supported rectangular plates subjected\nto longitudinal compression and to a uniform temperature rise is\ninvestigated in detail by solving the first few of the equations .\n experimental data are presented for the compression problem .\ncomparisons are made for total shortening and local strains and deflections\nwhich indicate good agreement between experimental and theoretical\nresults ."}, {"doc_id": 864, "text": "status of flutter of flat and curved panels .\nrepresentative results are presented to show the current status of\nthe panel flutter problem . the discussion includes flat panels with\nand without midplane stresses, buckled panels, and both unstiffened and\nstiffened infinitely long circular cylinders ."}, {"doc_id": 865, "text": "a study of the thermal fatigue behaviour of metals .\n the effect of test conditions on nickel-base high\ntemperature alloys .\nan attempt has been made to identify the significant factors governing\nthe thermal-fatigue behaviour of nickel-base high-temperature alloys,\nmainly by using a laboratory technique with hot and cold fluidized beds\nas the heating and cooling media . a succession of heating shocks is\ngenerally more damaging than a succession of cooling shocks between the\nsame temperature limits . the duration of the heating shock and the\nupper temperature of the cycle are dominant factors . the\nthermal-fatigue cracks are initiated at the surface and are intercrystalline in\norigin and propagation . surface oxidation, which is intergranular in\nnature for nickel-base alloys, has a significant effect on\nthermal-fatigue life ."}, {"doc_id": 866, "text": "regularities in creep and hot fatigue data .\n published experimental results are assembled to support a\npreviously-given theory of uniaxial deformation, and the theory is then used to\nanalyse published data on the creep-rupture and hot-fatigue of\nengineering materials . the theory enables data for different times and\ntemperatures to be classed together, thereby providing information over\na much greater range of times than could practicably be covered by\nexperiments at a single temperature . an underlying numerical pattern\ncommon to all the widely different group 8 materials considered then\nshows through the experimental scatter . data for further engineering\nmaterials is considered in these terms in part 2 ."}, {"doc_id": 867, "text": "low frequency fatigue of nimonic 90 . low frequency\nfatigue - a rheological approach .\nan alloy of nimonic 90 type has been tested under cyclic loads at\ntemperatures of 800 deg., 850 deg. and 900 deg. cent . graham's\ndescriptive theory of deformation has been developed in detail for the\ntests reported here, and shown to provide a satisfactory description of\nthe experimental results . the variation of cumulative strain with\nnumber of cycles can be described by the sum of powers of cycle number,\nn, n, n, and n . there is qualitative agreement between the observed\nand the calculated stress-strain loops . the effect of variation of\nmaximum stress per cycle can be described by the sum of power terms with\nsimple exponents . within the scatter of observation, the total time to\nfracture is independent of the frequency ."}, {"doc_id": 868, "text": "design and operation of the n. g. t. e. thermal shock\nanalogue .\n a description is given of the n.g.t.e. thermal shock analogue which\nis suitable for estimating the temperature in a turbine blade section as\na function of position and time when the blade is subjected to a step\nchange in gas temperature . the method of operating the analogue and\nobtaining results has also been described .\n the limitations of the analogue have been stated, but they are\nconsidered a small penalty in view of the essential simplicity of the\ndesign ."}, {"doc_id": 869, "text": "the calculation of transient temperature in turbine\nblades and tapered discs using biot's variational method .\n transient temperatures in aerofoil\nsections and tapered discs are\ncalculated taking advantage of simplifications\nin heat flow analysis\nachieved in biot's variational method .\ncross-sections are represented by\na line of adjacent squares of various\nsizes suitable for the local\ndimensions, e.g. small squares near the leading\nand trailing edges . the\npotential, dissipation and surface dissipation\nfunctions of biot's method are\nset up, and the lagrange equations lead,\nby automatic procedures, to an\neigenvalue formulation in matrix form for\nthe temperatures and their first\ntime derivatives . solutions are sums\nof exponentials in time, and are\nevaluated by digital computer, requiring\nabout five minutes for each\ncross-section and heat transfer coefficient .\ntransient temperatures in a\nparticular aerofoil section for variation\nof heat transfer coefficient and for\nexternal temperature depending exponentially\non time agree with results\nobtained on an analogue computer .\nmaximum transient temperature\ndifferences are evaluated for tapered discs\nby a simple electrical analogue) with\nvariation of edge radius and heat\ntransfer coefficient . peculiarities\nin the solution for cyclic\ntemperature external to an aerofoil over\na range of frequencies indicate\nlimitations in the mathematical formulation .\na successful solution for cyclic\nexternal temperature might enable\neigenvalues to be separated out in\nexperimental measurements using\nelectronic equipment, and this might be\nextended to exponential external\ntemperature if a relationship between\ncyclic and exponential external\ntemperature could be established .\neigenvalues and eigenvectors as discrete\nvalues arise fictitiously from the\nsub-division into squares and the\npossibility of an integral formulation\nis mentioned . there is a possible,\nbut not immediate, extension to\ncooled blades, whose cross-sections\nare multiply-connected regions .\ntransient stresses due to creep, and\nviscoelasticity might be included ."}, {"doc_id": 870, "text": "effect of rheological behaviour on thermal stresses .\n since the conventional elastic analysis of thermal stress problems\ncoupled with limiting creep rates and time-dependent fracture stresses\nas (inelastic) design criteria, results in design procedures for thermal\nstresses (in heat exchangers, nuclear reactors, flight structures at\nsupersonic speeds, etc.) of considerable unreality, the effect of\nvarious types of rheological behavior (viscoelastic, plastic, work\nhardening) on the level of thermal stresses is analyzed under simplified\nassumptions, such as uniaxial stress and polar or cylindrical symmetry .\nthe effect on the thermal stress intensity of the rheological behavior\nof the material is shown to be very significant, particularly with\nrespect to stress relaxation and the development of residual stresses ."}, {"doc_id": 871, "text": "steady-state creep through dislocation climb .\n a dislocation climb creep model is considered which does not require\nthe production of immobile dislocations . the creep equation that\nresults from the analysis is\nwhere a and b are constants, is the stress, q is the activation energy\nof creep and kt has its usual meaning . this equation is quite similar\nto one previously proposed ."}, {"doc_id": 872, "text": "fundamentals of boundary layer heat transfer with streamwise\ntemperature variations .\n boundary-layer heat transfer is analyzed for the case of a\nsinusoidal distribution of temperature in the direction of flow . it is\nshown that for both laminar and turbulent flow the spatial\ndistribution of heat transfer is generally out of phase with the wall\ntemperature by an angle of 30 to 45 . this leads to the\nconclusion that in some areas the heat flow is opposite to the\ntemperature difference as used in the definition of the heat-transfer\ncoefficient, and points to the basic shortcomings of this concept .\nthe physical explanation for this behavior is found to be the\ntemperature-field distortion by the fluid motion . the distortion\nis measured by the peclet number . approximate equations\nrepresenting a /conduction analogy/ were used in this analysis\nand the validity of these equations for unsteady flow is examined\nwith reference to limitations in frequency and wavelength . a\nsolution of these equations is given for the case of a velocity\nprofile which is not a straight line . the use of previously developed\nvariational principles for the evaluation of convective heat\ntransfer including cases of three-dimensional unsteady flow,\nturbulence, and nonparallel streamlines is also discussed ."}, {"doc_id": 873, "text": "lagrangian thermodynamics of heat transfer in systems\nincluding fluid motion .\n the lagrangian thermodynamic equations of irreversible\nprocesses are extended to convective heat transfer . this\ngeneralization provides equations for the unified analysis of transient\nheat flow in complex systems comprising solid structures and\nmoving fluids in either laminar or turbulent flow . the concept\nof a surface-heat-transfer coefficient is eliminated from the\nformulation . the theory is developed along two different lines . in\none approach a new concept referred to as the /trailing function/\nis introduced . it represents the surface-heat-transfer properties\nand may be evaluated by quite simple but remarkably accurate\nvariational procedures . the method of /associated fields/ is also\ngeneralized to convective phenomena . the second line of\napproach extends to convective heat transfer the thermodynamic\nconcept of entropy production for both laminar and turbulent\nflow . the theory amounts to an extension of the\nthermodynamics of irreversible processes to systems for which onsager's\nrelations are not valid ."}, {"doc_id": 874, "text": "the use of models for the determination of critical flutter speeds .\nthe use of model tests in the prediction of full-scale critical flutter\nspeeds is now well established, and the technique of such tests is\ntherefore worthy of discussion . in order to obtain critical speeds for\nthe model within the speed range of ordinary wind tunnels it is\nnecessary that the model should differ in some respect from a mere small\nsuggested by mckinnon wood the modification of the model consists in a\nreduction of its effective stiffnesses . this method has the defect /in\nmost cases probably not serious/ that the model experiment is conducted\nat a reynolds number much below that for full-scale . in the present\npaper it is pointed out that an alternative method of reducing the\ncritical speed is to increase the mass loading of the model and to make\nthe flutter tests in compressed air . * it is then quite feasible to\nreach the full-scale reynolds number . this method of reducing the\ncritical speeds by a proportionate increase of all effective densities\nmay also be combined with a reduction of the elasticity of the model .\nthe relation of model and full-scale stresses at the critical flutter\nspeeds is considered . where the reduction in critical speed is effected\n by increase of density only, the model and full-scale stresses are\nequal . in a model of reduced elasticity the stresses in the wires are\nthe same as for full-scale, whereas, the stresses in the spars are less\n than for full-scale . this is in accord with the usual experience that\nthe wires of such a model are the first parts of the structure to fail\nin a flutter .\nlastly, the influence of gravity on flutter is considered . this is\nnegligibly small for full-scale, but not necessarily so for the model .\ngravitational effects can sometimes be corrected by suitable orientation\n of the model ."}, {"doc_id": 875, "text": "models for aeroelastic investigation .\n this addendum provides a short note on two aspects omitted from the\noriginal paper, viz. gravitational effects and structural damping . a\nshort list of references to earlier papers dealing with the subject is\nalso added ."}, {"doc_id": 876, "text": "on flutter testing in high speed wind tunnels .\n the requirements for simulating in a wind tunnel flutter conditions\nappropriate to high-speed flight are discussed, and an assessment is\nmade of the desirable features of a wind tunnel suitable for flutter\ntesting at transonic and supersonic speeds .\n it is concluded that such a tunnel should have either the mach number\nor the stagnation pressure variable during the tunnel run, and that it\nis of considerable advantage, and for some purposes essential, for high\nstagnation pressures to be available . the stagnation pressure required\nto allow flight conditions to be simulated with a flutter model is\nconsidered to range from at least 2 atmospheres for transonic speeds to\nabout 15 atmospheres for m = 4 . no attempt to simulate kinetic heating\nis envisaged, although its effect on stiffness should be allowed for in\nthe design of the model . to minimise uncertainties due to the\nvariation of the model stiffness with temperature it is desirable that\nmeans for controlling the stagnation temperature should be incorporated\nin the tunnel ."}, {"doc_id": 877, "text": "the influence of aerodynamic heating on the flexural\nrigidity of a thin wing .\n this report considers the loss of flexural rigidity of a thin wing due\nto the presence of middle-surface stresses resulting from aerodynamic\nheating . the spanwise properties of the wing are assumed constant but\nthe wing section is arbitrary . the loss of flexural rigidity is\ncomparable with the corresponding loss of torsional rigidity ."}, {"doc_id": 878, "text": "experimental model techniques and equipment for flutter\ninvestigations .\nan outline is given of the uses of flutter models as an\naid to the designer in the avoidance of flutter . details\nare given of the different types and methods of\nconstruction that are used for flutter models and of the\nvarious test facilities that are available for high speed\nand low speed tests .\n the procedure followed in the u.k. for flutter\nclearance of the full scale aircraft is described, and the value\nof the electronic flutter simulator in this field is\ndiscussed ."}, {"doc_id": 879, "text": "flutter model testing at transonic speeds .\nflutter research on reflection plane models of straight, swept, and\ndelta wings in a 3 x 4 foot transonic test facility . techniques of\nmodel construction and testing developed ."}, {"doc_id": 880, "text": "the design and testing of supersonic flutter models .\nthe basic problems of flutter testing in the low supersonic speed range\nsimulate full-scale airplanes when mach number is included as a\nparameter are reviewed and are compared with those where velocity is scaled\nwhen the leading edges become transonic,. these are compared with\nresults given elsewhere and serve as a check on the results of tables\ni and ii ."}, {"doc_id": 881, "text": "cumulative damage in fatigue .\n the phenomenon of cumulative damage under repeated\nloads was assumed to be related to the net work absorbed\nby a specimen . the number of loading cycles applied\nexpressed as a percentage of the number to failure at a\ngiven stress level would be the proportion of useful life\nexpended . when the total damage, as defined by this\nconcept, reached 100 per cent, the fatigue specimen should\nfail . experimental verification of this concept for an\naluminum alloy, using different types of specimens,\nvarious stress ratios, and various combinations of loading\ncycles is presented . these data are also analyzed to\nprovide information on different stress ratios when an s-n\ncurve for any one ratio is known . results of a sample\nanalysis based on experiments are given . it is\nconcluded that a simple and conservative analysis is possible\nusing the concept of cumulative fatigue damage ."}, {"doc_id": 882, "text": "the variation of gust frequency with gust velocity\nand altitude .\n information on atmospheric turbulence obtained from counting\naccelerometer records is examined and relations giving the variation of\ngust frequency with gust velocity and altitude are obtained . the\nresults are summarized in a form convenient for use in estimating the\nfatigue life of an aircraft ."}, {"doc_id": 883, "text": "correlated fatigue data for aircraft structural joints .\n results of fatigue tests carried out at r.a.e. on typical aircraft\nwing structural joints are correlated to give an indication of general\nfatigue behaviour . the results are plotted in the form of s - log n\ncurves, and these indicate that the mode of behaviour cannot be\nattributed to any single factor, such as the type of aluminium alloy,\nthe ultimate tensile strength, or the mean stress of the fatigue cycle .\nthe detailed method of design undoubtedly has a predominant influence on\nbehaviour, but this quality is not revealed by a broad classification\naccording to the proportion of load transmitted at holes ."}, {"doc_id": 884, "text": "the estimation of fatigue damage on structural elements .\n a method is presented for the estimation of fatigue damage to\naircraft structural elements . the gust spectrum to which the aircraft\nis subjected is analysed in terms of infinitesimal loading intervals .\ngust data supplied by j. taylor for flying below 15,000 ft are used to\nstudy fatigue damage in a number of aircraft structural joints and one\nwhole structure ."}, {"doc_id": 885, "text": "buckling of thin cylindrical shells under hoop stresses\nvarying in axial direction .\n the buckling of a thin cylindrical shell simply supported\nalong the perimeter of its end sections is analyzed under\nhoop compressive stresses varying in the axial direction .\nthe thermal stresses arising from a uniform increase in\nthe temperature of the cylinder are determined . it is\nfound that such thermal stresses are not likely to cause\nelastic buckling . simple approximate formulas are\ndeveloped for buckling stress and thermal stress ."}, {"doc_id": 886, "text": "thermal buckling of clamped cylindrical shells .\nthe problem of thermal buckling of shells arises in\nconnection with air-frame bodies subject to aerodynamic heating at\nsupersonic speeds . the case of the shell with clamped edges is\npresented, as this case typifies all structures with a tubular shell\nstiffened at intervals with stiffening rings . the shell is assumed\nto be unrestrained longitudinally and fully restrained laterally at\nthe edges ."}, {"doc_id": 887, "text": "buckling due to thermal stress of cylindrical shells\nsubjected to axial temperature distributions .\n thermal stress distributions in uniform circular cylindrical shells\ndue to axial temperature distributions are investigated . the\ndiscontinuity effect due to the presence of a cooler stiffening bulkhead is\nconsidered, and the possibility of thermal buckling of the shell due to\nthe circumferential discontinuity stress is examined . the buckling\nanalysis is based on donnell's shell equation, and particular attention\nis given to shells having clamped edges .\n an experimental investigation of this buckling problem is discussed,\nand the results obtained are seen to agree reasonably well with theory ."}, {"doc_id": 888, "text": "combinations of temperature and axial compression required\nfor buckling of a ring-stiffened cylinder .\n a theory is presented to predict the buckling temperature of an\naxially compressed, uniformly heated ring-stiffened cylinder . the\ncylinder buckles because of the interaction of the axial stress due to\napplied compressive loads and the circumferential stress resulting\nfrom restraint of thermal expansion by the rings . buckling charts\ncovering a wide range of cylinder proportions are presented for both\nclamped and simply supported cylinders . the buckling temperature for a\ngiven axial loading is determined from a simple equation involving a\ncoefficient given in the buckling charts and the radius-thickness ratio\nof the cylinder ."}, {"doc_id": 889, "text": "a simplified method of elastic stability analysis for\nthin cylindrical shells .\n this paper develops a new method for determining the buckling\nstresses of cylindrical shells under various loading conditions .\nfor convenience of exposition, it is divided into two parts .\n in part 1, the equation for the equilibrium of cylindrical\nshells introduced by donnell in naca report no. 479 to find\nthe critical stresses of cylinders in torsion is applied to find\ncritical stresses for cylinders with simply supported edges under\nother loading conditions . it is shown that by this method\nsolutions may be obtained very easily and the results in each case may\nbe expressed in terms of two nondimensional parameters, one\ndependent on the critical stress and the other essentially\ndetermined by the geometry of the cylinder . the influence of boundary\nconditions related to edge displacements in the shell median\nsurface is discussed . the accuracy of the solutions found is\nestablished by comparing them with previous theoretical solutions\nand with test results . the solutions to a number of problems\nconcerned with buckling of cylinders with simply supported\nedges on the basis of a unified viewpoint are presented in a\nconvenient form for practical use .\n in part 2, a modified form of donnell's equation for the\nequilibrium of thin cylindrical shells is derived which is\nequivalent to donnell's equation but has certain advantages in physical\ninterpretation and in ease of solution, particularly in the case\nof shells having clamped edges . the solution of this modified\nequation by means of trigonometric series and its application to\na number of problems concerned with the shear buckling stresses\nof cylindrical shells are discussed . the question of implicit\nboundary conditions also is considered ."}, {"doc_id": 890, "text": "comments on 'thermal buckling of clamped cylindrical shells' .\nin the recent paper by zuk, an expression was presented for\nthe critical buckling temperature of a clamped cylindrical shell\nin terms of the material and geometrical properties of the shell .\nrestraint at the edges of the shell was assumed to be provided by\nrigid frames experiencing no temperature rise .\nthe circumferential stress induced in the shell when it experienced\na temperature rise, t, may be approximated by the function .\nin other words, there is a compressive circumferential stress along\nthe entire length, l, of the shell .\nit is well known, however, that the discontinuity stresses introduced at\nthe junction of a shell and a rigid frame (or bulk-head) are extremely\nlocalized, and the circumferential stresses induced in the shell\ndecrease rapidly away from the joint ."}, {"doc_id": 891, "text": "buckling of a finite length cylindrical shell under\na circumferential band of pressure .\n this paper is concerned with buckling of a circular cylinder of\nfinite length subjected to a symmetrical band of external pressure .\nboth experimental and theoretical results are presented . the\nexperimental data were obtained from tests of three thin-walled\nsteel cylinders subjected to external pressure by a pneumatic\ntube encircling the test cylinder at mid-length . the theory is\nbased on the principle of minimum potential energy, and the\nrayleigh-ritz procedure is used to expand the displacement\ncomponents in trigonometric series .\n theoretical results are given in the form of graphs which show\nbuckling pressure as a function of the following ratios ..\n cylinder radius thickness\n cylinder length radius\n pressure bandwidth cylinder length\n theoretical results are in close agreement with existing\nsolutions to special cases in which (1) the pressure is applied over the\nentire lateral surface, and (2) the pressure is concentrated along a\ncircumferential line . the theoretical results are also in\nagreement with the test results ."}, {"doc_id": 892, "text": "research on unsteady flow .\n this is a survey of certain recent advances made in the study\nof aerodynamic unsteady flow and of some of the new problems\narising which require further investigation . no attempt is made to\nreproduce classical theory, but emphasis rather is laid on validity\nand general usefulness, particular attention being given to\nunsteady boundary-layer effects, especially when there is flow\nseparation . coverage is broad and author thus provides a useful review\nfor those interested in this field ."}, {"doc_id": 893, "text": "a new design of pitot-static tube with a discussion\nof pitot-static tubes and their calibration factors .\n the report describes experiments devised to investigate\nsome of the previously unexplained peculiarities of normal types of\npitot-static tube . in the process use was made of what was as nearly\nas could be a standard static pressure tube .\n the experiments led to a new alternative design of instrument\nhaving a nose of modified ellipsoidal shape and for which the main\ncharacteristics have been investigated .\n it has been found to be necessary as well as desirable to\ninclude a discussion of the implications of the term /calibration\nfactor/ and (although not in this respect comprehensive) of the special\nfeatures and limitations of various pitot-static tubes ."}, {"doc_id": 894, "text": "flutter of a two dimensional simply supported buckled\npanel with elastic restraint against edge displacement .\n the critical flutter speed is evaluated for a two-dimensional thin\nbuckled panel with one surface exposed to a supersonic airstream and the\nother to still air at the same static pressure . the panel is simply\nsupported along the leading and trailing edges by rigid edge members\nseparated by an elastic member represented by a compression spring .\nthe whole system is acted upon by a constant compressive force uniformly\ndistributed along the edge members . the aerodynamic forces acting on\nthe deflected panel are found from two-dimensional /quasi-steady/\ntheory, valid for slow oscillations where the downwash velocity is small\ncompared with the speed of flow and provided that the mach number is\nsufficiently greater than . the elastic behaviour of the panel is given\nby von karman's large deflection equations modified to cover initially\ncurved plates . the solution of the equations is carried out by means\nof galerkin's method, which has been shown to give valid results for\na panel with a non-zero bending rigidity .\n the influence of the midplane compressive force carried by the panel\nitself, the initial buckle amplitude and the elastic restraint against\nedge displacements is investigated, and curves are presented giving the\ncritical dynamic pressure ratio as a function of these variables ."}, {"doc_id": 895, "text": "the airforces on the low aspect ratio rectangular wing\noscillating in sonic flow .\n approximate expressions for the\ngeneralised airforces acting on a\nrectangular wing of low aspect ratio\noscillating harmonically in sonic flow\nat low frequencies are derived in this\npaper . the modes of oscillation\nconsidered are rigid modes and a small\nselection of flexible modes . results\nare presented as the first few terms of\ninfinite expansions .\n a brief description of the modes\nof oscillation and of the generalised\nairforces is given towards the end of\nthe paper so that the results may be\nused without the main text of the paper\nhaving to be read ."}, {"doc_id": 896, "text": "the calculation of loads on a supersonic weapon in\nthe steady circling case .\n the economy of a design depends\non the accuracy with which it is possible\nto solve the various structural problems\nas this has a direct bearing on\nstructure weight . this paper describes\nthe calculation of the bending moments\non a specific weapon for the high-g steady\ncircling case . a hybrid method is\nused to obtain the aerodynamic loads .\n the results presented show the effect\nof a number of parameters, such\nas - altitude, weight, acceleration and mach\nnumber - on the magnitude of the\nmaximum bending moment ."}, {"doc_id": 897, "text": "some results on buckling and postbuckling of cylindrical\nshells .\n in this summary paper, the\neffects of initial deformations on the\nbuckling and postbuckling characteristics\nof circular cylindrical\nshells under hydrostatic pressure\nis determined in an approximate\nmanner . the influence of initial\naxisymmetric deformations is stressed .\nalso, the classical buckling of\nan axially compressed, noncircular\nthe results show that the\nmajor-minor axis ratio of the cross section\nhas a marked effect on the\ncritical load, and that use of the\nmaximum radius of curvature in the\nformula for the classical buckling\nstress of a circular cylindrical\nshell leads to good results for moderate\neccentricities ."}, {"doc_id": 898, "text": "a survey of buckling theory and experiment for circular\nconical shells of constant thickness .\n a survey of the state-of-the-art\nfor the stability of thin-walled\nconical shells is presented . known\ntheoretical results are summarized\nand compared with experiment . the\nshortcomings of present knowledge\nand recommended work for the future\nare discussed ."}, {"doc_id": 899, "text": "aerodynamic effects on boundary layer unsteadiness .\n with a view to the study of\naerodynamic problems, a review is made\nof boundary layer theory for a flat\nplate moving with a time-dependent\nvelocity . unsteady effects are shown\nto enter according to the magnitude\nof the ratio of time for diffusion to act\nthroughout the boundary layer to the\ncharacteristic time of the imposed unsteadiness .\n it is concluded that a boundary layer\nmay be considered quasi-steady\neven during extreme flight manocuvres .\ngeneration of acoustic noise purely\nby boundary layer unsteadiness is generally\nsmall . thermal and heat-transfer\neffects are cited .\n unsteady boundary layer considerations\nare important in damping or\namplifying certain instabilities, such as flutter\nof panels and stalling flutter of\naerofoils . in connection with the aerofoil\nproblem, laminar separation\nconcepts and the stagnation-point boundary\nlayer are described for unsteady\nflow .\n an analysis of aerofoil lift hysteresis\nis described, using unsteady\nlaminar boundary layer considerations, which\nleads to a prediction of\ncounter-clockwise hysteresis at maximum lift ."}, {"doc_id": 900, "text": "some measurements in the vortex flow generated by a\nsharp leading edge having 65 sweep .\n the report is concerned with the vortex flow which arises\nwhen separation occurs at a highly swept leading edge . measurements\nwere made in the flow over flat plates at 15 incidence each having\na sharp leading edge of 65 sweep . the pressure and velocity\ndistributions both along the axis of the vortex and for one\ncross section of the flow are presented together with a preliminary\ndiscussion of their significance ."}, {"doc_id": 901, "text": "long slender delta wings with leading edge separation .\n the slender-body approximation of linearized compressible flow is\napplied to the problem of a delta wing in which flow separation occurs\nat the leading edges . the vortex sheets found in the real flow are\napproximated by concentrated vortices with feeding lattices, and a\nplausible adaptation of kelvin's theorem is applied to simulate the\nforce-free nature of the vortex sheet .\n the computations show that leading-edge separation produces an\nincrease in lift over that given by the jones slender-wing theory and\nthat the lift does not vary linearly with angle of attack . computed\npressure distributions and span loadings are presented and the\ntheoretical lift results are compared with the results of simple force tests\nmade at a mach number of 1.9 ."}, {"doc_id": 902, "text": "some current and proposed investigations into the flow\nfor slender delta and other wings in unsteady motion .\n the practical need for research\ninto the aerodynamics of\nslender delta wings in unsteady motion has\nbeen emphasized in a recent\npaper by zbrozek . two important aspects\nare .. - formation and presence of\n leading-edge vortices .\n with oscillatory or transient\n modes of longitudinal (or\n chordwise) bending .\n the first of the aspects\nabove, has already been briefly\ndiscussed in ref. 2 . one feature of\nthe flow with leading-edge vortices\nwhich seems to be of particular\nsignificance to the dynamic behaviour\nof a wing is the shedding of vorticity\nat the leading edge as well as at\nthe trailing edge . any time-dependent\nmotion, or distortion, of the wing\nleads to a change in the rate at which\nvorticity is shed . with more\nconventional types of flow, the free\nvorticity being shed only from the\ntrailing edge has diminishing influence\non the wing, but when the free\nvorticity is shed from the leading edge,\nin passing downstream, it\nremains close to the upper surface of the\nwing . it might be expected\nthen, that, although the magnitudes of the\nunsteady forces may not be\ngreatly affected for a slender delta, the\ntime delays associated with\nthe forces may be significantly different\nfor the attached and\nseparated regimes of leading-edge flow ."}, {"doc_id": 903, "text": "two dimensional transonic unsteady flow with shock\nwaves .\n a study is made of the unsteady flow around an\nairfoil at transonic mach numbers, the situation being\nsuch that local supersonic regions terminated by\nshock-waves are present in the vicinity of the airfoil . for\nthe unsteady part of the flow, small perturbations\ntechnique is employed and the interaction with the shock\nwave is taken into account . the case of an oscillating\naileron is considered first, and a solution is derived\nfor the pressure distribution on the aileron . it is\nfound that the solution has a simple form when the\nshock-wave is well ahead of the hinge axis of the\naileron . as the shock approaches the hinge-axis a\ncorrection must be added to the solution . an\ninterpretation of these results is given . the results are\ncompared with results of a theory which neglects the\npresence of the shock and it is found that both agree\nfor m = 1 . for m 1, however, neglecting the presence\nof the shock waves introduces errors of the order of\nmagnitude (1 - m), where m is the local mach number\nbehind the shock .\n the theory is finally extended to include the case\nin which the whole airfoil oscillates, but only the\nsolution for the subsonic region behind the shock is\ntreated . the role of the unsteady shock-boundary layer\ninteraction is discussed and it is shown that this\nmechanism can be included in the results of the present\ntheory ."}, {"doc_id": 904, "text": "calibration of the standard pitot-static head used\nin the rae low speed wind tunnels .\n recent results of tests in the\nr.a.e. wind tunnels concerned with\nthe measurement of pressure distributions\nhave shown slight discrepancies\nbetween the readings of various static\npressure tubes and calculated\npressure distributions . as a consequence\nsome doubt was felt concerning\nthe calibrations of tunnel static pressure\nand upon the validity of the\nreading given by the standard pitot-static\nhead .\n it was therefore decided to check the\nstandard pitot-static head\nused in the r.a.e. wind tunnels, against an\ninstrument similar to the\nmeasurements of static\npressure were also made using a long tube where\nthe interference from head\nand support is calculated to be small .\n this note gives the results of tests\nmade in the 5 ft open jet wind\ntunnel and the no. 1 11 ft wind tunnel\nin order to determine the\nnecessary correction to the reading of static\npressure given by the r.a.e.\npitot-static head . the tests were made\nduring september and october, 1951 ."}, {"doc_id": 905, "text": "comparative tests of pitot-static tubes .\n comparative tests were made on seven conventional\npitot-static tubes to determine their static, dynamic, and\nresultant errors . the effect of varying the dynamic\nopening, static openings, wall thickness, and inner-tube\ndiameter was investigated . pressure-distribution measurements\nshowing stem and tip effects were also made . a tentative\ndesign for a standard pitot-static tube for use in\nmeasuring air velocity is submitted .\n this report covers an investigation conducted under\nthe auspices of the national research council ."}, {"doc_id": 906, "text": "review of the pitot tube .\n this paper is an attempt to bring together the\nimportant information regarding pitot tubes and their use,.\nto summarize the available data on the application of\nvarious types of impact and velocity probes for the\nguidance of engineers and research workers,. and to aid\nthem in the design of flow instruments for specific\napplications ."}, {"doc_id": 907, "text": "cavitation and pressure distribution\nhead forms at zero angle of yaw .\nearly in the fall of 1943 the iowa institute of hydraulic research\nundertook the design and fabrication of a variable-pressure water\ntunnel . as the tunnel neared completion, however, its immediate use\nfor the study of the pressure distribution around various body forms\nwas requested .\nthe original request for this investigation was a natural out-growth\nof the need for systematic data on the distribution of pressure\nin flow around various bodies, particularly under conditions leading to\ncavitation, information which is desirable for the design of a wide\nvariety of navy equipment . ultimately the study is to include data\nfor two- and three-dimensional head and tail forms at various angles of\nyaw . the first phase of the study, namely the investigation of\nthree-dimensional head forms at zero angle of yaw, is described herein .\nthree general geometric series have been studied.dash rounded,\nellipsoidal, and conical.dash together with other related forms .\nthe data obtained have been systematized to yield information for\na wide variety of geometrical forms either directly or by\ninterpolation . whenever possible, analytical methods have been used to\ncorroborate the experimental data and to provide a reliable means\nof generalizing the results ."}, {"doc_id": 908, "text": "random vibration .\n random vibration is vibration which results\nfrom an excitation which is not well represented by any simple\nfunction (sinusoid, step, etc.) or any simple combination of\nsuch functions but which is satisfactorily modeled by a\nstochastic process . it is perhaps not too much of an exaggeration\nto say that /all vibration is random vibration ./ every\nvibration record contains /hash/ at some level . nevertheless,\nuntil recently, engineering vibration theory has been able to\nget along without including the consideration of random\nexcitations .\n now in several fields simultaneously there has occurred a\nburst of activity in the application of random processes . the\nresponse of aircraft to buffeting from atmospheric turbulence\nand the response of ships to confused seas have been put on\nreasonably firm footing . possibly the most dramatic problems\nhave been posed by the development of large jet and rocket\nengines which produce spectacular amounts of random\nvibrational energy . the high level of random vibration in a jet\nplane or a missile provides a severe environment with respect\nto fatigue failure of structural members and with respect to\nmalfunctions of sensitive equipment ."}, {"doc_id": 909, "text": "the effect of jet noise on aircraft structures .\n the present state of knowledge on the\nproblem of fatigue failure due\nto vibrations excited by jet noise is reviewed .\nit is concluded that it should\ncurrently be possible to make reasonable\nestimates of the stress levels set up\nin a structure by jet noise but, in general,\nthe resultant fatigue life of the\ncomponents cannot be estimated\nwith any confidence ."}, {"doc_id": 910, "text": "natural frequencies of continuous beams of uniform\nspan length .\n a simple graphical network is used to determine the\nnatural frequencies of flexural vibration of continuous\nbeams having any number of spans of uniform length .\nthe network is based upon a relatively few calculated\nvalues ."}, {"doc_id": 911, "text": "experimental study of the random vibrations of an aircraft\nstructure excited by jet noise .\n recordings have been made of the strains induced in a\nfull scale rear fuselage test structure of the caravelle\nair-liner when one jet engine is running at maximum\ntake-off thrust . the analysis has been concentrated on the\nstrains in the centres of panels . correlation\nmeasurements indicate that the larger panel strains occur above\nresonance peak in each panel has been identified with the\nfundamental stringer-twisting mode but the mode-shapes for\nthe two smaller peaks have not been completely determined .\nan attempt has been made to calculate the panel resonant\nfrequencies theoretically ."}, {"doc_id": 912, "text": "the axisymmetric free-convection temperature field\nalong a vertical thin cylinder .\n with a view to studying the effect of strong transverse\ncurvature on boundary-layer problems, the axisymmetric free-\nconvection problem along a vertical thin cylinder is investigated\ntheoretically as well as experimentally . a theory is developed\nas an extension of the pohlhausen solution of a thick\naxisymmetric laminar boundary layer by mark and by glauert and\nlighthill . experiments consist of a thermocouple survey of the\ntemperature field over an electrically-heated brass cylinder of\ndiameter and 10 ft. height and an interferometric study\nof the density field over a bare tungsten wire of 0.02-in. diameter\nand 5 ft. height . the thermal-layer thicknesses are about five\nand fifty times the radii of the cylinders, respectively .\nexperimental results of the local heat-transfer coefficient are in excellent\nagreement with the theory . this, in turn, justifies the theories\nof laminar boundary layer along a thin cylinder, at least indirectly ."}, {"doc_id": 913, "text": "vibrations of beams on many supports .\n the natural frequencies of a continuous\nbeam resting on an arbitrary\nnumber of uniformly spaced supports are\ndetermined from a difference equation\nformulation . these frequencies fall in\nperiodically spaced groups that are\nseparated by spectral gaps of widths\nequal to approximately half the interval\nbetween the natural frequencies of a\nsingle beam on a square root frequency\nscale . these groups tend to uniform\nspectra as the number of supports tends\nto infinity, but the gaps remain, giving\na band-pass character to the entire\nspectrum . wave propagation along an\ninfinite, periodically supported beam\nis discussed and the phase and group\nvelocities evaluated as functions of\nfrequency ."}, {"doc_id": 914, "text": "transtability flutter of supersonic aircraft panels .\nfor certain aero-elastic configurations it is possible to ascertain\ncritical flutter conditions from static considerations alone . the\nidea is simply one of negation.. when the air speed exceeds a certain\nvalue statically stable equilibrium - and sometimes equilibrium itself\ntake place . there are times when the dynamics of a situation are\ncomplex enough to defy a tractable analysis . the value of being able\nto indicate a flutter criterion from the simpler statics is clear .\nwe will suppose flutter begins when some critical value of the air\nspeed (or some parameter simply related the to) is exceeded . here\nwe will show that there is a critical value which, when exceeded,\nprecludes static equilibrium . underlying our work is the premise\nthat these two critical values are the same . this assumption begs\ndiscussion .\nwe will call the lowest value of our air speed parameter to preclude\nstatically stable equilibrium of the system the transtability value .\nin some cases, excess of this value will ban all possibility of\nstatic equilibrium - stable or not., we will then call it a strong\ntranstability value ."}, {"doc_id": 915, "text": "a buckled plate in a supersonic stream .\nthe forcible buckling of an\nexternal skin plate from a guided missile, with a pinned end,\nis considered in a supersonic air flow . conidtions of dynamic stability\northogonality and expansion of the buckling mode, the degree of\nfreedom and cases of small deflection are considered .\nwithout a 50 half angle conical afterbody\nin a pressurized ballistic\nof range at nominal mach numbers of 3.5 and\nof 90000 and 220000, respectively . it"}, {"doc_id": 916, "text": "the flow around oscillating low aspect ratio wings at transonic\nspeeds .\nwhen certain conditions are fulfilled for thickness ratio, aspect ratio,\n and reduced frequency for a three-dimensional wing, it can be shown\nthat the partial differential equation for the non-steady perturbation\npotential can be reduced to a comparatively simple linear equation .\nthe solution is then obtained by applying a fourier transformation in\nthe free-stream direction and then using an iterative process developed\nby adams and sears for steady flow . the method gives solutions valid\nfor low combinations of aspect ratio and reduced frequency .\nthe method is applied to a delta wing oscillating in some selected rigid\n and elastic modes . from the results it can be seen that the special\nnon-steady forces in the potential equation, which are neglected in\nslender-body theory, are very important . stability derivatives can also\n be obtained by the method and it is seen that the damping in pitch may\nbe negative at m 1 for delta wings of too high aspect ratio ."}, {"doc_id": 917, "text": "a method of calculating the short period longitudinal\nstability derivatives of a wing in linearised unsteady\ncompressible flow .\n a method is developed for the\ncalculation of the pressure\ndistribution and the aerodynamic forces and\nmoments on a wing performing harmonic\npitching and heaving oscillations .\nthe calculation is based on the\nassumption of inviscid potential flow\nwithout shock waves and is\nrestricted to small incidence, so that the\nlinearized theory is valid .\n in contrast to other work in the\nfield the theory applies to all\nmach numbers . it is restricted to small\nvalues of the reduced frequency\nand should be valid for the usual range\nof short periods occurring at\npresent in flight . the formal solution\nyields two integral equations for\nthe parts of the load, which are in phase\nand go out of phase with the\noscillation,. these are of the same form\nas the corresponding equation\nin steady flow .\n the way is thus opened for solutions\nover the whole mach number\nrange at small frequencies, if the\ncorresponding steady solutions can\nbe found . the calculation is in fact\neasiest for m = 1 and has been\ndone here for delta-wings to supplement\na previous supersonic calculation,\nmade on different frequency assumptions,\nwhich broke down near m = 1 .\nit appears from the two sets of results\nthat the short period oscillation\nwill be unstable near m = 1, if the apex\nangle of the delta wing is\ngreater than about 60 . this confirms a\nnow generally recognised trend .\n such results near m = 1 must of\ncourse be invalidated to an\nunknown extent by thickness viscosity and\nshock waves at their maximum\neffect . nevertheless it is unlikely that\nthese factors will remove\nthe critical nature of the transonic damping\nas calculated by this method .\nwith all its obvious limitations this method,\nwhen extended to other\nplanforms, should provide a useful tool in\nstudying the effect of\ngeometrical parameters on the stability of\nan aircraft at transonic\nspeeds ."}, {"doc_id": 918, "text": "on the low aspect ratio oscillating rectangular wing\nin supersonic flow .\n the laplace transform of\nthe lift distribution on an oscillating\nrectangular wing in a supersonic flow is obtained\nby separating the linearised equation\nfor the velocity potential in elliptic (cylindrical)\nco-ordinates . the results for the case\nof no spanwise distortion are expanded in ascending\npowers of the aspect ratio in order\nto compare with the slender body theory, and the\nlongitudinal stability derivatives are\ncalculated . it is found that at either supersonic\nor transonic speeds single-degree-\nof-freedom instability in pitch is impossible insofar\nas the fourth power of the aspect\nratio is neglected ."}, {"doc_id": 919, "text": "theoretical studies of unsteady transonic flow . part iii . the\noscillating low aspect ratio rectangular wing .\nby expanding the velocity potential in an asymptotic series, the\naerodynamic forces on an oscillating low aspect ratio rectangular wing are\ncalculated . the approximate theory is valid for small values of ko /o\nsemi-span-to-chord ratio,. k reduced frequency/ and complements an\nearlier low-aspect-ratio-wing theory by the author valid only for\npointed wings like delta wings . the present report gives formulas for\nthe calculation of generalized forces for any smooth, flexible or rigid\nmode of oscillation with spanwise symmetry .\ncomparisons with the slender-wing theory show that, except for wings of\nvery low aspect ratio, unsteady-flow effects are appreciable even at\nfairly low reduced frequencies . near the upper limit in ko for the\napplicability of the present theory good agreement is obtained with a\nrecent theory for high aspect ratios ."}, {"doc_id": 920, "text": "supersonic flow over an inclined wing of zero aspect ratio .\nan asymptotic expression is found for the lift distribution on a long,\nnarrow, laminar wing, at incidence in a supersonic stream . the\napproximations of the linearized potential theory are used ."}, {"doc_id": 921, "text": "slender-body theory-review and extension .\nthe approximate theory of flow about slender bodies and wings originated\n by munk and jones is reviewed . it is presented here in a form that\nemphasizes the relation to the source-sink methods of von karman and\nothers . the extension to noncircular bodies is made for subsonic flow,\nparalleling ward's extension for supersonic flow . the calculation of\npressures and forces and the extension of the theory to unsteady flows\nare reviewed, and some discrepancies in the published literature are\nexplained .\nfinally, interpreting the jones slender-wing result as the first term of\n an expansion in powers of a breadth parameter /e.g., aspect ratio/, it\nis shown how a more accurate theory can be developed by carrying\nadditional terms for both subsonic and supersonic speeds . this theory of\nnot-so-slender wings is applied to some practical wing problems,\nincluding direct problems of flow past given wings and problems of wing\ndesign for minimum drag . the accuracy of the new results is assessed by\n comparison with linearized supersonic-airfoil theory for the special\ncase of a flat delta wing ."}, {"doc_id": 922, "text": "supersonic flow past slender bodies of revolution,\nslope of whose median section is discontinuous .\n the theory of supersonic flow around\nslender bodies of revolution, yawed or\nunyawed, with pointed or open bows, based\non the linearized equation, is extended\nto the case when the meridian section of\nthe outer surface has discontinuities in\nslope . expressions for the pressure distribution\non the surface are obtained . it is\nfound that the drag coefficient is no longer\nindependent of mach number, and tends\nto zero more slowly than the square of the\nthickness of the body . the large pressure\nchange behind a discontinuity is made up\nremarkably rapidly . the first\napproximation to the lift coefficient is unchanged ."}, {"doc_id": 923, "text": "methods for estimating lift interference of wing-body\ncombinations at supersonic speeds .\n the modified slender-body method\nused by nielsen, katzen, and tang\nin rm a50f06, 1950, to predict the\nlift and moment interference of\ntriangular wing-body combinations has\nbeen adapted to combinations with\nother than triangular wings . that\npart of the method for predicting the\neffect of the body on the wing has\nbeen retained, but a new method for\npredicting the effect of the wing on\nthe body has been presented . these\nmethods have been applied to the\nprediction of the lift-curve slopes of\nnearly 100 triangular, rectangular,\nand trapezoidal wing-body\nconfigurations . the estimated and experimental\nvalues for the lift-curve slopes\nagree for most of the cases within 10\npercent . some of the\nhigher-order effects that must be taken into\naccount in a theory that is to\ngive greater accuracy than the present\none are discussed . a numerical\nexample illustrating the method is included ."}, {"doc_id": 924, "text": "a method for calculating the lift and centre of pressure\nof wing-body-tail combinations at subsonic, transonic\nspeeds .\n a method is presented for\ncalculating the lift and pitching-moment\ncharacteristics of circular cylindrical\nbodies in combination with\ntriangular, rectangular, or trapezoidal\nwings or tails through the subsonic,\ntransonic, and supersonic speed ranges .\nthe method covers unbanked\nwings, sweptback leading edges or\nsweptforward trailing edges, low\nangles of attack, and the effects of\nwing and tail incidence . the\nwing-body interference is handled by the\nmethod presented in naca rm's a51j04\nand a52b06, and the wing-tail interference\nis treated by assuming one\ncompletely rolled-up vortex per wing\npanel and evaluating the tail load\nby strip theory . a computing table\nand set of design charts are\npresented which reduce the calculations\nto routine operations . comparison\nis made between the estimated and\nexperimental characteristics for a\nlarge number of wing-body and wing-body-tail\ncombinations . generally\nspeaking, the lifts were estimated to\nwithin 10 percent and the centers\nof pressure were estimated to within\neffect of wing deflection on wing-tail\ninterference at supersonic speeds\nwas not correctly predicted for triangular\nwings with supersonic leading\nedges ."}, {"doc_id": 925, "text": "factors affecting loads at hypersonic speeds .\n this paper gives a brief summary of current loads information at\nhypersonic speeds . several methods which the designer can employ in\nestimating the loads on various aircraft components are discussed . the\npaper deals with the characteristics of both slender and blunt\nconfigurations and touches upon the effects of boundary-layer and\naerodynamic interference ."}, {"doc_id": 926, "text": "post buckling behaviour of circular cylinderical shells\nunder hydrostatic pressure .\n the postbuckling behavior of initially perfect, thin-walled,\ncircular cylindrical shells under hydrostatic pressure is\ninvestigated with the aid of the principle of stationary potential energy\ntogether with appropriate approximate deflection functions .\ncalculations show that postbuckling equilibrium configurations\nexist for loads greater than as well as loads slightly less than the\ncritical load calculated from small-deflection theory . loads\nless than the critical load are obtained only for a finite range of a\nparameter indicative of shell geometry . for loads corresponding\nto radial displacements of the order of the shell thickness, it is\nfound that the number of circumferential waves remain\nessentially constant with increasing deflection and equal to the\nnumber of waves developed at buckling ."}, {"doc_id": 927, "text": "investigation of normal force distributions and wake\nvortex characteristics of bodies of revolution at supersonic\nspeeds .\n the supersonic aerodynamic characteristics of inclined bodies\nof revolution at high angles of attack have been investigated in\norder to provide a more basic understanding of the body vortex\nwake flow and its relation to the problem of body-wing\ninterference . the results of wind-tunnel tests, whereby the normal\nforce, pitching moment, normal force distributions, and the local\nflow properties in the vicinity of the body were determined, are\ndiscussed and analyzed .\n comparisons of experimental normal force coefficient and\ncenter of pressure data with values calculated in accordance with\ntheories which include methods for estimating the effects of\nviscosity show that the accuracy of these estimates is strongly\ndependent on the body fineness ratio and the angle of attack .\nfurther comparisons of the distributions of theoretical and\nexperimentally derived cross-flow drag coefficients clearly show that,\nin general, the disagreement between experiment and existing\ntheories is due to the inadequate prediction of the magnitude and\ndistribution of the forces resulting from flow separation .\n the circulation strengths of the concentrated vortices and the\ncirculation strengths of the vortex feeding sheets in the body\nvortex wake are determined by closed-contour velocity-perimeter\nintegrations for paths enclosing the vortex or the feeding sheet .\nthe values of vortex strength calculated in this manner are in\nclose agreement with the values predicted by vortex strength\nformulas written for a simple theoretical model for which it is\nassumed that the cross-flow in any plane along the cylindrical\nportion of the body is represented by the steady incompressible\npotential flow about a cylinder, two symmetrical vortices of\nequal strength, and the attendant image vortices . however,\nin computing these strengths it is necessary to use the vortex\nlocations and the viscous normal force distributions determined\nfrom experiment .\n the experimentally determined values of vortex strength are,\nin turn, used to calculate--by means of the aforementioned\nincompressible cross-flow potential--the local flow inclination\nangles which are in good agreement with the measured values,\nexcept in the vortex core, in the vicinity of the feeding sheet,\nand in regions for which transonic cross-flow velocities are\nexpected . a consideration of these various regions with simple\nmethods which account for the observed phenomena leads to\nsubstantial improvement in the agreement between theory and\nexperiment .\n it is indicated that the complete vortex wake flow may be\nadequately predicted for a body of revolution (for conditions\nrepresented by the theoretical flow model), provided that the\ndistribution of the viscous normal force and the vortex locations are\naccurately known ."}, {"doc_id": 928, "text": "a new theory for the buckling of thin cylinders under\naxial compression and bending .\n the results of experiments on axial loading of cylindrical\nshells (thin enough to buckle below the elastic limit and\ntoo short to buckle as euler columns) are not in good\nagreement with previous theories, which have been based on the\nassumptions of perfect initial shape and infinitesimal\ndeflections . experimental failure stresses range from 0.6\nto 0.15 of the theoretical . the discrepancy is apparently\nconsiderably greater for brass and mild-steel specimens\nthan for duralumin and increases with the radius-\nthickness ratio . there is an equally great discrepancy between\nobserved and predicted shapes of buckling deflections .\n in this paper an approximate large-deflection theory is\ndeveloped, which permits initial eccentricities or\ndeviations from cylindrical shape to be considered . true\ninstability is, of course, impossible under such conditions,.\nthe stress distribution is no longer uniform, and it is\nassumed that final failure takes place when the maximum\nstress reaches the yield point . the effect of initial\neccentricities and of large deflections is much greater than for\nthe case of simple struts . measurements of initial\neccentricities in actual cylinders have not been made,.\nhowever, it is shown that most of these discrepancies can be\nexplained if the initial deviations from cylindrical form are\nassumed to be resolved into a double harmonic series, and\nif certain reasonable assumptions are made as to the\nmagnitudes of these components of the deviations . with\nthese assumptions the failing stress is found to be a\nfunction of the yield point as well as of the modulus of\nelasticity and the radius-thickness ratio . on the basis of this\na tentative design formula (5) is proposel, which involves\nrelations suggested by the theory but is based on\nexperimental data .\n it is shown that similar discrepancies between\nexperiments and previous theories on the buckling of thin\ncylinders in pure bending can be reasonably explained on the\nsame basis, and that the maximum bending stress can\nbe taken as about 1.4 times the values given by equation\nbuckling problems can probably be explained by similar\nconsiderations, and it is hoped that this discussion may\nhelp to open a new field in the study of buckling problems .\nthe large-deflection theory developed in the paper should\nbe useful in exploring this field, and may be used in other\napplications as well .\n the paper presents the results of about a hundred new\ntests of thin cylinders in axial compression and bending,\nwhich, together with numerous tests by lundquist, form\nthe experimental evidence for the conclusions arrived at ."}, {"doc_id": 929, "text": "stability of the cylindrical shell of variable curvature .\nthe report is a first attempt to devise a calculation method\nfor representing the buckling behavior of cylindrical shells\nof variable curvature . the problem occurs, for instance, in\ndimensioning wing noses, the stability behavior of which is\ndecisively influenced by the variability of curvature . the\ncalculation is made possible by simplifying the stability\nequations (permissible for the shell of small curvature) and\nby assuming that the curvature as a function of the arc\nlength s can be represented by a very few fourier terms .\nwe evaluated the formulas for the special case of an\nellipse-like half oval with an axis ratio under\ncompression in longitudinal direction, shear, and a combination of\nshear and compression . however, the results can also be\napplied approximately to an unsymmetrical oval-shell segment\nunder compression, shear, and bending so that the numerical\nvalues contained in the diagrams 10 to 12 represent directly\ndimensioning data for the wing nose ."}, {"doc_id": 930, "text": "general theory of large deflections of thin shells\nwith special applications to conical shells .\n a general theory is developed for the case of large deflections\nbut with rotations of the elements negligible compared to unity . the\nderivation is carried out in tensor form and therefore any coordinate\nsystem on the surface of the shell can be used . the effect of initial\nimperfections is included . it is shown that for shells of negligible\ngaussian curvature (shallow shells and developable surfaces), the\nproblem can be reduced to the solution of two fourth-order partial\ndifferential equations in a stress function and the deflection normal to the\nshell . for shells forming a surface of revolution the results are\nindicated in terms of the equation of the generating curve . the\ndifferential equations for the conical shell are then listed ."}, {"doc_id": 931, "text": "stability equations for conical shells .\n the author rewrites v. s. vlasov's equations for (linear)\nstability theory of shells (prikl. mat. meh. 8(1944),\n109-placements . the result is a single eighth-order equation\nfor normal deflection, and two fourth-order equations\nrelating the displacement components in the shell middle\nsurface to the normal displacement ."}, {"doc_id": 932, "text": "buckling of circular cones under axial compression .\npresented are the results of an experimental\ninvestigation to determine the buckling\nstrength of right circular cones under axial\ncompression . correlation of these data is\nmade with existing theory and with previously\npublished experimental data on circular\ncylinders,. thus a recommended procedure\nfor predicting the buckling load of right\ncircular cones under the foregoing loading\ncondition is presented ."}, {"doc_id": 933, "text": "the characteristics of roughness from insects as observed\nfor two-dimensional, incompressible flow past airfoils .\n advances in the practical development of boundary-layer\ncontrol for the maintenance of extensive laminar flow have drawn\nattention to the problem of surface roughness, due not only to\nartificial irregularities such as rivet heads, lap joints, window\npanels, etc., but also to the kind generated in flight from impact\nwith insects . this natural form of roughening, the effects of which\nhave been noted, though not investigated previously, is the\nsubject of the present paper .\n the phenomenon may be divided into two parts--namely,\nand (2) its effect upon the stability of the laminar boundary\nlayer . wind-tunnel experiments with the fruit fly, drosophila,\nand the common housefly for the investigation of both (1) and\nairfoils are fully described . the former problem has also been\ntreated mathematically in a separate paper, not yet published,\nagreement between theory and experiment being satisfactory in\nall essentials .\n the characteristics of the roughness profile consist principally\nof a pronounced peak near the leading edge, followed by an\nextensive area of surface over which there is a much reduced and\ngradually diminishing value of the excrescence height . further,\nit is shown that, if the severe leading-edge roughness, or its effect\nupon the boundary layer, can be eliminated, then the\ndown-stream roughness causes no disturbance to the passage of a\nlaminar layer--i.e., the surface, though roughened, is aerodynamically\nsmooth . moreover, it appears that the conditions defining the\nupstream boundary to this region of insignificant roughness are\nfundamentally the same as those which determine the critical\nstate for transition at an artificial disturbance of a three-\ndimensional character ."}, {"doc_id": 934, "text": "stability of cylindrical and conical shells of circular\ncross section, with simultaneous action of axial compression\nand external normal pressure .\n we consider in this report the\ndetermination of the upper limit of\ncritical loads in the case of simultaneous\naction of a compressive force,\nuniformly distributed over plane cross\nsections, and of isotropic external\nnormal pressure on cylindrical or\nconical shells of circular cross\nsection . as a starting point we use\nthe differential equations for neutral\nequilibrium of conical shells (ref. 1)\nwhich have been used for the\nsolution of the problem of stability of conical\nshells under torsion and under\naxial compression (ref. 2),. upon solution\nof the problem it is possible\nto satisfy all boundary conditions, in\ncontrast to the report (ref. 3)\nwhere no attention is paid to the fulfillment\nof the boundary conditions\nand to the report (ref. 4) where only part\nof the boundary conditions are\nsatisfied by solution of the problem\naccording to galerkin's method .\napproximate formulas are used for the\ndetermination of the critical\nexternal normal pressure with simultaneous\naction of longitudinal\ncompression . let us note that the formulas\nsuggested in reference 5 are\nnot well founded and may lead, in a number\nof cases, to a substantial\nmistake in the magnitude of the critical load ."}, {"doc_id": 935, "text": "buckling of thin single- and multi-layer conical and cylindrical\nshells with rotationally symmetric stresses .\nthe buckling of simply supported, thin, single- and multi-layer conical\nshells under axially symmetrical loading is analyzed in this paper .\nthe results are presented in a compact manner so that they may be easily\nused for design and/or experimental purposes . the results are compared\nwith known experimental values ."}, {"doc_id": 936, "text": "a donnell-type theory for asymmetrical bending and\nbuckling of thin conical shells .\n equations, somewhat more accurate than those recently\npresented by n. j. hoff, are derived for bending and\nbuckling of thin circular conical shells under arbitrary loading .\nthese equations reduce to donnell's equations for thin\ncylindrical shells when the cone semivertex angle becomes\nvery small and the minimum radius of curvature of the\nmedian surface approaches a constant value . at the\nother end of the scale the equations reduce to the\nwell-known equations for flat circular plates when the cone\nsemivertex angle approaches a right angle . in addition,\nfor the entire range of cone semivertex angles the\nequations reduce to the known equations for axisymmetrical\nbending when variations of the displacements around the\ncircumference vanish . the problem of bending is\nreduced to the solution of a single fourth-order partial\ndifferential equation with variable coefficients ."}, {"doc_id": 937, "text": "on the buckling of truncated conical shells in torsion .\nthe problem of the buckling of thin circular\nconical frustums in pure torsion is solved in\na manner similar to that employed previously\nby the author for buckling under uniform\nhydrostatic pressure . synthesis of the numerical\nresults indicates that the critical torsion\nof a truncated cone is equal to that of an\nequivalent cylinder whose length and thickness\nare the axial length and wall thickness of\nthe cone and whose radius is a function of the\nsemivertex angle and the taper ratio of the\ncone . curves and equations to aid in the\nanalysis of conical frustums are given .\nit is shown that a previous recommendation for\nthe analysis of truncated cones in torsion\nmay be seriously unconservative in some cases ."}, {"doc_id": 938, "text": "calculations for the stability of thin conical frustums\nsubjected to external uniform hydrostatic pressure\nand axial loads .\n calculations are presented for the problem of the stability of\nconical shells subjected to combined external uniform\nhydrostatic pressure and axial tension or compression . stress\ninteraction curves are found to vary only slightly as a function of the\nratio of the end radii of the cone ."}, {"doc_id": 939, "text": "some explicit solutions for constant-temp . magnetogas\ndynamic channel flow .\nin order to simplify the process of estimating the aerodynamic\nloading on the after portions of slender vehicles, it is\nfrequently assumed that there is no nose-tail interaction . it is\nthe purpose of this note to show that, aside from boundary-layer\neffects, this assumption is not warranted when the nose\nhypersonic-similarity parameter, tan, is of the order of unity, or\ngreater . physically speaking, the entropy change associated\nwith a strong bow wave reduces the stagnation pressure\ndown-stream of the shock, and hence, lowers the dynamic pressure in\nthe vicinity of the tail ."}, {"doc_id": 940, "text": "of a turbulent free shear layer .\n the problem of predicting the mean velocity on streamlines\nthrough the pre-asymptotic turbulent free shear layer in two-dimensional\nincompressible flow is resolved into two parts . the linearized\nmomentum equation in terms of a generalized axial co-ordinate is\nsolved in the usual way . a relation between and the distance from\nthe separation point is then established analytically in contrast to the\nprevious use of empirical expressions .\n it is shown that except in the region close to separation the\nvelocity on the streamlines can be predicted by the simple approximation\nproposed by kirk ."}, {"doc_id": 941, "text": "viscous compressible and incompressible flow in slender\nchannels .\n an analytical study is made of viscous flow in slender\nchannels . similar solutions to the approximate equations of motion,\nvalid for flow at moderate or high reynolds numbers in slender\nchannels, are found for incompressible two-dimensional and\naxisymmetric flows and for compressible flows through\ntwo-dimensional channels with adiabatic walls . a study of\ncompressible flows in convergent-divergent channels yields results\nregarding the effect of viscosity on the location of the sonic line,\non the pressure ratio at the geometric throat and on the discharge\ncoefficient for such channels ."}, {"doc_id": 942, "text": "secondary gas injection in a conical rocket nozzle .\n data are presented on side forces generated\nby secondary gas injection in a 15 conical\nrocket exhaust nozzle . the side force was measured\ndirectly with a force transducer and the\ndata examined in terms of an amplification\nfactor, where is the measured effective\nspecific impulse of injectant, and is the\nspecific impulse of injectant for sonic flow into a\nvacuum . injection was normal to the axis\nof the nozzle through a single circular orifice at a\nfixed point in the diverging portion of the nozzle .\na variety of ambient temperature gaseous\ninjectants and orifice diameters were carefully studied .\ninjectant flow rate was varied for each configuration .\nthe main propellant was hot gas (\ncatalytically decomposed), and motor conditions\nwere held essentially constant ."}, {"doc_id": 943, "text": "compressible free shear layer with finite initial thickness .\n the momentum equation was uncoupled from\nthe other conservation equations for the case\nof a finite initial profile in a laminar free shear layer .\nthe equation was solved numerically, in\nthe crocco coordinate system, using an implicit\nfinite difference method . profiles of velocity\nand shear function were obtained as a function of\nstreamwise distance . the initial profiles as\nthe flow separates from the rear of the body\ncorrespond to the blasius profile in transformed\ncoordinates . for large distances downstream,\nthe profiles approach the chapman\ndistribution, corresponding to the case of zero initial\nfree shear layer thickness . the effect of these\nresults on calculations of base pressure and wake\nangle is discussed . a method for the\ncalculation of finite chemical kinetic effects on the\nprofiles of temperature and chemical\ncomposition in the free shear layer with finite initial\nthickness is outlined ."}, {"doc_id": 944, "text": "one dimensional heat conduction through the skin of\na vehicle upon entering a planetary atmosphere at constant\nvelocity and entry angle .\n closed-form solutions of the\none-dimensional heat-conduction\nequations for the flow of heat into a\nplate with a laminar boundary layer\nhave been obtained for a configuration\nentering a planetary atmosphere\nwith constant velocity and negative\nentry angle . the atmospheric density\nwas assumed to obey an exponential law\nand the temperature was assumed\nconstant initially . the solution is in\nthe form of a fourier series\nexpansion which, for most practical\napplications, can be approximated by\nretaining only one term of the expression .\nthe solution applies to the\ninitial part of the entry before the maximum\nheating conditions are\nencountered ."}, {"doc_id": 945, "text": "method for design of pump impellers using a high speed\ndigital computer .\n a method of designing pump impellers\nis derived from the equations of motion\nand continuity for incompressible nonviscous\nrelative flow . the flow is assumed\nto follow a known stream surface (representing\nblade shape) that extends from hub\nto shroud . equations are also derived for\napproximate blade-surface velocities\nand pressures . a detailed numerical procedure\nand block diagram are given for\nuse on a digital computer . a numerical example\nthat illustrates limited use of\nthe method is presented and further uses are\nindicated ."}, {"doc_id": 946, "text": "exploratory investigation of the effect of a forward\nfacing jet on the bow shock of a blunt body in a mach\nnumber 6 free stream .\n the effect of a forward-facing jet on\nthe bow shock of a blunt body in a\nmach 6 free stream was investigated\nexperimentally . the models tested had\nforward-facing jets using air and helium exhausting\nat mach numbers from 1 to 10.3 and\nwere run through a range of the ratio of jet\ntotal pressure to free-stream total\npressure of 0.03 (jet off) to 2.5 . the ratio\nof body diameter to jet-exit\ndiameter varied from 1.12 to 55.6 and the angle\nof attack was varied from 0 to 35 .\n the experimental results show that the\nmain-stream shock can be affected by\nthe jet in two significantly different ways .\none way is simply to move the strong\nshock away from the body without altering its\nshape . the second and perhaps more\ninteresting case occurs when the jet causes a\nlarge displacement of the main shock\nand considerably changes its shape . it was\nfound that the ratio of jet total\npressure to free-stream total pressure necessary\nto obtain the large displacements\nof the main-stream shock depended on the ratio\nof body diameter to jet-exit\ndiameter and also on the jet-exit mach number . the\nmaximum amount the shock could be\ndisplaced in percent of body diameter was seen\nto increase with increasing\njet-exit mach number and also with decreasing ratio\nof body diameter to jet-exit\ndiameter . for the models that were investigated\nthrough an angle-of-attack range, the\ndisplacement became very unsteady and fell off\nsharply as the angle of attack was\nincreased .\n simplified theoretical considerations applied\nto the shock-displacement\nphenomena provide a possible explanation for the\ntwo different types of\nmain-stream shock displacement . theoretical curves\nshow the regions where these types\nof displacement would occur for different exit\nmach numbers and pressure ratios\nfor a forward-facing jet in a mach 6 stream ."}, {"doc_id": 947, "text": "static aerodynamic characteristics of a short blunt\n10 semi-vertex angle cone at a mach number of 15 in\nhelium .\n axial force, normal force, pitching\nmoment, and shock-wave shape were\ndetermined for a body of revolution\nconsisting of a short blunt 10 semivertex\nangle cone with a flat base and also with\na conical afterbody having a\nsemi-vertex angle of 50 . measurements were\nmade in helium at a free-stream mach\nnumber of 15 and a free-stream reynolds\nnumber of 2.25x10 based on maximum body\ndiameter over an angle-of-attack range from\n the configuration with the conical\nafterbody was statically stable in the\nnose-forward attitude only, whereas the\nconfiguration with no afterbody was\nstatically stable in both the nose-forward\nand base-forward attitudes . the force\nand moment data of both shapes were predicted\nreasonably well by modified\nnewtonian theory at all angles of attack,\nexcept the pitching-moment coefficient\nfor the model without afterbody near 180\nangle of attack . in this region,\nmeasurements indicated static stability, whereas\ntheory indicated static instability .\nthe helium data agreed reasonably well with\na limited amount of force and moment\ndata obtained in a ballistic range at small\nangles of attack in air at a mach\nnumber of 15 and also with force and moment\ndata obtained in air over a complete\nangle-of-attack range at a mach number of 5.5 .\nthe value of axial-force\ncoefficient and the shape of the bow shock wave at\nzero angle of attack for both models\nobtained from a numerical flow field calculation\nagreed very well with the data .\nthe value of the axial force coefficient at 180\nangle of attack for the model\nwith afterbody agreed reasonably well with the\ntheoretical value for a cone . the\nposition and shape of the shock envelope near\nthe stagnation point also could be\npredicted accurately by an approximate method\nover an angle-of-attack range from"}, {"doc_id": 948, "text": "panel flutter tests on full scale x-15 lower vertical\nstabilizer at mach number of 3. 0.\n panel flutter tests were conducted\non two full-scale vertical\nstabilizers of the x-15 airplane at a\nmach number of 3.0 in the langley\nat dynamic pressures from 1,500 psf\nto 5,000 psf and stagnation temperatures\nfrom 300 f to 660 f . flutter\nboundaries were obtained for four of\nthe five distinct types of panels\nwhich make up the vertical sides of\nthe stabilizers . the boundaries\nconsisted of a flat-panel boundary\nand a thermally buckled-panel\nboundary . the flat-panel boundaries were\ncharacterized by a reduction in\ndynamic pressure with increasing skin\ntemperature,. whereas, after thermal\nbuckling the trend was reversed . the\nminimum dynamic pressure for\nflutter occurred at the intersection of\nthe flat-panel and buckled-panel\nboundaries and represented a large\nreduction in the dynamic pressure\nover the extrapolated, unstressed value .\nas a result of panel flutter,\nthree of the five distinct types of\npanels were modified to provide the\nrequired flutter margin on the design\nflight dynamic pressure of the\naircraft ."}, {"doc_id": 949, "text": "charts for equilibrium flow properties of air in\nhyper-velocity nozzles .\n for initial stagnation pressures\nup to 1,000 atmospheres and\nstagnation enthalpies up to 10,000 btu per\npound, nozzle-flow properties for\nequilibrium air have been computed and\nplotted on charts . the work of\nnasa tn d-693 has been extended to\ninclude flow properties for closer\nintervals of specified stagnation\nenthalpies . properties which have been\ncharted as a function of mach number\nare as follows .. temperature,\npressure, density, velocity, area ratio,\ndynamic pressure, reynolds number,\nisentropic exponent, and molecular weight\nratio . ratios of temperature,\npressure, and density across normal shock\nwaves are also charted, and\nweight-flow rate is plotted as a function\nof stagnation enthalpy ."}, {"doc_id": 950, "text": "comparison of theoretical and experimental creep buckling\ntimes of initially straight, centrally loaded columns .\n the creep-buckling times of initially straight, centrally loaded\ncolumns as predicted by the hypotheses of shanley, gerard,\nand rabotnov and shesterikov are compared with appropriate\nexperimental data . it is found that the theoretical predictions\nare generally conservative, due possibly to the fact that the\nhypotheses predict initial instability times while the experiments\nnormally record final collapse times . of the three hypotheses,\nthat of gerard generally gives predictions which agree best with\nthe experimental data ."}, {"doc_id": 951, "text": "a unified theory of creep buckling under normal loads .\n a general theory of creep buckling, with the initial\nimperfection as a parameter, is developed for the case of normal loading .\na hyperbolic-sine law is used to describe the process of creep . the\ntheory is believed to be applicable to, among other structures,\ncolumns, tubes, and possibly conical shells . the wall of the\nstructure is idealized as a sandwich in order to simplify the\nintegration of the equations .\n experimental data on columns and tubes, from two different\nsources, are compared with the predictions of the theory ."}, {"doc_id": 952, "text": "study of creep collapse of a long circular cylindrical\nshell under various distributed force systems .\n an analysis is presented for determining the collapse of circular\nrings and long cylinders subjected to primary and secondary creep\nconditions at elevated temperatures . the types of loading\nconsidered for the present investigation are dead loading and\nhydrostatic pressure-type forces . the method of solution is based on\nan application of the variational theorem for creep described in\nref. 1 with some additional terms being introduced for the\npressure-type loading case . the general results are reduced to a\nrelatively simple form for the theoretical predictions of collapse\ntime and are graphically illustrated for a typical sample material ."}, {"doc_id": 953, "text": "vibrations of infinitely long cylindrical shells under\ninitial stress .\n the general bending theory of shells under the influence of\ninitial stress presented recently by herrmann and armenakas\nis applied in this investigation to study the effect of initial\nuniform circumferential stress, uniform bending moment and\nuniform radial shear on the dynamic response of an infinitely long\ncylindrical shell ."}, {"doc_id": 954, "text": "analysis of stress at several junctions in pressurized\nshells .\n theoretical and experimental results are\npresented for the discontinuity stresses arising at a\nchange of wall thickness in a cylinder, a\ncylinder-hemisphere junction, and a cone-spherical torus\njunction in pressure vessels . the effect of mismatch\nof nonconcurrence of the middle surfaces of two\njoined cylinders is considered . in addition, a\ncylinder with a special closure which has considerably\nreduced stresses is described, and curves with\ntheoretical and experimental stresses are presented ."}, {"doc_id": 955, "text": "the membrane approach to bending instability of pressureized\ncylindrical shells .\n recent theoretical and experimental\nresearch is briefly described\nto trace the development of deformation\nand the occurrence of collapse in\npressurized circular cylindrical membranes\nunder applied moment loading .\nthe collapse of pure membrane cylinders\nis then compared with instability\nof pressurized cylindrical shells .\nthis approach leads to a better\nunderstanding of the behavior of pressurized\ncylinders under bending loads .\nthe results suggest possibilities for\nfurther research utilizing the\nmembrane approach ."}, {"doc_id": 956, "text": "elastic stability of simply supported corrugated core\nsand- wich cylinders .\n theoretical buckling coefficients\nare obtained for the general\ninstability of simply supported, corrugated\ncore sandwich circular\ncylinders under combined loads with the core\noriented parallel to the\nlongitudinal axis of the cylinder . buckling\ncurves are presented for axial\ncompression, external lateral pressure,\ntorsion, and some typical\ninteractions . the differential equations of\nequilibrium used to obtain the\nbuckling equations were derived from the\nsmall deflection equations of\nstein and mayer which include the effect\nof deformation due to\ntransverse shear . these equations are solved\nby galerkin's equation .\nremarks are made concerning the probable\nvalidity of the results of the\nsmall deflection theory for sandwich shells ."}, {"doc_id": 957, "text": "axisymmetric snap buckling of conical shells .\n the authors give a brief account\nof some of their recent analytical and\nnumerical studies of cone buckling,\nlimiting the discussion to axisymmetric\ndeformations .\n pertinent numerical results for the\nrelaxation buckling of full cones\nsubjected to uniform external pressure and\nbelleville springs deformed by axial\nedge loads are presented . in addition,\nbifurcation buckling problems are\ndiscussed . for a specific case, the existence\nof friedrichs' intermediate buckling\nload, as applied to cones, is established .\nupper and lower bounds for\nits value are given ."}, {"doc_id": 958, "text": "air scooping vehicle .\n a satellite vehicle is described\nwhich collects gases from the\nupper atmosphere and stores them in\nliquid form . such a vehicle\ncould serve as a filling station in space,\nfurnishing liquid oxygen or\nair to other spacecraft . the vehicle\nrepresents an alternative to\nlaunching these liquids into orbit from\nthe surface of the earth . the\ntwo methods are compared on an\neconomic basis, and it is shown that\nthe proposed vehicle permits substantial\nsavings when operated beyond\nabout one year . the feasibility of\ndeveloping such a system for\nlong-time operation is investigated . several\npractical designs are discussed ."}, {"doc_id": 959, "text": "heat transfer in separated flows .\n results of an experimental heat-transfer investigation in\nregions of separated flow are presented and compared with the\ntheoretical analysis of naca tn 3792 . the average heat\ntransfer for both laminar and turbulent separated boundary\nlayers was found to be from 35 to 50 per cent less than that for\nequivalent attached boundary layers . the overall scope of the\nmeasurements included mach numbers from 0.3 to 4.0 and\nreynolds numbers from 10 to 4 x 10 . the results for laminar\nboundary layers agree well with the analysis of tn 3792 . the\nresults for turbulent boundary layers, however, disagree\nconsiderably . results of velocity and temperature surveys in the\nseparated turbulent boundary layer are presented and partially\nexplain the discrepancy between the experiments and analysis .\nthe maximum local heat-transfer rates were found to occur in\nthe reattachment region of the separated boundary layers\ninvestigated . the effect of transition on heat transfer in the separated\nlaminar boundary layers is described and data showing effects\nof mach number and wall temperature on the transition\nreynolds number of separated laminar flows are also included ."}, {"doc_id": 960, "text": "investigation of free turbulent mixing .\n a discussion of the integral\nrelations for flow of the\nboundary-layer type is presented . it is\nshown that the characteristic laws of\nspread of jets, wakes, and so forth,\ncan be obtained directly for the\nlaminar case and, with the help of\ndimensional reasoning, for the\nturbulent case as well .\n measurements of the mean velocity,\nthe intensity and scale of the\nturbulent fluctuations, and of the turbulent\nshear in a two-dimensional\nmixing zone are presented . the results of\nthese measurements are\ncompared with the mixing-length theories . it\nis shown that both mixing\nlength and exchange coefficient vary across\nthe mixing zone . the\ntheories based on the assumption of constant\nmixing length or exchange\ncoefficient are thus in error .\n a discussion of the energy balance of\nthe fluctuating motion is\ngiven and the triple correlation is estimated ."}, {"doc_id": 961, "text": "compressible two dimensional jet mixing at constant\npressure .\n an analysis is made of turbulent constant pressure mixing for a\ncompressible jet boundary, taking into consideration effects of the\ninitial boundary layer . velocity profiles in the mixing region are\nrepresented in a transformed plans by one-parameter families of curves,\nwith no specification for the mixing mechanism beyond that of an\nexchange coefficient concept being made . the exchange coefficient is\nrepresented by the bornel function of an integral transform for the x\ncoordinate of an intrinsic system of coordinates . this intrinsic\nsystem and the physical coordinate system are related by means of a\nmomentum integral .\n satisfactory correlation of theory and experimental low-speed data\nis obtained with a simple form of kernal function .\n an asymptotic solution, corresponding to a fully developed velocity\nprofile in the jet boundary, allows the calculation of the mechanical\nenergy level along the separating streamline in the jet boundary without\nthe use of empirical information ."}, {"doc_id": 962, "text": "contributions to the theory of heat transfer through\na laminar boundary layer .\nan approximation to the heat transfer rate across a laminar\nincompressible boundary layer, for arbitrary distribution of\nmain stream velocity and of wall temperature, is obtained by\nusing the energy equation in von mises's form, and approximating the\ncoefficients in a manner which is most closely correct near the\nsurface . the heat transfer rate to a portion of surface of length l\nbreadth is given as\nwhere k is the thermal conductivity of the fluid, o its prandtl number,\np its density, u its viscosity, r(x) is the skin friction,\nand t(x) the excess of wall temperature over main stream temperature .\na critical appraisement of the formula indicates that it should be very\naccurate for large, but that for of order 0.7 (for most gases) the\nconstant should be replaced by 0.73, when the error should not exceed\nthis yields a formula for nusselt number in terms of the reynolds number\nr and the mean square root of the skin friction coefficient c, in the\ncase of uniform wall temperature .\nhowever, for the boundary layer with uniform main stream, the\noriginal formula is accurate to within 3 percent even for . by\nknown transformations an expression is deducted for heat\ntransfer to a surface, with arbitrary temperature distribution\nalong it, and with a uniform stream outside it at arbitrary\nmach number (equation (42)) . from this the temperature distribution\nalong such a surface is deduced in the case (of importance at high mach\nnumbers) when heat transfer to it is balanced entirely by radiation\nfrom it . this calculation, which includes the solution of a non-linear\nintegral equation, gives higher temperatures near the nose,\nand lower ones farther back (figure 2), than are found from a theory\nwhich assumes the wall temperature uniform and averages the heat\ntransfer balance . this effect will be considerably mitigated\nfor bodies of high thermal conductivity., the author is not\nin a position to say whether or not it will be appreciable for\nmetal projectiles . but for stony meteorites at a certain stage\nof their flight through the atmosphere it indicates that\nmelting at the nose and re-solidification farther back may occur, for\nwhich the shape and constitution of a few of them affords evidence .\nan appendix shows how the method for approximating and solving\nvon mises's equation could be used to determine the skin friction\nas well as heat transfer rate, but this line seems to have no advantage\nover established approximate methods ."}, {"doc_id": 963, "text": "a variational principle for convection of heat .\nauthors extend variational principle of biot to various cases of heat\ntransfer due to forced convection . numerical results are given for\none-dimensional problems of fluid flowing between parallel walls with\nuniform or parabolic velocity profiles . agreement with exact solutions\nis excellent ."}, {"doc_id": 964, "text": "on the theory of discharge coefficients for round entrance flowmeters\nand venturis .\na theory of rounded-entrance flowmeters, based on a consideration of the\n potential and boundary-layer flows in a converging nozzle, is\nconstructed . curves are presented showing the discharge coefficient as a\nfunction of diameter reynolds number, with the /total equivalent length\ntional length-diameter ratio of the contraction section of the asme\nlong-radius nozzle is presented . the theoretical curves of discharge\ncoefficient versus diameter reynolds number are in good agreement with\nexperiment over a range of reynolds number from 1 to 10 . the theory\nprovides a rational framework for correlating and extrapolating\nexperimental results,. it shows the effects of contraction shape and\nlocation of pressure taps,. it furnishes values of discharge coefficient\n for untested designs,. and it suggests precautions to be taken in\ndesign, installation, and operation ."}, {"doc_id": 965, "text": "analytic determination of discharge coefficients of flow nozzles .\nintegration of the velocity profile at the throat of a flow nozzle\nyields the discharge coefficient as a function of the ratio of boundary\nsolution of the approximate momentum equation for the boundary layer .\nthe resulting expression for the discharge coefficient is then a\nfunction of the reynolds number based on nozzle diameter and of the geometry\n of the nozzle . good agreement is shown between this expression and\npublished experimental data on flow nozzles for reynolds numbers between"}, {"doc_id": 966, "text": "on fully developed channel flows,. some solutions and limitations, and\neffects of compressibility, variable properties, and body forces .\nan examination of the effects of compressibility, variable properties,\nand body forces on fully developed laminar flows has indicated several\nlimitations on such streams .\nin the absence of a pressure gradient, but presence of a body force\nliquid this follows also for the case of a constant streamwise pressure\ngradient . these motions are exact in the sense of a couette flow . in\nthe liquid case two solutions /not a new result/ can occur for the same\nboundary conditions . an approximate analytic solution was found which\nagrees closely with machine calculations .\nin the case of approximately exact flows, it turns out that for large\ntemperature variations across the channel the effects of convection /due\n to, say, a wall temperature gradient/ and frictional heating must be\nnegligible . in such a case the energy and momentum equations are\nseparated, and the solutions are readily obtained . if the temperature\nvariations are small, then both convection effects and frictional\nheating can consistently be considered . this case becomes the\nconstant-property incompressible case /or quasi-incompressible case for\nfree-convection flows/ considered by many authors .\nfinally, there is a brief discussion of cases wherein streamwise\nvariations of all quantities are allowed but only in such form that the\nindependent variables are separable . for the case where the streamwise\nvelocity varies inversely as the square root of distance along the\nchannel, a solution is given ."}, {"doc_id": 967, "text": "a study of laminar compressible viscous pipe flow accelerated by an\naxial body force, with application to magnetogasdynamics .\na study is made of the steady laminar flow of a compressible viscous\nfluid in a circular pipe when the fluid is accelerated by an axial\nbody force . the application of the theory to the magnetofluidmechanics\nof an electrically conducting gas accelerated by electric and magnetic\nfields is discussed . constant viscosity, thermal conductivity, and\nelectrical conductivity are assumed . fully developed flow velocity and\ntemperature profiles are shown, and detailed results of the accelerating\n flow development, including velocity and pressure as functions of\ndistance, are given for the case where the axial body force is constant and\n for the case where it is a linear function of velocity . from these\nresults are determined the pipe entry length and the pressure difference\n required ."}, {"doc_id": 968, "text": "rocket propulsion systems for interplanetary flight .\na comparison is made of several different propulsion systems for\ninterplanetary flight . liquid and solid propellant rockets, propulsion\nsystems which use nuclear energy sources, are heating rockets,\nmagneto-plasma devices, ion rocket propulsion, solar heating rockets, and solar\nsails are briefly described and their current status reviewed . engine\nperformance requirements for different interplanetary missions are\nestablished . these several propulsion systems are then compared on the\nbasis of several performance criteria, environmental characteristics,\nvehicle requirements, reliability, current status, growth potential, and\n efficiency . predictions on various propulsion system capabilities and\nan analysis of multiple rocket engine reliability is included . it is\nconcluded that electrical rockets are superior for long-time\ninter-planetary flight applications, and that chemical rockets are\nsatisfactory for most of the immediate applications in /near/ space . none of\n the several propulsion schemes discussed can be rejected until further\ntechnical work has been accomplished ."}, {"doc_id": 969, "text": "on the use of side-jets as control devices .\n wind tunnel experiments with side-jets, issuing laterally\nnear the base of slender bodies in a supersonic stream, have\nsuggested the existence of a sizable and usable interaction .\nwith this interaction force, the use of jet reaction controls\nmay be as attractive for flight within the atmosphere as it\nobviously is for flight outside the atmosphere . this note\nindicates the altitude regime of interest and the order of\nmagnitude of the interaction bonus for a lateral control\njet located near the base of a body of revolution ."}, {"doc_id": 970, "text": "loads induced on a flat plate wing by an air jet exhausting\nperpendicularly through the wing and normal to a free-stream flow of mach\nnumber 2.0 .\nmeasurements were made of loads induced on a flat-plate wing by an air\njet exhausting perpendicularly through the wing and normal to the\nfree-stream flow . the investigation was conducted at a free-stream mach\nnumber of 2.0 and a reynolds number per foot of 14.4 x 10 . an axially\nsymmetric sonic nozzle and two supersonic nozzles were employed for the\njets . the supersonic nozzles consisted of an axially symmetric nozzle\nwith exit mach number of 3.44 and a two-dimensional nozzle with exit\nmach number of 1.76 . the ratio of nozzle total pressure to free-stream\nstatic pressure was varied from 20 to 110 .\nnegative loads were induced on the flat-plate wing by all the jets . as\nthe nozzle pressure ratio was increased the magnitude of interference\nloads due to jet thrust decreased . the chordwise center-of-pressure\nlocation generally moved toward the nozzle center line as the pressure\nratio was increased ."}, {"doc_id": 971, "text": "surface pressure distributions with a sonic jet normal to adjacent flat\nsurfaces at mach 2.92 to 6.4 .\nan investigation was made to determine the interference effects on\nsurface pressure distributions caused by a sonic jet exiting normal to the\nsurface . two configurations, a flat plate and an arrow-wing\nreentry-type vehicle, with sonic nozzles near the leading edge were tested over\na range of pressure ratios and reynolds numbers for mach numbers from\nthe data indicate that jet pressure ratio had considerable effect on the\n pressure levels and distributions on both configurations . also, for a\nconstant jet pressure ratio, the free-stream mach number effect on the\ndistributions and levels was quite large . over the limited range\ninvestigated, the effect of reynolds number at constant mach number and\npressure ratio was small compared to the mach number and pressure ratio\neffect ."}, {"doc_id": 972, "text": "aerodynamic interaction effects ahead of a sonic jet exhausting\nperpendicularly form a flat plate into a mach number 6 free stream .\nan investigation of the effects of the interaction ahead of a\ntwo-dimensional sonic jet exhausting perpendicularly into a mach number\nwere made at an angle of attack of 0degree at a reynolds number per foot\n of approximately 6 x 10 and with conditions of both transitional and\nturbulent separation on the flat plate . the ratio of jet stagnation\npressure to free-stream static pressure was varied from 8 to 460 and the\n jet slot width was varied from 0.001 to 0.05 inch . the force ratio\n due to reaction of jet/, calculated ahead of the jet, was sizable and\nvaried from 0.5 to 9 . in general, the ratio increased with increasing\npressure ratio and decreasing slot width . for the turbulent\nboundary-layer separation tests it was found that the first peak pressure and the\n chordwise pressure distribution of the separated boundary layer ahead\nof the jet were similar to those for a separation caused by a\nforward-facing step at the same test conditions ."}, {"doc_id": 973, "text": "interaction effects produced by jet exhausting laterally near base of\nogive-cylinder model in supersonic main stream .\nthe experimentally determined interaction effects of a side jet\nexhausting near the base of an ogive-cylinder model are presented and\ndiscussed . the interaction force appears to be independent of\nmain-stream mach number, boundary-layer condition /laminar or turbulent/,\nangle of attack, and forebody length . the ratio of interaction force to\n jet force is found to be inversely proportional to the square root of\nthe product of jet stagnation-to-free-stream pressure ratio and jet-to-\nbody diameter ratio ."}, {"doc_id": 974, "text": "approximate analysis of thrust vector control by fluid injection .\na study has been made of the side force generated by injection of\nsecondary material into the main stream of a rocket nozzle . two cases\nhave been analyzed .. gas injection and liquid injection . for the gas\ninjection case, it is assumed that the turbulent boundary layer ahead of\n the injection point separates from the wall . the pressure in the\nseparated region and the extent of the separated region are determined\nby a consideration of turbulent boundary layer-shock wave interaction\nand the accommodation height of the injected gas stream . equations are\nderived for calculating the side force, and the side forces predicted by\n the theory are compared with experimental data . the agreement between\ntheory and experiment is fair . for the case of liquid injection, it is\nassumed that the liquid flows along the nozzle wall and evaporates into\nthe main stream . the resulting side force on the nozzle wall is\ndetermined on the basis of linearized theory, thus restricting the analysis\nto small rates of liquid injection . the effects of small rates of heat\naddition are also included in the analysis . a very simple equation for\ncalculating the side force is obtained ."}, {"doc_id": 975, "text": "one dimensional flows of an imperfect diatomic gas .\n with the assumptions that berthelot's equation of state\naccounts for molecular size and intermolecular force effects, and\nthat changes in the vibrational heat capacities are given by a\nplanck term, expressions are developed for analyzing\none-dimensional flows of a diatomic gas .\n the special cases of flow through normal and oblique shocks\nin free air at sea level are investigated . it is found that up to a\nmach number of 10 the pressure ratio across a normal shock\ndiffers by less than 6 percent from its ideal gas value,. whereas\nat mach numbers above 4 the temperature rise is considerably\nbelow and hence the density rise is well above that predicted\nassuming ideal gas behavior . it is further shown that only the\ncaloric imperfection in air has an appreciable effect on the\npressures developed in the shock process considered . the effects\nof gaseous imperfections on oblique shock flows are studied from\nthe standpoint of their influence on the lift and pressure drag\nof a flat plate operating at mach numbers of 10 and 20 . the\ninfluence is found to be small ."}, {"doc_id": 976, "text": "turbulent diffusion in the wake of a blunt nosed body\nat hypersonic speeds .\n at reynolds numbers greater than about 5 x 10\ncorresponding to altitudes below about 180,000 ft, the hot outer inviscid\nwake behind the bow shock wave produced by a blunt-nosed\nbody at hypersonic speeds is cooled mainly by turbulent diffusion\nand conduction . turbulence originates in the inner wake formed\nby the coalescence of the free shear layers (or annulus) shed from\nthe body surface when the boundary layer separates from the\nsurface . as this turbulence spreads outward, it swallows\nenthalpy or momentum defect originally contained in the outer\ninviscid wake . if the turbulence is locally similar--i.e., if it\nbehaves at each station like a slice of a low-speed /self-similar/\nwake--then the turbulent diffusivity grows from a low initial\nvalue near the body to a value corresponding to the total drag of\nthe body at about 300 body diameters downstream . at flight\nvelocities of the order of 9,000-10,000 ft per sec. the growth of the\nturbulent inner wake predicted on the basis of locally similar\nturbulence is in good agreement with shadowgraph measurements\nof wake widths behind spheres obtained in ballistic ranges in the\nregion from 200 to 4,000 body diameters downstream of the body .\ntentatively, one concludes that the turbulence mechanism in the\nwake with respect to a fixed observer is similar to the low-speed\ncase, in spite of the large mean temperature gradients .\n in order to illustrate the behavior of an observable such as\nelectron density in a turbulent wake behind a blunt body, the\ntwo limiting cases of thermodynamic equilibrium and pure\ndiffusion (zero electron-ion recombination rate) are calculated for\nm = 22 at altitudes of 100,000 and 200,000 ft . even for the\ncase of thermodynamic equilibrium, the predicted turbulent\nradar trail length is about 200 body diameters at l-band (1,300\nmc) at 100,000-ft altitude and about 150 body diameters for\nuhf (400 mc) at 200,000 ft . one interesting result is that the\nwidth of the plasma cylinder corresponding to the plasma\nrequency at l-band remains virtually constant at about 3.5 body\ndiameters in the range 30 150 at 100,000-ft altitude .\nthese results are sufficiently encouraging that one can consider\nincluding the effects of finite chemical and electron-ion\nrecombination rates in the analysis in order to give a more complete\npicture of the wake at hypersonic speeds ."}, {"doc_id": 977, "text": "concerning some solutions of the boundary layer equations\nin hydrodynamics .\n the boundary-layer equations for\na steady two-dimensional motion\nare solved for any given initial\nvelocity distribution (distribution along a\nnormal to the boundary wall,\ndownstream of which the motion is to be\ncalculated) . this initial velocity\ndistribution is assumed expressible\nas a polynomial in the distance from\nthe wall . three cases are considered ..\nfirst, when in the initial distribution\nthe velocity vanishes at the wall,\nbut its gradient along the normal\ndoes not,. second, when the velocity in\nthe initial distribution does not\nvanish at the wall,. and third, when both\nthe velocity and its normal gradient\nvanish at the wall (as at a point\nwhere the forward flow separates\nfrom the boundary) . the solution is\nfound as a power series in some\nfractional power of the distance along\nthe wall, whose coefficients are\nfunctions of the distance from the wall to\nbe found from ordinary differential\nequations . some progress is made\nin the numerical calculation of\nthese coefficients, especially in the first\ncase . the main object was to\nfind means for a step-by-step calculation\nof the velocity field in a boundary\nlayer, and it is thought that such a\nprocedure may possibly be successful\neven if laborious . the same\nmathematical method is used to calculate\nthe flow behind a flat plate along a\nstream . the results are shown in\ncurves in the original ."}, {"doc_id": 978, "text": "temperature profiles inafinite solid with moving boundary .\na numerical solution is presented to the transient heat conduction\nequation for a cylinder of finite thickness with one moving boundary .\nthe implicit method of solution is developed with conductivity as an\narbitrary function of temperature . application is made to a sample case\n of re-entry heating encountered by aerodynamic bodies, with erosion by\nsublimation and combustion occurring at the body surface ."}, {"doc_id": 979, "text": "correlation of base pressure and wake structure of\nsharp and blunt-nose cones with reynolds number based\non boundary layer momentum thickness .\nit has been established in the past that there is a certain\nrelationship between base pressure and boundary-layer\nbehavior . the base-pressure and wake-flow conditions were\nfound to be dependent upon the local flow characteristics at the\nsurface of supersonic vehicles directly upstream of the base or of\nthe region of wake-flow separation .\n in order to use existing data on cones and other shapes to\npredict wake angle and base pressure on blunt bodies, an attempt was\nmade recently at the naval ordnance laboratory to establish\na unique relationship between given local flow conditions at the\ndownstream end of sharp and blunt cones at supersonic speeds\nand the corresponding wake-flow conditions with zero heat\ntransfer ."}, {"doc_id": 980, "text": "a method of computing the transient temperature of thick walls from\narbitrary variation of adiabatic-wall temperature and heat-transfer\ncoefficient .\na method of calculating the temperature of thick walls has been\ndeveloped in which are used relatively new concepts, such as the time\nseries and the response to a unit triangle variation of surface\ntemperature, together with essentially standard formulas for transient\ntemperature and heat flow into thick walls . the method can be used\nwithout knowledge of the mathematical tools of its development . the\nmethod is particularly suitable for determining the wall temperature in\none-dimensional thermal problems in aeronautics where there is a\ncontinuous variation of the heat-transfer coefficient and adiabatic-wall\ntemperature . the method also offers a convenient means for solving the\ninverse problem of determining the heat-flow history when temperature\nhistory is known .\na series of diversified problems were solved by exact analysis as well\nas by the new method . a comparison of the results shows the new\nmethod to be accurate . the labor involved is very modest in\nconsideration of the nature of the thick-wall temperature problem .\nlimiting solutions for the /infinitely thick/ wall and for walls so\nthin that thermal lag can be neglected were also obtained ."}, {"doc_id": 981, "text": "solutions to the heat-conduction equation with time dependent boundary\nconditions .\ndesign charts based on the analytical solution to the problem of\none-dimensional heat flow in a solid body of constant material properties\nwith time-dependent boundary conditions were presented by kaye and\nyeh . this solution dealt with aerodynamic heating at hypersonic speeds\nwhere the surface coefficient of heat transfer and the temperature\npotential were taken to be linear functions of time of flight . in order\n to make these charts of more general application, general solutions are\n presented which, together with the charts, enable rapid and reasonable\nestimates to be made of the transient temperature distributions in many\npractical cases ."}, {"doc_id": 982, "text": "the temperature history in a thick skin subjected to laminar heating\nduring entry into the atmosphere .\nduring high speed entry into the earth's atmosphere, a vehicle can be\nafforded thermal protection for the short period of entry heating by a\nthick outer skin, sometimes called a /heat sink/ . the temperature\ndistribution in such a heat sink has been found by integrating the\nproduct of the laminar aerodynamic heating rate and the appropriate\ngreen's function for a finite-thickness wall over the generalized\ntrajectory for a vehicle entering the earth's atmosphere at high speeds\ndimensional heat conduction problem for laminar heating . the maximum\nsurface temperature that occurs during the generalized entry trajectory\nfor any combination of wall thickness and thermal properties is obtained\nfrom which the performance of any material can be found, provided that\nthe average thermal properties may be used . as an example of the use of\n the solution, the performance of copper, graphite, molybdenum and\ntungsten are compared ."}, {"doc_id": 983, "text": "addendum to 'heat transfer to satellite vehicles re-entering the\natmosphere .\nthe original paper gave a correlation formula for stagnation point heat\ntransfer rate to a blunt body of revolution in hypersonic flow . this\nnote gives a somewhat refined version, based on further calculation and\nshock tube data . its effect on the conclusions of the original paper is\n negligible except at surface temperature parameters of over 5000\nr-ft1/8 . in other problems, where heat transfer rate itself is\nimportant, it can make a significant defference ."}, {"doc_id": 984, "text": "method of analysis for compressible flow through mixed-flow centrifugal\nimpellers of arbitrary design .\na method is presented for analysis of the compressible flow between the\nhub and the shroud of mixed-flow impellers of arbitrary design . axial\nsymmetry was assumed, but the forces in the meridional /hub to shroud/\nplane, which are derived from tangential pressure gradients, were taken\ninto account .\nthe method was applied to an experimental mixed-flow impeller . the\nanalysis of the flow in the meridional plane of the impeller showed that\n the rotational forces, the blade curvature, and the hub-shroud profile\ncan introduce severe velocity gradients along the hub and the shroud\nsurfaces . choked flow at the impeller inlet as determined by the\nanalysis was verified by experimental results ."}, {"doc_id": 985, "text": "a rapid approximate method for the design of hub shroud profiles of\ncentrifugal impellers of given blade shape .\na rapid approximate method for the design of centrifugal compressors of\ngiven blade shape with compressible nonviscous flow characteristics has\nbeen developed using techniques based upon stream-filament theory .\naxial symmetry is assumed, but meridional-plane forces derived from\ntangential pressure gradients are included .\nthe method was applied to the design of an impeller in order to\ndetermine the approximate maximum meridional streamline spacing that\ncould be used . three numerical solutions for different streamline\nspacings were made using the same hub profile, blade shape, and\nprescribed velocity distribution along the hub . the shroud profiles\nobtained from the three solutions, which utilized 3, 5, and 9\nstream-tubes, were negligibly different . the approximate computing time\nrequired was 15 hours per streamtube ."}, {"doc_id": 986, "text": "design and test of mixed-flow impellers, viii - comparison of\nexperimental results for three impellers with shroud redesigned by rapid\napproximate method .\nthree centrifugal impellers with parabolic, circular, and\nskewed-parabolic blading were modified by a recently developed design procedure\n to reduce the velocity gradients along the hub from inlet to outlet .\nall original dimensions except the shroud contours were retained .\nexperimental investigation showed that the modified impellers had better\nperformance characteristics than the original impellers at all speeds\ninvestigated, the greatest gains occurring at speeds of 1300 feet per\nsecond and higher . these large gains probably resulted primarily from\nmore favorable velocity gradients and from designing these impellers\nfurther away from the condition necessary for eddy formation . the\nmodified impellers were thus able to operate over a wider range of\nweight flows at high speeds .\nthe modified impellers were investigated over a range of equivalent\nspeeds of 900 to 1500 feet per second and flow rates from maximum to the\n point of incipient surge . at 1300 feet per second, the peak pressure\nratio and maximum adiabatic temperature-rise efficiency for the\nparabolic-bladed impeller were 3.07 and 0.825, respectively . for the same\nconditions, the circular-bladed impeller and the skewed-parabolic-bladed\n impeller had pressure ratios of 3.13 and 3.15 and efficiencies of 0.737\n and 0.805, respectively . of the three, the parabolic-bladed impeller\nhad the highest maximum efficiencies /0.854 to 0.800/ and the best\nweight-flow range over the speed range tested . on the basis of the\nparameters investigated, it appears that parabolic blading is superior\nto circular blading . the experimental results indicate that the design\nmethod of naca tn 3399 is a reliable method for use in designing\ncentrifugal impellers ."}, {"doc_id": 987, "text": "a general theory of three dimensional flow in subsonic and supersonic\nturbo-machines of axial-radial-and mixed-flow types .\na general theory of steady three-dimensional flow of a nonviscous fluid\nin subsonic and supersonic turbomachines having arbitrary hub and casing\n shapes and a finite number of blades is presented . the solution of the\n three-dimensional direct and inverse problem is obtained by\ninvestigating an appropriate combination of flows on relative stream surfaces\nwhose intersections with a z-plane either upstream of or somewhere\ninside the blade row form a circular arc or a radial line . the equations\nobtained to describe the fluid flow on these stream surfaces show\nclearly the several approximations involved in ordinary two-dimensional\ntreatments . they also lead to a solution of the three-dimensional\nproblem in a mathematically two-dimensional manner through iteration .\nthe equation of continuity is combined with the equation of motion in\neither the tangential or the radial direction through the use of a\nstream function defined on the surface, and the resulting equation is\nchosen as the principal equation for such flows . the character of this\nequation depends on the relative magnitude of the local velocity of\nsound and a certain combination of velocity components of the fluid . a\ngeneral method to solve this equation by both hand and high-speed\ndigital machine computations when the equation is elliptic or hyperbolic\n is described . the theory is applicable to both irrotational and\nrotational absolute flow at the inlet of the blade row and at both design\nand off-design operations ."}, {"doc_id": 988, "text": "nonviscous flow through a pump impeller on a blade-to-blade surface of\nrevolution .\nthe nonviscous incompressible flow through a typical pump impeller is\nanalyzed on a blade-to-blade surface of revolution . solutions are\nobtained for a variety of inlet conditions including several with prewhirl\n of the assumed location of the rear stagnation point . comparison of\nresults from two approximate methods of analysis showed good agreement\nfor the zero-angle-of-attack case and reliable indication of the\nexistence of an eddy on the driving face at a large positive angle of\nattack ."}, {"doc_id": 989, "text": "incompressible nonviscous blade-to-blade flow through a pump rotor with\nsplitter vanes .\nthe nonviscous flow through a mixed-flow pump impeller having one\nsplitter vane between adjacent main blades has been analyzed on a\nblade-to-blade surface of revolution using a previously reported\nanalysis method . solutions were obtained for a variety of flow\nconditions including several cases in which whirl is imparted to the\nflow upstream of the impeller .\nthe velocity distributions on the main-blade surfaces and on the\nsplitter-vane surfaces in the region of the splitter vane were strongly\ndependent on the assumed location of the rear stagnation points .\nsolutions were obtained by assuming values of slip factor and of division of\n flow around the splitter in addition to assuming the location of the\nrear stagnation points . these solutions indicated that the velocity\ndistributions in the splitter-vane region are largely determined by the\ndivision of flow around the splitter vane and that only the region in\nthe immediate vicinity of the trailing edge is affected by the slip\nfactor .\nblade surface velocities were obtained from two approximate methods by\nspecifying flow division and slip factor, and these results are compared\n with the more exact solutions of the analysis ."}, {"doc_id": 990, "text": "a rapid approximate method for determining velocity distribution on\nimpeller blades of centrifugal compressors .\na rapid approximate method of analysis was developed for both\ncompressible and incompressible, nonviscous flow through radial- or\nmixed-flow centrifugal compressors with arbitrary hub and shroud contours and\nwith arbitrary blade shape . the method of analysis is used to determine\n approximately the velocities everywhere along the blade surfaces, but\nno information concerning the variation in velocity across the passage\nbetween blades is given .\nin eight numerical examples for two-dimensional flow, covering a fairly\nwide range of flow rate, impeller-tip speed, number of blades, and blade\n curvature, the velocity distribution along the blade surfaces was\nobtained by the approximate method of analysis and compared with the\nvelocities obtained by relaxation methods . in all cases the agreement\nbetween the approximate solutions and the relaxation solutions was\nsatisfactory except at the impeller tip where the velocities obtained by\n the approximate method did not, in general, become equal on both\nsurfaces of the blade as required by the joukowski condition ."}, {"doc_id": 991, "text": "wing-flow study of pressure drag reduction at transonic speed by\nprojecting a jet of air from the nose of a prolate spheroid of fineness\nratio 6 .\na study was made at transonic speeds by the naca wing-flow method of the\n pressure-drag reduction obtained by projecting a high-energy jet of air\n from the nose of a prolate spheroid . supplementary information was\nobtained by taking shadowgraphs of the model mounted in a small\nsupersonic tunnel at a constant mach number of 1.5 .\nthe high-velocity jet was observed to alter the pressure distribution\nover the body in such a way that the pressure drag of the body was\nreduced,. thus, in a restricted sense, the nose jet produced a thrust on\n the body . under the conditions investigated, the thrust produced by\nthe nose jet was never so large as that which would be expected from a\nconventional rearward jet . for example, under the best conditions\ntested /mach number of 1.07/ the reduction in body pressure drag caused\nby the nose jet more than compensated for the negative thrust of the jet\n itself . however, the magnitude of the net reduction in drag /change in\n body pressure drag with jet on and jet off minus the adverse thrust of\nthe jet/ was only about one-half of the thrust which would be produced\nby the same jet exhausting rearward . the appearance of such an\nunexpectedly large effect in the first trial indicated the phenomenon to be\nworth further study ."}, {"doc_id": 992, "text": "the effects of a small jet of air exhausting from the nose of a body\nof revolution in supersonic flow .\nan investigation has been made at a mach number of 1.62 to determine\nthe effects of a small jet of air exhausting from the nose of an\nelliptical body of revolution upon boundary-layer transition and the\nviscous, pressure, and total drag of the forebody at three body stations\nbody nose were also obtained . the tests were conducted at reynolds\nnumbers of 2.13 x 10 and 7.66 x 10, based on body length . the maximum\nrange of thrust coefficients for the small jet was from 0 to about\nat the lower test reynolds number, for which the boundary layer was\nlaminar over the entire body in the jet-off condition, a very small flow\n from the jet moved the point of transition forward to the vicinity of\nthe 20-percent-body station . as the jet flow was increased, the\ntransition point moved abruptly to the nose at a thrust coefficient of about\ngardless of the type of boundary layer . at the higher test reynolds\nnumber for which the boundary layer was largely turbulent in the jet-off\n condition the total drag, including skin friction, was reduced somewhat\n by the action of the jet .\nalthough the forward-exhausting small jet was found to have the above\nfavorable effects upon the drag, these findings are not believed too\nimportant since the question arises as to the benefits of the same small\n jet exhausting from the rear of the body in the conventional manner .\nno attempt was made to establish geometric optimums in the present\ninvestigation, yet, from a general consideration of the benefits\nindicated by the present results and the phenomena known to occur in the\nvicinity of rearward-exhausting jets, the benefits of a small jet\nexhausting rearward would appear to exceed those of the same small jet\nexhausting forward, particularly so when the flow over the body is\nlaminar in the jet-off condition ."}, {"doc_id": 993, "text": "the extent of the jet interference flow fields .\njet effects on cylindrical afterbodies housing sonic and supersonic\nnozzles which exhaust against a supersonic stream at angles of attack\nfrom 90degree to 180degree .\n an investigation has been made to determine jet effects on\ncylindrical afterbodies housing sonic and supersonic nozzles which exhaust\nagainst a supersonic stream at angles of attack from 90 to 180 . the\ntests were conducted at a free-stream mach number of 2.91 and at\nfree-stream reynolds numbers, based on body diameter, of 0.15x106 and\nstream static pressure investigated was from jet off to about 400 .\n the data presented herein showed that, in general, variation of the\nratio of jet total pressure to free-stream static pressure, jet-exit\nmach number, and ratio of jet-exit diameter to body diameter had large\ninfluences on the body pressures on the windward halves of the\nafter-bodies and negligible influences on the leeward pressures . there was a\nnegligible effect of reynolds number on the body pressures . the ratio\nof jet total pressure to free-stream static pressure also had a large\ninfluence on the base pressures at all angles of attack . schlieren\nstudies showed details of the shock-wave structure caused by the jet\nand the extent of the jet interference flow fields ."}, {"doc_id": 994, "text": "investigation of a retrocket exhausting from the nose of a blunt body\ninto a supersonic free stream .\nthe pressure distribution and pressure drag of a blunt body with a\nsupersonic jet issuing upstream from its center were determined at\nfree-stream mach numbers of 1.60, 2.00, and 2.85 . the thrust of the jet\n issuing from the model nose was varied to study its effects on flow\naround the model and to determine variation of pressure distribution and\n pressure drag of the model with the thrust .\nat all mach numbers investigated, the pressure drag decreased with\nincreasing retrorocket thrust until a minimum value was reached .\nfurther increases in retrorocket thrust resulted in increases in the\npressure drag . the resultant drag /pressure drag plus retrorocket\nthrust but excluding base and skin-friction drag/ of the model was\nreduced by retrorocket operation below the drag for a jet-off condition,\n except at very low retrorocket thrust coefficients . the flow about the\n nose of the blunt body was very unstable throughout the range of mach\nnumbers and retrorocket thrust coefficients investigated ."}, {"doc_id": 995, "text": ""}, {"doc_id": 996, "text": "extension of boundary layer separation criteria to\na m=6 .5 utilizing flat plates with forward-facing\nsteps .\n an experimental investigation has\nbeen made of the separation\nphenomena on a flat plate to which\nforward-facing steps were attached to\nforce separation . both laminar and\nturbulent flows were investigated\nover a mach number range of approximately\ndistributions, shadowgraph and chemical\nfilm techniques, the pressure\nrise at separation, the laminar plateau\npressure, and the turbulent\npeak pressure were determined .\nboundary-layer surveys were made on a\nsmooth flat plate and on a flat plate with\nroughness to force\ntransition . examinations of the separated flow\nshowed that the predominant\nvariable in the determination of the pressure\ndistribution was the\nlocation of transition relative to the separation\npoint and reattachment .\npure laminar, transitional, and turbulent\ntypes of separation were found\nin this mach number range . the peak\nstatic-pressure-rise ratios for\nidentical forward-facing steps at a mach\nnumber of 6.25 were\napproximately 1.5 and 5.0, respectively, for pure\nlaminar and turbulent\nseparation . the effect of reynolds number on the\npeak pressure rise for\nturbulent separation for the lower mach number\nrange was found to be very\nminor provided the step height was of the\norder of the boundary-layer\nthickness . as the mach number is increased,\nthe peak pressure\ncoefficient for turbulent separation decreased\nfrom approximately 0.18\nat a mach number of 4 to about 0.13 at a mach\nnumber of 6.25 . the\npressure coefficient at the separation point for\nlaminar separation decreases\nfrom approximately 0.014 at a mach number of\nvalue at a mach number of 6.5 . the results\nobtained with forward-facing\nsteps agree with the trends predicted, based\nupon lower mach number\nstudies ."}, {"doc_id": 997, "text": "experimental and theoretical studies of axisymmetric free jets .\nsome experimental and theoretical studies have been made of axisymmetric\n free jets exhausting from sonic and supersonic nozzles into still air\nand into supersonic streams with a view toward problems associated with\npropulsive jets and the investigation of these problems .\nfor jets exhausting into still air, consideration is given to the\neffects of jet mach number, nozzle divergence angle, and jet\nstatic-pressure ratio upon jet structure, jet wavelength, and the shape and\ncurvature of the jet boundary . studies of the effects of the ratio of\nspecific heats of the jets are included as are observations pertaining\nto jet noise and jet simulation .\nfor jets exhausting into supersonic streams, an attempt has been made to\n present primarily theoretical curves of the type that may be useful in\nevaluating certain jet interference effects and in formulating\nexperimental studies . the primary variables considered are jet mach number,\nfree-stream mach number, jet static-pressure ratio, ratio of specific\nheats of the jet, nozzle exit angle, and boattail angle . the simulation\n problem and the case of a hypothetical hypersonic vehicle are examined"}, {"doc_id": 998, "text": "equations, tables and charts for compressible flow .\n this report, which is a revision and extension of naca tn\nuseful in the analysis of high-speed flow of a compressible fluid .\nthe equations provide relations for continuous one-dimensional\nflow, normal and oblique shock waves, and prandtl-meyer\nexpansions for both perfect and imperfect gases . the tables\npresent useful dimensionless ratios for continuous one-\ndimensional flow and for normal shock waves as functions of mach\nnumber for air considered as a perfect gas . one series of charts\npresents the characteristics of the flow of air (considered a perfect\ngas) for oblique shock waves and for cones in a supersonic air\nstream . a second series shows the effects of caloric\nimperfections on continuous one-dimensional flow and on the flow\nthrough normal and oblique shock waves ."}, {"doc_id": 999, "text": "static aerodynamic characteristics of short blunt cones\nwith various nose and base cone angles at mach numbers\nof 0. 6 to 5. 5 and angles of attack to 180 .\n wind-tunnel tests have been performed\nat mach numbers from 0.6 to 5.5\nto determine coefficients of normal force,\naxial force, and pitching\nmoment for short blunt cones, as affected\nby changes in nose and base\ncone angles . models with nose half-angles\nof 10 and 20 were investigated .\nthe 10 nose half-angle models were tested\nwith a flat base and with base\ncones of 50 and 70 half-angle . the 20\nnose half-angle model had a 50\nhalf-angle base cone . reynolds numbers\nfor the test ranged from about\nmaximum diameter .\n variations in the base cone angle\nresulted in significant changes in\nthe aerodynamic characteristics, with\nlesser effects resulting from changes\nin nose cone angle . in particular,\nthe model with the 50 half-angle\nconical base had only one trim angle\nflat base and 70 half-angle conical\nbase had two trim angles (a = 0 and\na = 180) . estimated variations of\nthe aerodynamic characteristics with\nangle of attack by means of a modified\nnewtonian theory were in good\nagreement with the experimental results .\nthe theory, however, failed to\npredict the trim point at a = 180 for\nthe flat-based model ."}, {"doc_id": 1000, "text": "free-flight measurements of the static and dynamic\nstability and drag of a 10 blunted cone at mach numbers\n3. 5 and 8 .5 .\ntests were made of a short blunt-nosed\nwithout a 50 half-angle conical afterbody\nin a pressurized ballistic\nrange at nominal mach numbers of 3.5 and\nof 90,000 and 220,000, respectively . it\nwas found that the models were\nstatically stable about the center-\nof-gravity location tested but\nexhibited neutral dynamic stability for flight\nat constant altitude . the\nstatic stability was not affected by the\nbut was nonlinear with angle of attack\nand varied with mach number . the\nnonlinear variation of the pitching moment\nwith angle of attack was\naccurately approximated by a cubic polynomial .\nthe static stability was only\nqualitatively predicted by modified newtonian\ntheory . the drag\ncharacteristics were in good agreement with values\ncalculated by use of modified\nnewtonian theory .\n calculations of the oscillatory\nbehavior of the configurations flying\nan example entry trajectory through\nthe martian atmosphere indicated the\nconfigurations to be dynamically\nsatisfactory . pitching motions should\nconverge to a small fraction of the\namplitude at entry, provided the\ninitial angle of attack and pitch\nrate are not large enough to cause\ntumbling ."}, {"doc_id": 1001, "text": "wind tunnel investigation of the static and dynamic stability\ncharacteristics of a 10degree semivertex angle blunted cone .\nthe static and dynamic stability characteristics of a blunted 10degree\nsemivertex angle cone were studied . the cone which had a modified\nspherical segment nose was tested with a flat base and with a truncated\nconical base .\nall tests were performed in air at mach numbers from 0.65 to 2.20 with\nthe angle-of-attack range from -4degree to +18degree . presented are\nmeasurements of the normal force, axial force, base pressure, and\npitching moment from the static tests, and the damping-in-pitch moment\nfrom the dynamic tests .\nboth models had satisfactory stability characteristics throughout the\ntest mach number range but the addition of the conical afterbody had a\nlarge destabilizing effect ."}, {"doc_id": 1002, "text": "preliminary investigations of spiked bodies at hypersonic speeds .\ngenerally accepted solutions for the problems of hypersonic flight\nappear, at the moment, to be centered around the use of blunt bodies to\nminimize the heat-transfer rates . there are, however, several other\nsolutions to the problem, and, as part of an exploratory study of these\nsolutions, a detailed examination has been made of the flow over blunt\nbodies equipped with a spike . these tests, carried out at a mach number\n of about 14 in the princeton helium hypersonic tunnel, have\ninvestigated the effect of varying spike lengths for flat-faced and\nhemispherically-nosed axially symmetric bodies . detailed pressure distributions\nhave been obtained as well as heat-transfer rates .\nthese exploratory studies have shown that the use of a spike protruding\nfrom a hemispherical-nosed cylinder at m 14 decreased the pressure\nlevel by an order of magnitude and the heat transfer to a fraction of\nthat measured on a hemisphere without a spike . the general technique\nappears to hold considerable promise for hypersonic flight ."}, {"doc_id": 1003, "text": "free-flight measurements of the static and dynamic .\n the real-gas hypersonic flow parameters for helium have been\ncalculated for stagnation temperatures from 0 f to 600 f and stagnation\npressures up to 6,000 pounds per square inch absolute . the results of\nthese calculations are presented in the form of simple correction\nfactors which must be applied to the tabulated ideal-gas parameters . it\nhas been shown that the deviations from the ideal-gas law which exist\nat high pressures may cause a corresponding significant error in the\nhypersonic flow parameters when calculated as an ideal gas . for\nexample, the ratio of the free-stream static to stagnation pressure as\ncalculated from the thermodynamic properties of helium for a stagnation\ntemperature of 80 f and pressure of 4,000 pounds per square inch\nabsolute was found to be approximately 13 percent greater than that\ndetermined from the ideal-gas tabulation with a specific heat ratio of"}, {"doc_id": 1004, "text": "free-flight measurements of the static and dynamic .\n the effects of contamination of helium by air upon static-pressure,\ntotal-pressure, heat-transfer, and temperature measurements have been\ninvestigated in the 2-inch helium tunnel at the langley research\ncenter . within the scope of the tests, even a small amount of air is\nshown to affect these measurements . the heat-transfer and temperature\nmeasurements were made on a 26.6 half-angle cone and demonstrated the\neffects of contamination qualitatively . the wall static and\ncenter-line pitot pressures show that if the contaminating air is held to less\nthan about 0.2 percent by volume, the error in indicated mach number is\nless than 1 percent as calculated from the rayleigh pitot equation .\nthe corresponding errors in wall static and center-line pitot pressures\nare about 1.7 and 0.4 percent, respectively ."}, {"doc_id": 1005, "text": "free-flight measurements of the static and dynamic .\n equations based on newtonian impact theory have been derived and a\ncomputational procedure developed with the aid of several design-type\ncharts which enable the determination of the aerodynamic forces and\nmoments acting on arbitrary bodies of revolution undergoing either\nseparate or combined angle-of-attack and pitching motions . bodies with\naxially increasing and decreasing cross-sectional area distributions are\nconsidered,. nose shapes may be sharp, blunt, or flat faced . the\nanalysis considers variations in angle of attack from -90 to 90 and\nallows for both positive and negative pitching rates of arbitrary\nmagnitude . the results are also directly applicable to bodies in\neither separate or combined sideslip and yawing maneuvers ."}, {"doc_id": 1006, "text": "free-flight measurements of the static and dynamic .\n the inviscid flow of a perfect gas over blunt-nosed axisymmetric\nand two-dimensional bodies at zero angle of attack has been calculated\nnumerically on an ibm 7090 computer . the computation consisted of the\nfuller blunt-body solution for the subsonic and transonic regions and\nthe method of characteristics for the supersonic region . the flow\nfields about a number of blunt bodies were studied, and the calculated\nresults showed good agreement with experimental shock-wave shapes,\nsurface-pressure distributions, and flow-field surveys ."}, {"doc_id": 1007, "text": "free-flight measurements of the static and dynamic .\n this report presents equations, tables, and figures for use in the\nanalysis of helium flow at supersonic and hypersonic speeds . the\ncontents of the report and presentation of the data parallel that of a\nsimilar reference work (naca rep. 1135) prepared for air flow .\n the perfect-gas relations for continuous one-dimensional flow,\nnormal- and oblique-shock waves, and prandtl-meyer expansions are the\nsame as for air but are presented here for completeness . the tables\npresent the values of useful dimensionless ratios for continuous\none-dimensional flow and for normal-shock waves as functions of mach\nnumber . the helium viscosity relation as a function of temperature,\nmass-flow rates as a function of mach number and temperature, and the\nreynolds number as a function of mach number and stagnation temperature\nare plotted . the oblique-shock characteristics of wedges and cones in\nhelium at mach numbers of 12, 16, 20, and 24 are presented in a series\nof plots . throughout all the computations, helium is considered to be\na perfect gas ."}, {"doc_id": 1008, "text": "free-flight measurements of the static and dynamic .\n representative experimental results are presented to show the\ncurrent status of the panel flutter problem . results are presented for\nunstiffened rectangular panels and for rectangular panels stiffened by\ncorrugated backing . flutter boundaries are established for all types\nof panels when considered on the basis of equivalent isotropic plates .\nthe effects of mach number, differential pressure, and aerodynamic\nheating on panel flutter are discussed . a flutter analysis of\northotropic panels is presented in the appendix ."}, {"doc_id": 1009, "text": "free-flight measurements of the static and dynamic .\n charts of thermodynamic properties for equilibrium air are presented\nwith sufficient accuracy to permit the calculation of flow parameters in\nhypersonic nozzles operating at stagnation temperatures up to 4,950 r\nand pressures up to 1,000 atm . flow parameters calculated from these\ncharts are presented for a series of stagnation temperatures between\nuse of these parameters, it is possible to calibrate a nozzle in the\nconventional way . a method is also presented from which the flow\nparameters for conditions other than those chosen herein may be\ncalculated . real-gas effects on the calculation of a hypersonic nozzle\ncontour are shown by an example calculation in which the nozzle contour\nfor mach number 12 was determined by including real-gas effects, and\nthis contour was compared with one calculated by ideal-gas\nconsiderations . also presented are the approximate limiting mach\nnumbers at which equilibrium air will just condense for various\ncombinations of stagnation temperatures and pressures ."}, {"doc_id": 1010, "text": "free-flight measurements of the static and dynamic .\n air-flow properties in nozzles were calculated and charted for\nequilibrium flow and two types of frozen flows . in one type of frozen\nflow, air was assumed to be in equilibrium from the nozzle reservoir to\narbitrary points where chemical reactions and molecular vibrations\nbecame frozen . in the other type, it was assumed that molecular\nvibrations were in equilibrium throughout the nozzle and that chemical\nreactions became frozen at arbitrary points . the calculations were\nmade for a range of stagnation pressures up to 10,000 poinds per square\ninch absolute and stagnation enthalpies up to 24,500 btu per pound .\nthe flow properties charted were temperature, pressure, density,\nvelocity, dynamic pressure, mach number, reynolds number, molecular\nweight fraction, and mass flow . equilibrium flow properties through\nnormal shock waves were also included ."}, {"doc_id": 1011, "text": "free-flight measurements of the static and dynamic .\n charts have been prepared relating the thermodynamic properties of\nair in chemical equilibrium for temperatures to 15,000 k and for\npressures from 10 to 10 atmospheres . also included are charts showing\nthe composition of air, the isentropic exponent, and the speed of\nsound . these charts are based on thermodynamic data calculated by the\nnational bureau of standards ."}, {"doc_id": 1012, "text": "principles of creep buckling weight-strength analysis\nof aircraft structures .\n the possibility of a gradual instability\nfailure of a column under\ncompressive load has been recognized\nfor some time . marin presented an\nanalysis of creep buckling based on\na theory of creep bending, but did not\ntake into account the average stress\ndue to axial loading . the theory also\nneglected the transient (nonlinear)\nportion of the creep curve .\n in efficient column design, the\naverage stress should be relatively high in\ncomparison with the bending stresses,.\nthat is, the column should be as straight\nas possible and the slenderness ratio\nshould not be too great . under these\nconditions marin's theory is not\ndirectly applicable, although it gives good\nagreement with tests of columns\nhaving large slenderness ratios or large\neccentricities ."}, {"doc_id": 1013, "text": "principles of creep buckling weight-strength analysis .\n published work on creep buckling has implied that failure\nof columns after a critical time is caused by initial imperfections .\nsuch analyses are relatively complex and ultimately leave the\nchoice of selecting the proper value of the initial imperfection to\nthe designer . furthermore, recent test results on creep buckling\nof columns have indicated that there is a random and relatively\nunimportant effect of small initial imperfections on the critical\ntime .\n to avoid the difficulties associated with initial imperfections,\na formulation of the creep buckling phenomenon in terms of\nclassical stability theory is presented . the theory permits the\nextension of known solutions for plastic buckling of certain thin\nplates and shells to creep buckling problems ."}, {"doc_id": 1014, "text": "principles of creep buckling weight-strength analysis .\na problem of creep stability of columns and plates\nis considered . in an analysis use is made\nof two forms of the creep theory based on the strain\nhardening hypothesis . for a uniformly\ncompressed palte a comparison is made between the\nresults according to the flow theory and strain\ntheory ."}, {"doc_id": 1015, "text": "principles of creep buckling weight-strength analysis .\n the determination of column deflections and\ncolumn buckling loads has been considered for\nmany years . the available theories, however,\ndo not provide for materials which creep with\ntime under constant loads . for the design of\nstructural members made of these materials, a\nconsideration of creep may be of practical\nimportance . plastics, concrete, and some metals\ncreep at normal temperatures while other\nmetals creep only at high temperatures and at stress\nvalues beyond the yield point . a consideration\nof creep in the design of some structures appears\nappropriate in view of the modern developments\nin plastics and the presence of high stress values\nwhich are sometimes beyond the yield stress .\nthis paper gives a rational theory for predicting\ncreep deflections in columns . a special case\nusing this theory is applied to the interpretation of\nsome preliminary tests of an aluminum alloy ."}, {"doc_id": 1016, "text": "principles of creep buckling weight-strength analysis .\n the relation of the time-dependent tangent-modulus\nload--as conceived by shanley--to actual column capacity\nis clarified . it may be interpreted as a limiting case of the\nconservative estimate . the time-dependent\ntangent-modulus load is, therefore, an approximation to a\nconservative estimate . the approximation, however, may\nbe either conservative or nonconservative when applied\nto imperfect or real columns . typical cases are discussed\nand experimental results for two alloys are cited ."}, {"doc_id": 1017, "text": "note on creep buckling of columns .\nit appears from librove's interesting analysis that, for\nthe case of creep buckling of columns, the initial\nimperfections contained in ordinary columns provide the mechanism by\nwhich failure due to creep occurs after a period of time . in fact,\nit can be concluded from this analysis that a theoretically perfect\ncolumn that is initially loaded below the time-independent critical\nload will not buckle at all . this is an interesting contrast to the\ncase of static buckling where small initial imperfections play an\ninsignificant role, since the failing load of an initially imperfect\ncolumn is substantially the same as that of a theoretically perfect\ncolumn . it is of interest, therefore, to conjecture whether there is\nany possible mechanism by which a column containing no initial\nimperfections can fail as a result of creep when the initial load is\nless than the theoretical buckling load ."}, {"doc_id": 1018, "text": "note on creep buckling of columns .\n the results of short-time elevated-temperature creep tests of\nobjective of obtaining procedures for predicting column lifetime .\nsemiempirical lifetime curves are obtained with the aid of a previously\npublished column creep theory and are used for deriving column curves .\nthe semiempirical lifetime curves are also used to study the effect of\nvarying applied stress and out-of-straightness . in the range\nconsidered, small variations in out-of-straightness are found to be of\nlittle practical significance,. whereas, small stress variations change\nthe column lifetime considerably . for the range of out-of-straightness\nencountered in the tests, the data can be presented in plots that do not\nexplicitly include out-of-straightness, and plots of this type should be\nsatisfactory for predicting column lifetime for design purposes ."}, {"doc_id": 1019, "text": "note on creep buckling of columns .\n a method for estimating allowable\nload capacities of columns subject\nto creep is presented . the method,\nwhich utilizes approximate stress\ndistributions derived from\nisochronous-stress-strain curves to estimate\ncolumn load capacities, is shown to\nbe conservative for the time for which\nthe estimate is made .\n an application of the method is\nmade to test data on as-received and\non stabilized 24s-t4 aluminum alloy .\na comparison of the computed column\ncapacities with experimental capacities\nindicates that the method is\nsatisfactory for estimating the decrease in\ncapacity with increasing time .\n easily obtained, time-dependent\ntangent-modulus loads are discussed .\nthey are interpreted as being approximations\nto allowable load-capacity\nestimates . a limited application is made to\ntest data, and the results\nappear promising . it is concluded that if\ncertain limitations are recognized,\nthe method may prove to be useful because\nof its simplicity .\n a presentation of the results of an\nexperimental investigation of the\neffects of column imperfection and\ncolumn-material variation is made . it\nis found that column-capacity variations of\nthe order of 10 per cent can\nresult from column-imperfection differences\nand column-material variation .\n the results of an experimental study of\nthe variation of column\ncapacity with temperature of exposure are presented .\nthey indicate that column\nefficiency, as measured by decrease in capacity,\ncan be acceptable for very\nshort times at the higher temperatures . the\nefficiency at these higher\ntemperatures falls rapidly, however, with increasing time ."}, {"doc_id": 1020, "text": "note on creep buckling of columns .\n the results of short-time\ncreep-buckling and creep-bending tests of\nslenderness ratio 111 are presented .\nthe tests were performed at 600 f,\nand strain measurements were taken\nwith high-temperature electric-resistance\nstrain gages . a description\nof the development of the gages is given\nin an appendix . the column\ntests show that the critical time decreases\nmuch more rapidly with\nincreasing load than with increasing initial\ndeviation from straightness .\nthe bending tests indicate that the steady\ncreep rate of the curvature\nis a simple power function of applied\nmoment . these latter results,\ntogether with a previously derived\ncreep-buckling theory, are used to\ndevelop a semiempirical formula suitable\nas a guide for the determination\nof the critical time for columns ."}, {"doc_id": 1021, "text": "note on creep buckling of columns .\n this paper describes theory and tests of the creep collapse\nof long thin aluminum-alloy cylinders under external radial\npressure . steady-state creep is assumed in the theoretical\nderivation . the test temperatures were between 300 and 500 f .\nthe collapse time for each cylinder was calculated theoretically .\nagreement between theoretical and test results was fair ."}, {"doc_id": 1022, "text": "note on creep buckling of columns .\n forty-three cylinders of 40-inch\nlength and 16-inch diameter, made\nof 5052-0 aluminum-alloy sheets of\nthickness, were subjected to bending\nmoments constant along the cylinder\nand in time in an oven which maintained\na constant temperature of 500 f\nduring the test . all the cylinders\nfailed by buckling . the time that\nelapsed between load application and\ncollapse was measured ."}, {"doc_id": 1023, "text": "note on creep buckling of columns .\n a theory of creep buckling is presented in which the instantaneous\nelastic and plastic deformations following the application of a load, as\nwell as the steady creep deformations, are considered in an approximate\nmanner . equations are given from which the critical time, that is, the\ntime elapsing between load application and the collapse of the column,\ncan be computed ."}, {"doc_id": 1024, "text": "note on creep buckling of columns .\n the general dynamic equation of\ncreep bending of a beam loaded\nlaterally and axially was derived for a\nlinearly viscoelastic material whose\nmechanical properties can be characterized\nby four parameters . the\nmaterial can exhibit instantaneous and retarded\nelasticity as well as pure\nflow .\n the equation derived was used to\nobtain the creep bending deflection\nof a beam in pure bending and of a column\nwith initial sinusoidal\ndeviation from straightness . as expected, the\nratio of the creep deflections\nof the beam in pure bending and the\ndeflections of a corresponding purely\nelastic structure is identical to the\nratio of the creep strain and the\ncorresponding elastic strain of a bar\nunder simple tension or compression .\n the results of the analysis of the\ncreep deflection of the column\nshowed that the deflections increase\ncontinuously with time and become\ninfinitely large only when the loading\ntime is correspondingly large .\nhowever, large deflections are obtained\nin reasonably short periods of\ntime if the applied load is near to the\neuler load of the column . the\ndeflection-time curves obtained from a\nnumerical example are of the same\ntype as those determined by experiment\nwith aluminum columns ."}, {"doc_id": 1025, "text": "note on creep buckling of columns .\n the creep of a slightly crooked section column carrying a\nconstant load is studied theoretically . the material of the\ncolumn is characterized by a strain-time relationship, under\nconstant uniaxial stress, of the form, where is\nthe total strain, is the constant stress, is the time, and e,a,b,\nand k are material constants . this form was selected because it\napplies to at least two alloys--75s-t6 aluminum alloy at 600 f .\nand a low-alloy steel at 800 and 1,100 f . however, the\nanalysis is intended for any material having creep properties of the\nsame form and for which the material constants are known . a\nstrain-time relationship under variable uniaxial stress, necessary\nfor the column analysis, is formulated from the constant-stress\nproperties with the aid of shanley's engineering hypotheses of\ncreep .\n the analysis leads to the conclusion that the lateral deflection\napproaches infinity--that is, the column collapses--in finite time .\nresults are given showing the maximum length of time the\ncolumn can support a given load before it collapses and the growth\nof stresses, strains, and deflections prior to collapse ."}, {"doc_id": 1026, "text": "note on creep buckling of columns .\n this paper is concerned with the solution of the creep buckling of\ncolumns . instantaneous elastic and plastic deformations, as well as\nthe transient and secondary creep, are considered . formulae for the\ncritical time at which a column fails are presented for integral values\nof the exponents appearing in the creep law ."}, {"doc_id": 1027, "text": "note on creep buckling of columns .\n a phenomenological relation between\nstress, strain rate, and\ntemperature is suggested to account for the\nbehavior of polycrystalline metals\nabove the equicohesive temperature .\nthe properties of the metal\nincluded in the relation are elasticity,\nlinear thermal expansion, and\nviscosity . the relation may be integrated\nunder various conditions to\nprovide information on creep rates, creep\nrupture, stress-strain curves,\nand rapid-heating curves . it is shown\nthat for one material - 7075-t6\naluminum-alloy sheet - the information\nyielded by the relation for these\nfour applications agrees reasonably\nwell with test data ."}, {"doc_id": 1028, "text": "note on creep buckling of columns .\n the phenomenological theory previously\nproposed in naca technical\nnote 4000 for the behavior of metals at\nelevated temperatures has been\nmodified to yield transient creep curves\nby assuming that the metal\nconsists of two phases, each with its own\nelasticity and viscosity . the\nextended theory satisfies the basic\nrequirements for a theory of\ntransient creep at elevated temperatures ..\nthat the transient creep be closely\nconnected with the subsequent steady\ncreep, and that the apparent\nexponent of the time in the transient region\nbe permitted wide variations\nbetween 0 and 1 . from this theory it is\npossible to construct\nnondimensional creep curves which extend continuously\nfrom the transient region\ninto the steady-state region . the\ncorresponding family of creep curves\nfor any metal may be obtained from\nthe nondimensional family by use of\nappropriate constants . the constants\nrequired are those obtained from\nsteady creep measurements, together\nwith two additional constants which\nrepresent the difference between the\nphases . the transient creep curves\nresulting from this theory are compared\nwith the experimental curves\nfor pure aluminum, gamma iron, lead, and\nagreement is found ."}, {"doc_id": 1029, "text": "note on creep buckling of columns .\n a variational theorem is presented for a body undergoing\ncreep . solutions to problems of the creep behavior of plates,\ncolumns, beams, and shells can be obtained by means of the\ndirect methods of the calculus of variations in conjunction with\nthe stated theorem . the application of the theorem is\nillustrated for plates and columns by the solution of two sample\nproblems ."}, {"doc_id": 1030, "text": "note on creep buckling of columns .\n some general topics in elastic stability are discussed . in\nparticular, attention is given to the relationship between\nadjacent-equilibrium-position and energy techniques, to the effects of\nnonlinearity, and to the sensitivity of certain stability problems to the\ncharacter of the loading ."}, {"doc_id": 1031, "text": "note on creep buckling of columns .\n a general variational theory of elastic stability that was\noriginated by e. trefftz (1) is applied to the problem of\nbuckling of rings of rectangular cross section subjected to\nuniform external pressure . the theory is believed to be\nmore rigorous than previous treatments of the problem,\nsince it avoids conventional assumptions of curved-beam\ntheory, such as the assumptions that plane sections\nremain plane and that radial stresses vanish . the classical\nresult of levy (2) is confirmed for a ring of infinitesimal\nthickness . new results are obtained which show the\neffect of the finite thickness of a ring on the coefficients in\nthe buckling formula ."}, {"doc_id": 1032, "text": "on the conservativeness of various distributed force systems .\nthe necessity of determining the conservativeness of force systems in\ninstability problems is discussed in reference 1 . it is shown that,\nwhereas kinetic methods are generally applicable for the determination\nof instability loads, the statical methods usually employed are valid\nonly for conservative and nongyroscopic systems . small changes in\nthe character of the loading could make an otherwise conservative\nsystem nonconservative and cause a large change in the magnitude of the\nbuckling load . the buckling load of the cantilever column example\nin reference 1 is, for tangential end loading, eight times that for\nconservative, constant directional loading ."}, {"doc_id": 1033, "text": "the design of tubes under uniform external pressure on the\nbasis of assumed inaccuracies .\nsince the failure of tubes under uniform external pressure depends\nvery much upon the various kinds of imperfections in them,\nit seems logical to derive a design formula for such tubes in\nwhich the quantities depending on imperfections will appear explicitly .\nthe most common imperfection in tubes is an initial ellipticity,\nthe limiting value of which in each type of tube is usually well-known\nfrom numerous inspection measurements . the deviation of the shape\nof the tube from a perfect circular form can be defined by the\ninitial radial deflections w' ."}, {"doc_id": 1034, "text": "note on creep buckling of columns .\n a long, thin-walled cylindrical shell is loaded by a uniform\nexternal pressure . equations are developed for the time behavior\nof the shape of the cross section under the following conditions ..\nformations expressible by a power creep law,. (b) the initial and\nsubsequent mode shape of the deviations from circularity of any\ncross section is two-lobed,. and (c) the shell construction is of the\nsandwich type, with concentric cylindrical membranes taking\nnormal stresses and an annular core supporting shear without\ndeformation . explicit solutions are obtained for the particular\ncase of the cubic creep law . it is shown that the nondimensional\namplitude of the cross-sectional mode shape (briefly, shape\nfactor) will become infinite in a finite time . curves of shape factor\nversus time and of collapse time versus initial value of the shape\nfactor are presented . also given are an explicit expression for\nand a curve of the expected variation in collapse time owing to\nuncontrollable deviations from a nominal initial value of the\nshape factor . it is shown that the expected variation is small\nif the nominal initial shape factor value is sufficiently large ."}, {"doc_id": 1035, "text": "note on creep buckling of columns .\n the stability of a compressed elastic\nring has been studied by a method which\ncan be extended to solve the problem\nof the stability of a flexible heavy structure\nspread by a system of hoops as in a crinoline\nskirt . the original work by levy, which\nwas developed by timoshenko and love,\ncannot be generalized to problems in\nwhich the compressing forces are affected by\nthe deformation of the ring .\n it is shown that the load at which a ring\nwill buckle depends not only upon the\nmagnitude of the load but also upon its first\nderivative relative to the radial distance .\na positive derivative causes the ring to\nbuckle at a higher load . when this result\nis applied to a cone of heavy and loosely\ndraped fabric spread by a rigid hoop of\nradius and a larger and flexible hoop\nof radius below it, both hoops being in\nhorizontal planes, then various modes\nof buckling other than oval are possible\naccording to the relative magnitudes of\nand . it is found that oval buckling\nchanges to three-wave buckling when\nthree-wave changes to\nfour-wave when, and as and\napproach nearer to equality the buckled\nform progressively changes to more waves .\nwhen applied to a structure spread by\nmany horizontal hoops of which the top\none is rigid and oval, it is found that all\nother hoops, if each is designed to the\ncriterion, will have the same\nabsolute deviation from circularity as the\nrigid hoop . if any one hoop is designed\nso that, then the oval shape of\nthe rigid hoop is magnified on all flexible\nhoops ."}, {"doc_id": 1036, "text": "on transverse vibrations of thin, shallow elastic shells .\n according to marguerre (proc. 5th internat. congress\nappl. mech., cambridge, mass., 1938, wiley, new york,\nshells are governed by three simultaneous differential\nequations in the three displacements . the author has\nconsiderably simplified this theory for the case of transverse\nvibrations by ignoring the longitudinal inertia terms, thus\nreducing the problem to that of solving two simultaneous\ndifferential equations in a stress function and one\ndisplacement component . this simplification is justified by an\norder-of-magnitude analysis, and illustrated by considering the\nvibrations of a paraboloidal shell with a rectangular\nboundary ."}, {"doc_id": 1037, "text": "on transverse vibrations of thin, shallow elastic shells .\nit is shown that a perfectly straight bar, subjected\nto a state of uniform shear stress, will\nbuckle, in a manner similar to a column under\ncompression, if the shear stress exceeds\na certain critical value . the buckling equations\nare obtained by the newtonian\napproach and also by the application of the principle\nof minimum potential energy . in\norder to provide additional insight into this buckling\nmechanism, a simple model is\nintroduced and analyzed ."}, {"doc_id": 1038, "text": "on transverse vibrations of thin, shallow elastic shells .\n the deformation and complete stress\ndistribution are determined for\neach of the following edge-loaded thin\nshells .. (1) a right circular\ncylinder, (2) a frustum of a right\ncircular cone, and (3) a portion of a\nsphere . the locations of maximum\ncircumferential and meridional stresses\nare also found . equations are\ndeveloped for discontinuity shear and\nmoment at the following junctions ..\ncircular cylinder, (2) axial change\nof thickness in a cone, (3) change\nof thickness in a portion of a sphere,\ncylinder and a portion of a sphere,"}, {"doc_id": 1039, "text": "on transverse vibrations of thin, shallow elastic shells .\n an experimental investigation was\nmade (1) to evaluate previously\npublished theoretical procedures for\nthe prediction of stress\ndistribution for cases of radially symmetric\nabrupt change in wall thickness of\nthin-walled cylinders subject to\ninternal pressure and (2) to\ninvestigate the significance of stresses\nattributable to the presence of\nthickness changes typical of design practice .\none theory was adequate in\nitself for solution of the case of continuous\nmiddle surface,. use of the\nsecond theoretical procedure was required\nto determine the additional\nstresses arising from discontinuous middle\nsurfaces at the change in\nthickness .\n comparisons were made between\ntheoretical and experimental stress\ndistributions for cases with continuous\nmiddle and continuous inner\nsurfaces for radially symmetric changes in\nwall thickness of a cylinder\nsubject to internal pressure for diameter\nto larger wall thickness ratios\nof 117 and 28 and for the case of a\ncontinuous outer surface for a ratio\nof 28 . in all tests the ratio of wall\nthicknesses at the change in wall\nthickness was 0.4 .\n there was reasonably good correlation\nbetween theoretical and\nexperimental curves of stress distribution .\non the basis of this\ncorrelation, it was concluded that the applicable\ntheories were valid . it\nwas shown that inclusion of the stresses\narising from the condition of\ndiscontinuous middle surfaces at a change\nin thickness has an important\neffect on stress distribution .\n in the case of a cylinder with a\ncontinuous outer surface, the\nmaximum mean effective stress was of sufficient\nmagnitude to indicate that\nthis geometry should be avoided in design\nif possible . the maximum\nmean effective stress was not increased to\na significant degree by the\npresence of a change in wall thickness in\nthe other cases ."}, {"doc_id": 1040, "text": "on transverse vibrations of thin, shallow elastic shells .\n experimental measurements of pressures and heat-transfer\nrates over three blunt afterbodies of small fineness ratio in fully\nseparated wakes are presented . the afterbodies are generally\nsimilar in shape but have different stepdown heights from the end\nof the forebody .\n tests were made by means of a new shroud technique over a\nrange of reynolds numbers closely corresponding to typical\nflight conditions at mach numbers on the order of 20, considering\nmodels on the order of 5 ft. in diameter at about 120,000 ft.\naltitude . stagnation temperatures on the order of 1,300 r. to\n strictly speaking, the test flows correspond to prototype flows\nwhich would be created by a forebody consisting of a sharp or\nslightly blunted 54 half angle cone which turns cylindrical for a\nshort distance and then connects with the afterbody . judiciously\ninterpreted, the results may be considered to have a somewhat\nwider applicability for approximation purposes . the results are\npresented and compared with each other in terms of\nnondimensional variables based on flow conditions at the end of the\nforebody .\n the pressure distribution along an afterbody is seen to be\nroughly uniform in each run . for a given point on an afterbody,\nthe ratio of pressure to the stagnation pressure at the forebody\nend (or exit) decreases with increasing stagnation pressure or\nreynolds number . the present pressures and pressure-reynolds\nnumber variations (fig. 8) are compared with values obtained\nfrom chapman's mach 2 or 3 base-pressure data,. qualitative and\nsome quantitative agreement is noted . in the reynolds number\nrange comparable to those of the present tests, chapman's exit\nboundary layers were considered to be laminar . an approximate\ncheck of the heat-transfer rate at the forebody end in the present\ntests also indicates a laminar rate . no information was obtained\nconcerning the possible transition of the free-mixing separated\nboundary layer covering the wake . an adverse pressure gradient\non the cylindrical end of the forebody figs. 7(a) and 7(c) was\nobserved .\n heat-transfer rates are seen to be roughly uniform over an\nafterbody in each run, although some increase in the streamwise\ndirection is noted . the afterbody nusselt number (n) varies\nwith the reynolds number (r evaluated at the forebody end)\nroughly in the manner n r where generally (fig. 13) .\n heat rates on the rear faces of the afterbodies are almost\ntwice the values on the sides . the heat rates on the large-step\nbody are higher than those on the body of zero stepdown height .\n in an addendum, it is shown that the prandtl-meyer expansion\nangle of the flow leaving the afterbody increases with increasing\ntest reynolds number, and that the corresponding local mach\nnumber square increases linearly with reynolds number . the\neffect is to keep the local wake reynolds numbers virtually\nconstant with increasing test reynolds number while the afterbody\nheat rates increase sharply . the expansion angle on the\nafterbody of zero stepdown height is significantly smaller than on the\nstepped down bodies,. this may affect the decreased heat rates on\nthis body ."}, {"doc_id": 1041, "text": "analysis of stresses in the elements of shell structure .\nthe love-meissner analysis for thin shells has previously been applied\nto cones of uniform wall thickness, and solutions for the stress\nresultants were given in terms of kelvin's functions . since\ntabulation of these functions for large arguments is not practical,\nconsiderable computation was still required . in the present paper, the authors\ndefine special functions which eliminate the necessity of evaluating\nkelvin/s functions and which may be used with simple algebraic and\ntrigonometric functions to compute the boundary forces and displacements\nfor cones for various loading conditions . these special functions also\nmake clear the magnitude of errors which result from geckeler/s and\nother approximate solutions ."}, {"doc_id": 1042, "text": "on transverse vibrations of thin, shallow elastic shells .\n the report presents information\non the stress problems in the\nanalysis of pressurized cabins of\nhigh-altitude aircraft not met with\nin other fields of stress analysis\nrelating to aircraft . the material\nmay be roughly divided into shell\nproblems and plate problems, the\nformer being concerned with the\ncurved walls of the cabin or pressure\nvessel and the latter being concerned\nwith small rectangular panels of\nits walls, framed by stiffeners, but\nnot necessarily plane ."}, {"doc_id": 1043, "text": "on transverse vibrations of thin, shallow elastic shells .\n a numerical analysis is given for the solution of the\ngeneral equations of thin shells of revolution subjected to\nrotationally symmetric pressure and temperature\ndistributions .\n the basic differential equations are in a very general\nform, which permits the geometry of the shells considered,\nto be specified by discrete data points .\n the analysis determines elastic stresses, strains and\ndisplacements for multi-layer and multi-sectional shells of\nrevolution . surface loads, temperatures, thicknesses and\nmaterial properties may vary arbitrarily in the meridional\ndirection . temperatures and material properties can also\nvary through the thickness .\n the solution is obtained by direct computation using a\nnumerical method that employs two by two coefficient\nmatrices,. and hence avoids the problems of slow convergence .\nthe solution has been programmed in a semi-algebraic\nlanguage which can be used on most high speed computers .\ncomparisons of numerical solutions to known exact and\napproximate solutions of the thin shell equations are made to\ndemonstrate the accuracy of this method ."}, {"doc_id": 1044, "text": "on the theory of thin elastic shells .\n general equations for the symmetrical finite deflection of\na rotationally symmetric thin shell are first obtained . for\nsmall deflections these equations are reduced to a pair of\nequations for the change of slope of the shell surface and\nthe product of the undeformed radius of the shell to the\nradial stress . this choice of dependent variable is shown to\nbe advantageous . two cases of shallow shells give\nparticularly simple solutions .. parabolic shells of nth degree and\nuniform thickness, and parabolic shells of mth degree with\nthickness varying as mth power of the distance from the\napex . for the first case, the solutions can be expressed in\nterms of cylinder functions,. for the second, in powers of\nthe paper concludes with a discussion of the asymptotic\nsolutions for small thickness ."}, {"doc_id": 1045, "text": "the bending strength of pressurized cylinders .\n discussion of previously presented experimental data for the\nloading of pressurized cylinders, in terms of membrane theory ."}, {"doc_id": 1046, "text": "the bending strength of pressurized cylinders .\n a theoretical solution is given\nfor the critical stress of\nthin-walled cylinders loaded in torsion .\nthe results are presented\nin terms of a few simple formulas and\ncurves which are applicable\nto a wide range of cylinder dimensions\nfrom very short cylinders of\nlarge radius to long cylinders of small\nradius . theoretical\nresults are found to be in somewhat better\nagreement with\nexperimental results than previous theoretical\nwork for the same range\nof cylinder dimensions ."}, {"doc_id": 1047, "text": "the bending strength of pressurized cylinders .\nbe described here is attributed to the russian\ninvestigator v. g. galerkin, whose original papers are\ninaccessible to the present writer . his knowledge\nof the method is derived from a description given in\na paper by e. p. grossman . grossman states\nthat the method was given by galerkin in his treatise\np. 897), and that applications to oscillation problems\nwere first made by v. p. lyskov . it is pointed\nout by grossman that galerkin's process in applications\nto mechanics leads to the same results as\nlagrange's principle of virtual work, but employs a\nspecial co-ordinate system .\n the method of galerkin belongs to the same general\nclass as those of rayleigh and ritz, for it seeks\nto obtain an approximate solution of a differential\nequation with given boundary conditions by taking\na function which satisfies these conditions exactly,\nand proceeds to specialise the function in such a\nmanner as to secure approximate satisfaction of the\ndifferential equation . the selected function is\na linear combination of n independent functions, and\nthe coefficients are determined by a process of\nintegration .\n the galerkin process can be considered from two\npoints of view, (a) simply as a means for the\napproximate solution of differential equations, and\ntreatment of problems concerning the statics and\ndynamics of elastic and other deformable bodies .\nthese two aspects are treated separately in parts 1\nand 2 of the paper respectively, and will now\nbe briefly discussed .\nwhich satisfies the boundary conditions, in\nthe differential equation be . since the result should be\nzero, is the error in the differential equation .\nthen the galerkin process consists in choosing the n\ncoefficients in the function in such a manner that\nn distinct weighted means of the error, taken throughout\na certain range of representation, shall all\nbe zero .\nas a generalised force, and the multipliers used\nto weight the errors are the virtual displacements\ncorresponding to increments of each of the generalised\nco-ordinates in turn . thus the vanishing of the\nweighted mean is here interpreted as the vanishing\nof the virtual work in the appropriate displacement .\n the degree of accuracy attaindd can be increased\nindefinitely by increasing the number of\nindependent functions employed, but this entails a great\nincrease of labour . however, when the functions\nare well chosen, an excellent approximation can be\nobtained by the use of a very small number, as is\nsufficiently shown by the examples included in this paper ."}, {"doc_id": 1048, "text": "a small deflection theory for curved sandwich plates .\n a small-deflection theory that takes into account deformations\ndue to transverse shear is presented for the elastic-behavior\nanalysis of orthotropic plates of constant cylindrical curvature\nwith considerations of buckling included . the theory is\napplicable primarily to sandwich construction ."}, {"doc_id": 1049, "text": "elastic constants for corrugated core sandwich plates .\n the sandwich plate consisting of\ncorrugated sheet fastened between\ntwo face sheets is considered . application\nof existing theories to the\nanalysis of such a sandwich plate requires\nthe knowledge of certain\nelastic constants . formulas and charts are\npresented for the evaluation\nof these constants . the formulas for three\nof these constants were\nchecked experimentally and found to give\nvalues in close agreement with\nthe experimental values ."}, {"doc_id": 1050, "text": "compressive buckling of simply supported curved plates\nand cylinders of sandwich construction .\n theoretical solutions are presented\nfor the buckling in uniform\naxial compression of two types of simply\nsupported curved sandwich\nplates .. the corrugated-core type and the\nisotropic-core type . the\nsolutions are obtained from a theory for\northotropic curved plates in\nwhich deflections due to shear are taken\ninto account . results are\ngiven in the form of equations and curves ."}, {"doc_id": 1051, "text": "the stability of thin-walled unstiffened circular cylinders\nunder axial compression including the effects of internal\npressure .\n in the design of high-speed aircraft the importance of\nunpressurized and pressurized monocoque cylinders necessitates a\nreliable analysis procedure for the compressive buckling of\ncylindrical shells . analysis by the classical small-deflection theory has\nproved inadequate . recent large-deflection theoretical\ntreatments of the problem have shown reasonable correlation with\nexperiments but require a prior knowledge of the initial\nimperfections of the cylinder . developed in this paper is a\nsemiempirical procedure which permits a compressive buckling analysis of\ncylindrical shells with a knowledge of the cylinder geometry only .\nthis analysis is achieved by correlating experimental data\nstatistically with theoretical parameters .\n in order to provide data not previously available, an extensive\nseries of axial compression tests of pressurized cylinders has been\nperformed . these data, together with all other known test data,\nare analyzed semiempirically . in the analysis best-fit curves\nare presented using theoretical parameters and shapes of curves\nwhere applicable . unpressurized and pressurized cylinder\ncompressive buckling curves are then developed as 90 per cent\nprobability curves from the test data . in general, these\nstatistically defined design curves are significantly lower than\npreviously available design curves ."}, {"doc_id": 1052, "text": "recent advances in the buckling of thin shells .\nthe importance of the field of shell analysis is evidenced by the\nfact that in august, 1959, the international union of theoretical\nand applied mechanics conducted a symposium on the theory of thin\nelastic shells in delft, holland . this special meeting was attened by\napproximately 65 scientists in this field from 14 countries . this\nsymposium indicated that considerable interest currently exists in\nsuch relatively new topics as the buckling of bimetallic shells,\npressurized shells, creep buckling, and dynamic buckling, as well as\nin the more traditional problems involving isotropic shells of various\ngeometries ."}, {"doc_id": 1053, "text": "spherical cap snapping .\n a nonlinear boundary value problem for the determination of\nthe rotationally symmetric deformations of a clamped spherical\ncap under external pressure is solved by finite differences . the\nnumerical solutions are obtained by employing a previously\ndeveloped iteration procedure . a special case of the difference\nequations is solved explicitly and yields a justification of the\niteration method as well as insight into the properties of the more\naccurate numerical solutions .\n buckled and unbuckled equilibrium states are obtained and\nthe shape of the pressure-deflection curve which is usually assumed\nfor these states is verified for a large class of caps . close\nestimates are given for the upper and lower buckling loads and an\nintermediate buckling load--i.e., the /dead-weight/ load . the\nstresses and deflections in the buckled and unbuckled states are\nexamined and compared with an asymptotic solution valid in the\ninterior of very thin shells . boundary layers are found to\ndevelop in the buckled states both as the loading increases and as\nthe thickness of the shell decreases ."}, {"doc_id": 1054, "text": "iterative solutions for the non-linear bending of circular\nplates .\n the authors study non-linear von karman equations\nfor bending of a thin circular plate under uniform normal\npressure . discussion is mainly concerned with plates\nclamped at the edges and with zero radial displacement,\nbut analysis is valid for other edge conditions . solution is\nby an iterative procedure whose convergence properties\nare studied by means of integral equations . method is\nthen applied to finite difference formulation of the\ndifferential equations in order to obtain numerical solutions .\nnumerical results are compared with previous work by\nother authors and the advantages of the present method\nare indicated ."}, {"doc_id": 1055, "text": "non-linear bending and buckling of circular plates .\n iterative solutions of finite difference\napproximations of the non-linear von karman\nplate equations are presented . results\nare obtained for circular plates under a\nvariety of boundary conditions subjected to\neither uniform lateral pressure or uniform\nedge thrust .\n the solution, carried out numerically on\nthe aec univac at new york university,\nyields a complete description of stresses\nand deflections for an apparently unlimited\nrange of load parameters . in addition, boundary\nlayer phenomena are discussed . for\ncomputing purposes, this iterative method proves\nto be superior to the previously used\npower series method and may be applicable to\nother non-linear problems ."}, {"doc_id": 1056, "text": "axisymmetric large deflections of circular plates subjected\nto thermal and mechanical load .\n this paper is concerned with the nonlinear\naxisymmetric analysis of circular plates with in-plane\nedge restraint . both temperature and mechanical\nloads are accommodated as an extension of\ninvestigations performed for the isothermal mechanical\nloading problem . an exact mathematical\nformulation within the framework of the v. karman large\nstrain-displacement relations is developed . the\nequilibrium equations and boundary conditions are then\nderived by utilizing the calculus of variations for\narbitrary axisymmetrical temperatures and normal\ndistributed loading . the satisfaction of equilibrium and\ncompatibility equations requires the solution of two\nsimultaneous nonlinear ordinary differential equations\nsubject to the prescribed boundary conditions .\nanalytical solutions of such equations are apparently not\npossible and therefore numerical procedures must be\nemployed .\n a finite difference procedure utilizing /relaxed\niterations,/ developed by h. keller and e. reiss, and\nemployed by them for the solution of isothermal\nproblems with apparently unlimited load parameter ranges,\nis used here for combined thermo-mechanical problems .\nnumerical results are presented for the special case of\na simply supported circular plate with radially\nimmovable boundaries, subject to a uniform pressure and an\narbitrary temperature variation through the thickness\ntained for a large range of temperature and load\nparameters . however, because of space limitations, only\na limited amount of data are presented in this paper ."}, {"doc_id": 1057, "text": "the uniform section disk spring .\n the authors point out in this paper that initially coned\nannular-disk springs of uniform cross section may be\nproportioned to give a wide variety of load-deflection\ncurves not readily obtainable with the more conventional\nforms of springs, and that, although the versatility of this\ntype spring has long been indicated, the formulas\navailable have not been presented in a manner to disclose\nreadily the effect of spring proportions on characteristics .\ntherefore the authors have derived the formulas presented\nin this paper with the intention that the formulas will aid\nthe designer in arriving at suitable characteristics by\nchoice of spring geometry . these new formulas have\nbeen in use for several years at the general motors\ncorporation research laboratories section, and their\nreliability has been checked by tests of springs used in a\nvariety of special test equipment ."}, {"doc_id": 1058, "text": "the conical disk spring .\n this paper presents approximate formulas\nto describe the behavior of the conical\ndisk spring . it is assumed that the shallow\nconical shell remains conical when\nsubjected to the axially symmetric edge loads .\nthe principle of stationary potential\nenergy is used to derive the relations between\nload and deflection . formulas relating\nthe applied loads, stresses, and deflections are\ngiven for several types of edge\nconstraint . the analysis is essentially a refinement\nand extension of the previous work\nof almen and laszlo ."}, {"doc_id": 1059, "text": "the nonlinear conical spring .\n the large symmetric deformations of shallow conical shells are\nof interest in the design of nonlinear conical disk springs . in most\napplications a uniformly distributed axial load acts at the inner\nand outer edges,. these edges are otherwise free . several\napproximations have been proposed to describe the behavior of\nthese springs . a first approximation (1) is based on the\nassumption that meridional strains are negligible . this requires that the\nshell remain conical after deformation and also that the\nextensional strain of meridional lines on the middle surface vanish .\nanother approximation (2) retains only the assumption that the\nshell remains conical . the first assumption satisfies neither of\nthe two boundary conditions at the free edges,. the latter\nviolates the condition of vanishing moment at the free edges .\nrecently the authors presented a series solution (3) for a special\ncase, namely, the case of an annular plate under similar loading .\nnumerical solutions for the shallow conical shell under these\nconditions of load have also been obtained (4) . an examination\nof these results indicates that the meridional bending stresses are\nof much smaller magnitude than the circumferential bending\nstresses . hence the present analysis is based on the neglect of the\nmeridional bending moment ."}, {"doc_id": 1060, "text": "buckled states of circular plates .\n authors discuss the thin elastic circular disk of constant\nthickness subjected to a constant compressive thrust applied at its\nedge . the analysis presented is based upon the nonlinear von\nkarman equations of plate theory and is applied to disks with\ncompletely clamped and completely, simply supported edges ."}, {"doc_id": 1061, "text": "turbulent mixing of a rocket exhaust jet with a supersonic stream\nincluding chemical reactions .\nthe equations for the turbulent mixing of a two-dimensional supersonic\njet issuing into an ambient supersonic stream are formulated . both\nstreams consist of a mixture of chemically active and possibly reacting\ngases, therefore any heat release by chemical reaction is included,. the\n net mass rate of production of species is obtained on the assumption\nthat the reaction rate constant is given by an expression reducible to\nthe classical arrhenius law . the equations first given in terms of the\nx, and y coordinates, are expressed in dimensionless form and in terms\nof the x and coordinates, where is the stream function . the resulting\nexpressions are all of the /heat conduction/ type,. they are put in a\nfinite difference form by using the crank-nicolson method of\nsubstituting finite difference approximations for both the /time/ and /space/\nderivatives . the mixture is assumed to consist of six species, namely\nh2o, h2, o2, co2, co, and n2, and the oxidation of h2 and co is assumed\nto take place according to a single-step chemical reaction . the\nsolution of the problem is based on the simultaneous solution of 8n linear\nalgebraic equations in 8n unknowns, n being the number of internal grid\npoints at every step in the x-direction, and 8 the total number of\nunknowns at each grid point, namely velocity, temperature, and\nconcentration for each of the six species . a method of obtaining initial and\nboundary conditions from available inviscid jet flow solutions is\ndiscussed . the equations are programed for calculation on an ibm-704\ncomputer . finally, one typical case is considered, and plots of velocity,\ntemperature, and concentration profiles are given for the initial stages\n of development of the mixing layer ."}, {"doc_id": 1062, "text": "an experimental and theoretical investigation of second-order\nwing-body interference at high mach number .\n the second-order wing-body interference theory\nof landahl and beane is used in the\ntheoretical calculation of the pressure distributions\nover the wing of a wing-body combination .\nresults are compared with experimental values\nobtained from wind-tunnel tests, at a mach\nnumber of 7.35, on a cone-cylinder non-lifting body\nwith a triangular wing of wedge section\nset at incidences of 0, 3, 6 and 10 . it is shown\nthat interference effects can be very large\nand can be calculated theoretically with good accuracy ."}, {"doc_id": 1063, "text": "on obtaining solutions to the navier-stokes equations\nwith high speed digital computers .\n the purpose of this paper is\nto show how to obtain steady\nstate solutions to the navier-stokes\nequations on a high-speed digital\ncomputer . first the relative merits\nof various finite difference\nformulae are discussed . thereafter\nthe main part of the paper is\nconcerned with the methods used to\nsolve the finite difference\nequations and an investigation is made\nof all the simpler iterative\nmethods ."}, {"doc_id": 1064, "text": "propeller slipstream effects as determined from wing\npressure distribution on a large-scale six-propeller\nvtol model at static thrust .\n during static-thrust tests of a\nlarge-scale general research model having a\ntilting wing and double-slotted flaps,\nstatic-pressure measurements were made on\na wing segment behind one propeller to\nsurvey the effects of the slipstream . for\nthe conditions of highest slipstream energy,\nthe hovering end point of aerodynamic\nparameters for aircraft having vertical and\nshort take-off and landing capability\nthe tilt-wing configuration (zero\nflap deflection) was a 6 spanwise variation\nin effective angle of attack in a\nspan of slightly less than 1 propeller diameter .\neffective changes in camber\non the tilt-wing configuration as a result of\nslipstream rotation, the radial\nvelocity gradient, and the resultant spanwise\nflow were negative and had a maximum\nmagnitude of less than 2-percent chord . for\nthe deflected-slipstream\nconfiguration (double-slotted flaps deflected), effects\nimportant to the hovering\nperformance were found, including a 40-percent spanwise\nvariation in effective thrust\nrecovery and a 20 spanwise variation in effective\nthrust turning ."}, {"doc_id": 1065, "text": "a free-flight investigation of ablation of a blunt\nbody to a mach number of 13 .1.\n a five-stage rocket-propelled\nresearch-vehicle system was flown to a maximum\nmach number of 13.1 at an altitude of\napproximately 78,000 feet to determine\nablation characteristics of teflon in free\nflight . continuous in-flight\nmeasurements were made using sensors developed by\nthe national aeronautics and space\nadministration . the sensors were located\non the blunted face of a nose cone\nconstructed from teflon, with one at the stagnation\npoint and two others at a surface\ndistance of 0.62 radius on opposite sides of the\nstagnation point . the\nablated-length measurements were in close agreement with\nanalytical predictions . the\nanalytical predictions, upon inclusion of the\npertinent material property values,\nshould be applicable to other materials as well\nas teflon ."}, {"doc_id": 1066, "text": "wind tunnel measurements of aerodynamic damping derivatives\nof a launch vehicle vibrating in free-free bending\nmodes at mach numbers from 0. 70 to 2. 87 and comparisons\nwith theory .\n the aerodynamic damping of a\nflexibly mounted aeroelastic model\nwith a blunted conical nose and a\ncylindrical afterbody was measured at\nmach numbers from 0.70 to 1.20 at\nseveral levels of dynamic pressure\nand two weight conditions and at\nmach numbers from 1.76 to 2.87 at one\nweight condition . the first two\nfree-free flexible modes of vibration\nwere investigated . also investigated\nat mach numbers from 0.9 to 1.2\nwas the aerodynamic damping in the\nfirst free-free modes of a model\nwhich had a /hammerhead/ nose (the\nbase diameter of the blunted cone\nwas greater than the diameter of the\nafterbody which necessitated a\nreflex angle downstream from the cone\nbase) .\n two basically different methods,\nthe /electrical power-input/ and\nthe /decaying oscillations/ methods were\nused to determine the damping\nand frequencies . the experimentally\ndetermined values are compared with\nsome applicable theories . the results\nof the investigation indicate\nthat the aerodynamic damping in the\nelastic modes of vibration was small\nfor all configurations tested . the\nmaximum aerodynamic damping measured\nin the first mode was on the order of\ndamping . the aerodynamic damping was\nfound to be even less for vibration\nmodes higher than the first .\nreduced-frequency effects were found to be\nnegligible for the range investigated .\nagreement of calculated\naerodynamic damping derivatives with the\nexperimental results was not good .\ngenerally, the experimentally determined\nderivatives were larger than\nthose predicted by the various theories\nused . the bond-packard theory\nappeared to give the best agreement for\nthe first free-free vibration\nmode but gave the worst agreement for the\nsecond mode . measurements\nmade on the configuration that had a\nhammerhead nose indicated small\nnegative aerodynamic damping in the mach\nnumber range from 0.95 to 1.00 .\naerodynamic stiffness effects were found\nto be small and within the\nexperimental scatter . (wind-on frequency\ndetermination was accurate\nonly to approximately 1 percent .)"}, {"doc_id": 1067, "text": "plastic stability theory of geometrically orthotropic\nplates and cylindrical shells .\n a linear eighth-order equilibrium differential equation for\nplastic buckling of geometrically orthotropic thin cylindrical\nshells is derived . this equation is used to obtain explicit\nsolutions for long flat plates and wide columns under axial\ncompression and moderate-length cylinders under external pressure,\ntorsion, and axial compression ."}, {"doc_id": 1068, "text": "instability analysis of cylindrical shells under hydrostatic\npressure .\n to determine the elastic buckling\npressure of simply supported\ncylindrical shells subjected to lateral\nand axial hydrostatic forces,\nvarious versions of linear bending\ntheories have been employed in the\npast . for certain shell dimensions,\nhowever, the expressions commonly\nused may yield substantially differing\nresults . in what follows,\nrecent work on this problem by\na. e. armenakas and the writer is\nbriefly reviewed . this work consisted\nprimarily in employing a general\nbending theory of circular cylindrical\nshells under the influence of\ninitial stress, developed earlier by\nthe same authors, to re-examine\nthe problem mentioned, and compare the\nresults with those of previous\ninvestigations . the outcome was the\nestablishment of a simple but\naccurate expression for the buckling\npressure applicable to a wide\nrange of shell dimensions ."}, {"doc_id": 1069, "text": "design and testing of honeycomb sandwich cylinders\nunder axial compression .\n experimental results for 36 diameter honeycomb cylinders\nfabricated with thin (0.010) aluminum faces and cores prove that it is\nquite feasible to stabilize thin faces so they can be loaded beyond\nthe yield point . the effect of initial imperfections and the various\nmodes of failure are discussed ."}, {"doc_id": 1070, "text": "buckling of orthotropic and stiffened conical shells .\n donnell type stability equations for thin circular orthotropic\nconical shells are presented and solved for external pressure, axial\ncompression and combined loading . the solution is likewise applied\nto stiffened conical shells . correlation with equivalent cylindrical\nshells yields a simple approximate stability analysis for orthotropic\nor ring-stiffened conical shells under hydrostatic pressure . the\ngeneral instability of stiffened conical shells under hydrostatic\npressure is also analysed by a more accurate approach . preliminary\nexperimental results for buckling of ring-stiffened conical shells\nunder hydrostatic pressure are presented and discussed ."}, {"doc_id": 1071, "text": "stability of thin torispherical shells under uniform\ninternal pressure .\n the stability of the toroidal portion of a torispherical shell\nunder internal pressure is considered from the point of view of the\nlinear buckling theory . a detailed stress analysis of the prebuckled\nshell is made employing asymptotic integration . the change in\npotential energy of the shell is then minimized using a rayleigh-ritz\nprocedure for actual computation of the critical pressure . numerical\nresults reveal that elastic buckling may occur for very thin shells\nwhose material has a relatively high value of the ratio of yield stress\nto elastic modulus ."}, {"doc_id": 1072, "text": "ignition and combustion in a laminar mixing zone .\n the analytic investigation of laminar combustion\nprocesses which are essentially two- or three-dimensional\npresent some mathematical difficulties . there are,\nhowever, several examples of two-dimensional flame\npropagation which involve transverse velocities that are small in\ncomparison with that in the principal direction of flow .\nsuch examples occur in the problem of flame quenching\nby a cool surface, flame stabilization on a heated flat plate,\ncombustion in laminar mixing zones, etc . in these cases\nthe problem may be simplified by employing what is\nknown in fluid mechanics as the boundary-layer\napproximation, since it was applied first by prandtl in his\ntreatment of the viscous flow over a flat plate . physically it\nconsists in recognizing that if the transverse velocity is\nsmall, the variations of flow properties along the direction\nof main flow are small in comparison with those in a\ndirection normal to the main flow . the analytic\ndescription of the problem simplifies accordingly . the present\nanalysis considers the ignition and combustion in the\nlaminar mixing zone between two parallel moving gas\nstreams . one stream consists of a cool combustible\nmixture, the second is hot combustion products . the two\nstreams come into contact at a given point and a laminar\nmixing process follows in which the velocity distribution is\nmodified by viscosity, and the temperature and\ncomposition distributions by conduction, diffusion, and chemical\nreaction . the decomposition of the combustible stream\nis assumed to follow first-order reaction kinetics with\ntemperature dependence according to the arrhenius law .\nfor a given initial velocity, composition, and temperature\ndistribution, the questions to be answered are .. (1) does\nthe combustible material ignite,. and (2) how far\ndownstream of the initial contact point does the flame appear\nand what is the detailed process of development . since\nthe hot stream is of infinite extent, it is found that ignition\nalways takes place at some point of the stream . however,\nwhen the temperature of the hot stream drops below a\ncertain value, the distance required for ignition increases\nso enormously that it essentially does not occur in a\nphysical apparatus of finite dimension . the complete\ndevelopment of the laminar flame front is computed using\nan approximation similar to the integral technique\nintroduced by von karman into boundary layer theory ."}, {"doc_id": 1073, "text": "a practical method for numerical evaluation of solutions\nof partial differential equations of the heat-conduction\ntype .\n three approximate methods for the solution of the\nnonlinear equation of heat flow in a medium where heat is\nbeing generated by a chemical reaction are compared . the\nequations are where\nsubscripts indicate partial differentiations and q, k, a are"}, {"doc_id": 1074, "text": "theoretical and experimental investigation of second-order supersonic\nwing-body interference .\napproximate second-order solutions for the supersonic flow around\nwing-body combinations are calculated, using two different theoretical models\nsmall and the wing sweep small in comparison with that of the mach cone\nare considered . the analysis is restricted to such high mach numbers\nthat m-2 1, and an approximate formula common to the two models is then\nfound for the second-order interference term . this formula can also be\nused to correct experimental pressure distributions for the effect of\nnonuniformities in the wind-tunnel flow .\nin order to test the theory, wind-tunnel experiments on non-lifting\ncone-cylinder bodies in combination with wings of simple shapes were\nperformed . pressure distributions were measured at m 3 and m 4, both\naround the bodies and on the wings separately, as well as in\ncombination, and it was found that the second-order interference was\npredicted reasonably well by the simplified theory ."}, {"doc_id": 1075, "text": "an experimental and theoretical investigation of second-order supersonic\n wing-body interference, for a non-lifting body with wings at incidence .\npressure distributions on the wing of two wing-body combinations are\nmeasured experimentally at mach numbers 3 and 4 with the wing at various\n incidences in the range 0degree to 10degree . the results are compared\nwith theoretical results which include interference effects calculated\naccording to the second-order supersonic wing-body interference theory\ndue to landahl and beane /1/ . this theory, having been tested\npreviously for non-lifting wing-body combinations, is thus tested also for\nwings at incidence . the agreement between theory and experiment is\nfound to vary with mach number and wing sweepback . for the higher mach\nnumber and moderate sweepback the theory gives a good prediction of\npressure distribution, but for the most adverse condition of low mach\nnumber and large sweepback the theory is found to overestimate the\ninterference effects . this is expected as the theory assumes the\nsweepback of the wings is small compared with that of the mach line . an\n empirical guide to the limit of application of the interference theory\nis given . within this limit the agreement between theory and experiment\n is found to deteriorate only a little with increase of incidence, over\nthe range tested ."}, {"doc_id": 1076, "text": "an approximate method for determining the displacement effects and\nviscous drag of laminar boundary layers in two-dimensional hypersonic\nflow .\na simplified approximate theory is presented by means of which the\nlaminar boundary layer over an insulated two-dimensional surface may be\ncalculated, a linear velocity profile being assumed, and an estimate\nmade of its effect in changing the pressure distribution over the\nprofile upon which the boundary layer is formed . skin friction is also\ndetermined . comparisons of results from this theory are made with\nexperimental results at a mach number of 6.86 and a reynolds number of"}, {"doc_id": 1077, "text": "a method of solution with tabulated results for the attached oblique\nshock wave system for surfaces at various angles of attack, sweep, and\ndihedral in an equilibrium real gas including the atmosphere .\na new method is derived for solving the attached oblique shock-wave\nsystem for surfaces at various angles of attack, sweep, and dihedral in\nany real gas in equilibrium . results are tabulated for the following\nranges .. angle of attack, 0degree to 65degree,. angle of sweep, 0degree\n to 75degree,. angle of dihedral, 0degree to 30degree,. mach number, 3\nto 30,. and /effective specific-heat ratio/ parameter, 1.10 to 1.67 .\nboth the method and tabulated solutions are easily adaptable to flight\nin any gas or in the atmosphere of any planet . an illustrative example\nis presented based on the ardc 1956 model atmosphere ."}, {"doc_id": 1078, "text": "the steady flow of a viscous fluid past a circular cylinder at reynolds\nnumbers 40 and 44 .\nthis paper describes the numerical solution of the complete\nnavier-stokes equations for the steady flow of an incompressible viscous fluid\nof unlimited extent past a circular cylinder at reynolds number 40 . a\nnew device developed for the numerical solution is described . the\nresults of the investigation are ..\ngood agreement with experimental results .\nhigher reynolds numbers even though they may not exist in nature . a\nsolution has been obtained at reynolds number 44 but it has not been\ncarried to the same accuracy as the solution at reynolds number 40 .\nportion of the cylinder continues to increase with reynolds number in\nsuch steady-state solutions up to a reynolds number 44 and no indication\n has been found that this process will not continue as the reynolds\nnumber is increased beyond 44 ."}, {"doc_id": 1079, "text": "finite difference formulae for the square lattices .\n the paper gives approximate formulae\nfor derivatives (including combinations\nlike and ), and integrals, of a function\nof two independent variables, in terms\nof its values at nodes of a square lattice,\nprimarily for use in the numerical solution\nof partial differential equations . consideration\nis given to the form, as well as to\nthe magnitude, of the leading terms in the\nerror, and what is believed to be for\nmost purposes optimum combinations are\nthus selected for the simpler compact\nsets of nodes ."}, {"doc_id": 1080, "text": "viscous flow round a sphere at low reynolds numbers . /l40/ .\nrelaxation methods are outlined, and the present problem formulated in\nmodified spherical polar co-ordinates . the results of calculations made\n for r 5, 10, 20, 40 are presented in the form of stream function and\nvorticity distributions,. and further results of pressure distributions,\n velocity distributions, and drag coefficients, calculated from them .\nthese results are shown to compare favourably with experimental work,\nshowing a steady trend from symmetrical stokes's flow, towards boundary\nlayer flow . the phenomenon of separation of the forward flow and\ndevelopment of a circulating wake, is explained and illustrated, the first\nformation of a wake being at r 17 ."}, {"doc_id": 1081, "text": "numerical solution of the navier-stokes equations for the flow around a\ncircular cylinder at reynolds number 40 .\nthe steady two-dimensional flow around a circular cylinder submerged in\na viscous fluid for the case r 40 is investigated, integrating\nnumerically the exact navier-stokes equations . the main results are as\nfollows . /i/ the steady flow solution exists even for the reynolds\nnumber as high as 40 . moreover, it seems that the solution goes over\nsmoothly to the solution of the kirchhoff discontinuous flow theory\nwhich seems to be the limiting flow for the case r . /ii/ the flow\npattern and the coefficients of pressure and drag are in good agreement\nwith the experimental data ."}, {"doc_id": 1082, "text": "the flow past pitot tube at low reynolds numbers, part 1-dash the\nnumerical solution of the navier-stokes equations for steady viscous\naxisymmetric flow, part 2-dash the effects of viscosity and orifice\nsize on a pitot tube at low reynolds numbers .\nin this report numerical methods used to solve the navier-stokes\nequations for steady viscous two-dimensional flow are extended to include\nthe case of axial symmetry . the equations and their finite difference\napproximations are derived working in cylindrical polar co-ordinates\nwith the stokes' stream function and the vorticity as variables . a new\nmethod of dealing with the boundary conditions is given .\nthe effects of viscosity and orlfice size on a blunt-nosed pitot tube\nhave been theoretically investigated up to a reynolds number of ten,\nwhere the reynolds number has been based on the radius of the tube .\nresults are expressed in terms of a pressure coefficient where p is the\npressure measured in the tube, p the density of the fluid, and p and u\nthe static pressure and velocity in an undisturbed flow at the position\nof the tube .\nthe values of c for a blunt-nosed tube are found to be less than those\nfor tubes with hemispheroidal heads, but always greater than unity in\nthe range considered . the effect of the orifice size is to decrease c\nas the orifice size increases, this decrease is very small but increases\n with the reynolds number . at a reynolds number of ten the decrease is\nat most five per cent of the value of c when there is no orifice .\nit is suggested that the decrease of c below unity found in some\nexperimental investigations at a higher reynolds number could be due to the\neffects of orifice size ."}, {"doc_id": 1083, "text": "an investigation of fluid flow in two dimensions .\nflow of an inviscid fluid . -dash there are in existence several methods\n of obtaining numerical solutions to the two-dimensional flow of a\nperfect fluid for given boundary conditions . part 2 of the present paper\ngives a method of obtaining a numerical solution for viscous steady flow\nsolution of the simpler problem, illustrating it with examples bearing\non the experimental work described in part iv ."}, {"doc_id": 1084, "text": "the flow past circular cylinders at low speeds .\nthis paper deals chiefly with calculations and experiments on the flow\npast circular cylinders, but the arithmetical methods of solution of the\n equations of steady viscous flow proposed and used in section i, are\napplicable to other equations and may be of interest ."}, {"doc_id": 1085, "text": "note on the convergence of numerical solutions of the navier-stokes\nequations .\na criterion is given for the convergence of numerical solutions of the\nnavier-stokes equations in two dimensions under steady conditions . the\ncriterion applies to all cases of steady viscous flow in two dimensions\nand shows that if the local 'mesh reynolds number', based on the size of\n the mesh used in the solution, exceeds a certain fixed value, the\nnumerical solution will not converge ."}, {"doc_id": 1086, "text": "a note on the numerical solution of fourth order differential\nequations .\n an old numerical method\nof solving fourth order differential equations\nis put in relaxation form . the higher\norder correction terms are included and the\ntechnique is illustrated by an example .\nthe method has the advantage of being more\nrapidly convergent than the usual relaxation\nprocedure for fourth order equations .\nsome comments are made on the numerical\nsolution of the viscous flow equation ."}, {"doc_id": 1087, "text": "convergence rates of iterative treatments of partial differential\nequations .\nthe development of high-speed digital computers has made feasible the\nnumerical solution by iterative methods of some partial differential\nequations . the convergence rates of several such iterative methods are\nestimated here . it is found that with the familiar elementary iterative\n methods some quite simple problems require prohibitive computational\nlabor .\nthe iterative methods here considered are related to the various forms\nof the southwell /relaxation method/ in that they involve successively\napplied local corrections to improve an approximate solution . however,\nthese iterative methods are routinized in conformity with the\nrequirements of automatic computers while the relaxation method is flexible and\n depends in an essential way on the skill of its practitioners ."}, {"doc_id": 1088, "text": "iterative methods for solving partial difference equations of elliptic\ntype .\nthis paper considers linear systems /1/ where a includes matrices of a\nsort frequently occurring in the solution of elliptic partial\ndifferential equations by difference methods /in particular, a o/ . rewriting\n superscript is number of iteration cycle/ are used to compute u\nwhen u are used . also, one may /over-relax/ ..\nser. a. 210, 307-357 /1910/ who suggested changing from time to time\nto speed up convergence . in the present paper over-relaxation /with\nfixed w/ is combined with immediate introduction of newly-computed u's,\na la gauss-seidel . various theorems on convergence are proved$. in\nparticular, it is shown that there exists an ordering of the equations\nand an optimum value wb such that in general /3/ converges much more\nrapidly than the gauss-seidel method /w 1/ . means are suggested for\nestimating wb,. the sensitivity of the rate of convergence to the choice\n of w is studied . the paper concludes with a theoretical comparison of\ngauss-seidel and the method proposed, /successive over-relaxation/, for\nsolving dirichlet's difference problem over a square using a high-speed\ncomputing machine ."}, {"doc_id": 1089, "text": "aerodynamic characteristics of propeller-driven vtol\naircraft .\n this paper discusses the two major configurations that are usually\nconsidered for achieving vtol while keeping the fuselage essentially\nhorizontal - that is, the tilt-wing and the deflected-slipstream\nconfigurations .\n because of the high turning losses incurred by deflected-slipstream\nconfigurations in hovering and because of the wing-stalling problem of\nthe pure tilt-wing configurations during the transition, it appears that\na combination of the two principles should be used . this tilt-wing and\nflap configuration should make use of a programed extensible-chord\nslotted flap together with a leading-edge high-lift device in order to\navoid the performance and handling qualities problems associated with\nwing stalling during the transition while keeping the wing area as low\nas possible for efficiency in cruising flight ."}, {"doc_id": 1090, "text": "pressure distribution and force measurements on a vtol\ntilting wing-propeller model . pt .ii, analysis of\nresults .\n this report presents in graphical\nform the results presented in\nreference 1 from pressure distribution and force\nmeasurements on a half-wing model\nof a twin-engined tilt-wing vtol configuration .\nthe profound influence of the\nslipstream on these results is discussed in some\ndetail ."}, {"doc_id": 1091, "text": "data from a static thrust investigation of a large\nscale general research vtol-stol model in ground effect .\n the model was tested at two different elevations with the wing\npivot at 1.008 and 2.425 propeller diameters above the ground . the\nslipstream of the propellers was deflected by tilting the wing and\npropellers, by deflections of large-chord trailing-edge flaps, and by\ncombinations of flap deflection and wing tilt . tests were conducted over\na range of propeller disk loadings from 7.41 to 29.70 pounds per square\nfoot . force data for the complete model and pressure distributions for\nthe wing and flaps behind one propeller were recorded and are presented\nin tabular form without analysis ."}, {"doc_id": 1092, "text": "wing-nacelle-propeller interference for wings of various\nspans . force and pressure distribution tests .\n an experimental investigation was made in the\nn. a. c. a. full-scale wind tunnel to determine the effect\nof wing span on nacelle-propeller characteristics and,\nreciprocally, the lateral extent of nacelle and propeller\ninfluence on a monoplane wing . the results provide a\ncheck on the validity of the previous research on nacelles\nand propellers with 15-foot-span wings tested in the\n the scale propeller and the n. a. c. a. cowling\nused in the former researches were tested in three typical\ntractor locations with respect to a thick wing of 5-foot\nchord and 30-foot span . the span was progressively\nreduced to 25,20, and 15 feet and the same characteristics\nwere measured in each case .\n the efficiency factors--propulsive efficiency, nacelle\ndrag efficiency, and net efficiency--were obtained for each\nwing length by means of force tests and the values are\ncompared to determine the effect of span .\npressure-distribution measurements show the lateral extent of the\nnacelle interference and the propeller-slipstream effect\non the span loading for the various conditions . complete\npolar curves and curves showing the variation of nacelle\ndrag with lift coefficient are also included .\n force and pressure-distribution tests concur in\nindicating that, for engineering purposes, the influence of a\nnacelle and of a propeller, in a usual combination, may\nbe considered to extend laterally on a wing the same\nmaximum distance, or about five nacelle diameters or two\npropeller diameters outboard of their common axes . all\nimportant effects of scale nacelle-propeller\ncombinations may be measured within practical limits of accuracy\nby tests of a 15-foot-span wing ."}, {"doc_id": 1093, "text": "induced interference effects on jet and buried-fan\nvtol configurations in transition .\n recent investigations of some jet and buried-fan configurations\nhave indicated that in the transition speed range, configurations with\nconsiderable area surrounding the jet or buried fan can encounter large\nlosses in lift and nose-up pitching moments due to the pressures induced\non the lower surfaces by the interaction of the jet and free-stream\nflow . the obvious way of minimizing these effects is to reduce the\nsurface area surrounding the jets or buried fans, that is, to consider\nthese effects in the preliminary stages of the airplane design ."}, {"doc_id": 1094, "text": "investigation of the effects of ground proximity and\npropeller position on the effectiveness of a wing with\nlarge chord slotted flaps in redirecting propeller\nslipstream downward for vertical take-off .\n an investigation of the effects\nof ground proximity and propeller\nposition on the effectiveness of a\nwing equipped with large-chord slotted\nflaps in redirecting the slipstreams\nfrom large-diameter propellers\ndownward for vertical take-off has been\nconducted in a static-thrust\nfacility at the langley aeronautical\nlaboratory .\n the results indicate that, with\nthe propeller thrust axis on the\nwing chord plane, both the angle through\nwhich the slipstream is\ndeflected and the ratio of resultant force\nto thrust are reduced as the ground\nis approached . at positions nearest\nthe ground some of the loss in\nresultant force is regained . lowering\nthe thrust axis below the wing\nchord plane reduces the adverse effects\nof the ground and also reduces\nthe large diving moments associated with\nthe slotted-flap arrangement .\nthe static-thrust efficiency of the\npropellers is slightly reduced by\nthe ground effect ."}, {"doc_id": 1095, "text": "investigation of effectiveness of large-chord slotted\nflaps in deflecting propeller slipstreams downward\nfor vertical take-off and low-speed flight .\n an investigation of the effectiveness\nof a wing equipped with\nlarge-chord slotted flaps in rotating the\nthrust vector of propellers through\nthe angles required for vertical\ntake-off and for flight at very low speeds\nhas been conducted in the facilities\nof the langley 300 mph 7- by 10-foot\ntunnel .\n under conditions of static thrust\nand with zero incidence between the\nthrust axis and the wing chord plane,\nthe slotted flaps were effective in\nrotating the thrust vector upward about\nthan 10 percent of the thrust . when an\nauxiliary vane was added above the\nwing, the thrust vector was rotated upward\nconfiguration, vertical take-off\ncould be achieved with an initial attitude\nof 16 and at airplane weights\nup to 90 percent of the total propeller\nthrust . the addition of 10\nincidence between the thrust axis and the wing\nincreased the upward rotation\nof the thrust vector about 10 . for the\nsame turning angle, the diving\nmoments associated with the slotted-flap\nconfigurations were approximately\ntwice as large as the diving moments of\nthe configurations with plain\nflaps and two auxiliary vanes ."}, {"doc_id": 1096, "text": "qualitative measurements of the effective heats of\nablation of several materials in supersonic air jets\nat stagnation temperature up to 11,000 f.\n the effective heats of ablation of a number of materials were\nderived from tests in supersonic air jets at stagnation temperatures\nranging from 2,000 f to 11,000 f . the materials included the plastics\nteflon, nylon, lucite, and polystyrene,. the inorganic salts ammonium\nchloride and sodium carbonate, several phenolic resins of varied resin\ncontent and type of reinforcement,. and a melamine-fiber glass\nlaminate ."}, {"doc_id": 1097, "text": "experimental ablation cooling .\n this paper presents the results\nof an experimental investigation on\nthe ablation of a number of promising\nmaterials for heating conditions\ncomparable to those which may be\nencountered by unmanned reentry\nsatellite vehicles, as well as for higher\nheating conditions comparable to\nthose associated with reentry ballistic\nmissiles . materials tested\nincluded the plastics teflon, nylon,\nand lucite,. the inorganic salts\nammonium chloride and sodium carbonate,.\ngraphite,. a phenolic resin and\nfiber glass composition,. and the\ncommercial material haveg rocketon .\nresults of these tests indicated\nheat-absorption capabilities which are\nseveral times greater than those of\ncurrent metallic heat-sink materials .\nthe results with teflon showed that\nfor hemispherical noses there was no\napparent effect of size or\nstagnation-point pressure on ablation rate\nfor the range of variables covered in\nthe tests . for flat-faced\nconfigurations, however, there was a definite\nincrease in the ablation rate with\nincreased stagnation-point pressure .\nthe results for the several\nmaterials tested at heating rates\nassociated with reentry ballistic\nmissiles showed considerable increase\nin the effective heats of ablation\nover the results obtained at lower\nheating rates . this trend of\nincreased effectiveness with increased\nheating potential is in\nagreement with the predictions of ablation\ntheories . comparisons of the\nresults for several materials tested\nat the higher heating rates showed\ngraphite to have the lowest ablation\nrate of all materials tested ."}, {"doc_id": 1098, "text": "an experimental investigation of ablating material\nat low and high enthalpy potentials .\n the ablation performance characteristics\nof a number of materials\nwere derived from tests conducted in\na mach number 2.0 ethylene-heated\nhigh-temperature air jet having a\nmaximum stagnation enthalpy potential\nof approximately 1,200 btu lb . the\ntests were conducted with 6-\ninch-diameter blunt nose shapes . the\nsurface of most of the materials after\ntesting was generally smooth and the\nunablated portions of the specimens\nwere in appearance the same as before\ntesting . in all cases, the back\nor inside surface of the specimens\nexhibited no evidence of heating .\n an evaluation of the enthalpy\npotential effect was obtained by\ncomparison of the present data with\nprevious tests conducted, on the\nin a subsonic arc-heated air\njet . the stagnation enthalpy potential\nof this facility was\napproximately 7,000 btu lb . for teflon, the\neffective heat of ablation increased\nfrom approximately 1,250 btu lb to\nenthalpy potential was increased from"}, {"doc_id": 1099, "text": "a theoretical study of stagnation point ablation .\na simplified analysis is made of the shielding mechanism which reduces\nthe stagnation-point heat transfer when ablation takes place at the\nsurface . the most significant result of the analysis is that the\neffective heat capacity of the ablation material increases linearly with\n stream enthalpy . the automatic shielding mechanism is discussed and\nthe significant thermal properties of a good ablation material are given\nparameters ."}, {"doc_id": 1100, "text": "an analytical investigation of ablation .\nan analytical procedure is described which enables the derivation of\neffective heat of ablation relationships for any type of boundary layer\nfrom transpiration cooling results . the procedure enables the inclusion\n of such effects as the ratio of wall temperature to local stream\ntemperature, surface radiation, and surface combustion .\nthe predicted effective heats of ablation for a three-dimensional\nlaminar stagnation boundary layer for teflon material were in agreement\nwith those derived from tests conducted at boundary-layer enthalpy\npotentials of 800 and approximately 7,000 btu/lb .\nthe predicted equilibrium surface temperatures on nonablating surfaces\nbehind an ablating material were in agreement with the values derived\nfrom tests conducted with inconel cylinders having teflon hemispherical\nnose pieces ."}, {"doc_id": 1101, "text": "a sensor for obtaining ablation rates .\na variable-capacitance ablation-rate sensor which allows continuous\nmeasurements of ablation rates for teflon and similar polymers has been\ndeveloped and tested in an ethylene-heated high-temperature jet at\nstagnation temperatures ranging from 2,400degree to 3,800degree f .\nthe data /length changes/ were measured by using the same telemeter\nequipment as that used in rocket-propelled flight vehicles . test\nresults indicate measurement error to be a maximum of 4 percent between\nthe telemetered length changes and the length changes that were obtained\n from photographic records of the test ."}, {"doc_id": 1102, "text": "a five-stage solid fuel sounding rocket system .\na five-stage solid-fuel sounding-rocket system which can boost a payload\n of 25 pounds to an altitude of 525 nautical miles and that of 100\npounds to 300 nautical miles is described . data obtained from a typical\n flight test of the system are discussed ."}, {"doc_id": 1103, "text": "pressures, densities and temperatures in the upper atmosphere .\naveraged and internally consistent values of atmospheric pressure,\ndensity, and temperature from the ground to an altitude of 219 km have\nbeen determined and compiled by the united states groups active in\nupper-atmospheric research by rockets . additional relevant data by\nsimilar groups engaged in research on meteors and on the anomalous\npropagation of sound are also included, particularly in a brief discussion\nof variations with time and with place of these three atmospheric\nparameters ."}, {"doc_id": 1104, "text": "aerodynamic heating of blunt nose shapes at mach numbers up to 14 .\nresults are presented from recent investigations of the aerodynamic\nheating rates of blunt nose shapes at mach numbers up to 14 . data\nobtained in flight and wind-tunnel tests have shown that the flat-faced\ncylinder has about 50 percent the stagnation-point heating rates of the\nhemisphere over nearly the entire mach number range . tests made at a\nmach number of 2 on a series of bodies made up of hemispherical segments\n of varying radius of curvature showed that slight amounts of curvature\ncan decrease the local rates at the edge of the flat-faced cylinders\nwith only a slight increase in the stagnation rate . the total heat\ntransfer to such slightly curved bodies is also somewhat smaller than\nthe total heat transfer to flat-faced cylinders .\ncomparison of several tests with theoretical heating-rate distributions\nshowed that both laminar and turbulent local rates can be predicted by\navailable theories /given the pressure distribution about the body/\nreasonably well, although the scatter of the available data still leaves\n open the choice between the theories at the edge of the bodies, where\nthey usually differ .\ntests on a flat-faced cylinder at a mach number of 2.49 and at angles\nof attack up to 15degree showed the movement of the apparent stagnation\npoint from the center of the body to the 50 percent windward station at\ncreased about 30 percent while that near the leeward edge decreased\nabout 20 percent at 15degree angle of attack .\npreliminary results on a concave nose have indicated the possibility\nthat this type of design may be developed to give heating rates\nsignificantly lower than even the flat-faced cylinder rates . the test results\n have also shown, however, the existence of an unsteady flow phenomenon\nwhich can increase the heating rates to extremely high values ."}, {"doc_id": 1105, "text": "numerical solutions for supersonic flow of an ideal\ngas around blunt two-dimensional bodies .\n the method described is an inverse one,. the shock shape is chosen\nand the solution proceeds downstream to a body . bodies blunter than\ncircular cylinders are readily accessible, and any adiabatic index can\nbe chosen . the lower limit to the free-stream mach number available in\nany case is determined by the extent of the subsonic field, which in\nturn depends upon the body shape . some discussion of the stability of\nthe numerical processes is given . a set of solutions for flows about\ncircular cylinders at several mach numbers and several values of the\nadiabatic index is included ."}, {"doc_id": 1106, "text": "free-flight observation of a separated turbulent flow\nincluding heat transfer up to mach 8. 5.\n a turbulent boundary layer separated\nby a forward-facing step was\nobserved on the cylindrical portion\nof a hemisphere-cone-cylinder test\nvehicle . tip blunting, producing a\nshear flow, was found to induce\nhigher pressures on the cylindrical\nportion than were predicted from\nballistic tunnel data of unblunted projectiles .\nan approximate method for\npredicting this blunt-body pressure\ndistribution was hypothesized . these\nfindings, along with the hypothesis,\nwere substantiated by a wind tunnel\ntest of a similar body . the peak pressure\nratios of the separation were\nsmaller in magnitude than flat plate\ntheory predicted because of the\neffect of the shear flow . the decrement\nin heating of the separated\nflow, relative to the corresponding\nattached flow, was found to compare\nwell with the expected results ."}, {"doc_id": 1107, "text": "the flow field over blunted flat plates and its effect\non turbulent boundary growth and heat transfer at a\nmach number of 4. 7.\n surface pressures, impact and\nstatic pressure distributions in the\nflow field over the plate, and local\nheating rates were measured on a\nflat plate with various leading-edge\ndiameters . the tests were conducted\nat a mach number of 4.7 and a\nfree-stream reynolds number of 3.8x10 per\nfoot .\n it was found that the shape of\nthe shock wave indicated the existence\nof an outward deflection of the flow\nover the plate . the flow deflection\ncaused an outward deflection of the\nshock-wave asymptote of approximately\nthe shock-wave angle calculated\nincluding boundary-layer growth . the\nmach number distributions in the\nshear layer evaluated from pitot and\nstatic pressure surveys agreed with\npredictions based on shock-wave shape .\nthe predicted turbulent\nheat-transfer coefficients for the blunted\nflat plates agreed with the\nmeasured heat-transfer coefficients . a\ncomparison between the measured\nheat-transfer coefficients for the blunted\nflat plates and the calculated\ncoefficients for a sharp leading-edged\nplate indicated that the\ncoefficients were highest near the leading\nedge of the most blunted plate . the\nmeasured heat-transfer coefficients\ndropped to approximately 80 percent\nof the sharp-plate values at a\nconsiderable distance from the leading\nedge for all of the blunted flat plates ."}, {"doc_id": 1108, "text": "a study of second-order supersonic flow theory .\n an attempt is made to develop a second approximation to the\nsolution of problems of supersonic flow which can be solved by\nexisting first-order theory . the method of attack adopted is an\niteration process using the linearized solution as the first step .\n for plane flow it is found that a particular integral of the\niteration equation can be written down at once in terms of the\nfirst-order solution . the second-order problem is thereby\nreduced to an equivalent first-order problem and can be readily\nsolved . at the surface of an isolated body, the solution reduces\nto the well-known result of busemann . the plane case is\nconsidered in some detail insofar as it gives insight into the\nnature of the iteration process .\n again, for axially symmetric flow the problem is reduced to a\nfirst-order problem by the discovery of a particular integral .\nfor smooth bodies, the second-order solution can then be\ncalculated by the method of von karman and moore . bodies\nwith corners are also treated by a slight modification of the\nmethod . the second-order solution for cones represents a\nconsiderable improvement over the linearized result .\nsecond-order theory also agrees well with several solutions for other\nbodies of revolution calculated by the numerical method of\ncharacteristics .\n for full three-dimensional flow, only a partial particular\nintegral has been found . as an example of a more general\nproblem, the solution is derived for an inclined cone . the\npossibility of treating other inclined bodies of revolution and\nthree-dimensional wings is discussed briefly ."}, {"doc_id": 1109, "text": "unsteady laminar compressible boundary layers on an\ninfinite plate with suction or injection .\n this study deals with unsteady compressible laminar\nboundary layers on an infinitely extended porous plate . an integral\nsolution based on two types of assumed velocity and\ntemperature profiles is presented for the general case where the unsteady\nfree-stream velocity and rate of surface suction or injection are\nboth arbitrary . also indicated is an exact solution, applicable,\nhowever, only to certain specific unsteady free-stream and\nsurface suction or injection variations . the reliability and range\nof validity of the integral solutions is then established on the\nbasis of numerical results from the exact solution . finally,\nseveral general qualitative conclusions of the unsteady effects\nof free-stream velocity and surface suction or injection on laminar\nboundary-layer behavior are made ."}, {"doc_id": 1110, "text": "on supersonic flow past a slightly yawing cone .\n this paper is concerned\nwith the motion of a circular cone, of\nnot too blunt an angle, through air at high\nspeed . if the direction of motion of\nthe cone coincides with its axis of symmetry,\nthe resulting air flow is well known .\nhere we consider the perturbation produced\nby a small /yaw/--i.e., the case in\nwhich the cone is moving not quite in the\ndirection of its axis . the results are\nconfirmed experimentally, and have applications\nto ballistics, though we are not\nconcerned with the latter here,. they may\nalso be useful as providing a check on\nvarious approximate methods of wider\napplicability . the square of the yaw is\nneglected--an approximation of which the\nvalidity is discussed . (similar\nmethods can be applied to the second-order effects\nof the yaw, which are also of ballistic\nsignificance,. but the computations have not\nyet been completed .) it should be\nobserved that, because of the lack of symmetry,\nthe flow will be neither\nirrotational nor isentropic ."}, {"doc_id": 1111, "text": "some research on high speed flutter .\npaper presents brief discussions of many topics currently of interest in\n the flutter field . these include /a/ the sonic speed case, /b/\noscillating pressure field of propellers, /c/ wing flutter with various\nconfigurations including effects of body modes, and /d/ propeller stall\nflutter ."}, {"doc_id": 1112, "text": "unsteady aerodynamic forces on a slender body of revolution\nin supersonic flow .\n linearized slender-body theory\nis applied to the computation of\naerodynamic forces on an oscillating,\nor deforming, body in supersonic\nflow . the undeformed body is a body\nof revolution and the deformed body\nis represented by movement of a line\nthrough the centers of the cross\nsections which are assumed to remain\ncircular . the time dependence is\nbased on sinusoidal motion .\n for a body of vanishing thickness\nthe slender-body theory yields\nthe apparent mass approximation as it\nis obtained for incompressible\ncrossflow around a cylinder .\n both linearized slender-body theory\nand the apparent mass\napproximation are used to calculate the\npitching-moment coefficients on a rigid\nslender body with a parabolic arc nose\ncone, and these coefficients are\ncompared with some experimental results ."}, {"doc_id": 1113, "text": "an electronic apparatus for automatic recording of\nthe logarithmic decrement and frequency for oscillations\nin the audio and subaudio frequency range .\n an electronic apparatus for automatic\nevaluation of the damping of a harmonic\noscillation has been designed and constructed .\nthe apparatus is based on the idea\nof representing the harmonic damped\noscillation by a rotating vector on the screen\nof a cathode-ray tube in such a way, that\nthe rate of decrease of the length of the\nvector is a measure of the damping . the\nresults are obtained simultaneously with\nthe oscillation test as two numbers in\ndecimal digits, which are inversely\nproportional to the logarithmic decrement and\nthe frequency, respectively . the\napparatus, which is named the /dampometer/,\nhas been used for some time for free\noscillation measurements of the dynamic\nstability derivatives of aeroplane models\nin windtunnels, and has proved to be very\nsatisfactory . it gives results of usually\nhigher accuracy than evaluation methods in\ncommon use, and permits a most considerable\nsaving of time ."}, {"doc_id": 1114, "text": "steady and fluctuating pressures at transonic speeds\non two space-vehicle payload shapes .\n steady and fluctuating pressures\nhave been measured at mach numbers\nwhich were varied from 0.6 to 1.2 on\ntwo bodies of revolution typical of\ntwo space-vehicle payload shapes, the\ncentaur and the able v .\n the results of the investigation\nshowed that significant fluctuations\nof pressure occurred on both bodies\nbetween mach numbers of 0.75 and 1.00 .\nthe maximum fluctuations measured at\nany mach number and angle of attack\noccurred in the region of the normal\nshock wave as a result of\nshock-wave motion . large regions of unsteady\npressure also occurred as a result\nof separation on the converging afterbody\nof the able-v model . the maximum\npressure fluctuations occurring on the\nbodies increased with increasing\nangle of attack . for angles other than\nare indicated since pressure fluctuations\nwere larger on the upper half\nof the bodies than on the lower half .\n no definite conclusions could be\ndrawn regarding the form of the\nspectral densities of pressure\nfluctuations in the region of the shock\nwave . the spectral densities in regions\nof separation following the\nshock wave appeared flat except for some\nincrease in energy level below\ndue to slight model motions ."}, {"doc_id": 1115, "text": "measurements of aerodynamic forces for various mean\nangles of attack on an airfoil oscillating in pitch\nand on two finite-span wings oscillating in bending\nwith emphasis on damping in the stall .\n the oscillating air forces on a two-dimensional wing\noscillating in pitch about the midchord have been measured at various\nmean angles of attack and at mach numbers of 0.35 and 0.7 .\nthe magnitudes of normal-force and pitching-moment coefficients\nwere much higher at high angles of attack than at low angles of\nattack for some conditions . large regions of negative damping\nin pitch were found, and it was shown that the effect of increasing\nthe mach number from 0.35 to 0.7 was to decrease the initial\nangle of attack at which negative damping occurred .\n measurements of the aerodynamic damping of a 10-\npercent-thick and of a 3-percent-thick finite-span wing oscillating in\nthe first bending mode indicate no regions of negative damping\nfor this type of motion over the range of variables covered . the\ndamping measured at high angles of attack was generally larger\nthan that at low angles of attack ."}, {"doc_id": 1116, "text": "general instability of stiffened cylinders .\n theoretical buckling stresses\nare determined in explicit form for\ncircular cylinders with\ncircumferential and axial stiffening . the\nloadings are axial compression, radial\npressure, hydrostatic pressure,\nand torsion . analyses were confined\nto moderate-length and long\ncylinders . the investigation was based\nupon the use of a form of donnell's\nequation derived by taylor which is\napplicable to orthotropic cylinders .\nthe derivation of this equation is\npresented in this report ."}, {"doc_id": 1117, "text": "stability of orthotropic cylindrical shells under combined\nloading .\n the increasing use of fiber and whisker\nreinforced materials makes necessary the availability of\nmethods of analyzing cylinders and cones\ncomposed of an orthotropic material . this paper treats\nthe buckling of such shells under a combination\nof axial compression and uniform external pressure .\nthe differential equation approach of flugge is\nused, and the resulting buckling equation is\npresented in terms of axial and circumferential\nbending rigidities, shear rigidity, poisson's ratio,\ngeometry parameters and mode shapes . design\ncurves are presented which allow quick\ndetermination of critical loads on cylinders, and, by using\nthe equivalent cylinder concept, on conical shells\nof small included angle . the curves also lend\nthemselves to /tailoring/ of materials to fit the load\ncarrying requirements of the structure ."}, {"doc_id": 1118, "text": "elastic stability of orthotropic shells .\n a small-deflection theory for general instability of orthotropic\ncircular cylindrical shells has been derived for external pressure,\ntorsion, and axial compression . for the first two types of\nloading, comparison of the theory with experimental data for\northotropic cylinders reveals agreement comparable with that\nobtained for isotropic shells . for axial compression, experimental\ndata have been found to agree reasonably well with theory for\northotropic cylinders, in contrast to the agreement usually\nobtained for isotropic cylinders ."}, {"doc_id": 1119, "text": "plastic stability theory of thin shells .\n considerable interest is currently centered on the\nrole of deformation and flow types of plasticity\ntheories in the solution of stability problems . for\nthin flat plates, deformation theory combined with\nclassical stability theory appears to yield results which\nare in substantially good agreement with test data .\non the other hand, flow or incremental theories appear\nto require the introduction of initial imperfections in\norder to obtain a satisfactory degree of correlation with\ntests .\n thus, in view of the current state of development of\nplastic stability theory, it appears fruitful to exploit\nthe mathematical simplicity inherent in deformation\ntheory in the investigation of the plastic stability of\nthin shells . although there may be theoretical\nobjections to deformation theories as a class, test data on\nflat plates do suggest the predictive value of the results\nobtained from this theory .\n in this paper, a set of equilibrium differential\nequations for the plastic buckling of thin shells of constant\nunequal radii is derived . this set of three equations\napplies to flat plates, cylinders, and spheres under any\nloading system leading to buckling . for particular\nproblems such as buckling of cylinders under axial\ncompression, torsion or lateral pressure, and spheres\nunder external pressure, the set of equations can be\nreduced to a single eighth-order partial differential\nequation of the donnell type in terms of the radial\ndisplacement only . these donnell-type equations are\nused to obtain solutions for plastic buckling of spheres\nunder external pressure and long and moderate length\ncylinders under lateral pressure or torsion loads . the\nlimiting cases of a simply supported flat plate under\ncompression or shear, represent the solutions for short\ncylinders under lateral pressure or torsion, respectively ."}, {"doc_id": 1120, "text": "a unified theory of plastic buckling of columns and\nplates .\n on the basis of modern plasticity considerations, a unified\ntheory of plastic buckling applicable to both columns and plates\nhas been developed . for uniform compression, the theory\nshows that long columns which bend without appreciable\ntwisting require the tangent modulus and that long flanges\nwhich twist without appreciable bending require the secant\nmodulus . structures that both bend and twist when they\nbuckle require a modulus which is a combination of the secant\nmodulus and the tangent modulus ."}, {"doc_id": 1121, "text": "compressive and torsional buckling of thin-wall cylinders\nin the yield region .\n based on assumptions which have\nled to the best agreement between\ntheory and test data on inelastic\nbuckling of flat plates, a general set\nof equilibrium differential equations\nfor the plastic buckling of\ncylinders has been derived . these equations\nhave been used to obtain\nsolutions for the compressive and torsional\nbuckling of long cylinders in\nthe yield region .\n test data are presented which indicate\nsatisfactory agreement with\nthe theoretical plasticity-reduction\nfactors in most cases . where a\ndifference in results exists, test data\nare in substantially better\nagreement with the results obtained by use of\nthe maximum-shear law rather\nthan the octahedral-shear law to transform\naxial stress-strain data to\nshear stress-strain data ."}, {"doc_id": 1122, "text": "on the role of initial imperfections in plastic buckling\nof cylinders under axial compression .\nin a recent paper lee treated the complex problem of the\nplastic buckling and postbuckling behavior of an axially\ncompressed cylindrical shell containing initial imperfections,\nrepresenting an important step forward in our understanding of this\ncommon, yet perplexing, structural element . lee drew two\nmajor conclusions .. (a) even with initial imperfections the\nincremental theory of plasticity considerably overestimates the\nbuckling strength as compared with the deformation theory,\nwhich is in substantially good agreement with experiments, and\nstrength of cylindrical shells subject to axial compression are\nsignificant .\n it is the purpose of this note to discuss the second conclusion\nin terms of lee's experimental and theoretical results, other\nexperimental data on inelastic buckling of 7075-t6\naluminum-alloy cylinders, and recent theoretical results on the inelastic\nbuckling of cylinders in the axisymmetric and circumferential\nmodes . in particular, this writer does not believe that lee has\nproved that initial imperfections are important for the group\nof cylinders that he has tested . on the contrary, it is believed\nthat initial imperfections are completely insignificant for this\ngroup of cylinders although of probable significance in other\ncases ."}, {"doc_id": 1123, "text": "an extension of donnell's equation for a circular cylindrical shell .\nin 1933, donnell succeeded in simplifying the equations of equilibrium\nfor a circular cylindrical shell\nhe obtained simple relations between the critical buckling shearing\nstress and the physical properties of a thin circular cylinder under\npure torsion . his approach reduces the tedious computations involved\nin the classical solutions and is still in good agreement with them .\nfurthermore, it is easy to show that the well-known classical solution\nfor critical compressive stress of the cylinder under axial compression\ncan readily be obtained from donnell's equation ."}, {"doc_id": 1124, "text": "design of missile bodies for minimum drag at very high\nspeeds - thickness ratio, lift, and center of pressure\ngiven .\n newtonian flow theory has been used to develop a procedure\nfor the design of minimum drag bodies of revolution having a\ngiven thickness ratio and center of pressure .\n it is shown that the optimum body shape is independent of\nlift . center of pressure location, however, exerts a powerful\ninfluence on both the shape of the body and on the drag\ncoefficient at zero lift ."}, {"doc_id": 1125, "text": "collapse by instability of thin cylindrical shells\nunder external pressure .\n this paper discusses the collapse by instability of\nthin-walled cylindrical vessels subjected to external pressure .\nthe most important of the theoretical and empirical\nformulas that apply to this subject are presented in a\ncommon notation . a new and simple instability formula is\ndeveloped .\n three classes of tubes are considered .. tubes of infinite\nlength,. tubes of finite length with uniform radial\npressure only,. and tubes of finite length with both uniform\nradial and axial pressure . collapsing pressures\ncalculated by the various formulas are presented in tabular\nform as a means of comparing the formulas .\n the formulas are discussed briefly and checked against\nthe results of tests conducted at the u. s. experimental\nmodel basin for the bureau of construction and repair,\nnavy department .\n this paper is a sequel to one previously published as a\npart of the work of the a.s.m.e. special research\ncommittee on the strength of vessels under external pressure ."}, {"doc_id": 1126, "text": "an engineer's conceptual approach to the buckling of\ncylindrical shell (axial loading) .\nby using the well known analogy between\nthe bending of a beam on an elastic\nfoundation and the axial symmetric\ndisplacement of a cylinder, a physical\ninsight is obtained for the buckling of\ncylindrical shells under axial\ncompression . the technique is equivalent\nto classical small deflection theory\nand provides good agreement with the more\nelaborate solutions for the buckling\nstrength of various sandwich, multi-layered,\nand orthotropic cylinders,\nincluding the effects of internal pressure\nor an elastic core ."}, {"doc_id": 1127, "text": "the buckling of sandwich type panels .\n fifty-one flat rectangular sandwich-type panels were tested\nin edgewise compression with the unloaded edges of the panels\nrestrained by v-grooves . the sandwich consisted of papreg\nfaces and a cellular cellulose acetate core . the thickness of the\nfaces varied from 0.00675 to 0.02025 in.,. the core, from 0.066\nto 0.741 in.,. the width of the panel, from 4 to 11 in . the length\nof the panel was always 10.5 in . the buckled shape consisted of\na ripple of short wave length across the panel . it was either\nsymmetric, the two faces bulging out symmetrically according\nto sine curves, or skew, the two faces deflecting in the same sense\naccording to sine curves having a phase angle of 90 .\n a strain energy theory of buckling is presented for both the\nsymmetric and the skew cases, and the buckling load in the\nsymmetric case is also calculated by integration of the differential\nequation . the agreement between the theoretic and the\nexperimental buckling stress is reasonable, that between the predicted\nand actual buckled shape good . a simple formula is developed\nwhich permits a choice of the most suitable core material when the\nmechanical properties of the face material are given ."}, {"doc_id": 1128, "text": "face wrinkling and core strength in sandwich construction .\n the effect of initial waviness on the wrinkling of\nfaces in sandwich construction is studied . formulae are\nderived to determine the failing stress when the faces\nwrinkle due to failure of the core in tension, compression\nor shear . the importance of core strength requirements\nin maintaining surface smoothness is noted . a\ncomparison of theory with experiments is made, and the\nagreement between the two is found to be reasonably good .\nthe strength of the core . williams has related the strength\nof the core in tension and shear to an arbitrarily assumed\ninitial irregularity which, to ensure laminar flow in a wing\nis assumed to have a maximum admissible value (initial\nwave amplitude critical wavelength=0.0005 to 0.001) ."}, {"doc_id": 1129, "text": "general instability of a ring stiffened circular cylindrical\nshell under hydrostatic pressure .\n the general instability load of a ring-stiffened, circular\ncylindrical shell under hydrostatic pressure is determined\nby analyzing an equivalent orthotropic shell . a set of\ndifferential equations for the stability of an orthotropic\nshell is derived and solved for the case of a shell with simple\nend supports . the solution is presented in terms of\nparameters of the ring-stiffened, isotropic shell, and a\nrelatively simple expression for the general instability load\nis obtained . some numerical examples and graphs of\nresults are presented . in addition, an energy-method\nsolution to the problem is outlined, and the energy and\ndisplacement functions that could be used in carrying out a\nrayleigh-ritz approximation are indicated ."}, {"doc_id": 1130, "text": "handbook of structural stability . pt .vi . strength\nof stiffened curved plates and shells .\n a comprehensive review of failure\nof stiffened curved plates and\nshells is presented .\n panel instability in stiffened\ncurved plates and general instability\nof stiffened cylinders are discussed .\nthe loadings considered for the\nplates are axial, shear, and the\ncombination of the two . for the\ncylinders, bending, external pressure,\ntorsion, transverse shear, and\ncombinations of these loads are considered .\n general instability in stiffened\ncylinders was investigated . for\nbending and torsion loads, test data\nand theory were correlated . for\nexternal pressure several existing\ntheories were compared . as a result\nof this investigation a unified theoretical\napproach to analysis of\ngeneral instability in stiffened cylinders\nwas developed ."}, {"doc_id": 1131, "text": "the effect of axial constraint on the instability of\nthin conical shells under external pressure .\n author considers elastic axial restraint which may be (1)\nactive from the beginning of loading and (2) active only at the onset\nof buckling . buckling loads for the two cases are related by a\nsimple conversion factor . effect of the restraint on the\naxisymmetric type buckling is negligible, but the amplification of the\ncritical load for the nonaxisymmetric type buckling may be very\nlarge for type (1) restraint . design curves are included for a\nrange of l d.and restraint stiffness . results are of doubtful\nvalue considering the known inadequacy of the linear theory of\nbuckling under axial compression ."}, {"doc_id": 1132, "text": "general instability of ring stiffened cylindrical shells\nsubject to external hydrostatic pressure - a comparison\nof theory and experiment .\n tests are described of a number of machined-stiffened\ncylinders subjected to external hydrostatic pressure, and the\nobserved general instability strengths compared with predictions\nfrom theories of kendrick and nash . agreement with kendrick\nwas found rather good . results also are presented from\nelectrical strain gages which show in detail the growth of embryonic\nlobes and nonlinear characteristics of deformation at the\nthreshold of buckling . weakening effects of imperfect circularity are\ndiscussed ."}, {"doc_id": 1133, "text": "a simple extension of southwell's method for determining the elastic\ngeneral instability pressure of ring-stiffened cylinders subject\nto external hydrostatic pressure .\na simple extension of southwell's method is presented whereby the\nelastic general instability pressure of ring-stiffened cylindrical\nshells subject to external hydrostatic pressure may be determined . an\nactual application of the method is illustrated in the paper and the\nresults of several other examples are summarized ."}, {"doc_id": 1134, "text": "torispherical shells - a caution to designers .\n it has recently become apparent, through\na rigorous stress analysis of a specific case\nthat designing torispherical shells by the\ncurrent edition of the asme code on unfired\npressure vessels can lead to failure during\nproof-testing of the vessel . the purpose\nof the present paper is to show in what\nrespects the code fails to give accurate results .\nas an illustrative example, a hypothetical\npressure vessel with a torispherical head\nhaving a diameter-thickness ratio of 440 was\nselected . the supports of the vessel were\nconsidered to be either on the main cylinder\nor around the torus . the vessel was\nsubjected to internal pressure and the elastic\nstresses in it were determined rigorously and\nby the code . a comparison of the two\nrevealed that the code predicted stresses in the\nhead which were less than one half of those\nactually occurring . furthermore, the code\ngave no indication of the presence of high\ncompressive circumferential direct stresses\nwhich exceeded 30,000 psi for practically\nthe entire torus . if the head had been\nfabricated using a steel with a yield point of\nwould have failed or undergone large\ndeformations, whereas the code would have\npredicted that it was safe . the code's rules\nfor torispherical heads are thus in need of\nrevision for certain geometries . the\nimplications of the foregoing results are currently\nbeing studied by the asme,. in the interim,\nhowever, designers should exercise care in\napplying the code to torispherical shells .\n it is also shown in the paper that the use\nof the membrane state as a particular\nsolution of the differential equations is not a\ngood approximation for toroidal shells of the\ntype considered ."}, {"doc_id": 1135, "text": "limit analysis of symmetrically loaded thin shells\nof revolution .\nthe yield surface for a thin cylindrical shell\nis shown to be a very good approximation to\nthe yield surface for any symmetrically\nloaded thin shell of revolution . hexagonal\nprism approximations to this yield surface,\nappropriate for pressure vessel analysis, are\ndescribed and discussed in terms of limit\nanalysis . procedures suitable for finding\nupper and lower bounds on the limit pressure\nfor the complete vessel are developed and\nevaluated . they are applied for illustration\nto a portion of a toroidal zone or knuckle held\nrigidly at the two bounding planes . the\ncombined end force and moment which can be\ncarried by an unflanged cylinder also is discussed ."}, {"doc_id": 1136, "text": "design of thin walled torispherical and toriconical\npressure - vessel heads .\n the failure under hydrostatic test of a large storage vessel\ndesigned in accordance with current practice stimulated earlier\nanalytical studies . this paper gives curves and a table useful for\nthe design and analysis of the knuckle region of a thin\ntorispherical or toriconical head of an unfired cylindrical vessel . a simple\nbut surprisingly adequate approximate formula is presented for\nthe limit pressure, np, at which appreciable plastic deformations\noccur ..\nwhere p is the design pressure, is the yield stress of the\nmaterial, and n is the factor of safety . the thickness t of the knuckle\nregion is assumed uniform . upper and lower bound calculations\nwere made for ratios of knuckle radius r to cylinder diameter d\nof 0.06, 0.08, 0.10, 0.12, 0.14, and 0.16, and ratios of spherical cap\nradius l to d of 1.0, 0.9, 0.8, 0.7, and 0.6 . toriconic1a heads may\nbe designed or analyzed closely enough by interpreting in\ntable 1 as the complement of the half angle of the cone ."}, {"doc_id": 1137, "text": "on the theory of thin elastic toroidal shells .\n the author obtains asymptotic solutions to the problem\nof rotationally symmetric small deflection of thin toroidal\nelastic shells . he first reduces the problem to that of\nintegrating a single linear nonhomogeneous ordinary differential\nequation involving two parameters . asymptotic formulae\nfor the complementary function are obtained by applying\nthe general method of langer (trans.amer.math.soc.33,\nadvantage of yielding results valid near the points where\nthe tangent plane is perpendicular to the axis of revolution,\nwhere the methods of asymptotic integration customary in\nshell theory fail (see the preceding review) . for two\nproblems in which only the complementary function is required,\nthe author's results are compared with those obtained by\nwissler (dissertation, zurich, 1916) by a method of power\nseries expansion,. the agreement is within 4 or better . the\nauthor observes that the usual method of obtaining\nasymptotic expressions for a particular integral, being based on\nusing as an approximation the complementary function\nobtained from the membrane theory, will fail near points\nwhere the tangent plane is perpendicular to the axis of\nrevolution . he therefore introduces a new method, which\nhe states was developed jointly with e. reissner . he applies\nhis results to the cases of an joint loaded symmetrically\nand parallel to its axis, a corrugated pipe subject to axial\nload, and a corrugated cylinder subject to axial pressure .\nmany numerical calculations are involved and there are two\ntables of functions occuring in the solutions ."}, {"doc_id": 1138, "text": "asymptotic solutions of toroidal shell problems .\n method of asymptotic integration developed by e. reissner and\nauthor is refined, and solutions previously obtained for problems\nof bending of curved tube and of a toroidal expansion joint\nsubject to an axial force are generalized and extended . results are\ncompared to those obtained by l. beskin . for large values of a\ncertain parameter, agreement is good ."}, {"doc_id": 1139, "text": "the effect of entrance velocity on the flow of a rarefied\ngas, through a tube .\n the flow of a rarefied gas through a circular tube is considered .\nmolecules entering the tube have a mass velocity directed down\nthe tube, as well as a randomly directed thermal velocity . it is\nassumed that the conditions for free-molecule flow hold, and that\nmolecules striking the tube wall are reflected diffusely . the\nmass velocity and tube dimensions are restricted only by the\nlimitation to free-molecule flow . the theory is illustrated by an\nexample of the effect of an entrance tube on the measurement of\npressure and density by a gage placed on a satelite ."}, {"doc_id": 1140, "text": "shock-standoff distance for spherical bodies at high\nmach numbers .\n usaf-sponsored development of a simple expression for\nshock-standoff distance, by consideration of an apropriate specific-heat\nratio behind the shock . the theory gives predictions which are\nalmost as accurate as those of the van dyke and hays methods ."}, {"doc_id": 1141, "text": "the wake behind an oscillating vehicle .\n the incompressible laminar far wake behind an oscillating\nvehicle is analyzed with the use of the oseen linearization, and\nthe assumption that the wake cross section is axisymmetric .\ntime-wise drag variations are thus represented as changes in the\nwake diameter and velocity defect . it is shown that the\nunsteadiness in this flow can be predicted by a quasi-steady theory ."}, {"doc_id": 1142, "text": "effect of wall divergence on sonic flows in solid wall\ntunnels .\n the effect of wall divergence (in excess of the normal\nvalue given for compensating the boundary layer growth\non the tunnel walls), on the simulation of sonic flows in\nsolid wall wind tunnels is presented in this note which is\na condensed version of ref. 1 ."}, {"doc_id": 1143, "text": "a one-foot hypervelocity shock tunnel in which high-enthalpy\nreal gas flows can be generated with flow times of\nabout 180 milliseconds .\n a shock tunnel is described in\nwhich high-enthalpy, real-gas air\nflows can be generated with flow times\nof about 180 milliseconds . this\nshock tunnel is operated with a\ncombustion-heated driver gas and consists\nof a combustion chamber, shock tube,\nsupersonic nozzle, test section, and\nvacuum tank . an essential feature of\nthis shock tunnel is a means for\nachieving a constant-pressure air reservoir\nfor the duration of the test .\nair streams with velocities in excess of\nachieved at a mach number of about 10 .\nthe corresponding stream total\nenthalpy is about 4,500 btu lb and the\nstagnation pressure is 3.25 psia ."}, {"doc_id": 1144, "text": "slipstream flow around several tilt-wing vtol aircraft models\noperating near the ground .\na collection of data from a number of brief investigations made with\nthree different models to determine the character of the slipstream flow\nalong the ground is presented for multiple-propeller tilt-wing vtol\naircraft configurations operating near the ground . in general, the tests\ninvolved tuft surveys and slipstream dynamic-pressure measurements for\nseveral tilt-wing vtol models . a more extensive series of tests,\nincluding some measurements of the erosion of gravel by the slipstream\nand some measurements of the unsteady rolling, yawing, and pitching\nmoments, was also made on one of the models operating in the hovering\ncondition near the ground .\nthe results of the flow studies indicated the presence of a stronger\nand deeper slipstream flow along the center line of the aircraft, and to\nsome extent along parallel planes between adjacent propellers (on one\nwing), than to the side of the aircraft . this effect is caused by an\nintensification of the individual slipstreams as they meet at the planes\nof flow symmetry . the intensified flow along the center line of the\naircraft is amplified by the presence of the fuselage and causes the\ndynamic pressure to be greater in front of the aircraft than would be\nexpected on the basis of the slipstream of the individual propellers .\nin the erosion tests it was found that gravel, if sufficiently small,\nwas rapidly eroded by the slipstream and that this gravel could be\nthrown high into the air if it struck even very small fixed obstacles on\nthe ground (obstacles with a height less than the diameter of the\ngravel) . results of the investigation of moment fluctuations\nindicated that there are large, erratic variations of rolling, yawing,\nand pitching moments and that the propellers, reacting to an erratic\ninflow from the recirculating slipstream, are the primary source of\nthese moments ."}, {"doc_id": 1145, "text": "buckling of core-stabilized cylinders under axisymmetric external\nloads .\nan equation is derived for the elastic stability of a circular\ncylindrical shell which is filled with a soft elastic core and is subjected to\ngeneral axially-symmetric lateral pressure combined with a central\naxial force . numerical results are given for three lateral pressure\ndistributions of interest in rocket motor case analysis.. uniform\npressure, linearly varying pressure, and a circumferential band\nof pressure located at an arbitrary distance from one end of the\ncylinder . comparison is made with results of previous theoretical\nand experimental investigations, where available ."}, {"doc_id": 1146, "text": "thermal buckling of cylinders .\nseveral theoretical and experimental investigations on the buckling\nof cylinders due to both axial and circumferential thermal stresses are\nreviewed . differences that exist among the various results are\ndiscussed and areas of future work are indicated ."}, {"doc_id": 1147, "text": "heat transfer to bodies traveling at high speed in the upper\natmosphere .\na general method has been developed, using the methods of kinetic\ntheory, whereby the surface temperatures of bodies can be calculated for\nsteady flight at any speed in a rarefied gas . the particular solution\nwas made for a flat plate., however, the calculations can be easily\nextended to bodies of arbitrary shape .\nit was found that the aerodynamic heating problem in the absence of\nsolar radiation, that is, for the case of nocturnal flight, becomes of\nnegligible importance at altitudes of 125 miles and higher and up to\nsteady flight speeds of 36,000 feet per second . the effect of solar\nradiation, for the case of daytime flight, becomes increasingly\nimportant as the flight altitude is increased . at an altitude of 150\nmiles and higher, solar radiation is the predominating factor that\ndetermines skin temperature . owing to the strong effect of solar\nradiation on skin temperatures at high altitudes, the desirability of\nnocturnal flight is indicated in order to minimize skin temperatures .\nin order to maintain low skin temperatures, it was found that the\nangle of inclination of the body with respect to the flight path should\nbe kept as small as possible . this may be accomplished in practice\nby designing the body to be finely tapered and by flying the body at\nsmall angles of attack .\nit is pointed out that skin temperatures may be reduced by insuring\nthermal contact between portions of the skin inclined at positive\nand negative angles with respect to the flight path . as much surface\nas possible should be inclined at negative angles . practically,\nthis may be accomplished by boattailing the body .\nin the event that an internal skin-cooling system is employed, it is\nshown that the rate of internal cooling must be of the same order of\nmagnitude or greater than the rate at which heat is lost naturally\nby emitted radiation . if the cooling rate is below the natural\nradiation rate, cooling has little effect upon skin temperatures .\nit is shown that, in the case of a missile designed to fly over a wide\nrange of altitudes and speeds, it is desirable to make the emissivity\nof the skin as high as possible . this conclusion, however, is\nbased upon a skin surface for which the emissivity is independent\nof the wave length of the emitted and absorbed radiant energy .\na possible method of reducing surface temperatures is indicated by\nthe decrease in skin temperature which accompanies a decrease in\nthermal accommodation coefficient . this phenomenon may be\nused to advantage if it is possible to decrease the accommodation\ncoefficient by altering the surface characteristics of the skin ."}, {"doc_id": 1148, "text": "knudsen flow through a circular capillary .\nthe problem of knudsen flow through a circular capillary has been\noften discussed, usually by the momentum transfer method . however,\np. clausing gave a rigorous formulation for the problem and obtained an\nintegral equation for which he gave an approximate solution . from\ntime to time the accuracy of clausing's solution has been questioned\nand since clausing did not give a rigorous estimate of his error we\nhave reinvestigated the problem ."}, {"doc_id": 1149, "text": "similar temperature boundary layers .\nconditions for the existence of similar solutions are known for (a)\ntwo-dimensional, incompressible, steady and nonsteady laminar boundary\nlayers and (b) three-dimensional, incompressible, steady, laminar\nboundary layers for a body of revolution rotating in a fluid at rest or\na body of revolution in a rotating fluid flow . corresponding\nconditions for the existence of similar temperature boundary layers in\nboth cases are given for constant and variable wall temperatures . the\ngeneral conclusion is that, in all these cases, with or without viscous\nheating, and with constant wall temperature, conditions for the\nexistence of similar velocity boundary layers are at the same time the\nconditions for the existence of similar temperature boundary layers .\nif the wall temperature is variable, the conditions for the existence\nof similar velocity boundary layers are at the same time the\nconditions for the existence of similar temperature boundary layers if the\nwall temperature varies as a power of the local free-stream velocity\nor surface velocity . numberical solutions are given for the\nnondimensional temprature distributions function and the nondimensional\ntemperature gradient at the wall for several prandtl numbers in the case\nof a rotating flow over an infinite plate at rest ."}, {"doc_id": 1150, "text": "preliminary results of density measurements from an air force satellite.\natmospheric density was determined from a singly mounted ionization\ngauge flown on an air force satellite . included is a brief description\nof the experiment and theory as well as a discussion of some of the\nproblems involved in performing these measurements . density data are\ngiven for the altitude range of 370 to 400 km during early morning hours\n for the two days 17 and 18 june 1961 . results are compared with those\nof the 1961 revised u.s. standard atmosphere ."}, {"doc_id": 1151, "text": "experiments on supersonic blunt-body flows .\n recently, progress has been made in the theoretical calculation of\nthe inviscid flow between the detached shock wave and the surface of\na blunt body travelling at supersonic speed . detailed experimental\ndata are needed for comparison . experiments have been made in the\nsupersonic wind tunnels of the jet propulsion laboratory on spheres,\ndisks, and blunted cones over the mach number range 1.8 to 5.0 in air .\nsurface pressures, shock wave shape and detachment distance, certain\nvelocity gradients, the sonic line location, and some streamline paths\nwere determined . the sonic line is found as the trace of the\ntermination point of a weak shock generated by a probe ahead of the model .\nfor a sphere, good agreement between theory (of van dyke) and experiment\nis found ."}, {"doc_id": 1152, "text": "on periodically oscillating wakes in the oseen approximation .\n studies in maths . and mechs .,\n the oscillating vortex wake behind an obstacle at\nreynolds numbers of order 10 is studied by means of the\noseen approximation ."}, {"doc_id": 1153, "text": "a study of the simulation of flow with free stream mach number 1 in a\nchoked wind tunnel .\nthe degree to which experimental results obtained under choking\nconditions in a wind tunnel with solid walls simulate those associated with\nan unbounded flow with free-stream mach number 1 is investigated for the\n cases of two-dimensional and axisymmetric flows . it is found that a\nclose resemblance does indeed exist in the vicinity of the body, and\nthat the results obtained in this way are generally at least as accurate\n as those obtained in a transonic wind tunnel with partly open test\nsection . some of the results indicate, however, that substantial\ninterference effects, particularly those of the wave reflection type, may\nbe encountered under certain conditions, both in choked wind tunnels and\n in transonic wind tunnels, and that the reduction of these interference\n effects to acceptable limits may require the use of models of unusually\n small size ."}, {"doc_id": 1154, "text": "on the influence of wall boundary layers in closed transonic test\nsections .\nthe boundary layers at the test section walls of a transonic wind tunnel\n are known to reduce the wall interference . in the present paper this\neffect is studied by means of small perturbation theory, assuming\nviscosity to be negligible when perturbing a turbulent boundary layer . an\napproximation for thin boundary layers leads to a modified boundary\ncondition at the wall of the test section, expressing the normal\nstreamline slope induced by changes in mass flow density and crossflow\nwithin the boundary layer . this boundary condition is applied to the\nlinearized equations of subsonic flow and to the non-linear transonic\nequations at choking, the cases of plane and circular test sections only\n being treated in detail .\nthe results of linear theory show that all corrections except the\nthree-dimensional angle-of-attack correction are considerably reduced by\n the presence of the boundary layers at mach numbers greater than 0.9,\nthe essential part of their influence being due to the change of mass\nflow density with pressure . in the case of choking the analysis\nindicates that the presence of boundary layers will increase the maximum\nmodel size for which the flow can be interpreted as corresponding to\nmach number one in free flight . finally, the technique of using\nartificial thickening of the wall boundary layers for a reduction of wall\ninterference is considered, though without reaching a definite\nconclusion as to its value as compared to other techniques ."}, {"doc_id": 1155, "text": "some experimental investigations on the influence of wall boundary\nlayers upon wind tunnel measurements at high subsonic speeds .\npressure distribution measurements and drag determination by means of\nbalance measurements have been carried out for a number of models at\nhigh subsonic velocity in wind tunnels, where the boundary layer of the\nwalls has been varied . within the investigated range it appeared that a\n thickening of the boundary layer reduced the disturbing influence of\nthe walls, which also caused an increase of the choking mach number .\nthe phenomenon described should be of a certain importance from the\npoint of view of wind tunnel technique, since it is possible to increase\n the choking velocity for a given model by means of thickening the\nboundary layer ."}, {"doc_id": 1156, "text": "experimental investigation of attenuation of strong\nshock waves in a shock tube with hydrogen and helium\nas driver gases .\n an experimental investigation\nhas been made of the attenuation of\nstrong shock waves in air in a shock\ntube . time-history measurements\nwere made of the static pressure at\nseveral stations in the wall of the\ntube . the internal diameter of the\ntube is 3.75 inches . shock-\nwave-velocity data were taken for a distance\nalong the tube of about 120 feet .\nthe range of the shock-wave mach number\ncovered was from 5 to 10 and\nthe initial pressure ahead of the shock\nwave varied from 5 to 100\nmillimeters of mercury . hydrogen and helium\nwere used as driver gases .\n a helium-driven shock wave was found\nto decay only about one-half\nas rapidly as a hydrogen-driven shock wave .\nthe pressure level had\nlittle effect on the attenuation rate of\na shock wave of given strength\nfor the pressure range investigated . the\nstatic-pressure measurements\nindicated that a severe pressure gradient\nexisted in the latter portion\nof the air flow . this gradient limits the\ntesting time useful for\nobtaining reliable aerodynamic data ."}, {"doc_id": 1157, "text": "hypersonic shock tunnel .\na hypersonic shock tunnel has been developed for obtaining fluid\nmechanic information at the high mach numbers and corresponding stagnation\ntemperatures encountered in flight by long range ballistic vehicles and\nsatellites . this report describes the hypersonic shock tunnel and\npresents some of the results obtained in the driven tube and in the nozzle\nhelium is ignited in the driver to produce strong shock waves in air .\na shock velocity in air as high as 55,000 fps with a calculated\nequilibrium temperature of 16,000 k has been produced in the driven tube . the\n effects of high stagnation temperatures upon the detached shock wave\nand the pressure distribution for blunt bodies have been observed in the\n nozzle test section . the detachment distance devreased greatly at high\n temperatures . the pressure distribution for the hemisphere was found\nto be less than that predicted by the modified newtonian theory . shock\nwave boundary layer interaction at the leading edge of a flat plate was\nobserved, and the results agreed with the analytical prediction . a\ndetached shock wave was observed for a blunt two-dimensional body at very\nlow densities in the test section with a flow mach number of 19.6 ."}, {"doc_id": 1158, "text": "the tailored-interface hypersonic shock tunnel .\nthe /tailored-interface/ hypersonic shock tunnel provides a means for\nproducing the high mach number, high stagnation temperature flow\nconditions encountered in hypersonic flight . various gasdynamic\nphenomena associated with shock tunnels are discussed, and experimental\nevidence of the successful application of this technique is presented .\nas an indication of its research application, the results of\nheat-transfer experiments on a hemisphere-cylinder model are presented\nand compared with theory ."}, {"doc_id": 1159, "text": "experimental investigation of the effect of yaw on\nrates of heat transfer to transverse circular\ncylinders in a 6500-foot-per-second\nhypersonic air stream .\na technique has been developed by which air can be shock-compressed\nby helium to 3660 degrees rankine to generate a 6500-foot-per-second\nair stream with a flow duration of 40 milliseconds . the resulting\nequipment is described . experiments were conducted to determine\nrates of heat transfer to transverse circular cylinders of 0.003-,\ngreater than 100 . the cylinders were tested at a nominal mach number\nof 11 with a stagnation reynolds number (evaluated with free-stream\nmass flow and stagnation viscosity of 4.00 times 10 to the 4th power\nper foot ."}, {"doc_id": 1160, "text": "recent advances in gaseous detonation .\n a review of recent work in gaseous detonation\nis presented . early work is briefly mentioned and\ntreatises listed . theoretical calculations of\nchapman-jouguet detonations are reviewed,\ncompared and the ambiguity concerning the speed of\nsound in a reacting gas mixture discussed .\nexperimental chapman-jouguet measurements are\nreviewed . recent studies of the interior of a\ndetonation wave are presented . standing detonation\nwave research, detonation limits, two-dimensional\ndetonations, spectra, ionization and magnetohydrodynamic\ntreatments are brought to the reader's\nattention . a qualitative description of the\ndevelopment of a flame to a detonation is presented .\nexperimental observations are examined and\nrecent theoretical attempts to explain these\nobservations are reviewed ."}, {"doc_id": 1161, "text": "stagnation point heat transfer measurements in dissociated\nair .\n the results of an experimental investigation of the laminar heat\ntransfer at the stagnation point of a blunt body in partially\ndissociated air are presented and are compared to the theoretical\ntreatment of fay and riddell . heat-transfer results are\npresented for air temperatures as high as 8,000 k. where more than\nperiments were performed in a shock tube and the new\nexperimental techniques and principles are discussed briefly .\nsimulation of flight stagnation conditions at velocities up to satellite\nvelocity of 26,000 ft. sec. is shown to be possible in shock tubes and\ndata has been obtained over a large altitude range at these\nvelocities ."}, {"doc_id": 1162, "text": "force-test investigation of the stability and control\ncharacteristics of a 1/8 scale model of a tilt-wing\nvertical take-off and landing airplane .\n a force-test investigation has\nbeen made to determine the\naerodynamic characteristics of a scale\nmodel of a tilt-wing\nvertical-take-off-and-landing airplane in the\nshort- and long-wing configurations .\nthe model had two 6-blade dual-rotating\npropellers that were not\ninterconnected mounted on a wing that could\nbe tilted up to an incidence angle\nof about 90 for vertical take-off and landing .\n the investigation included measurements\nof both the longitudinal\nand lateral stability and control\ncharacteristics in the normal-\nforward-flight, transition, and hovering ranges .\ntests in the forward-flight\nand transition conditions were made at\nvarious wing incidences and power\nconditions . tests in the hovering\ncondition were made in the presence\nof the ground . the data are presented\nwithout analysis ."}, {"doc_id": 1163, "text": "force-test investigation of the stability and control\ncharacteristics of a scale model of a tilt-wing vertical\ntake-off and landing aircraft .\n a wind-tunnel investigation has\nbeen made to determine the\naerodynamic characteristics of a scale\nmodel of a tilt-wing vertical-\ntake-off-and-landing aircraft . the model\nhad two 3-blade single-rotation\npropellers with hinged (flapping)\nblades mounted on the wing, which\ncould be tilted from an incidence\nof 4 for forward flight to 86 for\nhovering flight .\n the investigation included\nmeasurements of both the longitudinal\nand lateral stability and control\ncharacteristics in both the normal\nforward flight and the transition\nranges . tests in the forward-flight\ncondition were made for several values\nof thrust coefficient, and tests\nin the transition condition were made\nat several values of wing incidence\nwith the power varied to cover a range\nof flight conditions from\nforward-acceleration (or climb) conditions to\ndeceleration (or descent) conditions\nthe control effectiveness of the\nall-movable horizontal tail, the ailerons\nand the differential propeller pitch\ncontrol was also determined . the\ndata are presented without analysis ."}, {"doc_id": 1164, "text": "effect of ground proximity on the aerodynamic characteristics\nof a four- engined vertical take-off and landing transport\nairplane model with tilting wing and propellers .\n an investigation has been made\nto study the effect of ground\nproximity on the aerodynamic characteristics\nof a four-engine vertical-\ntake-off-and-landing transport-airplane\nmodel with tilting wing and\npropellers . tests were made with the wing\nat an angle of incidence of 90,\nthe position used for vertical take-off\nor landing . with the model at\nvarious heights above the ground, the\nlift, drag, and pitching moment\nwere measured and tuft studies were\nmade to determine the flow field\ncaused by the propeller slipstream .\ndata were obtained for the complete\nmodel, for the model with horizontal\ntail removed, and for the\nwing-propeller combination alone .\n the results of the investigation\nshowed that, when the model was\nhovering near the ground, there was a\nstrong upwash in the plane of\nsymmetry and also an increase in lift\nof about 10 percent of the\npropeller thrust . about one-half of this\nlift resulted from an increase\nin propeller thrust and one-half resulted\nfrom an up load on the\nfuselage induced by the upwash . as the model\napproached the ground, it also\nexperienced an increasing nose-down\npitching moment that evidently\nresulted from the up load on the fuselage,\nthe rear part of which was\nlonger than the front part . the addition\nof the horizontal tail which\nwas located about halfway up the vertical\ntail did not increase the\nnose-down pitching moment because the\nfuselage decreased the energy of\nthe upwash before it reached the tail ."}, {"doc_id": 1165, "text": "an investigation of the effect of downwash from a vtol\naircraft and a helicopter in the ground environment .\n dynamic-pressure measurement,\nin ground effect, have been obtained\nabout a single-rotor helicopter and\na dual-propeller vtol aircraft . the\nresults indicate that the slipstream\ndynamic pressure along the ground,\nsome distance from the center of\nrotation, is not a function of disk\nloading but merely a function of\nthe gross weight or thrust of the\naircraft . furthermore, for a given\ngross weight the thickness of this\noutward flowing sheet of air is less\nfor a small-diameter propeller (higher\ndisk loading propeller) .\n the variation of the dynamic-pressure\nflow field for single and\ndual propellers or rotors is significantly\ndifferent in the plane of\nsymmetry between the two rotors than\nin a direction normal to this\nplane . the interaction of the two\nflows produces a region of upflow\nin this plane where the fuselage is\nlocated, and the decay of the\nmaximum dynamic pressure with distance\nahead of the fuselage is slower ."}, {"doc_id": 1166, "text": "an investigation to determine conditions under which\ndownwash from vtol aircraft will start surface erosion\nfrom various types of terrain .\n results of an investigation with\nsmall-scale equipment of the\nconditions under which the downwash from\na hovering vertical-take-off-\nand-landing (vtol) aircraft will start\nsurface erosion indicate that the\nonset of erosion depends only on the\ndynamic pressure of the outward\nflow of air near the surface . for a\nrotor or propeller at a height of\nabout 1 slipstream diameter above the\nsurface, this surface dynamic\npressure was found to be equal to the\ndisk loading . for the vtol\naircraft supported by a ducted fan, the\nsurface dynamic pressure with the\nducted fan exit at a height of about\none-half the exit-area loading . the\nsurface dynamic pressure decreases\nrapidly with increasing height of the\nvtol device .\n erosion of sand and loose dirt\nstarted at surface dynamic pressures\nof 1 to 3 lb sq ft, which is in general\nagreement with helicopter\nexperience . thoroughly soaking the sand and\nloose-dirt surfaces increased the\nresistance to erosion to surface dynamic\npressures of 30 to 50 lb sq ft .\nspray from water started at surface\ndynamic pressures of 1.5 to\npressures up to about 1,000 lb sq ft ."}, {"doc_id": 1167, "text": "an experimental study of the effect of downwash from\na twin-propeller vtol aircraft on several types of\nground surfaces .\n a full-scale, twin-propeller\nvtol aircraft with a maximum gross\nweight of 3,400 pounds has been\noperated on the ground to study the\neffect of downwash on several types\nof ground surfaces .\n static operation over loose snow\nindicated a zone of obliterated\nvision ahead of the pilot in an arc of\napproximately 10 on each side\nof the plane of symmetry . an arc 10\nto 45 each side of the center\nline was found to be an area of fair\nvisibility while the arc from 45\nto 90 was an area of poor visibility .\n static operation in the presence\nof loose surface material\nindicated that the downwash cleared the\narea near the aircraft of these\nparticles without recirculation or\ndamage to any components .\n short-time operation at moderate\nforward speed over loose gravel,\nwith the thrust axis at an angle of\nin propeller-blade erosion and numerous\nsmall dents and fabric\npunctures in the sides of the fuselage .\nthe propeller-blade erosion was\nsuperficial except for the leading\nedges where several layers of glass\nfiber were eroded ."}, {"doc_id": 1168, "text": "damage incurred on a tilt-wing multipropeller vtol/stol\naircraft operating over a level, gravel-covered surface .\n a summary is presented of the\ndamage experienced by a tilt-wing\nvtol stol aircraft as a result of\noperating from a level surface covered\nwith loose gravel . the damage was\ninadvertently incurred as the aircraft\nwas performing a taxiing-turn maneuver\nover an area of level macadam\nsurface containing loose and embedded\ncrushed stone . observers from a chase\naircraft commented that the wing was\ntilted at approximately 76 with\nrespect to the ground when the damage\noccurred . deposits of stone in the\nopen fuselage, punctures in the rotor\nblade skin, and damage to the\ncompressor blades of the engine occurred\ndue to the circulation of the\ncrushed gravel ."}, {"doc_id": 1169, "text": "hangling qualities experience with several vtol research\naircraft .\n all of the vtol research aircraft\ndiscussed in this paper have\nsuccessfully demonstrated conversion from\nhovering to airplane flight and\nvice versa . however, control about one\nor more axes of these aircraft\nhas been inadequate in hovering flight .\nfurthermore, ground interference\neffects have been severe in some cases\nand have accentuated the inadequacy\nof control in hovering and very low\nspeed flight .\n stalling of wing surfaces has resulted\nin limitations in level-flight\ndeceleration and in descent, particularly\nfor the tilt-wing aircraft, which\nin this case is a very rudimentary type .\nminor modifications to the wing\nleading edge have, however, produced\nsurprisingly large and encouraging\nreductions in adverse stall effects .\n height control in hovering and in\nlow-speed flight has proved to\nbe a problem for the aircraft not having\ndirect control of the pitch of\nthe rotors . the other systems have shown\nundesirable time lags in\ndevelopment of a thrust change ."}, {"doc_id": 1170, "text": "structural loads surveys on two tilt-wing vtol configurations .\n the results of two structural-loads\nsurveys are summarized . the\nfirst loads program discussed concerns\nthe airframe vibratory loads\nencountered during flight tests of the\nvz-2 tilt-wing vtol aircraft\nthroughout the operational range from\nhover to cruise flight . the\nprimary sources of airframe vibration\nwere wing-stall buffeting and\ntail buffeting in descents . the second\nloads program discussed\nconcerns the initial results of a\nstructural-loads survey conducted as\npart of the wind-tunnel test of a\nlarge-scale tilt-wing research model .\nthis loads program deals with the\nsteady wing loads measured throughout\nsimulated transition from hover to\ncruise ."}, {"doc_id": 1171, "text": "the stability under axial compression and lateral pressure\nof circular cylindrical shells with a soft elastic\ncore .\n the stability under axial compression and lateral pressure of a\nfinite circular-cylindrical shell with an elastic core is treated by\nmeans of donnell's equations . the stability criterion is\ninvestigated in detail for the general cylinder under axial compression or\nlateral pressure and for a particular cylinder under combined\nloading . comparisons are made with available experimental\ndata ."}, {"doc_id": 1172, "text": "elastic stability of circular cylindrical shells stabilized\nby a soft elastic core .\n the effect of a soft elastic core upon the\nbuckling strength of a thin, circular, cylindrical shell is\ninvestigated experimentally . two types of loading are\nconsidered .. (a) axial compression, and (b) uniform\nradial-band loading, where the width of the band is small\ncompared to the length of the shell .\n for each type of loading it is shown that the\nstrengthening effect of the elastic core becomes more significant\nwith the increasing values of the radius-thickness ratio .\nfor example, it is shown that for the geometric and\nelastic constants considered it is possible, with the presence\nof the core, to increase the axial buckling stress by as\nmuch as 65 percent over the values found for those\nwithout an elastic core . the elastic core is even more\neffective in stabilizing the shell against buckling due to band\nloading, the peak pressure required to buckle the filled\nspecimen being 7.30 times that required to buckle the\nunfilled shell ."}, {"doc_id": 1173, "text": "the buckling of cylindrical shells under longitudinally varying loads .\ntwo problems illustrating the effect of nonuniformity of loading\non the buckling characteristics of circular cylinders are\ninvestigated . the first problem deals with the effect of\nlinearly varying axial compressive stress, such as would be\nproduced by the weight of the propellant in a solid-propellant\nengine case . the results indicate that the ratio of the maximum\ncritical compressive stress induced by the shear load to the\ncritical uniform compressive stress varies from 1.9 for\nthe curvature parameter z equal to 1.6 as z\nbecomes infinite . in particular, the increase in stress is\nless than 20 per sq. ft. for z greater than 100 .\nthe stability of thin cylinders loaded by lateral external\npressure varying linearly in the longitudinal direction is also\ninvestigated . the results indicate that for z greater than 100,\nthe buckling coefficients are proportional to square\nroot z ."}, {"doc_id": 1174, "text": "general theory of buckling .\nvarious aspects of the theory of buckling are expounded\nin many treatises (1 to 15) . the books of bleich (2)\nand salmon (3) contain large bibliographies . goodier\ndevelopments in buckling theory . numerous references are\nappended to hoff's article . nearly all publications on\nbuckling of shells, available in the u.s.a. (to 1956), are listed in\nthe bibliographies on shells by nash (18) . the section\nready guide to recent literature ."}, {"doc_id": 1175, "text": "stresses from local loadings in cylindrical pressure\nvessels .\n a short discussion is given of the possible methods for\ncomputing the stresses caused in cylindrical shells by local\nloadings . it is concluded that the method of developing\nthe loads and displacements into double fourier series\nleads to formulas which are best suited for numerical\nevaluation . with this method the pertinent expressions\nfor the displacements caused by radial loads are found by\nreducing the three partial differential equations of the\nshell theory to an eighth-order differential equation in the\nradial displacements, which is similar to, but not identical\nwith, those derived by donnell and yuan . insertion of the\nfourier series for the radial displacements and the external\nloading in this equation leads directly to a double series\nexpression of the radial displacement w in terms of the load\nfactors of the radial load . this results in the pertinent\nexpressions for the other displacements and for the\nbending moments and membrane forces . the cases of radial\nloading considered here and those which can be reduced to\nit are (a) a load uniformly distributed within a rectangle,\ntion, uniformly distributed over a short distance in the\ncircumferential direction, (d) a moment in the\ncircumferential direction, uniformly distributed over a short\ndistance in the longitudinal direction . for all these\nloadings the load factors, which have to be used in the\npertinent formulas for the displacements, bending\nmoments, and membrane forces, are computed . for the case\nof tangential loading an eighth-order differential\nequation is derived in terms of the radial displacement and the\ntangential load . using this equation, formulas for the\ndisplacements, bending moments, and membrane forces for\ntangential loading within a rectangle are found ."}, {"doc_id": 1176, "text": "bending tests of ring-stiffened circular cylinders .\n twenty-five ring-stiffened circular\ncylinders were loaded to\nfailure in bending . the results are\npresented in the form of design curves\nwhich are applicable to cylinders with\nheavy rings that fail as a result\nof local buckling ."}, {"doc_id": 1177, "text": "effects of rapid heating on strength of airframe components .\n results of several experimental\ninvestigations are presented which\nindicate the effects of rapid heating\non the bending strength of multiweb\nbeams and ring-stiffened cylinders .\nit is shown that thermal stresses\nreduce the bending load carried at\nbuckling by both beams and cylinders .\nthe influence of thermal stress on\nmaximum load is found to depend\nlargely on the mode of buckling .\nfor beams that buckle locally, no\napparent effect of thermal stress on\nthe maximum load has been found .\na reduction in maximum load has been\nobserved for beams that buckle in\nthe wrinkling mode and for cylinders ."}, {"doc_id": 1178, "text": "buckling of ring-stiffened cylinders under a pure bending\nmoment and a nonuniform temperature distribution .\n thirteen stainless-steel ring-stiffened\ncylinders were subjected to a pure\nbending load and heated rapidly until\nbuckling occurred . for most of the\ncylinders the heating was not uniform around\nthe circumference so that appreciable\naxial thermal stresses were present .\nelementary thermal stress theory was found\nto be inadequate for the prediction of\nthese thermal stresses, but a method was\ndeveloped that would give satisfactory\nthermal stress results . by properly\naccounting for the thermal stress, the\nbuckling load could be correlated with a\ntheory for the buckling of an axially\ncompressed ring-stiffened cylinder that is\nuniformly heated ."}, {"doc_id": 1179, "text": "a theory of asymmetric hypersonic blunt-body flows .\ntwo-dimensional asymmetric and three-dimensional\ninviscid blunt-body flows are analyzed\nusing a new method . the method is inverse, that\nis, the shock-wave shape and freestream\nconditions are taken as known, and the body shape\nand flow field are to be determined .\nresults at zero angle of attack are obtained as a special\ncase of the general problem . solutions at\nzero angle are calculated for a variety of body shapes\nat freestream mach numbers ranging from\ninfinity to 1.85 . the ratio of specific heats, is taken\nas 1.4 . comparison with results obtained\nusing van dyke's and garabedian's numerical\nsolutions indicates that the method under\nconsideration is more accurate than the van dyke\nmethod for determining stand-off distance .\nsolutions are obtained for parabolic and paraboloidal\nshock waves at small angle of attack and\ninfinite freestream mach number,. assumes the\nvalues 1.4, 1.2, 1.1, and 1.05 . for all cases,\nthe streamline that wets the body passes through\nthe shock wave slightly above the point\nwhere the shock is normal and thus does not possess\nmaximum entropy . these results\nprovide counter examples to the conjecture that any\nisolated convex body in a supersonic stream\nis wetted by the streamline of maximum entropy ."}, {"doc_id": 1180, "text": "approximate analysis of the slot injection of a gas\nin laminar flow .\n the laminar diffusion and combustion of a gas\ninjected into a high-speed uniform stream by\nmeans of a wall slot are considered . the\ndorodnitzin-howarth transformation is employed to\nreduce the boundary layer equations to\nincompressible form,. the nonsimilar flow field is\ntreated by a modified oseen approximation in\nconjunction with the integral method . thermal\nboundary conditions corresponding to an adiabatic\nwall and to constant wall enthalpy are\ndiscussed . the injection of homogeneous, heterogeneous,\nnonreactive, and reactive gases is\ntreated . for the latter case, the models usually\nemployed for chemical behavior, namely,\nfrozen and equilibrium flow, are considered . the\nanalysis is applicable to a wide variety of\nlaminar flows, e.g., those involving cooling, thermal\nprotection, skin-friction reduction, and\nsupersonic deflagration . a numerical example of\npractical interest in connection with the\nventing of gaseous hydrogen boiloff from a rocket\nbooster is presented ."}, {"doc_id": 1181, "text": "steady magnetohydrodynamic flow past a non-conducting\nwedge .\n this paper presents a study of the steady\ntwo-dimensional magnetohydrodynamic flow of an\ninfinitely conducting fluid past a nonconducting\nwedge with nonaligned flow and magnetic\nfield . the flows considered are in the /superfast/\nor fully hyperbolic regime . the flows consist\nof several regions of uniformity connected by\nshocks and expansion waves . because of the\nboundary condition on the magnetic field, the\nmagnetic field must be the same in the regions\nabove and below the wedge,. thus the flows in these\nregions are coupled, unlike in the case of\nordinary supersonic gasdynamics . only small wedge\nangles and weak waves (characteristics) are\nconsidered . the problem thus is linearized, and\nexplicit solutions are obtained which are\nqualitatively similar to the nonlinear solutions .\nsome interesting and unexpected features\narise, and they are discussed in detail ."}, {"doc_id": 1182, "text": "an approximate solution for laminar boundary layer flow .\nthis paper presents an approximate solution for two-dimensional,\nincompressible, laminar boundary layer flow with arbitrary pressure\ngradient . von mises' form of the boundary layer equation is linearized\nby making a change in the coefficient of one of the terms . the\nlinearized equation yields a solution that is accurate for the outer portion\nof the flow but inaccurate near the surface . a separate inner solution\nthen is developed which is accurate at the surface and which joins with\nthe outer solution at some point within the boundary layer . the\nmethod may be considered a major modification of one developed earlier\nby von karman and millikan, with changes in both outer and inner\nsolutions, and the point at which the two solutions are joined . the changes\nimprove the accuracy of the method and in some respects simplify the\ncalculations . as examples, results are presented for flow with a\nlinear variation of velocity (including flat plate and stagnation\npoint flow as special cases), flow with sinusoidal variation of\nvelocity, flow past a circular cylinder (heimenz' velocity\ndistribution), and flow past an ellipse (schubauer's data) . agreement\nwith theoretically exact solutions is good, and better than\nresults obtained using the pohlhausen method ."}, {"doc_id": 1183, "text": "laminar hypersonic trail in the expansion-conduction\nregion .\n the usual procedure in calculating the cooling\nprocess in a wake behind a blunt object is to\nassume a region of pure expansion up to a distance\nwhere the pressure has reached its ambient\nvalue, followed by a region where the mechanism\nof pure heat conduction is operative . in\nthe present paper both mechanisms are assumed\nto be valid simultaneously, and the result is\ncompared with previous calculations . the\nfollowing criterion is established .. the minimum\nradius of a hemisphere-cylinder configuration,\nabove which a simultaneous\nconduction-expansion calculation is not needed, is given by\nthe approximation\nwhere is the nondimensional value\nof the enthalpy at the axis of the wake below\nwhich the two methods of computation give the\nsame result, and m is the flight mach number ."}, {"doc_id": 1184, "text": "three dimensional effects in viscous wakes .\n three-dimensionality in wakelike or jetlike\nfree mixing may stem from initial geometric\nconfigurations, nonuniformities in flow variables\nover a cross section, or boundary conditions\nalong the flow . these may be generated by\nbodies at angle of attack, nonaxisymmetric\nbodies, mixing of nonaxisymmetric jets with\nan outer flow, finite wings, or more artificial\nmeans . this paper is devoted to studies bearing\non such configurations . the first section\ndeals with the general mathematical model, in\nwhich the boundary layer approximations\nare used, and with methods of solution .\nlaminar and turbulent flow, compressibility,\nunsteadiness, and streamwise pressure gradients\nare admitted initially . the flux forms of the\nequations are given . algebraic integrals of the\nenergy equations and the diffusion (\nfrozen-flow) equations are obtained . a simplification\nof the convective terms, roughly\ncorresponding to the oseen approximation, is used\nin the asymptotic downstream region .\nthe second section contains explicit solutions\nfor specific configurations, in particular\nfor flows whose initial isovels are of elliptic shape .\nthese flows may be wakelike or jetlike .\ncompressibility is admitted,. however, the flows\nmust have uniform pressure and must be\nsteady . the final section deals with interpretation\nand evaluation of the results ."}, {"doc_id": 1185, "text": "an integral method for calculating heat and mass transfer\nin laminar boundary layers .\n an integral method previously used successfully\nin several kinds of boundary layer problems\nhas been extended to treat simultaneous heat and\nmass transfer in a binary-mixture laminar\nboundary layer when the pressure is uniform .\nthe principal results are two pairs of dual\nintegral relations arising from solutions to the\nintegral concentration and energy equations .\none pair connects the surface mass transfer rate\nand surface concentration of injected gas,. the\nother relates surface temperature and heat transfer\nrate in the presence of mass transfer .\nonly the cases of helium and air injection into an\nundissociated air stream are discussed in\ndetail, but the method can be applied to problems\ninvolving other gases . the approximate\nresults agree quite well with some numerical solutions\nand with recent experimental results\nfor which no numerical solutions are available ."}, {"doc_id": 1186, "text": "lift of slender delta wings according to newtonian\ntheory .\n an approximate system of equations is derived to\ndescribe the inviscid flow past a flat slender\nwing at angle of attack, in the limit and .\nthe aspect ratio is required to\napproach zero at the same rate as the mach angle in\nthe flow behind the shock wave . only a\nsingle parameter appears in the resulting equations,\nand a similarity law therefore can be\nwritten expressing a correction to the newtonian\nnormal-force coefficient . for the delta wing,\na correlation of experimental data according to the\nsimilarity law is shown, and the first terms\nof the solution are derived under the assumption\nthat the similarity parameter is small (\nvertex angle much smaller than mach angle) ."}, {"doc_id": 1187, "text": "shock-induced boundary layer separation in overexpanded conical exhaust\nnozzles .\nthe flow in overexpanded supersonic nozzles is reviewed . although five\nessentially different flow regimes can be discerned, depending on the\nnozzle pressure ratio, the regime of most interest to the engine\ndesigner is the one characterized by oblique shock patterns in the nozzle\nand flow separation from the nozzle wall . it is shown that the pressure\n rise associated with the separation correlates well with the mach\nnumber at the separation point . a simple analytical formulation for the\npressure rise required to separate the flow provides excellent agreement\n with experimental data over a wide range of nozzle operating conditions\n and allows prediction of overexpanded nozzle performance ."}, {"doc_id": 1188, "text": "factors affecting lift-drag ratios at mach numbers\nfrom 5 to 20 .\n yawed-cone working charts and an engineering\nmethod are presented and used to calculate\nlift-drag ratios of flat-top conical wing-body\narrangements at mach numbers from 5 to 20 .\nviscous interaction effects are considered, but\nbluntness effects are neglected . correlations\nof wind-tunnel data in the range\nshow that boundary layer\ndisplacement corrections to surface pressure and skin\nfriction are required to calculate lift-drag ratios\nby this method whenever\nis greater than 0.2 . is the freestream mach\nnumber and is the freestream reynolds\nnumber based on body length . double- and\nsingle-type shock patterns, transition from one\npattern to the other, and the variation of inner-shock\nposition with angle of attack are described .\nlift-drag ratios are calculated at selected flight\ndesign points for flat-top, conical body\narrangements with triangular and hyperbolic wing\nplanforms . the hyperbolic wing arrangement\noffers a potential l d benefit at mach 5 but\nnot at mach 10 or above ."}, {"doc_id": 1189, "text": "nonequilibrium flow past a wedge .\n an exact numerical solution is obtained for\nthe chemically reacting flow past a wedge . the\nfreestream is either in equilibrium or out of\nequilibrium but nonreacting . the attached\nshock wave is shown to be either concave, convex,\nor straight, depending on the values of the\namount of dissociation in the freestream and\na parameter describing the amount of energy\ncontained in the freestream relative to the gas\ndissociation energy . numerical examples are\npresented illustrating these regimes . the flow\nfield is characterized by the presence of an\nentropy layer and a relaxation layer, both easily\nidentifiable in the presentation of the numerical\nresults ."}, {"doc_id": 1190, "text": "flow of a gas near a solid surface .\n the state of a gas near a solid surface is investigated .\nit is assumed that at a sufficiently\nlarge distance from the surface the particle distribution\nfunction is of the chapman-enskog\nform . the half-range analysis previously employed for\nparallel plate geometrics (symmetric\nproblems) can be adapted to the single-plate problem .\nalthough the mathematical analysis\ndiffers, the slip coefficients are essentially identical\nwith those obtained from the parallel\nplate problem (e.g., couette flow) . detailed calculations\nare presented for both hard sphere\nand maxwellian molecules . the recent work of\nbakanov and deryagin for hard sphere\nmolecules, which is based on incorrect approximations, is discussed ."}, {"doc_id": 1191, "text": "heat transfer to a hemisphere-cylinder at low reynolds\nnumbers .\n measurements of the local heat flux to\nhemisphere-cylinder models in a supersonic rarefied\nair stream are presented . two different steady-state\nmethods were developed, and five\nindividual models were used . data were obtained\nthroughout the mach number range of 2 to 6,\nwith reynolds numbers (based on conditions\nbehind the bow shock and model diameter)\nvarying from 38 to 1730 . the stagnation point data\nindicated a gradual increase from continuum\nboundary layer theory at the higher reynolds\nnumbers to about 10 above at the lower end\nof the range investigated . pressure distribution\nmeasurements on cooled and uncooled models\nwere found to agree well with modified newtonian\ntheory . local recovery factor\nmeasurements showed a small rarefaction effect at the\nlowest reynolds numbers ."}, {"doc_id": 1192, "text": "an integral method for calculation of supersonic laminar\nboundary layer with heat transfer on yawed cone .\n an integral method for calculating the three-dimensional\nboundary layer over the surface of\na cone at angle of attack is investigated .\nthe numerical procedure of integration for that\nmethod on the basis of a simplifying assumption\nconcerning the boundary layer development\nalong the cone generator is developed and illustrated\nby applying the method to find the\nsolutions of integral equations for a specific example .\nthe results obtained for the example for the\nrange of circumferential angle of 40 investigated\nare summarized and given as heat transfer\ncoefficients, coefficients of friction, and other\nfriction parameters . the distribution of heat\ntransfer coefficients checked with available\nexperimental data fairly well ."}, {"doc_id": 1193, "text": "some exact solutions for cavitating curvilinear bodies .\n a special case of cavitating flow solutions is\npostulated and transformed to a semi-infinite\nplane . the complete, exact solution then is\nsynthesized by superposition of singularities .\nthe solution is relevant to a general, two-parameter\nfamily of curvilinear bodies . the\nparameters are the flow angles at the two points of flow\nseparation . the body reduces, in the special\ncase, to the rayleigh solution for a flat plate .\nthe equations of the cavity boundaries are\ngiven in explicit form . the body form and the\nstagnation streamline are given as the locus of\nthe roots of a cubic equation . local static\npressures and, hence, lift and drag, also may be\ncalculated . the generated solutions constitute\na technique involving simple computation\nfor exact solutions of a special family of cavitating\ncurvilinear bodies at finite angles of attack ."}, {"doc_id": 1194, "text": "magnetohydrodynamic flow past a thin airfoil .\n the steady flow of a perfectly conducting\nmagnetohydrodynamic fluid past a thin\nnonconducting airfoil is studied with the usual model\nin which the fluid variables obey the lundquist\nequations linearized about a constant unperturbed\nflow . /hyperliptic/ flows, in which\nhyperbolic and elliptic fields are superimposed,\nare considered . results of grad, mccune and\nresler, and sears and resler are extended and\nconsidered in detail for the case of an arbitrarily\ninclined unperturbed field . the general solution\ncontains four line singularities along the\ncharacteristics through the ends of the body and\nhas two arbitrary constants . by a /\ngeneralized kutta-joukowski condition,/ these constants\nare fixed so that two of the line singularities\ndisappear . specifically, it is required that the\nsolution be locally square integrable . behavior\nof the exponents of the singularities is investigated\nby numerical computation and, in limiting\ncases, analytically . the singular parts of some flows\nare investigated numerically ."}, {"doc_id": 1195, "text": "experiments with two-dimensional, transversely impinging jets .\n experiments on the interaction of transversely\nimpinging two-dimensional jet flows were\nperformed in which a low pressure control jet\nflow interacted with a relatively high pressure\npower jet flow . the ratio of the control jet to\nthe power jet supply chamber gauge stagnation\npressure was adjusted at 0, 10, and 15 .\nshadowgraphs of the power jet alone, as well as the\ncorresponding interacting jet flows, were\nrecorded to establish the nature of and changes in\nthe shock structure . the jet flows were\ntraversed by a pitot tube to record the pitot pressure\ndistributions at various locations downstream\nof the power jet exit . it was discovered that\nwith the addition of only a small percent\ncontrol jet flow, the normal shock front of the highly\nunderexpanded power jet flow changed to\nan oblique shock structure and, downstream of the\nprevious location of the normal shock which\nappeared in the power jet flow alone, the\nmaximum recovery stagnation pressures were\nproportionally much higher . the mechanism for\nthis behavior of the normal shock is proposed .\npossible practical importance of this behavior\nof interacting jet flows with reference to aerodynamic\nnoise, supersonic diffuser losses, etc., is\nalso pointed out . for the power jet flow alone it\nwas found that by considering the actual jet\nboundaries as simply an extension of the actual\nnozzle, the average axial flow quantities,\ncomputed from the area-mach number relation using\nthe observed cross-sectional area of the jet\nflow, agreed quite favorably with the experimental results ."}, {"doc_id": 1196, "text": "growth of the turbulent wake behind a supersonic sphere .\n experimental data are presented on the growth\nof turbulent wakes up to 8000 calibers\nbehind and spheres traveling at supersonic\nvelocities . experimental determination\nof the exponential coefficient in the growth law is\nvery difficult, if not impossible . data are\npresented in the form of both .\nin the representation, two\nregions of different wake growths are observed .\nby means of a quasi-steady state assumption,\nthe effect of drag deceleration is eliminated\nand growth of the far wake compared with\ntheoretical predictions . the agreement with the\nlees-hromas theory in this region was found to\nbe quite good ."}, {"doc_id": 1197, "text": "unsteady aerodynamic forces on slender supersonic aircraft\nwith flexible wings and bodies .\n the present paper derives generalized aerodynamic\nforces for slender supersonic aircraft on\nthe basis of slender-body theory . particular\nconsideration is given to configurations which\nare spanwise flexible . to treat configurations\nwith flexible wings and bodies, the slender\nwing-body problem is first reduced to a simple body\nproblem whose solution is well known, and a\nsolution of the latter is obtained, utilizing the\ncircle theorem or method of images and a known\nsolution of the airfoil equation for a double\ninterval . with this approach, it is not necessary\nto apply conformal mapping techniques,\nand the solution so obtained is valid for arbitrary\nspanwise downwash distributions . on the\nbasis of slender-body theory, the velocity potential\nand, subsequently, the generalized\naerodynamic forces are derived for a general class of\nspanwise flexible wing-body configurations ."}, {"doc_id": 1198, "text": "the blunt-leading-edge problem in hypersonic flow .\n the present paper is mainly concerned with\nthe hypersonic flow over a flat plate with a\nblunt nose . the analysis is based on the flow\nmodel in which the flow field behind the shock\nwave may be divided into two regions .. the\ninviscid-hypersonic-flow region and the entropy\nlayer, across which the pressure has no appreciable\nchange . the equations for the entropy\nlayer can be reduced to those of the usual\nboundary-layer problem with the exception that\nthe outer edge of the entropy layer, as well\nas the pressure remain unknown . these\nunknowns are determined so as to approximately\nmatch the entropy-layer solution with the\ninviscid hypersonic solution in which the shock\nwave has the shape of the power law of the\ndistance from the leading edge . the assumed\nflow model is shown to be valid over a restricted\nrange depending on the wall-to-stagnation\ntemperature ratio and (where is\nthe reynolds number based on half the thickness\nof nose t, m the freestream mach number,\nand c the chapman-rubesin constant .\nactual calculations have been carried out for the\ncase with typical values of and\nthe wall-to-stagnation temperature ratio .\nthe calculated values for both the surface\npressure and heat-transfer rate are compared\nwith the experimental data . as regards surface\npressure in particular, a satisfactory\nagreement with the data is obtained . the validity\nof the assumptions upon which the present\nanalysis is based has been examined from the\nnumerical results, and the region of the validity\nhas been found to extend over a certain large range\nof the nondimensional distance from the\nleading edge ."}, {"doc_id": 1199, "text": "theoretical investigations of a supersonic laminar\nboundary layer with foreign-gas injection .\n the phenomena arising from the uniform injection of helium,\nair, argon, and iodine into the laminar boundary layer of a\nsupersonic stream of air in a tube were investigated theoretically .\nthe partial differential equations describing the energy, mass,\nand momentum transfers through the boundary layer were\nobtained, and a series solution was found for the case of uniform\ninjection through the tube wall . the results of the analysis are\nin the form of axial distributions of wall temperature and\nrecovery factor and of radial distribution of concentration,\nvelocity, static, and stagnation temperatures . the gas mixture\nwas assumed to be a perfect gas . properties of the mixture were\ncalculated in accordance with the gibbs-dalton rule and the\nmixing rules based on the kinetic theory of dilute gases .\ntransport properties for pure air were taken from the n.b.s.\ntabulations . transport properties for the other gases were calculated\nby kinetic-theory methods, employing a lennard-jones 6-12\nmodel for the interaction potential . the theoretical predictions\nfor the recovery factor along the tube with air or argon injection\nagree with experimental data to within one percent . the\ntheoretical predictions for helium injection indicate an 8-percent\nrise in the recovery factor along the tube, while experiments\nhave shown only a 1-percent rise . these differences between\ntheory and experiment are attributed to inaccuracies in the\napproximations to the transport properties of the binary mixtures ."}, {"doc_id": 1200, "text": "hypersonic viscous flow over a sweat-cooled flat plate .\n this paper presents a theoretical analysis of the hypersonic\nviscous flow over a sweat-cooled flat plate . the physical\nsystem under consideration is the hypersonic laminar boundary\nlayer over a porous flat plate with homogeneous, normal\ninjection of a coolant into the external stream . a heat balance at\nthe porous surface is made between the heat transferred to the\nsurface and the heat absorbed by the coolant . the existence\nof similar solutions requires a nonuniform distribution of coolant\ninjection . the method of solution consists of the integration of\nthree simultaneous first-order equations, the momentum and the\nenergy integral equations in the boundary layer, and the\ntangent-wedge approximation in the inviscid layer . first-order\nasymptotic formulas are given in both the strong and the weak pressure\ninteraction regions for the induced surface pressure, the\nskin-friction coefficient, and the nusselt number . numerical\nresults for three specific cases are presented and discussed ."}, {"doc_id": 1201, "text": "a study of slender shapes of minimum drag using the\nnewton-busemann pressure coefficient law .\n the problem of minimizing the drag of a slender, two-\ndimensional or axisymmetric body in hypersonic flow at zero angle of\nattack is considered under the assumption that the pressure\ncoefficient law is newton's impact law as modified by busemann in\norder to include centripetal acceleration effects . after the\ncondition that the pressure coefficient be nonnegative is accounted\nfor and after arbitrary conditions are imposed on, in addition\nto the thickness and the length, the enclosed area and the moment\nof inertia of the contour in the two-dimensional case and the\nwetted area and the volume in the axisymmetric case, the\nminimal problem is formulated as a problem of the mayer type and\nsolved by the combined use of the euler-lagrange equations,\nthe transversality condition, the erdmann-weierstrass corner\ncondition, and the properties of the switching function .\n particular attention is devoted to the class of problems such\nthat, among the four quantities being considered, two are\nprescribed while the remaining are free . for these problems, the\nextremal arc is composed of two subarcs .. one is characterized by\na positive pressure coefficient and is called the regular shape,. the\nother is characterized by a zero pressure coefficient and is called\nthe free layer . in this connection, the analysis shows the\nexistence of two different types of solutions depending on whether the\nthickness is given or free .\n if the thickness is given, the expression for the regular shape is\na power law, and the transition from the regular shape to the free\nlayer occurs in the second half of the body . in the two-\ndimensional case, the exponent of the power law is 1 if the length is given\nif the enclosed area is given, and 3 if the moment of inertia\nof the contour is given,. the transition point from the power\nbody to the free layer is located at 50 percent of the length if the\nlength is given, at 66 percent if the enclosed area is given, and at\nthe axisymmetric case, the exponent of the power law is if\nthe length is given, 1 if the wetted area is given, and if the\nvolume is given,. the transition point from the power body to the\nfree layer is located at 60 percent of the length if the length is\ngiven, at 70 percent if the wetted area is given, and at 80 percent\nif the volume is given .\n on the other hand, for problems where the thickness is free,\nthe equation governing the regular shape is not that of a power\nbody, and the point of transition to the free layer is located in the\nfirst half of the body . in the two-dimensional case, the\ntransition point is at 28 percent of the length if the length and the\nenclosed area are given, at 32 percent if the length and the moment\nof inertia of the contour are given, and at 45 percent if the\nenclosed area and the moment of inertia of the contour are given .\nin the axisymmetric case, the transition point is located at 35\npercent of the length if the length and the wetted area are given,\nat 39 percent if the length and the volume are given, and at 46\npercent if the wetted area and the volume are given .\n for all of the cases considered, analytical expressions are\nobtained for the optimum shapes, the thickness ratios, and the drag\ncoefficients ."}, {"doc_id": 1202, "text": "uniformly valid second-order solution for supersonic\nflow over cruciform surfaces .\n considered is the second-order supersonic flow over a\ncruciform configuration consisting of two intersecting rectangular\nwings of high aspect ratio . the practical interest is in\napplication to supersonic inlets, wing-body junctions and vehicle fins .\nthe fundamental interest centers about identification and\nadjustment of the severe local failures of the ordinary second-order\ntheory . for wings with discontinuous slopes, discontinuous\npotentials occur across the planar shock and square-root\nsingularities in the velocities occur at the intersection of these shocks\nwith the cruciform surfaces . the problem is simple enough so\nthat these interesting features stand out clearly .\n a second-order solution uniformly valid to first order is\nconstructed by adjustment of the ordinary second-order solution\nobtained first . the uniformly valid solution has two different\nseries representations in the thickness parameter . one is the\nordinary second-order series in ascending integral powers of the\nthickness parameter which is valid in the interior of the\nvertex-centered undisturbed mach cone, and the other is a series\ncontaining fractional powers which is valid adjacent to and upstream\nof this mach cone . the uniformly valid solution gives the\ndetailed wave structure and shows a flow regime upstream of the\nvertex-centered undisturbed mach cone not predicted by the\nordinary theory . the two solutions are otherwise identical .\nthe wave structure consists of a pyramidal arrangement of planar\nshocks adjacent to and upstream of the above cone, followed by\nweaker oblique expansion fans and finally by two extremely\nweak shocks coincident with the vertex-centered undisturbed\nmach cone . as an example of the above, detailed results are\npresented for the case of two intersecting wedges . application\nof the techniques to other quasi-cylindrical problems is discussed ."}, {"doc_id": 1203, "text": "the propagation of a nonuniform magnetohydrodynamic\nshock wave into a moving monatomic fluid .\n an initially uniform magnetohydrodynamic shock wave of\narbitrary strength propagates through a channel which consists of\ntwo portions of which one has uniform cross-sectional area while\nthe other is of varying cross-sectional area . it is assumed that\nthe flow in the nonuniform section in front of the shock is initially\na uniform state and no perturbations (due to the area variations)\nof this flow reach the shock until the area variation is encountered .\nwhen the shock enters the nonuniform section, it is perturbed,\nthe shock strength altered and the subsequent flow is\nnonisentropic . in addition to the perturbation due to the effect of the\narea variations on the initially uniform upstream flow, there are\ntwo further contributions--viz., a permanent perturbation\ncaused directly by the area changes and a transient\ndisturbance--which propagates with true sonic speed with respect to the flow\nbehind the shock, due to reflections of the permanent\nperturbation at the shock . expressions for these various contributions are\nobtained . the results presented include as special cases\npropagation of a nonuniform conventional gas dynamic shock into a\nmoving nonconduction fluid and propagation of a nonuniform\nhydromagnetic shock wave into a stationary fluid ."}, {"doc_id": 1204, "text": "experimental effect of bluntness and gas rarefaction\non drag coefficients and stagnation heat transfer on\naxisymmetric shapes in hypersonic flow .\n inverted hemispheres, circular discs (normal to stream),\nspheres, 26 total angle 0.368 blunt hemisphere cones, 18\ntotal-angle sharp cones, and other axisymmetric shapes were run in a\nhypervelocity wind tunnel . hypersonic drag coefficients at zero\nangle of attack were measured in the air velocity range, 7,000-\nefficient is defined as drag force . knudsen number is\ndefined as mean free path behind shock sphere shock\ndetachment distance . in the case of nonsphere shapes, the knudsen\nnumber is defined as the knudsen number of a sphere with the\nsame base diameter .\n these drag coefficients cover the range of gasdynamics to free\nmolecule flow and are given in graphical form . the drag\ncoefficients were measured by means of a ballistic balance in\nmillisecond intervals, and referenced to the drag coefficient of a\nsphere in the gasdynamics region, for a gamma of 1.4, of 0.92 .\n tunnel stagnation conditions of pressure, temperature, density,\nand pressure drop with time were measured directly . in the\ntunnel test section, velocity, q density, total pressure, and static\npressure were measured directly .\n these experimental curves have been found useful in the\nanalysis of complex shapes if the complex shapes can be easily broken\ndown into simple components with small interactions between\ncomponents .\n heat-transfer distributions have also been obtained on these\nand other complex shapes in the hypervelocity wind tunnel, by\nmeans of a special paint which changes through several visible\nspectral orders within a heat transfer range of x10 for a single\napplication . heat transfer rates, so obtained, have been\nperformed in the hypersonic gasdynamic and slip flow regions and\nare presented for spheres . these data, in the vorticity interaction\nregion, agree with the data of ferri and zakkay ."}, {"doc_id": 1205, "text": "effects of cooling on boundary layer transition on\na hemi- sphere in simulated hypersonic flow .\n an experimental investigation of the effects of cooling on\nboundary-layer transition on a 9-in. diameter hemisphere in\nsimulated hypersonic flow is reported . the newtonian pressure\ndistribution was obtained by use of a shroud and boundary layer\ncooling was achieved by internally cooling the model . transition\nwas detected with hot wires and with a pitot tube at the surface .\nattained .\n transition was observed in the subsonic and near-sonic flow\nregion at and upstream of n = 45 . in this region the stagnation\nreynolds number at which transition occurred when the surface\nwas highly polished was only slightly affected by cooling within\nthe temperature range . thus, transition\nreversal does not occur on a polished spherical surface within the\nrange of these tests, and we therefore conclude that the cooling\ndid not cause the linear stability of boundary layer to decrease\nsignificantly .\n an essential feature of transition studies with boundary-layer\ncooling is the close control of surface roughness . in the present\nexperiments this control required, in addition to a highly polished\nsurface, the necessity for low water vapor dewpoint, the\navoidance of carbon dioxide condensation and the utilzation of every\navailable means for removing the dust from the airstream ."}, {"doc_id": 1206, "text": "magnetohydrodynamic mach cones .\n features of the surfaces of main disturbance created by a small\nobject in steady motion through a conducting fluid are examined .\nthese surfaces are found by drawing tangent cones from the\nobject to the relevant wave-front diagrams . the outer wave\ncone (when present) is smooth, but the two inner cones have\ncross sections similar to the cusped figures of the inner\nwave-front diagram . it is conjectured that the disturbance may be\nconcentrated along such line cusps . this has particular\nrelevance in the application of known two-dimensional results to\nthree-dimensional problems, say in the well-known techniques\nof aerodynamics . in mhd the omission of the large disturbance\ncharacteristics implicit in a two-dimensional solution may\ninvalidate its use in any practical three-dimensional problem ."}, {"doc_id": 1207, "text": "supersonic airfoil performance with small heat addition .\n an analytical method is presented which permits a very rapid\nevaluation of the acrodynamic effects arising from the addition\nof small amounts of heat near supersonic two-dimensional\nairfoils . this method applies to shockless inviscid flow without heat\nconduction . also, the mechanism by which the sesired heat\naddition is achieved is not considered .\n it is shown that even small amounts of heat generate a\nsubstantial pressure rise and thus cause appreciable changes in the\nacrodynamic coefficients . the results of this analysis compare\nfavorably with those obtained by a more accurate, but also more\ntedious, graphical method of characteristics .\n two possible modes of application to an airplane design are\nconsidered from the energy requirements standpoint . in this\nconnection, it is shown that the decrease of the required wing\narea resulting from heat addition may, in some cases, lead to\nsavings in the rate of the fuel consumption . in general, however,\none should not expect any substantial reduction in energy\nrequirements resulting from the application of the wing heat\naddition ."}, {"doc_id": 1208, "text": "a linearized analysis of the forces exerted on a rigid\nwing by a shock wave .\n solutions are obtained in closed form for the pressures exerted\non a rigid half plane by an incident, plane acoustic shock wave .\nthe angle of incidence of the wave front is arbitrary and the half\nplane is considered to be traveling at constant velocity, subsonic\nof supersonic with respect to the acoustic medium . a\nclosed-form solution is obtained also for a rigid wedge which is\nmotionless with respect to the acoustic medium . the analysis is carried\nout by transforming the wave equation to laplace's equation\nby the busemann conical transformation and then applying\nconformal mapping ."}, {"doc_id": 1209, "text": "aerodynamic processes in the downwash-impingement problem .\n theoretical and experimental data relating to the downwash\nimpingement problem are examined in order to arrive at a\ncoherent understanding of the process of entrainment of ground\nparticles in the flow . it is demonstrated that a key mechanism\nin the process is the interaction of nonuniform flow in the ground\nboundary layer with bluff ground particles . this interaction\nproduces a lift force which, under typical conditions, equals or\nexceeds the particle weight .\n in the interest of quantitative prediction of the conditions\nnecessary for particle entrainment, four subsidiary problem areas\nin the impinging jet are examined . these are the viscous decay,\nthe inviscid flow field, the ground boundary layer, and the forces\non a bluff body in nonuniform flow . applicable theories are\nused in conjunction with experimental data to assess the accuracy\nand range of validity of the theories, and to define the stream\nconditions which will cause particle entrainment .\n available data are applied to the establishment of criteria for\nparticle entrainment in the vicinity of the impinging-jet\nstagnation point . these criteria show that entrainment occurs in a\nfinite annular region on the ground plane, and that the particles\nmost readily entrained are those with a diameter equal to about\ntwo-thirds the thickness of the ground boundary layer . the\nconfiguration size is shown to influence the process in that the\nonset of entrainment is fixed by the jet diameter and velocity,\nand the size of the ground particles . the criteria established\nprovide a quantitative estimate of the conditions causing\nentrainment and provide a basis for scaling experimental results to\na variety of full-scale situations ."}, {"doc_id": 1210, "text": "on slender airfoil theory for nonequilibrium flow .\n an exact linear theory for nonequilibrium flow past a thin\nairfoil is given . green's function technique is used to solve the\nboundary value problem for the governing third order equation .\nupon satisfying the boundary condition on the airfoil surface an\nintegral equation is obtained which has an exact solution . the\nfinal expression for the velocity potential, given as an integral over\nthe source strength times the green's function, shows that the\nsolution is dependent not only on the slope variation of the airfoil\nbut also on its curvature variation . this turns out to be the case\nfor all free-stream mach numbers .\n as an example, the supersonic flow past a wedge is considered ."}, {"doc_id": 1211, "text": "boundary layer transition at supersonic\nspeeds-three-dimensional roughness effects (spheres).\n further experiments carried out in the 12-in. supersonic wind\ntunnel of the jet propulsion laboratory of the california\ninstitute of technology to investigate the effect of three-dimensional\nroughness elements (spheres) on boundary-layer transition on a\nthe local mach number for these tests was 2.71 . the data show\nclearly that the minimum (effective) size of trip required to bring\ntransition to its lowest reynolds number varies as the one-fourth\npower of the distance from the apex of the cone to the trip . use\nof available data for other mach numbers indicates that the\nmach-number influence for effective tripping is taken into\naccount by the simple expression .\nsome remarks concerning the roughness\nvariation for transition on a blunt body are made ."}, {"doc_id": 1212, "text": "effect of uniformly distributed roughness on turbulent\nskin-friction drag at supersonic speeds .\n an experimental program was carried out in the 18-in. by\n20-in. supersonic wind tunnel of the jet propulsion laboratory to\ndetermine the effect of uniformly distributed sand-grain\nroughness on the skin-friction drag of a body of revolution for the case\nof a turbulent boundary layer . the mach number range\ncovered was 1.98 to 4.54, and the reynolds number varied from\nabout 3 x 10 to 8 x 10 . some data were also obtained at a\nmach number of 0.70 .\n at speeds up to a mach number of 5 and for roughness sizes\nsuch that the quadratic resistance law holds, the compressibility\neffect is indirect, and the skin-friction drag is a function of only\nthe roughness reynolds number, exactly as in the\nincompressible case . it is shown that the entire compressibility effect\nis a reduction of the fluid density at the surface as the mach\nnumber increases . the critical roughness, below which the\nsurface is hydraulically smooth, is,. this is equal\nto the thickness of the laminar sublayer for a smooth surface for\nboth compressible and incompressible flow . over the range of\nroughness sizes considered here, there appears to be no wave drag\nassociated with the drag due to roughness . the shift in the\nturbulent veocity profile for a rough surface at supersonic\nspeeds is a function of only the roughness reynolds number\nand quantitatively follows exactly the same law as that\nfor the incompressible case ."}, {"doc_id": 1213, "text": "heat transfer to slender cones in hypersonic flow,\nincluding effects of yaw and nose bluntness .\n as part of a general study of the aerothermodynamic\ncharacteristics of flight of hypersonic vehicles, an investigation of\nlaminar heat transfer to slender yawed cones has been conducted .\nexperiments have been made in the cal 11- by 15-in. shock\ntunnel at mach numbers from 11 to 13 and at yaw angles up to\nwere tested .\n the heat-transfer rates are compared with theoretical\npredictions . the effects on the local heat-transfer rates of the\nboundary-layer displacement thickness, transverse curvature, yaw,\nnose bluntness, and the entropy sublayer are discussed . it is\nshown that, at zero yaw, the experimental data for the sharp\ncone are in good agreement with theory when boundary-layer\ndisplacement and transverse-curvature effects are included .\nfor the yawed sharp cone, the heat-transfer rates along the\nmost windward streamline are in good agreement with reshotko's\ntheory for yaw angles up to 3 . at larger yaw angles, the\nexperimental heat transfer was found to be greater than that\npredicted theoretically . however, at these yaw angles the\nheat-transfer distribution on the windward side was in good\nagreement with laminar-boundary-layer calculations based on an\nassumption of local similarity . the zero-yaw tests of the blunted\ncones showed qualitative agreement with cheng's shock-layer\ntheory for slender blunt-nose bodies ."}, {"doc_id": 1214, "text": "the drag of elongated bodies over a wide reynolds number\nrange .\n the resistance of bodies in motion through an incompressible\nviscous fluid is predictable from stokes- or oseen-type solutions\nin the creeping-motion range, while some test information is\navailable in the boundary-layer range . with the exception of\nexperimental results for spheres or circular cylinders and\nanalytical and experimental results for flat plates, almost no information\nis available on other bodies, particularly in the intermediate\nrange of reynolds numbers extending from unity to a million .\n experimental results as obtained from hydroballistic studies\nin water and glycerin-water solutions are presented for finned\nellipsoids of fineness-ratio .4 over a 20,000-fold range and are\ncorrelated with available information on other bodies . although\nresults do not extend down to the creeping-motion region where\nanalytical predictions are available, comparison with the drag\ncoefficient trends for spheres and flat plates indicates that an\nappropriate curve for the ellipsoid could be extended so as to cover\nthe entire laminar-viscous range . less extensive results are\npresented on the drag of fineness-ratio 8 ellipsoids and on\nlaminar-turbulent transition occurrences ."}, {"doc_id": 1215, "text": "the effect of slip particularly for highly cooled walls .\n it is found that for boundary conditions on the velocity slip\nand on the temperature jump which are not oversimplified in an\nunrealistic way, the effect of these phenomena on the heat transfer\nand the shear at a stagnation point is of the order of the ratio of\nthe mean free path outside the boundary layer to the\nboundary-layer thickness, even for highly cooled walls . a simplified\ntheory of this effect is given, which puts the physical reasons for\nthe results in evidence and agrees closely with the more accurate\ncalculations . it is concluded that the effects of slip and jump\nare not negligible in comparison with other low-reynolds-number\ncorrections, even for very cold walls ."}, {"doc_id": 1216, "text": "pressure distribution in regions of step-induced turbulent\nseparation .\n an analysis is made of the pressure distribution in the\nseparated-flow region ahead of a step, using the concept of the\nturbulent mixing coefficient of crocco and lees and the /jet-flow/\nmodel of chapman with some modification . on the basis of\na variable mixing coefficient, a differential equation for the\npressure distribution is derived, which gives the pressure rise as a\nfunction of the distance from the separation point . this\nequation contains the separation length as an unknown . a second\nequation is obtained by making a mass balance of the air entering\nand, leaving the /dead-air/ region ahead of the step . the\npressure rise and the separation distance for a given mach\nnumber are determined by solving the two equations simultaneously .\n the analysis yields results which are in close agreement with\nthe experimental data on steps, obtained at princeton,\nparticularly for m = 3.85 . for lower mach numbers, a maximum\nvariation of 5 percent is found between theory and experiment .\nuse of the velocity profiles of jets, as required by the jet-flow\nmodel, necessarily restricts the applicability of the present study\nto flows with thin boundary layers at the separation point ."}, {"doc_id": 1217, "text": "application of inequality constraints to variational\nproblems of lifting re-entry .\n inequality constraints are introduced into the variational\nformulation of the optimum re-entry problem for a lifting\nvehicle to prevent human and or structural tolerances from being\nexceeded . these constraints consist of minimum and maximum\nangle of attack, maximum load factor, and maximum convective\nheat transfer (equilibrium temperature) .\n the equations have been programed for the ibm 704\ncomputer, and sample trajectories are presented for which the total\nheat transferred to certain critical areas on the windward\nsurface of the vehicle is minimized . these trajectories indicate the\ndominant effect of the constraints on the optimum flight path,\nwhich is shown to consist of both unconstrained and constrained\narcs ."}, {"doc_id": 1218, "text": "experimental lift and drag of a series of glide configurations\nat mach numbers 12 .6 and 17 .5.\n a series of semiballistic-type bodies consisting of three half\nsphere cones of 0.3 bluntness ratio with half-cone angles of 8.6,\nlaboratory hypersonic shock tunnel at m = 17.5 and 12.4 .\nin addition, a representative winged glide configuration\nconsisting of a sharp-edged, 60 swept delta wing with cone-segment\nthe range of angle of attack for the half sphere-cone tests was\n the technique for force coefficient determination consists of\nanalyzing high-speed motion pictures of the motion of very light\nbalsa and isofoam plastic models which are literally free-flown\nfor several milliseconds in the test section of the shock tunnel .\n because of viscous effects the newtonian prediction of half\nsphere cone drag is consistently less than, but generally parallel\nthese bodies is generally well predicted by the newtonian theory\nexcept at small and moderate positive angles of attack where it is\ngenerally less than newtonian . this lift deficiency appears to\nincrease with cone half angle . maximum lift-drag ratios fall\nconsiderably short of the newtonian predictions . several\nexploratory tests at mach 11.7 and low reynolds number (\napproximately reduction in) on the 13 model produced an\napproximate doubling of minimum drag and a 35 percent\ndecrease in (l d) max,. this demonstrates the importance of viscous\neffects for blunt bodies in the reynolds number range of these\ntests .\n the sharp leading-edge, 60 sweep delta wing-body\nconfiguration exhibited the same (l d) max, as the wing alone, about 2.80\nat both positive and negative angles of attack ."}, {"doc_id": 1219, "text": "determination of lift or drag programs to minimize\nre-entry heating .\n a study of single-pass re-entry from escape speed and from\ncircular satellite speed is made to determine the lift program for a\nhypersonic glider and the drag-modulation program for a\nnon-lifting vehicle that minimize the heating of the vehicles within\nacceleration or range constraints . a new method of numerical\nsolution is used, similar to kelley's /method of gradients,/ that\npermits rapid convergence to the optimum lift program starting\nwith an original good estimate . this method avoids the\ntwo-point boundary-value problem of the calculus-of-variations\nformulation, and is applicable to any optimum-programing\nproblem . an acceleration-tolerance limit is introduced which\ndescribes the human pilot's capability to withstand acceleration\nmore accurately than a simple acceleration limit ."}, {"doc_id": 1220, "text": "boundary layer transition in the presence of streamwise\nvortices .\n results of an experimental investigation of instability leading\nto transition in the subsonic boundary layer flow along a flat\nplate are presented . a series of wings was placed outside the\nboundary layer to produce streamwise vortices, which in turn\nmade the boundary layer three-dimensional--i.e., periodic in\nthickness in the spanwise direction . hot-wire measurements\nwere made to trace the downstream development of the\ndisturbance or wave created by the vibrating ribbon . as the wave\ntravels downstream, it is deformed into a three-dimensional\nconfiguration by the three-dimensionality of the boundary-layer\nflow, but it is eventually damped out so long as it remains small in\nintensity . it is only after the wave intensity exceeds a certain\namount (which depends on the degree of boundary-layer\nthree-dimensionality) that the nonlinear effect manifests itself by the\nrapid amplification of wave intensity, the rapid increase in wave\nthree-dimensionality, and the distortion in mean velocity profile .\nthe appearance of nonlinear development inevitably leads to the\nbreakdown of laminar flow, and hence the onset of turbulence .\nthere is present a mechanism by which the energy is transferred\nfrom one spanwise position to another so that the breakdown of\nlaminar flow occurs as a consequence of three-dimensional\ndevelopment of the wave as a whole ."}, {"doc_id": 1221, "text": "steady flow of conducting fluids in channels under\ntransverse magnetic fields, with consideration of hall\neffect .\n an approximate method of solution based on a minimum\nprinciple is presented for the steady laminar incompressible flow of an\nelectrically conducting fluid through a straight channel of\narbitrary cross section with conducting or nonconducting walls in the\npresence of a uniform transverse magnetic field . the hall effect\nis taken into account by making simplifying assumptions that the\ngas is fully ionized and that both reynolds number and magnetic\nreynolds number are small . numerical calculations are carried\nout for the case of a rectangular channel ."}, {"doc_id": 1222, "text": "axisymmetric magnetohydrodynamic channel flow .\n the axisymmetric subsonic and supersonic flow fields, and the\nskin friction and heat transfer of an electrically conducting\ncompressible fluid flowing in a channel of constant circular area\nthrough a magnetic field are investigated when the magnetic\nreynolds number is small . the inviscid-flow field for flow\nthrough a dipole field is solved by the method of characteristics\nin the supersonic case . for the subsonic case, linearized\nequations are derived for small values of the magnetic interaction\nparameter . numerical results are obtained by the relaxation\nmethod .\n the inviscid-flow-field solutions are used as boundary\nconditions for the laminar boundary layer along the wall, in which\naxial pressure gradients form an important feature . the exact\ncontinuum-flow equations are reduced by an order-of-magnitude\nanalysis to the boundary-layer equations, which are solved\nnumerically by an integral method using a fourth-degree velocity\nprofile and a fifth-degree stagnation-enthalpy profile .\n pressure, temperature, and heat-transfer measurements are\nmade with a shock tube under supersonic-flow conditions closely\napproaching those used in the numerical computations .\ngeneral agreement is found between the theoretical and the\nexperimental results ."}, {"doc_id": 1223, "text": "inviscid-incompressible-flow theory of static two-dimensional\nsolid jets, in proximity to the ground .\n the inviscid-incompressible-flow theory of static two-\ndimensional solid jets impinging orthogonally on the ground is\npresented using conformal mapping methods .\n it is shown that the thrust of a solid jet at constant power\ninitially decreases as the ground is approached . the\nmagnitude of the thrust out of ground effect is regained only at a very\nlow height-to-jet width ratio (approximately 0.55) . the\nmaximuin decrease is about 6 percent . the ground effect on solid\njets is thus largely unfavorable ."}, {"doc_id": 1224, "text": "on the plk method and the supersonic blunt-body problem .\n detailed analysis of the subsonic and transonic portious of the\nflow field about either very blunt or asymmetric configurations\nrequires successive approximations,. these can be carried out in a\nsystematic fashion only when an appropriate convergent\nperturbation procedure is available . the problem of producing\nsuccessively refined sets of initial conditions for either /direct/\nor /inverse/ analysis of the flow is formulated in the following\nterms .. given reasonable estimates for shock shape and\npressure distribution on the body, can one determine the flow field\nof interest to any desired degree of approximation by a\nperturbation approach .qm\n a procedure to this effect is developed which involves\nstretching of coordinates in the spirit of the poincare-lighthill-kuo\nare transformed along body, shock, and intermediate lines so as\nto annul perturbations of the local resultant velocity,. (b) for the\nintegral method the coordinate along the boundary of each strip\nis shifted so as to control perturbations of the velocity component\nthat determines the critical point .\n the approach is justified by a study of the equations governing\nthe direct method, and by consideration of model transonic flow\nproblems for which closed form solutions are available . the\nrange of validity of the proposed procedure is assessed by\npractical application and comparison with experiment,. results are\npresented for a disk set normal to a low-termperature air stream\nat m = 4.76, and for a highly asymmetric two-dimensional\nconfiguration at m = 8 ."}, {"doc_id": 1225, "text": "the effect of adverse pressure gradients on the characteristics of\nturbulent boundary layers in supersonic streams .\ntests were conducted at mach numbers from 2.0 to 3.5 to determine\nthe thickness and profile shape characteristics of turbulent boundary\nlayers on two-dimensional and axisymmetric curved-surface models\nhaving adverse pressure gradients . the magnitude of the gradients\nrelative to the boundary-layer thickness at the beginning of the\ngradient was varied by employing models having different radii of\ncurvature and by changing the boundary-layer thickness at the\nbeginning of the gradient . the overall pressure rise in most cases was\ngreater than the value which would cause a turbulent boundary layer\nto separate if the pressure rise were created by an oblique shock wave .\nan analytical investigation was also conducted so that the results of\nthe experimental investigation could be applied to the prediction of\ncases outside the range of the experiments .\nit is shown that boundary-layer momentum thickness can be predicted\nfrom the von karman boundary-layer momentum equation, but that measured\nvalues of boundary-layer profile shape are in poor agreement with\nvalues computed from procedures derived by extending conventional\nmethods for predicting profile shape in subsonic flow . a new\nprocedure for calculating boundary-layer profile shapes, developed in this\npaper, is shown to provide a good correlation between experimental\nand calculated values of boundary-layer profile shapes in adverse\npressure gradients created by curved surfaces . this procedure is based\non the experimental observation that the station at which high-energy\nfree-stream flow actually mixes into a turbulent boundary layer in\nan adverse pressure gradient is well downstream of the station at\nwhich flow would have to mix in order to maintain a flat-plate profile ."}, {"doc_id": 1226, "text": "heat transfer in the laminar boundary layer with ablation\nof vapor of arbitrary molecular weight .\n the reduction of heat transfer in the laminar boundary layer\nunder the condition of vaporizing ablation is analyzed for\narbitrary molecular weight of the vapor . primary assumptions are\nthat the pressure gradient is zero, the individual components of\nthe binary system are perfect gases, the prandtl number is\nconstant, and the viscosity is proportional to temperature .\nvariations through the boundary layer of the schmidt number for\nbinary diffusion and the density-viscosity product, are\nincluded in the analysis . the wall temperature is held constant .\nnumerical results are obtained for prandtl numbers of 0.75 and\nvarying from 0.25 to 4.00, wall concentration of the foreign gas\nas high as 0.9 (corresponding to the high heat rates encountered\nduring re-entry), and ratio of specific heats of foreign gas equal\nto that of air . kinetic theory is used to obtain schmidt number\nas a function of molecular weight and concentration .\n the departure of schmidt number and prandtl number from\nunity and the variation of reynolds analogy factor with prandtl\nnumber, blowing parameter, wall concentration, and molecular\nweight ratio are found to have relatively minor influence on the\nheat block ratio at high rates of ablation . the primary factor\ngoverning the influence of molecular weight ratio on the heat\nblock ratio is the variation of across the boundary layer .\nlittle loss of accuracy is incurred, in the range of molecular weight\nratios considered here, by assuming schmidt and prandtl\nnumbers of unity as long as the variation is properly taken into account ."}, {"doc_id": 1227, "text": "pressure-gradient effects on the preston tube in supersonic\nflow .\n this paper is concerned with an experimental investigation of\nthe effects of a longitudinal pressure gradient in a supersonic\nstream of air over a bounding surface on the performance of a\npreston or impact-pressure tube at the surface . evidence is\npresented which indicates that for the mach number considered and\nfor the range of pressure gradients covered, the preston tube\nfunctions in a completely satisfactory manner for the determination\nof local shear stress ."}, {"doc_id": 1228, "text": "leading-edge separation of laminar boundary layers\nin supersonic flow .\n a brief description of the flow field is given for the interaction\nof shock wave and laminar boundary layer on a compression\ncorner in supersonic flow . a special sub-case--that of\nleading-edge laminar separation--is analyzed by extension of chapman's\nlaminar mixing-layer theory . results are tabulated for ranges\nof mach number, and compression-corner angle .\na limited region of possible leading-edge laminar\nseparation with an attached leading-edge shock (or in certain\ncases an expansion) followed by a second shock due to the\nreattachment flow is found to exist . comparison with existing\nexperimental data is found to be satisfactory in several cases ."}, {"doc_id": 1229, "text": "the effect of sweep angle on hypersonic flow over blunt\nwings .\n a series of tests were carried out in the princeton university\nhelium hypersoule wind tunnel on blunt two-dimensional wings\nat zero angle of attack with sweep angles up to 70 at mach\nnumbers from 7 to 15 . the leading edge reynolds number varied\nfrom 3,000 to 25,000 . the measured pressure distributions were\ncompared with the simple summation of the theoretical inviscid\neffect (based on blast wave theory using the normal mach\nnumber) added to the viscous effect (calculated as if no sweep\nwere present) . for the unswept wing, the slope of the pressure\ndecay was reasonably well predicted by the theoretical\ncalculations . the viscous theory reasonably predicted the variation in\nthe pressure distribution due to changes in leading-edge\nreynolds number . by subtracting the theoretical viscous effects, an\ninviscid mach number dependence of the 2.2 power was found\nas compared to the value of 2.0 predicted by the inviscid theory .\nthe same approach for the swept wing did not give consistently\nsatisfactory results . deviations avove and below the calculated\nvalue by as much as 40-50 percent were measured and there\nseemed to be no systematic variation with either mach number or\nreynolds number . at a constant high reynolds number, it was\nfound that the pressure distribution varied with the distance\nalong the wing with an exponent between about--0.53 and--0.58\nexcept for a rather sharp decrease which occurred for the 70\nsweep case . the pressure at a given station for a fixed mach\nnumber and given leading edge thickness varied as the cosine of\nthe sweep angle to the 1.1 power as compared to the 1.3 power\npredicted from general geometrical considerations ."}, {"doc_id": 1230, "text": "hypersonic nozzle expansion of air with atom recombination\npresent .\n an experimental investigation on the expansion of high-\ntemperature, high-pressure air to hypersonic flow mach numbers in\na conical nozzle of a hypersonic shock tunnel has been carried out .\nthe equilibrium temperature and pressure ranges after the\nreflected shock wave were 1400 to 6000 k and 100 to 1000 psia .\nstatic-pressure measurements, which are sensitive to the state\nof the gas, were made along the axis of the nozzle for different\nreservoir conditions . these results are compared with the\ncalculated equilibrium and /frozen/ data for the same geometry\nand initial reservoir conditions .\n for reservoir pressures greater than 500 psia, the expansion of\nthe air in the nozzle is essentially in equilibrium up to reservoir\ntemperatures of about 4,500 k . for temperatures greater than\nalmost frozen . at a given area ratio for the nozzle and reservoir\npressure, the expansion process remains in equilibrium up to a\ncertain reservoir temperature, and beyond this temperature the\nflow expansion deviates rapidly from the equilibrium process and\napproaches the frozen case ."}, {"doc_id": 1231, "text": "hypersonic flow over an elliptic cone: theory and experiment .\n by applying hypersonic approximations to ferri's linearized\ncharacteristics method, simple results were obtained for the\nshock shape and surface pressure distribution for an unyawed\nconical body of arbitrary cross section . calculations were\ncarried out for an elliptic cone having a ratio of major to minor\naxes of, and a semivertex angle of about 12 in the meridian\nplane containing the major axis . an experimental investigation\nof the flow over this body conducted at a mach number of 5.8\nin the galcit hypersonic wind tunnel showed that the surface\npressure distribution at zero angle of attack agreed quite closely\nwith the theoretical prediction . on the other hand, the simple\nnewtonian approximation predicts pressures that are too low .\n surface pressure distributions and schlieren photographs of\nthe shock shape were obtained at angles of attack up to 14 at\nzero yaw, and at angles of yaw up to 10 at zero pitch . at the\nhigher angles of attack the newtonian approximation for the\nsurface pressures is quite accurate ."}, {"doc_id": 1232, "text": "the curtain jet .\n a detailed analytic study is made of the curtain jet, the\ntwo-dimensional fluid wall used to contain support pressure on the\nunderside of ground effect machines . two variations of the jet\nare studied in detail--the bifurcated jet, in which a portion of the\nflow streams into the support pressure region, and the deflected\njet, in which none of the flow penetrates into the support pressure\nregion . kirchhoff-helmholtz free steamline analysis is used\nto construct the flow field, and quantitative results are presented\nfor the effect of nozzle inclination and detailed geometry on flow\nrequirements and support pressure differential at varying\naltitudes ."}, {"doc_id": 1233, "text": "supersonic shear flow past an airfoil between two parallel\nwalls .\n the supersonic flow with assigned mach number gradient in\nthe span direction past a straight wing between two parallel\nwalls is studied using the small-disturbance theory . the\ngoverning equation for the disturbance pressure on the airfoil, together\nwith the boundary conditions on the airfoil and at the walls, is\nsolved by the method of separation of variables . upon\nseparation the problem is reduced to a sturm-liouville eigenvalue\nproblem and to the solution of the telegraph equation .\n as an application, a certain mach number profile is selected\nand the resulting pressure distribution on a parabolic arc airfoil\nis computed ."}, {"doc_id": 1234, "text": "direct calculation of pressure distribution on blunt\nhypersonic nose shapes with sharp corners .\n the method of belotserkovskii for calculating hypersonic\nflow fields past a circular cylinder is extended to deal with\naxially-symmetric flow past sharp-cornered nose shapes, in particular,\nspherical segments and flat-headed cylinders . results on\nspheres are also included . in the present paper belotserkovskii's\nfirst approximation is considered, and comparison of calculated\npressure distribution and shock shape with experimental results\nshows very good agreement ."}, {"doc_id": 1235, "text": "a theory of the two dimensional laminar bounary layer\nover a curved surface .\n the purpose of this paper is to present a theory to account for\nsurface curvature effects on the two-dimensional boundary-layer\nflow which approaches a potential flow at free stream .\n the problem of two-dimensional viscous flow is first formulated\nby using the streamlines and their orthogonal trajectories as the\ngeneralized coordinates . a boundary-layer approximation is\napplied to the navier-stokes equations and the gauss equation\nin the generalized coordinates to yield the boundary-layer\nequations . the conditions under which similar solutions of the\nboundary-layer equations exist are determined . by a simple\ntransformation, the governing differential equation can be\nexpressed in a form which reduces to the falkner-skan equation\nfor zero surface curvature .\n numerical results for a similar solution which corresponds to a\nflow over a curved surface with zero surface pressure gradient\nhave been obtained . the velocity profiles in the boundary layer\nand the wall skin-friction distribution for concave and convex\nsurfaces are presented . the wall skin friction for a convex wall\nis found to be higher than the blasius value for a flat plate . on\nthe other hand, for a concave wall, the skin friction will drop\nbelow the blasius value as the curvature increases, but it appears to\nreach a minimum, and beyond this minimum point it will increase\nagain . the same flow problem was treated by murphy by a\ndifferent method of analysis . comparison of murphy's results\nwith those obtained by the present method reveals some basic\ndifferences in the boundary-layer characteristics . in particular,\nmurphy's results indicate that the wall skin friction for a convex\nsurface is smaller than the blasius value, while for a concave wall\nit is higher ."}, {"doc_id": 1236, "text": "the stagnation point boundary layer in the presence\nof an applied magnetic field .\n similarity equations for axisymmetric compressible flow are\nobtained, assuming that the magnetic field is uniform, normal to the\nsurface, and unaffected by the flow, and that the conductivity\nvaries as the nth power of the enthalpy . numerical solutions are\ngiven for a number of values of n and of the field strength, and are\nused to modify the estimates of heat-transfer made by the author\nusing inviscid theory (title source 26, 536-537, 1959) ."}, {"doc_id": 1237, "text": "foreign-gas injection into a compressible turbulent\nboundary layer on a flat plate .\n the distributed injection of a foreign gas into a compressible,\nturbulent boundary layer in the absence of a pressure gradient is\nconsidered . the analysis is performed within the framework of\nthe binary-mixture concept, that is, the primary fluid flowing\nover the surface represents one component while the injected\nspecies represents the second .\n calculations have been performed for the injection of helium\ninto undissociated air . the results indicate an effect of mach\nnumber on surface shear and energy transfer when distributed\nlight-gas injection normal to the surface exists . a comparison\nwith experimental data indicates reasonable agreement over a\nrange of mach numbers ."}, {"doc_id": 1238, "text": "the newtonian approximation in magnetic hypersonic\nstagnation-point flow .\n the hypersonic flow of an electrically conducting fluid around\nthe stagnation region of a sphere carrying a radial magnetic field\nis examined .\n by assuming a newtonian pressure distribution and constant\ndensity, the differential equation of the inviscid flow is integrated\nand a simple closed-form solution is obtained .\n it is found that the ratio of the stand-off distances of the shock\nwave for the magnetic and nonmagnetic cases does not depend\nexplicitly on the magnetic parameter s (ratio of the ponderomotive\nforce to the free-stream inertia force) nor on the density ratio (the\nvalue at the free stream divided by the value behind the shock\nwave) but on the product s at least for values of between\nand .\n the velocity gradient on the body is also calculated and the\nratio of the magnetic to the nonmagnetic case is shown to depend\non the parameter .\n the case of cylindrical shocks is also examined,. the same\ngeneral conclusions are drawn ."}, {"doc_id": 1239, "text": "body under lifting wing .\n an investigation is made of supersonic-aircraft configurations\ncomposed of a cambered body positioned a certain distance\nbeneath an arbitrary lifting wing . the geometry of the wing is\nregarded as given and the geometry of the body may be given or\noptimum . expressions for the drag and lift are obtained from\nreverse-flow considerations,. these greatly implement such a\nstudy when interference cross flows must be cancelled . the\ndrag advantage to be gained when a given body and wing\nassume a given orientation is studied . treated more extensively\nis the variational problem of determining the optimum wing\nincidence and optimum body shape, for the given volume and\nlength, to yield the minimum drag for prescribed lift .\nnumerical results are provided to indicate the significance of the large\nnumber of parameters appearing in the problem . of these, the\ngap between the wing and the body is found to be particularly\nimportant . it is found that at low gap moderate body\ndistortions have a significant influence on the drag . drag reductions\nof up to 44 relative to the case of no interference have been\nfound at a mach number of 2.24 in a configuration having a\ngap approximately equal to the maximum diameter of the body,\nand a wing chord of about three eighths of the length of the body .\ncomparison is made with the conventional wing-body\ncombination including the effects of skin friction, and it is concluded that\nthe advantage suggested by the preceding considerations is not\nappreciably diminished . finally, it is shown that the\nconfigurations studied lead to bodies of fineness ratios much lower\nthan are appropriate to conventional wing-body combinations .\n tests were made on an arrangement consisting of a\nscars-haack body located under a lifting rectangular diamond-profile\nwing . the mach number was 1.6 and the reynolds number\nwas 9.17 x 10 based on the body length . it was found that the\nmeasured lift developed on the wing due to the flow field of the\nbody agrees very well with the theoretical value . downstream\nof the impinging shock from the wing, flow separation was\nobserved on the exterior of the body but not in the interior . the\nseparation is attributed not to the pressure rise across the shock\nbut to the pressure field arising from the reflection from the\nbody of the shock-induced cross flow . further observations\nsuggest that the separation can be avoided by pitching the body\nor by kinking the body at the shock wave to accommodate the\nshock-induced cross flow ."}, {"doc_id": 1240, "text": "nonsimilar solutions of the compressible laminar boundary\nlayer equations with applications to the upstream-transpiration\ncooling problem .\n a new method is presented for predicting the boundary-layer\ncharacteristics downstream of the porous region of an\ninjection-cooled surface . the method consists of a general scheme for\nobtaining nonsimilar solutions of the compressible-\nlaminar-boundary-layer equations and is formulated along the following\nlines . the viscous domain is divided into n curvilinear strips .\nthe governing equations are then integrated along the\ncoordinate normal to the body from the surface to the boundary of each\nstrip . as a result, one obtains a set of independent\nintegro-differential relations . the integration is carried out by\nexpressing the integrands as polynomials, the coefficients of which\nare functions of the unknown values of the velocity and\ntemperature on the strip boundaries as well as of the imposed\nboundary condition at the wall and at the outer edge . after the\nintegration is performed, a set of ordinary first-order differential\nequations is obtained . the set of equations may be solved for\ngiven initial conditions by a numerical integration scheme such\nas the runge-kutta method . several numerical examples of\ninterest are presented ."}, {"doc_id": 1241, "text": "the turbulent boundary layer on chemically active ablating\nsurfaces .\n incompressible turbulent-boundary-layer analysis is\nextrapolated analytically to the case of a compressible turbulent\nboundary layer with ablation or mass injection at the surface .\nthe effects of chemical reactions such as dissociation and\nrecombination as well as combustion are included . the analysis\napplies to blunt as well as sharp bodies which are either\naxisymmetric or two-dimensional . when the turbulent lewis and\nprandtl numbers are unity, it is found that, as in the laminar\ncase, little detailed knowledge of the chemistry inside the\nboundary layer is required in most instances . the conditions at the\nsurface and the outer edge of the boundary layer are often\nsufficient for prediction of heat and mass transfer .\n comparison is made with experiments on the combustion of\ngraphite under turbulent flow conditions . prediction of ablation\nrates within about 30 percent accuracy is obtained when\nempirical constants obtained from incompressible velocity profiles\nwith no mass injection are used ."}, {"doc_id": 1242, "text": "some considerations on the laminar stability of time-dependent basic\nflows .\nas a stability criterion for infinitesimal disturbances in an\nincompressible, parallel but time-dependent basic flow, it is proposed\nto introduce the concept of /momentary stability,/ which is said\nto prevail at the instant if the kinetic energy of the disturbances,\nas a fraction of the kinetic energy of the basic flow, tends to\ndecrease . the significance of such a criterion is briefly discussed .\nfor special time-dependent basic flows which are described by similar\nvelocity profiles at all times (except for changes in amplitude),\nin the inviscid limit only a change of the time scale is needed to\nreduce the solution essentially to that for the steady case . the\ndisturbances may be of either the transverse-wave or the\nlongitudinal-vortices type . the result indicates a very strong destabilizing\ninfluence of deceleration, which is likely to overshadow that of the\nvelocity profile under normal circumstances . the observations of fales\nrotating cylinders) are believed to be largely due to the deceleration .\nat finite reynolds numbers, the usual procedure of calculating the\nstability solution on the basis of the instantaneous profile is further\nshown to be valid only for extremely slow acceleration or deceleration .\neven when the solution is acceptable, the condition for neutral\nstability may not be used without reservation . to calculate\nmomentary stability properly, a procedure for a slowly varying but more\ngeneral profile is also described ."}, {"doc_id": 1243, "text": "supersonic boom of wing-body configurations .\n the supersonic boom in steady, level flight of a wing-body\nconfiguration is due to the effects of body volume, wing volume,\nwing incidence or lift, and wing-body interference . the\ncontribution in the far field of each of these factors can, in any given\nazimuthal plane, be represented as that of an equivalent body\nof revolution . this concept is developed to investigate the\npossibilities of using interference among the components of a\nwing-body configuration to reduce or suppress the boom due to\nlift . results of wind tunnel experiments are also presented and\ndiscussed in light of the theoretical indications ."}, {"doc_id": 1244, "text": "on the aerodynamic noise of a turbulent jet .\n a new model is advanced for analyzing the broad-spectrum\nnoise of a turbulent jet . the shear layer bounding the turbulent\njet is assumed to play an important role in modifying the /\nquadrupole sound radiation/ from the interior . to the sound-\nemitting small-scale turbulent eddies (with frequencies much higher\nthan those of large-scale eddies), the laminar shear layer has an\nirregular contour, as if the large-scale turbulent motions were\nfrozen . the linearized analysis is then applied to the laminar\nshear layer to relate the acoustic oscillations across it .\n the concept of geometrical acoustics is generalized to represent\nthe passage of an acoustic ray through a laminar shear layer .\nacoustic rays may be traced across the shear layer as\ntransmission and refraction, but they may also be apparently /absorbed/\nor /generated/ by the laminar layer . this /generation/ is\nvisualized as the schematic representation, within the framework of\ngeometrical acoustics, of the action of the reynolds stress in\ntransferring energy from the shearing mean flow to the acoustic\nwaves . such action of the reynolds stress can be neglected in\nordinary acoustics when the acoustic medium is not moving at\nspeeds comparable to the speed of sound in the medium .\nhowever, this action is of crucial importance in the aerodynamic noise\nof high-speed turbulent jets where the reynolds stress is the\nfundamental element of the radiating quadrupoles, according to\nlighthill .\n those acoustic waves that become /stationary/ with respect\nto the local mean flow somewhere in the interior of the shear layer\nare significantly modified by the viscous action through the\ncritical layer . the shear layer therefore serves as a selective\namplifier of the acoustic waves passing through it .\nkinematically, the shear layer brings about the preferred downstream\nemission .. dynamically, the shear-layer augmentation\nsignificantly increases the polar peak noise level . the acoustic power\noutput per unit solid angle for such downstream emissions\naugmented by the shear layer (including the polar peak) varies as,\npredicted by lighthill, but without lighthill's convective\ncorrections . on the other hand, the acoustic power output per\nunit solid angle nearly normal to the jet, due to the transmitted\ndownstream-propagating waves, varies roughly as . heating\nthe jet gas increases the shear-layer augmentation and may\nincrease the polar peak noise level by several db . the silencing\naction of the edge notches and edge teeth may also be\ninterpreted as due apparently to the result of possible distortion of\nthe shear-layer profiles ."}, {"doc_id": 1245, "text": "some aspects of nonequilibrium flows .\n in this paper are discussed some of the general features of\nnonequilibrium flow . in particular, vibrational relaxation is\ndiscussed in detail . this case is somewhat simpler than dissociation\nand ionization but it illustrates some of the main new features of\nnonequilibrium flow . those aspects of two-dimensional and\naxisymmetric flow behind shock waves are examined analytically\nwhich yield significant information without requiring numerical\nsolution of the governing equations .\n the thermodynamics of a vibrational relaxing gas are\ndiscussed . the conditions for simulating flows are noted . crocco's\ntheorem and the characteristic equations are derived . then a\nsimple method of obtaining the initial gradients of the flow\nvariables behind a shock is shown . these gradients are used in\ndiscussing two particular flows . an exact solution for flow over a\ncusped body is obtained . flow over a wedge near the tip and\nfar from the tip is considered . it is found that far from the tip\na boundary-layer type phenomenon occurs ."}, {"doc_id": 1246, "text": "solution of subsonic nonplanar lifting surface problems\nby means of high-speed digital computers .\n the method proposed in this paper is based on an approximate\nsolution of the integral equation which represents the potential\nflow about a finite wing, with no restrictions beyond those\nnecessary for linearization . after assuming the usual series\nrepresentation of the wing surface vorticity distribution, the solution\nis achieved by approximating portions of the kernels of the\ntransformed integral equation by single and double fourier series and\nperforming termwise integrations analytically . this is followed\nby the routine inversion of the aerodynamic influence coefficient\nmatrix, after satisfying appropriate boundary conditions at\nselected control points . in this procedure the number of control\npoint used is limited only by the storage capacity of the\ncomputer . control points may be located so as to cover the entire\nwing surface, with due regard to certain physical requirements,\npermitting the accurate representation of complicated mean\nsurface shapes .\n an evaluation of the proposed method is included .\ncomparisons with other theoretical methods and electrical analogy tank\nresults are used to substantiate the accuracy of the proposed\nmethod when applied to plane wings . a final evaluation\ninvolves a comparison of calculated surface pressure distribution\nwith wind-tunnel measurements on a swept, tapered wing with\na cambered and twisted mean surface . the agreement evidenced\nin the latter comparison has the same order of overall accuracy as\nsimilar comparisons on plane wing planforms . in either case,\nthe results given by the proposed method are within the accuracy\nrequirements for most aircraft design studies ."}, {"doc_id": 1247, "text": "the supersonic boom of a projectile related to drag\nand volume .\n the whitham theory predicting the far-flow field around a\nprojectile is used to derive body shapes which produce extreme\nbow shock-wave pressure jump or /boom,/ subject to\nconstraining conditions regarding the drag due to the bow shock and\nfineness ratio of the bodies . it is found that the minimum drag\nbody is also the minimum boom body . the body-volume effect\nand the effect of discontinuities in slope of the body meridian\nsection on the boom intensity is investigated .\n as a general result of the investigation, it can be said that the\nboom of a projectile for given mach number and flight altitude\nis primarily determined by its length and fineness ratio . the\nmaximum variation in the boom intensity for pointed bodies\nwith given length and fineness ratio is of the order of 10 per cent .\nthe geometry of the bodies is thus found to play a minor role ."}, {"doc_id": 1248, "text": "an analytic extension of the shock-expansion method .\n the problem is considered of calculating approximately the\ninviscid rotational flow field and pressure distribution about a\nsmooth two-dimensional airfoil with sharp leading and trailing\nedges in a uniform supersonic or hypersonic stream . the\nassumption of a perfect gas is made, and the basic flow pattern for\nthe analysis is taken to be given by the simple isentropic\nshock-expansion method with straight characteristics . an elementary\ncharacteristics treatment is discussed to show when the simple\nshock-expansion method should be satisfactory for computing\nthe surface pressure distribution, and under what circumstances\nit may be expected to break down . by utilizing characteristic\nvariables the isentropic shock-expansion method is then\nformulated analytically, and an analytic result is obtained for the shock\nshape corresponding to this zero-order approximation . in the\nspecial case where hypersonic similitude is applicable, that is,\nfor slender bodies and high mach numbers, the shock-shape\nexpression for large distances is found to reduce to the result\npreviously given by mahony, which for weak shocks and slender\nbodies in turn reduces to the simple-wave result first given by\nfriedrichs .\n employing the analytic form of the isentropic shock-expansion\nmethod as a zero-order approximation, an analytically consistent\nperturbation method is developed by expanding the dependent\nflow variables in the exact partial differential equations in powers\nof the reflection coefficient for simple waves interacting with an\noblique shock . the scheme by its nature helps to define those\nregions in which shock expansion can be used, in addition to\ntaking into account in a perturbation sense the factors neglected\nin simple shock-expansion theory, namely, the curvature and\nreflection of the mach waves and the correct boundary\nconditions at the shock wave . analytic solutions are obtained for\nthe first-order corrections, including the surface pressure\ndistribution . the necessary numerical computation of the integrals\ninvolved is considerably simpler than a direct application of the\nmethod of characteristics . to illustrate the method and its\naccuracy, the zero-order shock shape and first-order pressure\ndistribution are calculated for a family of parabolic arc airfoils at\nan infinite free-stream mach number . these results are\ncompared with rotational characteristic solutions where available,\nand the present method is found to be in excellent agreement ."}, {"doc_id": 1249, "text": "plasma flow over a thin charged conductor .\n the flow of a dense plasma over a wavy conducting wall of\nsmall amplitude is investigated where magnetic effects are\nnegligible . these results are then used to analyze the flow over\na thin conductor with cusped edges . it is found that the\ncoulomb drag vanishes identically, while the fluid-pressure drag\ncorresponds to the ackeret value for a neutral particle gas at the\nreduced-plasma mach number ."}, {"doc_id": 1250, "text": "high-speed viscous corner flow .\n a boundary-layer integral method analysis is set up for\ncompressible laminar flow in a symmetric corner with varying angle\nand streamwise pressure gradient . it represents an extension\nand modification of the constant density analysis of loitsianskii\nand bolshakov . the analysis is applied to the case of constant\npressure, constant corner angle, and isothermal surfaces, for\nwhich the crocco velocity-enthalpy relation holds . although\nsimplifying assumptions limit the quantitative accuracy outside\nthe 60 to 120 angle range, some qualitative trends are\nprobably correct outside this range . the limiting cases near 0\nand 180 are not considered .\n favorable agreement between some results obtained by the\nintegral method and by other methods is demonstrated for the\nisothermal, constant-density case .\n results show an increasingly sharp merger of the outermost\nisovels of streamwise velocity as the mach number increases .\nthis sharp merging of the outer isovels is increased by increasing\ncorner angle and by insulation of heating of the surfaces . within\nthe interior of the viscous layer the spreading or contraction of\nthe disturbed region of merging is influenced by surface\nheat-transfer conditions . surface shear and heat flux are decreased\nin the disturbed region, and are zero at the apex . for cases\ncorresponding roughly to the higher mach numbers of wider\ncorner angles, the /specific momentum-area/ exhibits the same\ndecrease with mach number as its two-dimensional counterpart,\nwhereas the /specific displacement-area,/ a measure of\nstream-tube dilation, increases more rapidly with mach number than\nthe comparable two-dimensional parameter ."}, {"doc_id": 1251, "text": "viscous flow past a quarter infinite plate .\n a study is made of the motion of an incompressible viscous\nfluid past a quarter-infinite plate, whose leading edge is\nperpendicular to and whose side edge is parallel to the undisturbed\ndirection of the stream . it is assumed that the kinematic\nviscosity is small . the first approximation is taken to be the\nundisturbed motion, and successive approximations are obtained\nby iferation . the second approximation is the blasius shear\nlayer necessary to satisfy the boundary conditions on the plate .\nin turn, this layer leads to a velocity component normal to the\nplate which needs a potential solution, in which the velocities\nare 0, to match with the conditions at infinity . further,\nthe match at the edge of the blasius shear layer must be\ncompleted to 0 by introducing a secondary shear layer . the\nregions near the leading and side edges are considered separately,.\nin particular, the neighborhood of the side edge needs special\ncare, because the determination of the chief terms is complicated\nby the presence of powers of log . in particular it is shown\nthat the effect of the edge is to change the skin-friction coefficient\nby a factor"}, {"doc_id": 1252, "text": "on the approach to chemical and vibrational equilibrium\nbehind a strong normal shock wave .\n the concurrent approach to chemical and vibrational\nequilibrium of a pure diatomic gas passing through a strong normal\nshock wave is investigated . it is demonstrated that the\nequilibrium degree of dissociation behind the shock front, and hence the\ndensity, for the case where the vibrational degrees of freedom are\nfrozen out can exceed the degree of dissociation, and hence the\ndensity, for the case where all degrees of freedom are in\nequilibrium . thus the necessary condition for a maximum of the\ndensity between the shock front and the position of full\nequilibrium flow downstream of the shock front is established . the\nsufficient condition that such a maximum be observable is shown\nto be that the approach to equilibrium of the vibrational degrees\nof freedom (or any other internal degrees of freedom) must lag\nthe approach to dissociation equilibrium by a significant amount,.\nthat is, there must be at least an order of magnitude difference in\nthe respective relaxation times before such a maximum might be\nobserved . an example calculation for a mach 13 strong shock\nwave in oxygen illustrates the appearance of such a maximum of\nthe density and its dependency upon the relative values of the\nvibration and dissociation relaxation times ."}, {"doc_id": 1253, "text": "hypersonic viscous flow near the stagnation point in\nthe presence of magnetic field .\n the present study investigates the hypersonic viscous flow\npast blunt-nosed bodies with hydromagnetic interaction .\nlocal-similarity solutions of flow field and temperature distribution are\nnear the stagnation-point region . the discussions may be\ngrouped into two parts .. the two-dimensional problem (circular\ncylinder) and axisymmetric problem (sphere) .\n numerical computations have been carried out for the sphere\nproblem for the /viscous-layer regime,/ with various magnetic\nfield strengths and electrical conductivities ."}, {"doc_id": 1254, "text": "combustion in the boundary layer on a porous surface .\n the position of the diffusion flame in a boundary layer with\nuniform mixture injection from a porous wall parallel to a uniform\nair stream is determined under the conditions of laminar, steady\nflow with zero streamwise pressure gradient . under the\nassumption of fast forward reaction rate, solutions of the boundary\nlayer forms of the conservation laws of acrothermochemistry are\nobtained leading to a formula for the downstream velocity at\nthe flame in terms of composition and flow variables . the\nrates of change of conditions at the wall in the streamwise\ndirection are assumed to be relatively small . methods of\ntreating complex reaction systems are described, and generalized\nform of the reynolds analogy is developed ."}, {"doc_id": 1255, "text": "the flow about a charged body moving in the lower atmosphere .\n the flow about an electrically charged body traveling at high\nspeeds through the lower ionosphere is analyzed . a simple\ngas model composed of electrons, ions, and neutral particles is\nused and the hydrodynamic description given is based on\nmaxwell's transfer equations for a mixture .\n the conditions under which local statistical equilibrium can\nbe assumed are discussed, and different approaches to determine\nthe gasdynamic force in the subsonic, supersonic, and hypersonic\ncases are indicated . the reciprocal action of the electric field\nof the flow on the body is also analyzed and a formula for the\nresultant electric force is given . the total force on the body\nis equal to the sum of the gasdynamic force and the electric force .\n the negative potential acquired by a plane body is also\ncalculated . finally, the lack of validity of debye's linearization\nin this case and the solution of the exterior nonlinear problem\nwhich characterize the electric potential and the electron\ndistribution are discussed ."}, {"doc_id": 1256, "text": "fluctuating lift and drag acting on a cylinder in a\nflow at supercritical reynolds numbers .\n the fluctuating lift and drag acting on a circular cylinder in a\nflow of an incompressible fluid at large reynolds numbers were\nmeasured . data on the root-mean-square values of the lift and\ndrag coefficients, the extreme values of these coefficients, and\ntheir power spectra at various reynolds numbers are presented ."}, {"doc_id": 1257, "text": "an optical boundary-layer probe .\n the applicability of the schlieren-photomultiplier technique to\nobtain quantitative density measurements in the laminar\nboundary layer induced by a traveling shock wave in a shock tube is\ninvestigated . tests were conducted at a mach number of 1.58\nso that the data could be compared with the exact theoretical\nsolution tabulated by mirels . the data obtained are in good\nagreement with the theory if the distance of the light beam above\nthe floor of the shock tube is adjusted to fit the theoretical curve,.\nthis would not be necessary if a larger shock tube were used .\nvalues of the transition reynolds number were also determined\nwhich are slightly less than those found by martin using an\ninterferometer . it is shown that this technique is sensitive enough\nto detect changes in density that are only 0.000 per cent of\natmospheric density ."}, {"doc_id": 1258, "text": "heat transfer, recovery factor and pressure distributions\naround a circular cylinder normal to a supersonic rarefied\nair stream .\n measurements of the heat transfer, recovery factor, and\npressure distributions around a circular cylinder normal to a\nsupersonic rarefied-air stream (total temperature 300 k.)\nare described for the mach number range of 1.3 to 5.7, the\nreynolds number range of 37 to 4,100 and at cylinder wall\naverage temperature levels of 90 k. and 210 k . study of the\nresults yielded .. (1) a correlation equation for the\nstagnation-point nusselt number as a function of the reynolds number just\nafter the normal part of the detached bow shock wave,. and (2)\nfourier series expressions for the heat-transfer coefficient and\npressure coefficient distributions in terms of the stagnation point\nvalues .\n in comparing these measurements with predictions based on\nrecent analytical studies, exceptionally good agreement for the\nheat-transfer coefficient distribution was obtained with lees'\ntheory . in the mach number range of 3.55 to 5.73 the\npressure decreased less rapidly with distance from the stagnation point\nthan predicted by the modified newtonian theory ."}, {"doc_id": 1259, "text": "second-order theory for unsteady supersonic flow past\nslender pointed bodies of revolution .\n an analysis is made of the second-order effects of thickness on\nthe unsteady aerodynamic forces on a slender pointed body of\nrevolution in supersonic flow . the theory is restricted to\nharmonic oscillations for small angles of attack . the solution is\nobtained by approximating the nonlinear terms in the second-order\npotential equation by their first-order values and solving the\nresulting inhomogeneous partial differential equation, subject to\nmore refined boundary conditions . the pressure equation is\nlikewise refined and integrated to give the second-order\ncorrections to lift and pitching moment coefficients . the analysis can\nbe considered as an extension of the second-order, slender body\ntheory of lighthill to the case of unsteady flow .\n the results indicate appreciable reductions in unsteady lift\nand damping moment coefficients when applied to slender cones .\nthe present theory is estimated to be reliable provided that\nis less than 0.7 ."}, {"doc_id": 1260, "text": "on the response of the laminar boundary layer to small\nfluctuations of the free-stream velocity .\n the linearized treatment of small time-dependent disturbances\nof a laminar boundary layer, initiated by lighthill, is extended in\nseveral ways . in particular, the high-frequency expansion is\ncontinued beyond the leading (stokes) term . several interesting\nquestions of /joining/ occur, which are discussed but left\nunresolved . in addition, a practical method for obtaining the\nresponse to the laminar boundary layer to an impulsive change in\nvelocity is presented . the methods are applied to the case in\nwhich the basic steady flow belongs to the falkner and skan\nfamily of similarity solutions ."}, {"doc_id": 1261, "text": "a method of calculating velocity distribution for turbulent\nboundary layers in adverse pressure distributions .\n a new method of calculating the behavior of turbulent\nboundary layers in adverse pressure distributions is developed which\npermits direct determination of the velocity profile rather than\nthe gross integral parameters normally used to infer the general\ncharacter of the boundary layer . the method offers the\nsimplicity of algebraic equations coupled with the use of charts\nrather than the laborious simultaneous solution of coupled\ndifferential equations required by existing methods . the method also\naffords, for the first time, a means of determining the total\nboundary-layer thickness, thus allowing calculation of the absolute as\nwell as the nondimensional velocity distribution .\nthe velocity profile is considered to be composed of two\nregions--an inner region which is described by the law of the wall\nand an outer region which is described by a function depicting\nthe deviation from that law . the deviation function involves\ntwo parameters which are uniquely dependent upon the\nskin-friction coefficient and a third parameter which, for practical\npurposes, can be considered a constant . since the entire\nvelocity distribution was found to be almost uniquely dependent\nupon the local skin friction, serious doubt is cast upon the\ngenerally accepted /history concept/ which considers the outer region\nof the boundary layer to be dependent on integrated upstream\nconditions .\n agreement between experimental velocity distributions and\nthose calculated by the method presented here is generally very\ngood . the analysis and calculation procedures which are\npresented are applicable to two-dimensional, pseudo-two-\ndimensional, and axisymmetric conical flows ."}, {"doc_id": 1262, "text": "an extension of the linearized characteristics method\nfor calculating the supersonic flow around elliptic\ncones .\n the method of linearized characteristics as applied by ferri to\nthe flow about elliptic cones can be used to determine the surface\npressure distribution, even when only linear terms are kept in the\nboundary conditions, provided an area rule requirement is\nsatisfied . in addition, the method can be applied for angles of attack\nprovided the elliptic body geometry is specified in a manner that\ndoes not distort the cross section . the surface pressure\ndistribution obtained by this modified method is in reasonable\nagreement with experiment over the range of mach numbers and\nsemidiameter ratios considered . experimental results for several\nconical bodies are presented ."}, {"doc_id": 1263, "text": "turbulent heat transfer through a highly cooled, partially\ndissociated boundary layer .\n the problem of heat transfer from high-temperature air\nthrough a turbulent boundary layer to a cold surface is\nconsidered both analytically and experimentally . heat-transfer\ndata obtained in shock tubes are presented and correlated by a\nsemiempirical theory which includes the effect of atomic diffusion .\n the distinguishing characteristics of turbulent boundary\nlayers with dissociation and large cooling are considered . it is\nshown that the equations governing such flow, after certain\napproximations, can be represented in a form similar to the\nclassical equations for a turbulent boundary layer .\n an approximate theory is proposed for turbulent heat transfer\nfor a highly cooled boundary layer on portions of the body where\nthe pressure gradient is negligible in the case of blunted bodies\nof revolution in high-speed flight .\n experimental results obtained on the cylindrical portion of a\nhemisphere-cylinder model are presented for conditions\nsimulating flight speeds to 21,350 ft. sec., where up to 30 per cent of\nthe molecules are dissociated . reynolds numbers of 2.5 x 10,\nbased on local fluid properties external to the boundary layer,\nwere achieved . the larger values of reynolds number and\nflight speed were not obtained simultaneously, due to structural\nlimitations of the shock tubes,. however, the experiments were\nconducted in such a way that the important effects of each could\nbe determined .\n in the experiments the mach number external to the\nboundary layer varied between 1.7 and 2.2 . the corresponding mach\nnumber for blunted nonslender bodies in flight would have a\nmaximum value between 2.5 and 4,. however, it is shown that\nthese differences in mach number are not important for such\nbodies ."}, {"doc_id": 1264, "text": "boundary layer transition and heat transfer in shock\ntubes .\n an experimental study is made of the wall boundary layer in a\nshock tube operated over a wide range of shock mach numbers\nand pressure levels in air, including those for which real-gas effects\nexist . transition distances are determined and correlated in\nterms of the transition reynolds number based on a\ncharacteristic length for this boundary layer . data from independent\nshock-tube studies are also included in this correlation .\n the results indicate a weak dependence of transition reynolds\nnumber on shock strength up to moderate values of shock mach\nnumber, followed by a larger stabilizing tendency . comparison\nof these data with transition data obtained in the same manner\nin argon indicate that the increased cooling rates are largely\nresponsible for the stabilization .\n a dependence of transition reynolds number on the unit\nreynolds number is found at the lower shock strengths .\nspecifically, higher transition reynolds numbers are achieved at\nlarger unit reynolds numbers .\n the phenomenon of transition reversal does not appear within\nthe range of the experiments reported .\n laminar- and turbulent-flow heat-transfer rates to the walls\nof the shock tube are determined experimentally . the results\nof the heat-transfer measurements substantiate existing theories\nin both the laminar- and turbulent-flow regimes ."}, {"doc_id": 1265, "text": "on the thrust hypothesis for the jet flap including\njet-mixing effects .\n this paper is concerned with the thrust generated by a jet\nflap . it is shown that a /linear/ thrust hypothesis can be\nobtained, provided linearized potential flow is assumed . in fact,\nthe linearized problem of a jet-flap system is found to be the\nlinear combination of a lift problem and a thrust problem . the\nlift problem gives all the lift generated, but it is of interest to note\nthat the thrust problem would yield all the thrust developed by\nthe jet flap within the limitation of the linearized theory .\n the mixing of the jet flap with the surrounding fluid is analyzed\nby the momentum-integral method . the analysis substantiates\nstratford's suggestion for obtaining an increase of thrust by\ncausing the jet to mix with the main stream in a region of high\nsuction . finally, some approximate formulas, relating the thrust\nand the jet angle, are derived . the drag of the airfoil section and\nother viscous effects are, however, not considered ."}, {"doc_id": 1266, "text": "minimum wing wave drag with volume constraint .\n a numerical method is developed for calculating the minimum\nthickness drag for a given wing planform and volume using\nlinearized supersonic flow theory . the corresponding optimum\nvolume distribution is also determined . the results show that\nconsiderable drag reduction is possible by improved volume\ndistribution ."}, {"doc_id": 1267, "text": "on supersonic flow past thick airfoils .\n the inviscid rotational supersonic flow behind the shock wave\nattached to the sharp leading edge of an airfoil is studied by a\ntransformation of coordinates which introduces the crocco stream\nfunction as an independent variable .\n using expansions in the power series of, an iterative process\nis developed for the determination of pressure distribution along\nthe airfoil surface ."}, {"doc_id": 1268, "text": "stable combustion of a high-velocity gas in a heated\nboundary layer .\n it is generally recognized that stable combustion processes in\nheated boundary layers may be achieved by either of two\nconceptual mechanisms . in one mechanism it is pictured that the heat\ntransfer to the wall quenches the propagating flame at a certain\ndistance from the surface . the equality between the flow velocity\nand the normal burning velocity at this quenching distance\ndetermines the position of the propagating flame . in the second\nmechanism it is conceived that the hot surface provides a\ncontinuous source of ignition in much the same manner that the hot\nrecirculation zone of a bluff body flame holder provides continuous\nignition to the gas flowing around it . in this case it is the\ncharacteristic time during which the gas must be heated that determines\nthe position of the flame .\n all experimental work reported to date has been concerned with\nconditions where the first picture has apparently been applicable .\nin the present paper, experiment and analysis are given that show\nunder what conditions the continuous ignition mechanism provides\nthe appropriate model and also how the two models are related .\nto differentiate the two mechanisms an experiment was set up to\nstudy flame stabilization in high-velocity boundary layers over a\nwall heated in the form of a step function . with a turbulent\nboundary layer and a wall temperature above 1,700f., the\ncharacteristic time was found to be a systematic and reproducible\nvariable . these observations led to the conclusion that a\ncontinuous ignition mechanism governs stabilization in heated\nturbulent boundary layers . a rational explanation is made for the\ntransition from the low-speed mechanism known to be applicable\nin unheated turbulent boundary layers and heated laminar\nboundary layers to the ignition mechanism applicable in heated\nturbulent boundary layers .\n as a further verification of the continuous ignition mechanism\nan apparent ignition energy was found . the logarithm of the heat\nadded at the lower stability limit was found to be a linear function\nof the reciprocal of the limiting wall temperature . the activation\nenergy derived from this arrhenius type of relation agreed\nreasonably well with the estimated value for the fuel used ."}, {"doc_id": 1269, "text": "a study of supersonic combustion .\n steady, stable, plain, and oblique detonation waves were\ncreated in a high-temperature, steady flow supersonic tunnel .\nignition conditions and properties across the wave were\nmeasured . the local-wave fluid-dynamic properties agree well\nwith detonation theory . experimental data are presented in\ndetail and compared with other studies and theory .\nexperimental behavior of these detonations and their possible utility\nare discussed ."}, {"doc_id": 1270, "text": "supersonic inlet dynamics .\n an approximation of the differential equation for compressible\nduct flow is presented . the equation is linear and of the second\norder . the duct transfer function and response characteristics\nare obtained by applying small-perturbation theory to the\ndifferential equation . the resulting equations describe duct\nnatural frequency as a function of duct areas and volumes, and\ndamping ratio as a function of the slope of the steady-state mass\nflow, pressure-recovery curve .\n the calcualted response agrees, to a first approximation, with\nmeasured response as obtained from tests of a fixed-geometry,\nsugar-scoop inlet model with hypass for matching airflows .\ntesting was done in the 10 x 10 and 8 x 6 ft. supersonic tunnels\nat nasa lewis flight propulsion laboratory . further\nagreement was obtained during flight tests of the f8u-3 airplane ."}, {"doc_id": 1271, "text": "theory of supersonic propeller aerodynamics .\n a supersonic propeller with blades attached to an infinite\ncylinder as a hub is studied . the forward speed may be subsonic, but\nthe relative speed at each section is supersonic . the lightly\nloaded blades are represented by a surface distribution of\nappropriate /modified/ sources in a fashion similar to ordinary\nsupersonic thin-wing theory . these sources are found by\napproximating the exact potential for a constant-strength\ncompressible source traveling along a helical path . the usual\nrelationship between the source strength and boundary condition is\nfound,. and subsequently the source distribution is given, to the\nappropriate order, in terms of the blade geometry .\n tip effects are considered by extending the theory of evvard\nand krasilshchikova . the present investigation, however, is\nrestricted to those planforms for which no vortex sheet appears\noff the tip . for points in the tip region, the potential is obtained\nthrough the appropriate distribution of /modified/ sources in the\nupwash region off the tip . by transforming to a curvilinear,\nnonorthogonal coordinate system coincident with the modified mach\nlines described by the infinities of the potential, an integral\nequation for the required source distribution in the upwash region is\nderived . without having to solve this equation, it is shown that\nthe potential for a point in the tip region can be obtained in terms\nof an integration of known source distributions over the blade\nsurface only .\n the case of a twisted flat plate of particular planform is treated,\nand a sample calculation is made of the pressure distribution at\nselected radial positions within the noncommunicating portion\nof the blade, as well as over the entire tip region .\n though this analysis is carried out explicitly for the supersonic\npropeller, it could also be extended to calculate various rotary\nderivatives for highspeed flight vehicles ."}, {"doc_id": 1272, "text": "oscillatory aerodynamic coefficients for a unified\nsupersonic hypersonic strip theory .\n this investigation presents a derivation of the oscillatory\naerodynamic coefficients for wings with supersonic leading edges\nfrom the second-order, nonlinear, unsteady, supersonic flow theory\nof van dyke . the theory is considered applicable throughout\nthe supersonic-hypersonic regime at mach numbers normal to\nthe leading edge and reduced frequencies for which .\nthe coefficients are modified for sweep, and a finite-span\ncorrection is suggested to increase the accuracy of strip-theory flutter\nanalyses . the limiting values of the coefficients in steady flow\nare also discussed ."}, {"doc_id": 1273, "text": "magnetohydrodynamic effects on the formation of couette,\nflow .\n this paper is concerned with the problem of the formation of\ncouette flow--i.e., the problem of how the velocity profile varies\nwith the time tending asymptotically to that of the steady flow of\nan electrically conducting viscous fluid in the presence of a\nmagnetic field . the governing equations and boundary conditions\nare established and discussed . the cases of both vanishing and\nnonvanishing mean induced electric field strengths are solved in\nterms of complimentary error functions as well as some\nelementary functions . it is shown that the solutions are reducible to\nthat of the steady case as the time approaches infinity, and to that\nof the nonmagnetic field as the hartmann number becomes zero .\nsome numerical calculations are given . the results indicate\nthat in the presence of a magnetic field the flow rate is reduced\ndepending on the magnitude of the hartmann number, and that\nthe magnetic field /assists/ the flow to reach its steady\ncondition ."}, {"doc_id": 1274, "text": "real gas effects in flow over blunt bodies at hypersonic speeds .\na hypersonic shock tunnel has been developed to investigate the\naerodynamic characteristics of flow over bodies at conditions comparable to\nthose encountered by ballistic missiles and satellites re-entering the\natmosphere . some results for a shock velocity of over 50,000 ft. per\nsec. in the shock tube portion of the facility are presented . static\npressure investigations were made in the nozzle to determine the flow\ncondition and the expansion process .\nthe results of the investigation of representative blunt bodies at\nhypersonic mach numbers and nozzle stagnation temperatures up to\napproximately 6,000degreek. are presented . these include body pressure\ndistributions, shock-wave shapes, detachment distances, and photographs\nof the luminous gas region in the shock layer . it is seen that the\nshock detachment distance is smaller at higher stagnation temperatures\ndue to the real gas effects . for the hemisphere the pressure\ndistribution was less than that predicted by the modified newtonian theory for\n all stagnation temperatures . for a 50degree cone-hemisphere the\npressure distribution and the shock detachment distance were appreciably\naffected by the real gas effects .\nthe observed shock-wave shape and the approximate boundary layer on a\nflat plate are compared with the analytical prediction . some\npreliminary results for the detached shock wave produced by a blunt two-\ndimensional body in a low density flow at a mach number of 19.6 are presented"}, {"doc_id": 1275, "text": "flow about an unsteadily rotating disc .\n an analysis is made of the unsteady laminar flow about a\nrotating disc whose angular velocity may vary with time .\nthe deviation of the actual instantaneous state of the flow from\nthe quasi-steady state (instantaneous steady state) is\ndetermined . from this, a simplified criterion, is\nderived to define the conditions under which the flow can be\nconsidered as quasi-steady for the purposes of shear stress and\ntorque computations . since a turbulent flow responds more\nrapidly than a laminar flow, the quasi-steady criterion found here\nshould also serve for the turbulent situation ."}, {"doc_id": 1276, "text": "a three-dimensional linearized analysis of the forces\nexerted on a rigid wing by a shock wave .\n the pressure distribution on a moving flat plate induced by an\nacoustic shock front striking the edge of the plate obliquely has\nbeen found in terms of the two-dimensional solution of the authors"}, {"doc_id": 1277, "text": "a study of vortex cancellation .\n the cancellation of a vortex by means of another concentric\nvortex of equal strength but opposite spin is investigated . when\nsuch a cancellation occurs, there is a recovery of static pressure .\nthe vortices are generated by means of two three-dimensional\nairfoils cantilevered from the duct wall, one being situated in the\nwake of the other . the airfoils have opposite effective angles of\nattack and therefore have trailing vortices of opposite spin, as\nrequired .\n it is demonstrated experimentally that there exists an optimum\nangle of attack for the second airfoil which cancels the vortex\nfrom the first airfoil and restores uniform flow downstream of\nthe two airfoils . a theoretical solution of this optimum angle of\nattack is presented, and it is found to depend upon the angle of\nattack of the first airfoil and upon the geometrical properties of\nthe wings . the pressure recovery accompanying the vortex\ncancellation is also studied . theoretical considerations, based on\nthe model of a vortex filament in the center of a circular tube\nshow that a maximum of 62 per cent of the static pressure drop\nacross the first airfoil can be recovered . this maximum is\nimposed, irrespective of skin friction and separation losses, by the\nirreversibility associated with establishing a vortex field .\nexperimental pressure recoveries of 50 per cent are realized .\n perhaps the primary value of the present study is the\nopportunity it provides to verify certain of the fundamental concepts\nof fluid mechanics which are brought into play when the trailing\nvortex system of a lifting wing is cancelled by a second wing ."}, {"doc_id": 1278, "text": "transition in a separated laminar boundary layer .\n transition to turbulence was studied in a separated laminar\nboundary layer on a flat plate 24 in. long and thick . steps\nwith a height of to were provided at a distance of 4 to\ntransition was observed through a hot-wire anemometer . the\nauthor concludes that transition was always initiated by\ntollmien-schlichting waves . two types of transition were observed . in one\ntype, bursts suddenly appeared in the wavy flow . the other type\nconsists of amplification, distortion, and breaking up of the waves .\nwhich type of transition occurs depends on the value of the\nfollowing parameter .. boundary-layer displacement thickness times\nstep height times free-stream velocity squared divided by\nkinematic velocity squared . the burst type has been observed for\nvalues of this parameter larger than 4.2 x 10 . the separated\nlaminar boundary layer becomes unstable and develops waves when\nthe critical reynolds number based on boundary-layer\ndisplacement thickness at the step location exceeds a value of 350 . some\nconclusions on the development of separation bubbles on air foils\nare drawn from the present studies ."}, {"doc_id": 1279, "text": "sublimation in a hypersonic environment .\n a priori knowledge of the response of materials subjected to a\nsevere aerothermal environment is essential in the space age .\nthe successful design of space and re-entry vehicles demands\nthat the fundamental problem of the interaction between a\nmaterial and dissociated air be properly formulated and solved . in\nthis paper, the problem of sublimation in a hypersonic\nenvironment is considered .\n in this study of hypersonic ablation, the pertinent\nconservation equations are derived and the simultaneous processes of\ndiffusion, convection, and thermal exchange are analyzed for the\nvaporization of a refractory material which is subjected to the\nenvironmental conditions encountered during hypersonic\nreentry .\n for simplicity, only the forward stagnation point of an axially\nsymmetric body is treated . it is shown that the quantity,\ncalled the effective heat of vaporization, which includes all heat\nabsorbing or heat blocking effects, is an increasing function of\nflight speed, independent of body size, except where\nnonequilibrium vaporization effects or radiative effects appear ."}, {"doc_id": 1280, "text": "wings with minimum drag due to lift in supersonic flow .\n it has been shown by r. t. jones that, in order to produce\nminimum drag, the given lift must be distributed over the wing\nsurface in such a way that the sum of the downwash induced by\nthis distribution and the downwash induced in reversed flow is\nconstant over the wing surface . this combined downwash can be\nexpressed by an integral which contains the load as a function\nof the spanwise and chordwise coordinate . the problem of\nfinding the appropriate load distribution is thus reduced to the\nproblem of finding the solution of a rather cumbersome integral\nequation .\n the severe spanwise singularity of the kernel function is\nhandled most easily, as in corresponding subsonic problems, by an\napproximate integration over interpolation polynomials . the\nchordwise load distribution is represented by a limited series\ndevelopment in legendre polynomials . the sigularity of the\nkernel function along the mach lines through any pivotal point\ncan be avoided by a similar legendre development of the\ncombined induced downwash which is constant . the integral\nequation is thus converted into a system of linear equations for the\nunknown coefficients of the legendre functions of the load\ndistribution at a limited number of spanwise stations .\n practical calculations are carried out on an electronic\ncomputer . the solutions yield the optimum load distribution and the\nlocal incidence (twist, camber, etc.) necessary to realize this\ndistribution . for many wing plan forms, considerable gains\nover a plane wing appear possible ."}, {"doc_id": 1281, "text": "turbulent heat transfer on blunt-nosed bodies in two-dimensional\nand general three-dimensional hypersonic flow .\n recent results obtained for three-dimensional laminar\nboundary layers are extended to the turbulent case . it is shown that\nin the presence of highly cooled surfaces and of moderate mach\nnumbers of the outer stream, the crossflow and the pertaining\nreynolds stresses in a general three-dimensional turbulent\nboundary layer are negligible even for large transverse pressure\ngradients . a correlation due to mager between two-\ndimensional compressible and incompressible turbulent boundary\nlayers is extended to the problem in question . from a study of\nthe transformation and of its implications, a rapid method for\nthe analysis of the boundary-layer flow under the subject\nconditions is established . in the absence of general three-\ndimensional data, a comparison with experiments and with the\npredictions of other known analyses is carried out for several\naxisymmetric configurations,. the results of the method presented\nhere exhibit good agreement with the data . the range of\nvalidity of the cold wall approximation for general three-dimensional\nproblems is estimated qualitatively on the basis of recent\nmeasurements in laminar flow, the argument being that, for either\nzero or favorable streamwise pressure gradients, smaller\nthree-dimensional effects are to be expected in a turbulent boundary\nlayer, as compared to a laminar layer ."}, {"doc_id": 1282, "text": "compressible flat-plate boundary-layer flow with an\napplied magnetic field .\n the laminar boundary-layer equations are formulated and\nsolved for a flat plate in high-speed compressible air flow where\nequilibrium dissociation and ionization are assumed and where\nthere is an applied magnetic field having its component normal\nto the plate proportional to . the skin-friction and\nheat-transfer characteristics are determined for free-stream velocities\nof up to 17,500 meters sec. and magnetic fields of up to about\n the results show that the skin friction and heat transfer at a\ngiven free-stream velocity decrease with increasing magnetic\nfield strength, and the percentage reduction is constant along\nthe length of the plate . they also exhibit the same hysteresis\nbehavior as was first found in the case of magnetoaerodynamic\ncouette flow,. however, for the flat plate the hysteresis effect\ndisappears at a higher mach number . furthermore, it was\nfound that the reduction in heat transfer with increasing field\nstrength is opposite in behavior from that for couette flow ."}, {"doc_id": 1283, "text": "on shearing flow between porous coaxial cylinders .\n the flow between concentric porous cylinders in relative axial\nmotion with a pressure gradient is considered . the analysis is\nrestricted by the assumption that the velocity distribution is a\nfunction of the radial coordinate only so that there is no net\ninjection or withdrawal of fluid at any station . this assumption\nreduces the problem to a soluble system of ordinary differential\nequations . an associated heat-transfer problem is also discussed\nbriefly ."}, {"doc_id": 1284, "text": "the transition to tubulence in a boundary layer on\na blunt cone in supersonic flow .\n experiments were made with a series of cones, each having an\nincluded angle of 15 degrees, and having different tip radii (sharp\nto blunt nose) . the cones were tested in streams, undisturbed\nmach numbers of 3.12 and 3.81, and the position of transition to\nturbulence was observed with a shadowgraph technique . for each\nmach number the distance to transition (distance downstream from\nthe tip of the cone) increased with increase in tip radius, reached\na maximum at a certain tip radius, and then decreased with\nincrease in tip radius . a study indicates that a reynolds number\nbased on the momentum thickness, instead of the length from tip to\ntransition, is a more appropriate parameter for correlating the data .\nthe research scientist active in this field probably would derive\nthe most benefit from the original paper ."}, {"doc_id": 1285, "text": "experiments at hypersonic speeds on circular cones\nat incidence .\n pressure distribution measurements\non five circular cones with total\napex-angles ranging from 25 to 45 degrees\nare described . the tests covered\na range of angles of incidence from 0 to\nand 8.60 . the extent to which various\nanalytical and empirical theories\npredict the measured pressures is assessed ."}, {"doc_id": 1286, "text": "equilibrium real-gas performance charts for a shypersonic\nshock-tube wind-tunnel employing nitrogen .\n charts are presented covering\na wide range of reflected-shock\nwind-tunnel operating conditions, using\nnitrogen as the working gas . a\nstatistical-mechanical model of the gas\nis assumed which takes account of\nmolecular vibration, electronic excitation\nand dissociation . the gas is\nassumed to be constantly in\nequilibrium that is, the reaction rates are\ntaken to be infinitely fast . the equations\nof motion are solved with the\naid of a digital computer, previously reported\nresults for the state of the\nshock-processed gas in the shock-tube being used ."}, {"doc_id": 1287, "text": "progress report on an experiment on the effect of surface\nflexibility on the stability of laminar flow .\n this paper describes the flexible\nsurfaces whose properties have\nbeen examined and which have been tested on\nan aerofoil in a wind tunnel .\nthe experiment has been rather inconclusive\nas no drag reductions have been\nfound in turbulent flow, whilst the only\nrearward movements of transition\noccurred in conditions where the alteration\nhas been inhibited by the onset\nof laminar separation . the limitations of\nthe experiment are discussed\ncarefully in order to clarify the next steps\nwhich are to be taken with\nmore flexible surfaces with less damping ."}, {"doc_id": 1288, "text": "analysis of the fluid mechanics of secondary injection\nfor thrust vector control .\n an analysis is made of the interaction of an injected\ngas or liquid with a supersonic stream,\nand the force induced on an adjacent wall is predicted .\nthe study deals only with the\nfreestream-injectant interaction,. the modifications to the\nflow introduced by the boundary layer\nare not considered . in the case of liquids, it is shown\nthat the momentum deficit of the\ninjectant relative to the freestream may play a larger part\nin producing the side force than the\nvolume generation by vaporization and reaction . the\nanalytical results are compared with\nthose obtained from experiments in a wind tunnel and in nozzles ."}, {"doc_id": 1289, "text": "numerical technique to lifting surface theory for calculation\nof unsteady aerodynamic forces due to continuous sinusoidal\ngusts on several wing planforms at sobsonic speeds .\n a numerical lifting-surface method has\nbeen used to calculate direct gust\nforces and moments on wings of several\nplanforms . the gust velocities are\ncontinuous and vary sinusoidally in the stream\ndirection and are also uniform across\nthe wing span . the procedure has the\nadvantage of rapid machine calculation and\nincludes the effects of wing planform,\nnonsteady subsonic flow, and induced flow\neffects . the method provides for calculation\nof gust forces on a basis\nconsistent with that for the calculation of forces\ndue to motion and deformation . the\nresults include the in-phase and quadrature\ncomponents of the following\nquantities .. (a) spanwise distribution of\nsection lift coefficient, (b) total\nlift coefficient, and (c) total pitching-moment\ncoefficient . in addition,\ngeneralized gust forces on approximate fundamental\ncantilever bending modes (\nparabolic) are also included . results have been\nobtained for 60 and 75 delta wings,\nratio 11.60, and an unswept wing of aspect\nratio 6.00 . conditions for which\ncalculations were made include two mach numbers\nreduced-frequency range of 0 to 1.0 . the\ndirect gust forces and moments are in\nforms suitable to be inserted in equations\nof motion used in the calculation of\nthe dynamic responses of flexible lifting\nvehicles to random turbulence and to be\ncompared with results from other methods ."}, {"doc_id": 1290, "text": "measured and calculated subsonic and transonic flutter\ncharacteristics of a 45 sweptback wing planform in\nair and in freon-12 in the langley transonic dynamics\ntunnel .\n in order to investigate the\nreliability of flutter data measured\nin the langley transonic dynamics\ntunnel, an experimental and theoretical\nsubsonic and transonic flutter study\nhas been conducted in air and in\nfreon-12 in this facility . the wing\nplanform employed had an aspect\nratio of 4.0, a taper ratio of 0.6,\nand 45 of quarter-chord sweepback .\na sting-mounted full-span model was\ntested in addition to three sizes of\nwall-mounted semispan models . a wide\nrange of mass ratio was covered by\nthe tests in air and by flutter\ncalculations made by the modified\nstrip-analysis method of naca research\nmemorandum l57l10 . a limited amount of\ndata was obtained in freon-12 .\n results of the tests in air\nand in freon-12 are in good agreement\nwith the flutter calculations at\nall mach numbers . the test data\ncompare favorably with previously\npublished transonic flutter data for the\nsame wing planform . the results\nindicate that flutter characteristics\nobtained in freon-12 may be interpreted\ndirectly as equivalent flutter\ndata in air at the same mass ratio and mach number ."}, {"doc_id": 1291, "text": "atmosphere entries with spacecraft lift-drag ratios\nmodulated to limit decelerations .\n an analysis has been made of\natmosphere entries for which the\nspacecraft lift-drag ratios were\nmodulated to limit the maximum\ndeceleration . the parts of the drag polars\nused during modulation were from\nmaximum lift coefficient to minimum\ndrag coefficient . five drag polars\nof different shapes were assumed for\nthe spacecraft . the entries covered\nwide ranges of initial velocity,\ninitial flight-path angle, initial\nand maximum lift-drag ratio .\ntwo-dimensional trajectory calculations were\nmade for a nonrotating, spherical\nearth with an exponential atmosphere .\nthe results of the analysis indicate\nfor four of the five drag polars that,\nrelative to the maximum deceleration\nof an unmodulated entry at maximum\nlift-drag ratio, the greatest reduction\nin maximum deceleration obtainable\nby modulation depends upon a single\nparameter . this parameter is the ratio\nof the value of the aerodynamic\nresultant-force coefficient at minimum\ndrag coefficient to the value at\nmaximum lift coefficient . thus, the\nreduction in maximum deceleration\nis independent of initial velocity,\ninitial flight-path angle, initial\nmaximum lift-drag ratio, and\nthe shape of the drag polar . for\nthe fifth drag polar, the reduction in\nmaximum deceleration was found to\ndepend upon the maximum lift-drag ratio .\nalso, relative to the depth of a\ngiven deceleration-limited corridor, the\ngreatest increase in corridor depth\nobtainable by modulation (for four of\nthe five drag polars) depends upon\nthe same ratio of aerodynamic\nresultant-force coefficients . the fractional\nincrease in corridor depth can be\nexpressed as an empirically determined\nanalytical function of this ratio ."}, {"doc_id": 1292, "text": "effect of jet pluming on the static stability of cone-cylinder-flare\nconfigurations at a mach number of 9. 65 .\n the effects of jet pluming on\nnormal force and pitching moment of\nhave been measured at a free-stream\nmach number of 9.65 with reynolds\nnumbers based on model length of 500,000\nto 600,000 . geometric variables\nincluded nose bluntness, flare half-angle,\nand nozzle geometry and exit displacement .\ntwo test nozzles with design\nmach numbers of 3.74 and 4.60 were operated\nwith compressed air to\nsimulate the initial jet-boundary shape of a\nparticular solid-propellant\nrocket motor operating between altitudes\nof 165,000 and 215,000 feet .\nthe ratio of the jet pressure to free-stream\nstatic pressure varied from\na jet-off condition to approximately 1,300\nfor the nozzle with design mach\nnumber of 3.74, and from a jet-off condition\nto approximately 280 for the\nnozzle with design mach number of 4.60 .\nthe angle-of-attack range was\nfrom 0 to approximately 6 .\n the results indicate that as the\njet-pressure ratio was increased\nthe size of the jet plume increased,\nand as a result the model static\nstability was decreased . increasing\nthe angle of attack resulted in a\nreduction in static instability during\nthe jet-on condition . increasing\nnose bluntness resulted in a more forward\nmovement of the center of\npressure when jet-plume interference was not\npresent and a rearward movement\nin the center of pressure when jet\ninterference was present . increasing\nthe nozzle-area expansion ratio and\ndisplacing the nozzle exit downstream\nof the flare base resulted in a more\nrearward location of the center of\npressure ."}, {"doc_id": 1293, "text": "design of stiffened cylinders in axial compression .\n the problem of optimum design\nof axially compressed cylinders\nstiffened by rings and stringers is\ndiscussed . particular\nattention is devoted to configurations\nsuitable for large launch\nvehicles . consideration is given to\nthe analytical techniques for\ndetermining strength as well as\nthe procedures for optimization ."}, {"doc_id": 1294, "text": "non-linear shallow shell analysis by the matrix force\nmethod .\n the matrix force method of redundant\nstructure analysis is currently\nbeing extended by various users to cover\na number of non-linear problems .\none of these is the non-linear analysis\nof heated cambered wings, such as\nmight be used in advanced flight vehicles .\nin this case the approach used\nby the present authors is equally applicable\nto shallow shells, the\nformulation of the strain-displacement and\nequilibrium relations being a\nfinite element equivalent to that used\nby marguerre . the solution is\nobtained by a combined iteration and step\nby step procedure utilizing a\ntangent flexibility matrix . divergence\nin the calculations indicates\nthat the range of stable configurations\nhas been exceeded . cambered\nplates subjected to several loadings are\ngiven as examples,. for one, an\nexact solution is available for comparison .\n it is believed that the basic concepts\ninvolved in this shallow\nshell analysis can be extended to apply\nto other, more general shell\ninstability problems, and that useful\nsolutions to the latter are\nprobably within the capability of present day digital computers ."}, {"doc_id": 1295, "text": "recent advances in nonequilibrium dissociating gasdynamics .\n the purpose of this paper is to review some recent\nadvances in the study of gasdynamic problems including\neffects of chemical reactions . to provide a background for\nthe study the general concepts shall be outlined briefly . the\ndiscussions of the recent developments are restricted to\ninviscid flow problems only, neglecting viscosity, heat\nconduction and diffusion . particular attention is directed to recent\nadvances in analyses of nonequilibrium dissociating gas\nflows . in the hypersonic flight regime, high stagnation\nenthalpies sufficient to cause dissociation are realized . when\nthe time to reach equilibrium is comparable with the time it\ntakes for a fluid particle to pass through the flow, then there\nexist regions of the flow field where nonequilibrium states are\nencountered . a brief survey of both the linear and the\nnonlinear methods of treatment of these nonequilibrium flows,\nincluding some new developments that have not appeared\nelsewhere, will be presented ."}, {"doc_id": 1296, "text": "non-equilibrium expansions of air with coupled chemical\nreactions .\n analysis and solutions of the streamtube gas\ndynamics involving coupled chemical rate equations\nare carried out . results are presented for airflows\nalong the surface of blunt bodies and through\nhypersonic nozzles . speeds and altitudes corresponding\nto re-entry were selected to obtain initial\nconditions for the external flow calculations . conditions\nappropriate to hypersonic tunnel testing\nwere chosen for the nozzle flow calculations . composition\nhistories are shown for a kinetic mechanism\nincluding 6 species and 14 reactions . gas-dynamic effects\nof nonequilibrium processes qualitatively\nresemble those reported earlier . however, the freezing\nprocess is complicated by the coupling of the\nnitric oxide shuffle reactions with the dissociation-recombination\nreactions . in many cases of\nhypersonic nozzle flows where the energy in nitrogen dissociation\nis significant, the fast shuffle reactions\nprevent nitrogen-atom freezing which would otherwise occur\nif three-body recombination were the only\nprocess operating . nitric oxide concentrations\nundershoot the equilibrium values if the ratio of\nnitric oxide to oxygen molecule concentrations\nexceeds unity in the freezing region . this depletion\nof nitric oxide leads to nitrogen-atom freezing ."}, {"doc_id": 1297, "text": "ionization nonequilibrium in expanding flows .\n approximate methods are developed for solving\nthe electron-ion kinetic equations in expanding\nquasi one-dimensional airflows . results are obtained\nfor inviscid nozzle flows at conditions\nappropriate to shock tunnel testing and are compared\nwith exact numerical solutions . effects on rf\ntransmission and d-c conductivity are examined .\nsince two-body deionization never fully freezes\nin the flows considered here, the assumption of sudden\nfreezing gives an upper bound on the residual\nionization at large area ratios . the use of an\nasymptotic form of solution with the freezing\ncriterion provides an improved estimate for such cases .\nionization nonequilibrium is also\nconsidered for the plasma sheath associated with blunt\nhypersonic bodies flying at high altitudes .\nthe influence of atomic ions is examined for typical\nre-entry conditions ."}, {"doc_id": 1298, "text": "theory of radiation from luminous shock waves in nitrogen .\n the physical properties behind a normal shock in\nnitrogen are calculated as a function of time .\nthese include the variation of temperature, composition,\nionization, and the intensity of radiation\nfrom the n first negative band system . this calculation\nincorporates a rate equation for the\ndissociation of nitrogen, the conservation laws, an equation\ndescribing vibrational relaxation, and a\nmethod of coupling the vibrational relaxation with the\ndissociation rate . the n radiation is\ncomputed assuming excitation of the radiating state by\ncollision with vibrationally excited nitrogen\nmolecules . a particular case is considered for which\nexperimental data are available, and regions\nsensitive to particular rates are indicated ."}, {"doc_id": 1299, "text": "hypersonic viscous shock layer .\na decade ago tsien (1) (as well as others) and, more\nrecently, adams and probstein (2) have attempted to\ndefine the different regimes of gaseous interactions during high\naltitude flight . in this note some results are presented which\nare pertinent to the flight of hypersonic lifting vehicles\ncomposed of axially symmetric and two-dimensional elements,.\nsec. fig. 1 ."}, {"doc_id": 1300, "text": "some effects of bluntness on boundary layer transition\nand heat transfer at supersonic speeds .\n large downstream movements of transition observed when the\nleading edge of a hollow cylinder or a flat plate is slightly\nblunted are explained in terms of the reduction in reynolds\nnumber at the outer edge of the boundary layer due to the\ndetached shock wave . the magnitude of this reduction is\ncomputed for cones and wedges for mach numbers to 20 .\nconcurrent changes in outer-edge mach number and temperature occur\nin the direction that would increase the stability of the laminar\nboundary layer .\n the hypothesis is made that transition reynolds number is\nsubstantially unchanged when a sharp leading edge or tip is\nblunted . this hypothesis leads to the conclusion that the\ndownstream movement of transition is inversely proportional to\nthe ratio of surface reynolds number with blunted tip or\nleading edge to surface reynolds number with sharp tip or leading\nedge . this conclusion is in good agreement with the\nhollow-cylinder result at mach 3.1 .\n application of this hypothesis to other mach numbers yields\nthe result that blunting the tip of a slender cone or the leading\nedge of a thin wedge should produce downstream movements of\ntransition by factors ranging from 2 at mach 3.0 to 30 at mach\nthe possible reduction in over-all heat-transfer rate and friction\ndrag for aircraft flying at high supersonic speeds .\n mach number profiles near the surfaces of blunted cones and\nwedges are computed for an assumed shape of the detached\nshock wave at flight mach numbers to 20 . the dissipation and\nstability of these profiles are discussed, and a method is\ndescribed for estimating the amount of blunting required to produce\nthe maximum possible downstream movement of transition ."}, {"doc_id": 1301, "text": "compressible boundary layers on bodies of revolution .\n in a former paper (1) it has been shown that the\nbehaviour of the laminar boundary layer on a body of revolution can\nbe described mathematically by the same equations which are also\napplied to the processes in the laminar boundary layer in the\ntwo-dimensional flow along a body contour, the form of which is\ndetermined by the shape of the body of revolution . a simple\nrelation exists between the two-dimensional boundary layers and\nthe axially symmetrical ones . the flow had been assumed to be\nincompressible . in this report it shall be shown that this\nrelation is still valid when the compressibility is taken into\nconsideration . the distribution of velocity as well as that of\ntemperature in the laminar boundary layer of a body of revolution\ncan be calculated by solving the corresponding problem for the\ntwo-dimensional flow around a suitable contour . the method is\nmade clear by the example of the supersonic flow towards a cone\ntip,. this example has already been treated by another method\nby hantzsche and wendt (2) ."}, {"doc_id": 1302, "text": "the development of the boundary layer in supersonic\nshear flow .\n the development of the boundary\nlayer in a velocity shear layer is\ndiscussed for two-dimensional flow\nand for axisymmetric flow of both\ncompressible and incompressible fluids .\nit is shown that the solutions\nobtained by li and glauert for the\ntwo-dimensional flow of an\nincompressible fluid are applicable in the\nmore general case after suitable\ntransformations of coordinates have\nbeen made . new definitions are shown\nto be necessary, and are given, for\nthe displacement and momentum thicknesses\nof such a boundary layer . reynolds\nnumbers based on these thicknesses are\ngiven, and it is shown that any phenomenon\nwhich occurs at a constant value of such\na reynolds number will occur at a\npoint which, as the length scale of the\nflow increases, first moves\ndown-stream and then moves slightly upstream .\nthis is shown to be in qualitative\nagreement with experimental results on a\nblunt cone in a supersonic flow .\na quantitative comparison of the theoretical\nand experimental values of\ndisplacement and momentum thicknesses is\nattempted, and no disagreement is\nobvious,. unfortunately the accuracy of the\nexperiments so far available is\ninsufficient to give positive confirmation\nof the theory of this note ."}, {"doc_id": 1303, "text": "air pressure on a cone moving at high speeds .\n the cone is considered to be\nmoving at a velocity higher than that\nof sound, so that there is in front\nof it a shock wave, moving with the\nsame speed as the cone itself . in\nthe first part of the paper, the case is\ninvestigated mathematically where\nthe flow is irrotational, and the\npressure, velocity and density of the air\nstream are each constant over the\nsurfaces of cones coaxial with the\nmoving solid cone . the complete\nsolution is obtained in numerical\nform, for cones of semi-vertical angle\nof the paper, the results are compared\nwith experiment, both in respect of\npressure distribution as measured in a\nwind tunnel, and also (for the 30\ncone) by comparison with photographs\nof bullets in flight . in the latter case\nthe theory should only be applicable\nif the speed is 1.46 or more times the\nvelocity of sound, and it is in fact\nfound in the photographs, that the nature\nof the wave alters at about this\nvelocity . the exact solution found, is\ncompared with an approximation\ngiven recently by v. karman and moore .\nthis should be valid for thin\nspindle-shaped bodies, and does in fact\nagree well in the case of the cone\nof 10 semi-vertical angle, but diverges\nincreasingly from the truth as\nthe angle is increased ."}, {"doc_id": 1304, "text": "newtonian flow over a surface .\na general method is presented for\nthe study of a three-dimensional\nhypersonic flow about a body of arbitrary shape when .\nthe manner of constructing a double\nasymptotic development in\nand is shown . formulae are given\nwhich enable the first three terms of\nthis development to be obtained while neglecting .\nthe theory is then applied to the case of\na body of circular-cone shape . the\npressure is given as a triple development\nin accordance with the preceding\nparameters and the angle of attack,. this\ndevelopment neglects . a. ferri's\nvortical layer is brought into evidence .\na second application is devoted to\ncalculation of the total forces acting\nupon bodies of revolution at angles of\nincidence, while neglecting .\ngeneral formulae are\nestablished for the coefficients of axial\nforce, normal force and moments .\nthe formulae are developed according\nto the powers of incidence, the first\nterms of each formula being of very simple form ."}, {"doc_id": 1305, "text": "a proposed programme of wind tunnel tests at hypersonic\nspeeds to investigate the lifting properties of geometrically\nslender shapes .\n a programme of tests at hypersonic\nspeeds on slender bodies is\ndescribed, which has the aim of\ninvestigating how lift is generated, and\nthe compromises that may be enforced\nby aerodynamic heating . the programme\nis based on models of simple geometric\nshape, from which lifting\nconfigurations will later be built up ."}, {"doc_id": 1306, "text": "experiments on circular cones at yaw in supersonic\nflow .\n pressure measurements made in the fort halstead\nsupersonic tunnel on two circular cones, of semiapex angles 15 and\ncoefficients are compared with corresponding values calculated\nby theoretical methods, and the relative merits of these methods\nare then discussed ."}, {"doc_id": 1307, "text": "laminar heat-transfer and pressure measurements at\na mach number of 6 on sharp and blunt 15 half-angle\ncones at angles of attack up to 90 .\n two circular conical configurations\nhaving 15 half-angles were\ntested in laminar boundary layer at a\nmach number of 6 and angles of\nattack up to 90 . one cone had a sharp\nnose and a fineness ratio of\nblunted nose with a bluntness ratio\nof 0.1428 and a fineness ratio of 1.66 .\npressure measurements and\nschlieren pictures of the flow showed\nthat near-conical flow existed up\nto an angle of attack of approximately\nnear the base and the bow shock\nwave was considerably curved .\n comparison of the results with\nsimply applied theories showed that\non the stagnation line pressures may\nbe predicted by newtonian theory,\nand heat transfer by local yawed-cylinder\ntheory based on the yaw angle\nof the windward generator and the local\nradius of the cone . base effects\nincreased the heat transfer in a region\nextending forward approximately\ncircumferential pressure\ndistributions were higher than the\ncorresponding newtonian distribution\nand a better prediction was obtained\nby modifying the theory to match\nthe pressure at 90 from the windward\ngenerator to that on the surface\nof the cone at an angle of attack of 0 .\ncircumferential heat-transfer\ndistributions were predicted satisfactorily\nup to about 60 from the\nstagnation line by using lees' heat-flux\ndistribution based on the\nnewtonian pressure . the effects of nose\nbluntness at large angles of\nattack were very small in the region\nbeyond two nose radii from the\npoint of tangency ."}, {"doc_id": 1308, "text": "a guide to the use of the m. i. t. cone tables .\n the second and third volumes of the m.i.t. cone tables have\nbeen found to be unsatisfactory in two respects . they have been\ncriticized because of their inconvenient tabulation and because\nthe theory on which they are based is inadequate near the cone\nsurface . the former is climinated by means of a coordinate\ntransformation . empirical evidence is presented to show that\nthe latter may be ignored in practice . the exact nature of\ncertain numerical errors in the table is also pointed out ."}, {"doc_id": 1309, "text": "hypersonic flows past a yawed circular cone and other\npointed bodies .\na detailed treatment of inviscid hypersonic\nflow past a circular cone is given, for\nsmall and moderate yaw angles, within\nthe framework of shock-layer theory .\nthe basic problem of non-uniform validity\nassociated with the singularity of\nthe entropy field is examined and a valid\nfirst-order solution is obtained which\nprovides an explicit description of a thin\nvortical layer at the inner edge of the\nshock layer . analytic formulas for pressure\nand circumferential velocity are\ngiven consistent to the second-order\napproximation including the non-linear\nyaw effect .\n the study of the entropy field (which\nis not restricted to the hypersonic case)\nalso provides corrections to previous\nwork on the yawed cone and confirms the\nvalidity of the linear yaw effect on pressure\nfield in the stone theory .\n a related investigation of three-dimensional\nflow fields is presented with\nspecial reference to the flow structure near\nthe surface of a pointed, but\notherwise arbitrary body . the inviscid streamline\npattern on the surface is given by\nthe geodesics originting from the pointed\nnose as a leading approximation of\nshock-layer theory . associated with this\nstreamline pattern is a vortical sublayer\nwhich exists generally at small as well as at\nlarge angle of attack . at the base of\nthe sublayer, enthalpy and flow speed remain\nessentially uniform ."}, {"doc_id": 1310, "text": "survey of inviscid hypersonic flow theory for geometrically\nslender shapes .\n a survey is made of existing\ntheories for the calculation of pressure\ndistributions on slender bodies at\nhypersonic speeds . no account is taken\nof boundary layer displacement effects\nwhich are expected to become important\nabove a mach number of about 10 for a slender body .\n first the breakdown of linearised\nsupersonic theory is demonstrated as\nmach number increases above about 5, and\nthis is followed by a derivation of\nthe hypersonic similarity rule . this\nsection includes a description of the\npiston-analogy .\n next a physical interpretation\nof hypersonic flow is outlined and a\nsimple derivation of the modified\nnewtonian pressure formula is given .\n the equations of flow through\nan oblique shock wave are simplified by\nassuming a strong shock, and various\nresults are thereby derived . these\ninclude the tangent-wedge and tangent-cone formulae .\n this is followed by a description\nof the newtonian approximation for\nslender bodies, including the effect of\ncentrifugal forces, and the connection\nwith newtonian flow theory is emphasized for .\n the shock-expansion method is\ndescribed in some detail for both\ntwo-and three-dimensional bodies, and\nfinally some remarks are made about the\navailable data sheets and tables for\nestimating pressures on cones and\nogive-cylinders in yaw .\n the note does not claim to be\noriginal, even in presentation . the aim\nhas been to prepare a reasonably complete\nsurvey of available theory for\nhypersonic flow over slender bodies, excluding\nviscous and explicit real gas effects .\n this will provide the background\nfor further work in which experimental\ndata will be analysed and in conjunction\nwith which it is hoped to produce\naccurate design methods for estimating\npressures and forces on shapes intended\nfor sustained flight at hypersonic speeds ."}, {"doc_id": 1311, "text": "some simple solutions to the problem of predicting\nboundary layer self-induced pressures .\n simplified theoretical approaches\nare shown, based on hypersonic\nsimilarity boundary-layer theory,\nwhich allow reasonably accurate\nestimates to be made of the surface\npressures on plates on which viscous\neffects are important . the consideration\nof viscous effects includes\nthe cases where curved surfaces,\nstream pressure gradients, and\nleading-edge bluntness are important factors ."}, {"doc_id": 1312, "text": "tabulated solutions of the equilibrium gas properties\nbehind the incidents and reflected normal shock-wave\nin a shock-tube .\n tabulated solutions are\npresented for the equilibrium gas\nproperties behind the incident and\nreflected normal shock-waves in the\nshock-tube, for nitrogen and oxygen .\nthey cover the range of shock-wave\nmach numbers up to 12 at intervals of\nundisturbed gas pressure between 1 and\n the thermodynamic model of the\ngas used in the calculations\nis described in some detail, as is the\nmethod of solving the equations .\nthe limitations of the assumption of\nthermodynamic equilibrium are discussed\nwith regard to shock-tube applications,\nand the estimated accuracy of the\ntables is indicated ."}, {"doc_id": 1313, "text": "on the flow in a reflected shock tunnel .\nthe performance of a shock tunnel operated by the reflected-shock\ntechnique is examined theoretically neglecting viscous effects and\nhigh-temperature real-gas effects . particular attention is given to\ndisturbances to the flow at the nozzle entry caused by waves reflected from\n the contact surface when the operating conditions depart from those for\nthat the first disturbance reflected from the contact surface is weak\nenough to be tolerated only within a small range of primary-shock mach\nnumber, m /e.g., 5 7 m 6 3 if the pressure at entry to the nozzle is to\nremain constant to 10 per cent/ . within this range, running times much\nlonger than those obtained in 'straight-through' shock tunnels are\npredicted, the limitation usually being imposed by the arrival of the\nexpansion wave originating at the diaphragm .\noutside this range of mach number, the uniform-flow duration between the\n arrival at the nozzle entry of the primary shock and the first\ndisturbance reflected from the contact surface is shown to be approximately\n equal to the time between the arrival of the primary shock and the\ncontact surface in a 'straight-through' shock tunnel . at first sight it\n appears, therefore, that the advantages of reflected-shock operation\nare confined to a very narrow range of shock mach number, unless a\nheated driver gas is used in order to vary the mach number for\nfurther analysis suggests, however, that subsequent disturbances in the\nmultiple wave reflection process between the contact surface and the end\n of the tube are relatively weak over a useful range of shock mach\nnumber . thus, if the flow after the arrival of the early reflected\ndisturbances is used for test purposes, long running times seem possible in\n theory without severe restrictions to the shock mach number .\nexperiments have been made in a shock tube and a shock tunnel to\nprovide data for comparisons with the results of the simple theory . if\nallowance is made for viscous effects on the motion of the contact\nsurface, fair agreement is found for the disturbances reflected and\ntransmitted by the contact surface, and for the arrival of the expansion wave\nreflection process increases when the shock mach number is raised\nsubstantially above the 'tailored' value, and a limit to the usable flow\nduration may result .\na striking feature of the results is a fall of pressure at the end of\nthe tube immediately after reflection of the primary shock . this is\nattributed to attenuation of the reflected shock resulting from its\ninteraction with the boundary layer on the wall of the tube . further\nresearch is required to check this explanation, and to investigate the\neffects of reynolds number and of the cross-sectional shape and size of\nthe tube . the effects of the tail and reflected head of the expansion\nwave originating at the main diaphragm are discussed . it is shown that\nthe arrival of the reflected head at the nozzle entry may impose a\nsevere limitation to the duration of uniform conditions at low shock\nmach number, and that the arrival of the tail may limit the flow\nduration at high shock mach number . unless means can be devised to\nsuppress the expansion wave, it is demonstrated that it is desirable to\nhave alternative diaphragm positions in a tube required to operate over\na range of shock mach number .\nit is concluded that running times of order 10 milliseconds at a shock\nmach number of 4, falling to, perhaps, 1 millisecond at a shock mach\nnumber of 8 seem possible in a shock tunnel of reasonable size by using\nreflected-shock operation with unheated hydrogen driving air . because\nof the simplifying assumptions of the theoretical investigations, and\nthe deficiencies of the apparatus used for the experiments, the present\ninvestigation must, however, be regarded as preliminary in character .\nfurther research is required to check and extend the findings, and\ntopics particularly requiring investigation are listed in the paper ."}, {"doc_id": 1314, "text": "production of high temperature gases in shock tubes .\n this paper is intended to set forth aerodynamic and\nthermodynamic calculations which are useful in the\nproduction of strong shock waves . the experimental\nproduction of strong shock waves is discussed .\ncomparison of the experimental shock strengths with the\ntheoretical calcualtions is made, and finally, some\npreliminary results of shock tube studies in high temperature\ngases (up to 18,000k) are briefly surveyed ."}, {"doc_id": 1315, "text": "performance estimates for the rae 6in . high-pressure\nshock tube .\n estimates are made of the performance\nof the rae 6'' high pressure\nshock tube, with various driver gases, over\na range of pressure ratios giving\nshock mach numbers from 6 to 22 . the\ncalculations are based on a simplified\nmodel of shock tube flow, in which the\nworking fluid (argon-free air) is\nassumed to be always in chemical\nequilibrium, and the driver gas (either\nhydrogen, or the products of combustion\nof a hydrogen-oxygen mixture) is\nassumed to behave as an ideal gas with\nconstant specifiic heats .\n the results are presented in\ngraphical form and comprise charts\nnormal shock waves in argon-free air\nshock wave mach number and diaphragm\npressure ratio under various initial conditions, and\nof the shock-induced flows, both\nin the uniform-sectioned shock tube, and\nwhen expanded in a divergent nozzle"}, {"doc_id": 1316, "text": "temperature measurements of shock-waves by spectrum-line reversal, ii a\ndouble beam method .\nthe sodium-line reversal method, as previously described, using a\nphotomultiplier and oscillograph, has been modified . two light beams\nare now employed, and interference filters are used in front of the\nphotomultipliers instead of a spectrograph . in one beam the background\nsource is viewed directly, through the shock tube, and in the other beam\n the background source is viewed through the shock tube by a mirror\nsystem with a neutral filter interposed to reduce its effective\nbrightness temperature . with a suitably chosen temperature for the\nbackground, one oscillograph trace indicates absorption and the other\nindicates emission of the sodium lines . it is thus possible, from the\nrecords of a single shock, to determine the temperature history behind\nthe shock wave to about 20degreec . nitrogen and oxygen again show\nrelaxation effects near the front . temperatures in argon tend to come\nlow, owing to radiative disequilibrium,. excitation processes in argon\nare discussed . with this system it is possible to determine\ntemperatures rather higher than that of the background source . some work has\nalso been done, with a single-beam method, using a carbon arc as\nbackground and following reversal of the indium blue line . temperatures\n up to 3600degreek have been measured in shocks through nitrogen, but\nthe time resolution is not so good ."}, {"doc_id": 1317, "text": "shock-tube testing time .\nin a theoretical investigation of attenuation effects of the shock wave\nthe conservation of mass equation led to an explanation of the\ndifference between the ideal theoretical test time and the experimentally\nobtained time . a numerical example is given ."}, {"doc_id": 1318, "text": "stagnation temperature measurements in a hypersonic gun tunnel using the\n sodium-line reversal method .\nthe sodium line reversal /s.l.r./ method has recently been used to\nmeasure transient temperatures in the 1400degreek to 3000degreek range, for\n example ref.6 reports measurements of gun flash temperatures . in the\ngun tunnel, stagnation temperatures in the above range can be generated\nflow between a blunt body and its bow shock wave . the gas temperature\nin this zone is close to the stagnation value ."}, {"doc_id": 1319, "text": "real gas effects in flow over blunt bodies at hypersonic speeds .\na hypersonic shock tunnel has been developed to investigate the\naerodynamic characteristics of flow over bodies at conditions comparable to\nthose encountered by ballistic missiles and satellites re-entering the\natmosphere . some results for a shock velocity of over 50,000 ft/sec in\nthe shock tube portion of the facility are presented . static pressure\ninvestigations were made in the nozzle for different stagnation\nconditions in order to determine the flow condition and the expansion\nprocess .\nthe results of the investigation on representative blunt bodies at\nhypersonic mach numbers and nozzle stagnation temperatures up to\napproximately 6000degreek are presented . these include body pressure\ndistributions, shock wave shapes, detachment distances, and photographs\nof the luminous gas region in the shock layer . it is seen that the\nshock detachment distance is smaller at higher stagnation temperatures\nowing to the real gas effects . for the hemisphere the pressure\ndistribution was less than that predicted by the modified newtonian theory for\n all stagnation temperatures . for a 50degree cone-hemisphere the\npressure distribution and the shock wave detachment distance were\nappreciably affected by the real gas effects .\nthe experimentally obtained shock wave shape and the approximate\nboundary layer on a flat plate are correlated with the analytical\nprediction . some preliminary results for the detached shock wave produced\nby a blunt two-dimensional body in a low density flow at a mach number\nof 19.6 are presented ."}, {"doc_id": 1320, "text": "divergence of plate airfoils of low aspect ratio at\nsupersonic speeds .\n in part (1), as a first approach to a theoretical investigation\nof low aspect ratio rectangular plate wings of constant thickness,\nthe two assumptions are made that .. (a) the spanwise form of\nthe structural distortion is known, leaving the chordwise\ndistortion arbitrary,. and (b) the aerodynamic forces are\napproximations of the supersonic linearized theory . the form of the\nchordwise distortion is then deduced from the differential\nequation representing the state of neutral equilibrium for small\ndisplacements at the critical divergence speed .\n secondly, this problem is investigated using measured\nstructural flexibility coefficients together with theoretical\naerodynamic coefficients .\n thirdly, the usual series solution based on the rayleigh-ritz\napproach is discussed, using the same assumptions as in the first\nmethod .\n all the results of these methods are consistent and indicate that\nthe transonic regime at m = 1 is the most critical for\ndivergence .\n in part (2), it is established that sweeping the leading edge of\na plate airfoil of constant thickness increases its stability . for\nangles of sweep less than 30, the critical conditions occur when\nthe leading edge is sonic, but for angles greater than 30 the\ncritical conditions occur when m = 1 ."}, {"doc_id": 1321, "text": "effects of a flexible boundary on hydrodynamic stability .\npurpose of paper is to examine theoretically the use of coatings of\nelastic materials to prevent transition from laminar to turbulent flow .\n theory is extension to flexible boundary of the small-disturbance\ntollmien-schlichting stability theory and makes use of /tietjens\nfunction/ and other functions that occur in solution of orr-sommerfeld\nequation . it is shown how solutions for flexible wall can be obtained\nfrom solutions for rigid boundary .\noutline and discussion is given first for tollmien-schlichting stability\n theory for rigid wall, then for theory for flexible boundary . theory\nis given both for a nondissipative and a dissipative flexible boundary .\n behavior of flexible medium itself is also examined .\npractical requirements are discussed . for example, a conclusion is that\n to avoid tollmien-schlichting instability, the wave velocity of surface\n waves in absence of flow should coincide with tollmien-schlichting wave\n velocity at wavelength of /most dangerous/ tollmien-schlichting waves .\n moreover, damping should be large enough to prevent surface waves from\ndeveloping but not so large that tollmien-schlichting waves are\npermissable . author states that a boundary that is both soft and light,\none whose elastic constants are of same order as the dynamic pressure of\n the flow, may be practical for use at high speeds . this surface should\n have a small damping to avoid tollmien-schlichting type of instability\nand a large enough wave speed without flow to avoid surface wave\ninstability . although paper is somewhat sketchy in places, it gives\ncomprehensive coverage of stability of laminar flow over a flexible wall ."}, {"doc_id": 1322, "text": "qualitiative solutions of the stability equation for a boundary layer in\n contact with various forms of flexible surface .\nan appropriate form of the boundary layer stability equation is\ndeveloped for the condition where the fluid is in contact with an\nisotropic and homogeneous elastic medium, and various approximate\nanalytical solutions obtained for certain types of surface, so as to reveal at\nleast qualitatively the origin and characteristics of neutral\noscillations . in the worked solutions the elastic medium is treated as\nnondissipative, and the interior boundary is supposed either fixed, or free\n of stress, or exposed to fluid .. the boundary layer, also, is treated\nas that over a flat-plate in an incompressible fluid .\nthe results obtained show that the presence of such a resiliant surface\nintroduces the possibility of a number of other modes of oscillation\nschlichting waves . most of these modes have speeds of propagation\ndetermined largely by the properties of the elastic material, and their\npresence may well be effectively a matter of 'non-viscous' flow\nstability -dash a subject not treated here . the tollmien-schlichting\nmode has its minimum reynolds number increased by the presence of the\nsurface, but if the interior boundary is free there may be an upper\nlimit as well . indeed, a sufficiently thin free surface, or one of low\nrigidity, apparently eliminates neutral oscillations of this mode\naltogether, only at the expense, however, of the introduction of a mode of\nflexural waves ."}, {"doc_id": 1323, "text": "an investigation of the use of an auxiliary slot to\nre-establish laminar flow on low drag aerofoils .\n the use of an auxiliary slot on a laminar-flow\naerofoil has been investigated to check whether laminar\nflow can be re-established by suction at the rear of the region\nof deposited dirt, flies, etc .\n results indicate that in the absence of unfavourable pressure\ngradients, it is possible to re-establish a laminar\nboundary layer by removing a little more than the whole turbulent\nlayer reaching the slot, and preliminary estimates\nsuggest that with efficient ducting it should be possible to achieve\na reduction in overall effective drag coefficient by\nthis means ."}, {"doc_id": 1324, "text": "the effect on transition of isolated surface excrescences\nin the boundary layer .\n the effect of isolated surface excrescences in a\nlaminar boundary layer in producing disturbances\nwhich may lead to turbulent flow has been examined\nexperimentally by several methods . photographs of some\nof the flow patterns visualised by smoke and china-clay\ntechniques are given .\n the critical heights of pimple which just give rise to\nspreading wedges of turbulent flow have been measured\non a flat plate and on two aerofoils at several angles of\nincidence . the results are analysed and are presented in a\nform which enables approximate estimates to be made of the\nprotuberances permissible on laminar-flow surfaces at\nfull-scale flight reynolds numbers . the estimates suggest\nthat at an altitude of 30,000 ft the critical pimple height\nis 0.004 in. for a speed of 350 m.p.h., whilst 0.002 in.\nmay be permissible at all subsonic speeds . at sea-level,\nhowever, the tolerances are approximately halved ."}, {"doc_id": 1325, "text": "experiments on the use of suction through perforated\nstrips for maintaining laminar flow . transition and\ndrag measurements .\n wind-tunnel tests are described in which suction\nis applied at perforated strips, as an alternative to\nporous strips or slots, in order to maintain a laminar boundary\nlayer . a test was first carried out on a single row of\nperforations on a cambered plate, as a preliminary to the main\ntests which were performed on strips of multiple rows\nof perforations drilled through the surface of a low-drag-type\naerofoil 13 per cent thick and of 5-ft chord .\n up to a wind speed of 180 ft sec it has been ascertained that\nsuction may be safely applied to extend laminar flow\nprovided the ratio of hole diameter to boundary-layer displacement\nthickness is less than 2, the ratio of hole pitch to\ndiameter is less than 3 and there are at least three rows of holes\nin the strip . with less than three rows, the criteria\nare much more restrictive . it is possible to extend laminar flow\nby suction through perforations whose diameters and\npitches exceed these values slightly, but only with the risk that\nexcessive suction quantities will produce wedges of\nturbulent boundary layer originating at the holes .\n a uniform distribution of suction through the holes was\nnecessary . this was successfully obtained by two methods,\nthe use of cells and throttle holes, and with tapered holes .\nin particular, tests were carried out on some panels\nsupplied by handley page, ltd., in which the cells and tapered\nholes had been constructed by commercial methods, and\nthe suction distribution proved satisfactory .\n the resistance of some of the cellular arrangements was\nmeasured . it was found that when the suction quantities\nwere the minimum required to maintain laminar flow, the\nadditional losses in total head of the sucked air due to\nthe resistance of the throttle holes could be made small compared\nwith the loss in total head of the sucked boundary\nlayer ."}, {"doc_id": 1326, "text": "interaction of secondary injectants and rocket exhaust\nfor thrust vector control .\n tests were conducted with 1300- to 1500-lb thrust\nsolid rocket motors in order to investigate the\nside-force generation mechanisms associated with\nthe injection of a secondary fluid into the\nexpansion cone of a solid propellant rocket nozzle for\nthrust-vector control . the nozzles were 15\nconicals with a nominal expansion ratio of . all\nfirings were conducted in zero-flow ejectors .\nfreon-12, water, and gascous nitrogen were used as\nthe injectant . nozzle-wall pressure profiles,\nside thrust, and the nozzle-wall shock interface were\nrecorded . the general character of the\npressure disturbance was defined . the major portion of\nthe side force was generated by the pressure\ndisturbance downstream of the injector . the\naxial-thrust augmentation generated by the\ninjectant was calculated . the effects of nozzle-expansion\nratio and injector location on the side force\nwere clearly illustrated ."}, {"doc_id": 1327, "text": "on the propagation and structure of the blast wave .\n concerning blast waves with front surfaces of plane, cylindrical and\nspherical shape, the propagation velocity u and the distribution of\nhydrodynamical quantities are discussed . the solutions are constructed\nin the form of power series in (c u), where c is the sound velocity of\nundisturbed fluid . especially r, the distance of shock front from the\ncharge, is represented as,\nwhere r is the characteristic length related to the energy of explosion,\nj and are constants, and a=0,1,2 correspond to plane, cylindrical and\nspherical case, respectively . in this paper the first approximations\nfor a=0,1 are discussed (the case a=2 has been discussed by g. i.\ntaylor) . the solution is obtained numerically for the case of the\nadiabatic index . the approximate solution is also considered . using\nthese solutions, is found to be .\n the second approximation will appear in part 2 to be published\nsubsequently ."}, {"doc_id": 1328, "text": "the production of aerodynamic forces by heat addition\non external surfaces of aircraft .\n within the framework of linearized\nflow theory an equivalence between\na fluid mass source, a heat source,\nand streamwise body forces is\ndeveloped . the equivalence between\nthe fluid mass source and heat\nsource was first noticed by hicks(2)\nand later by chu . (3) using the\nequivalence the flow field produced\nby heat addition and by\nmagnetohydrodynamical body forces can be computed .\n examples for a two-dimensional\nflat plate, a delta wing, an axially\nsymmetric slender body, and a wedge-shaped\nafterbody are computed at\nsubsonic and supersonic speeds .\nthe efficiency of lift or thrust\nproduction by surface heat addition is\nvery low at subsonic speeds . at\nsupersonic speeds the efficiency is\ncompared with the efficiency of a\nconventional turbojet-powered aircraft\nconfiguration . it is found that\nthe efficiency of lift or thrust production\nby heat addition on\ntwo-dimensional bodies is approximately the same\nas that for a\nturbojet-powered two-dimensional body . the\nefficiency is somewhat higher at low\nsupersonic mach numbers and behaves\nas, decreasing to a\nconstant value as increases .\non the other hand, the efficiency of\nthrust production by heat addition\nincreases linearly with mach number\nwhen heat is added on the rear surface\nof an axially symmetric afterbody\nof parabolic shape ."}, {"doc_id": 1329, "text": "some aspects of non-stationary airfoil theory and its\npractical application .\n this paper consists of three notes on the theory of two-\ndimensional thin airfoils in non-uniform motion ..\noscillating airfoil are collected from an earlier paper and are\npresented in convenient forms for practical application .\nrigid airfoil passing through a vertical-gust pattern having a\nsinusoidal distribution of intensity . the lift is determined as a\nfunction of the reduced frequency (which in this case is\nproportional to the ratio of the airfoil chord and the wave length of the\ngust pattern) and is presented in the form of a vector diagram .\nit is shown that the lift acts at the quarter-chord point of the\nairfoil at all times .\ncalculation of the amplitude of torsional oscillation of a fan blade\noperating in the wake of a set of pre-rotation vanes . in a\nnumerical example the amplitude is found to be small even when\nthe vanes are spaced so that the exciting frequency coincides\nwith the natural frequency of the fan blade ."}, {"doc_id": 1330, "text": "on some fourier transforms in the theory of non-stationary\nflows .\n the growth of lift on a airfoil\nstarting impulsively from rest to a uniform\nvelocity has been given by wagner (1925) . the\nsteady-state lift due to circulation on an\nairfoil oscillating sinusoidally and moving with\nuniform velocity has been given by theodorsen\n the present paper based essentially on the\nmaterial of n. a. c. a. report no. 629 by the\nauthor, discusses some reciprocal relations of\nthe nature of fourier transforms existing\nbetween the functions of wagner and theodorsen .\nkussner (1936) has already shown that wagner's\nfunction may be derived from theodorsen's\nfunction . by means of a superposition principle it\nis possible to utilize these fundamental\nfunctions to treat general problems in transient\nexpression which is accurate to within 2\npercent is given for wagner's function . this\nexpression leads to a good approximate expression\nfor theodorsen's function in terms of the\nexponential integral, instead of hankel functions .\nan analogy is drawn between transient\nhydrodynamic flows and transient electrical flows .\n kussner (1936) has introduced a function\ndescribing the growth of lift on an airfoil\nentering a sharp edged vertical gust region . this\nfunction bears a certain relation to wagner's\nfunction which is briefly discussed ."}, {"doc_id": 1331, "text": "calculated responses of a large sweptwing airplane\nto continuous turbulence with flight-test comparisons .\n calculated responses of symmetrical\nairplane motions, wing\ndeformations, and wing loads due to gusts are\nshown to compare favorably with\navailable flight-test results . these\ncalculated responses are based on\nrandom-process theory, five degrees of\nfreedom, lifting-surface\naerodynamics, and one-dimensional vertical\nturbulence . the extent to which\nvarious degrees of freedom contribute\nto the responses is examined and\nin this connection the relative effects\nof static and dynamic\naeroelasticity are determined ."}, {"doc_id": 1332, "text": "calculated spanwise lift distributions, influence functions\nand influence coefficients for unswept wings in subsonic\nflow .\n spanwise lift distributions have been calculated for nineteen\nunswept wings with various aspect ratios and taper ratios and\nwith a variety of angle-of-attack or twist distributions, including\nflap and aileron deflections, by means of the weissinger method\nwith eight control points on the semispan . also calculated\nwere aerodynamic influence coefficients which pertain to a\ncertain definite set of stations along the span, and several\nmethods are presented for calculating aerodynamic influence\nfunctions and coefficients for stations other than those stipulated .\n the information presented herein can be used in the analysis\nof untwisted wings or wings with known twist distributions, as\nwell as in aeroelastic calculations involving initially unknown\ntwist distributions ."}, {"doc_id": 1333, "text": "aerodynamic forces on wings in non-uniform motion .\n the problem of determining the aerodynamic forces\nacting on wings of finite span in non-uniform motion\nin an incompressible, inviscid fluid is investigated . the underlying\ntheory is outlined in 2, and some known results\nfor the case of an aerofoil of infinite span are included in 3 . it is\nshown in 4, by the use of operational methods,\nthat the growth of lift function k (s) corresponding to a sudden unit\nchange of incidence can be derived from the lift\nfunction corresponding to simple harmonic translational motion .\nfrom results given by the writer for rectangular\nwings (1943) and tapered wings (1945) in simple harmonic motion\nthe corresponding values of k (s) are determined .\nthe growth of lift function k (s) for a wing penetrating a uniform\nvertical gust can then be estimated as shown in 4\nand 5 . by the use of approximate formulae for the growth of lift\ncurves given in fig. 2, the aerodynamic forces\ncorresponding to damped and growing translational oscillations are\nderived .\n certain integrals involved in the theory are evaluated in\nappendix 1, and in appendix 2 the method of determining\nk (s), when k (s) is known, is discussed in detail .\n it is suggested that the aerodynamic forces acting on wings\nof finite span for any type of motion can best be derived\nfrom a knowledge of the forces corresponding to purely\ndivergent motion, which can be calculated by the methods\noutlined in this report ."}, {"doc_id": 1334, "text": "calculated spanwise lift distributions and aerodynamic\ninfluence coefficients for swept wings in subsonic\nflow .\n spanwise lift distributions have been calculated for 61 swept wings\nwith various aspect ratios and taper ratios and with a variety of\nangle-of-attack or twist distributions, including flap and aileron\ndeflections, by means of the weissinger method with eight control points\non the semispan . also calculated for these plan forms were aerodynamic\ninfluence coefficients which pertain to a certain definite set of\nstations along the span . the information presented herein can thus be\nused both in the analysis of untwisted wings or wings with known twist\ndistributions and in aeroelastic calculations involving initially\nunknown twist distributions .\n this paper supplements and is intended to be used in conjunction\nwith naca tn 3014, where the same type of information, calculated in the\nsame way, is presented for 19 unswept wings ."}, {"doc_id": 1335, "text": "use of freon-12 as a fluid for aerodynamic testing .\n the thermodynamic properties\nof freon-12 have been\ninvestigated to determine the\npossibilities of the use\nof this gas as a fluid for\naerodynamic testing . the\nvalues of velocity of sound\nin freon-12, which are less\nthan one-half those in air,\nare presented as functions\nof temperatures and pressure,\nincluding measurements at\nroom temperature . the density\nof freon-12 is about\nfour times that of air . changes\nin state of freon-12\nmay be predicted by means of the\nideal gas law with an\naccuracy of better than 1 percent\nat pressures below\nfreon-12 is shown not\nto condense during an adiabatic\nexpansion from normal\nconditions up to a mach number\nof 3 . the values of the\nratio of specific heats\nfor freon-12 are lower than\nthat for air, and therefore\nan additional parameter is\nintroduced, which must be\nconsidered when comparisons\nare made of aerodynamic tests\nusing freon-12 with those\nusing air .\n the time lag of the\nvibrational heat capacity\nof freon-12 to a change in\ntemperature has been\nmeasured and found to be\nof the order of 2 x 10 second\nat atmospheric temperature\nand pressure . this time\nis so short that no important\nenergy dissipations\nshould result in most\nengineering applications ."}, {"doc_id": 1336, "text": "studies of the use of freon-12 as a wind tunnel testing\nmedium .\n a number of studies relating to\nthe use of freon-12 as a\nsubstitute medium for air in aerodynamic\ntesting have been made . the\nuse of freon-12 instead of air makes\npossible large savings in\nwind-tunnel drive power . because of the\nfact that the ratio of specific\nheats is approximately 1.13 for freon-12\nas compared with 1.4 for air,\nsome differences exist between data\nobtained in freon-12 and in air .\nmethods for predicting aerodynamic\ncharacteristics of bodies in air\nfrom data obtained in freon-12, however,\nhave been developed from the\nconcept of similarity of the streamline\npattern . these methods,\nderived from consideration of two-dimensional\nflows, provide substantial\nagreement in all cases for which comparative\ndata are available . these\ndata consist of measurements throughout\na range of mach number from\napproximately 0.4 to 1.2 of pressure\ndistributions and hinge moments on\nswept and unswept wings having aspect\nratios ranging from 4.0 to 9.0,\nincluding cases where a substantial\npart of the wing was stalled .\n the freon charging and recovery\nsystem used for the langley\nlow-turbulence pressure tunnel is described ."}, {"doc_id": 1337, "text": "study of effects of sweep on the flutter of cantilever\nwings .\n an experimental and analytical investigation of the flutter\nof sweptback cantilever wings is reported . the experiments\nemployed groups of wings swept back by rotating and by\nshearing . the angle of sweep ranged from 0 to 60 and\nmach numbers extended to approximately 0.85 . a theoretical\nanalysis of the air forces on an oscillating swept wing of high\nlength-chord ratio is developed, and the approximations\ninherent in the assumptions are discussed . comparison with\nexperiment indicates that the analysis developed in the present\nreport is satisfactory for giving the main effects of sweep, at\nleast for nearly uniform cantilever wings of high and moderate\nlength-chord ratios . a separation of the effects of finite span\nand compressibility in their relation to sweep has not been made\nexperimentally but some combined effects are given . a\ndiscussion of some of the experimental and theoretical trends is\ngiven with the aid of several tables and figures ."}, {"doc_id": 1338, "text": "investigation to determine effects of center of gravity location on the\ntransonic flutter characteristics of a 45degree sweptback wing .\nan experimental investigation has been conducted in the 26-inch langley\ntransonic blowdown tunnel to determine effects of center-of-gravity\nlocation on the transonic flutter characteristics of a 45degree\nswept-back-wing plan form of aspect ratio 4.0 and taper ratio 0.6 .\nsolid-construction models of the plan form with streamwise naca 65a004\nairfoil sections and center-of-gravity locations at approximately 34\npercent chord, 46 percent chord, and 58 percent chord, respectively, were\nfluttered at several mach numbers between 0.8 and 1.35 .\nit was found that, for streamwise mach numbers from 0.8 to 1.0, the\nvariation with mach number of the ratio of experimental flutter speed to\n a calculated incompressible flutter speed was not affected by\ncenter-of-gravity location . however, for mach numbers from 1.0 to 1.35, there\nwas an increase in flutter-speed ratio with mach number which was\ndifferent for each center-of-gravity position . data from wings with\nsuccessively more forward center-of-gravity locations showed\nsuccessively larger values of flutter-speed ratio at mach numbers from 1.0 to"}, {"doc_id": 1339, "text": "calculation of flutter characteristics for finite-span swept or unswept\nwings at subsonic and supersonic speeds by a modified strip analysis .\na method has been developed for calculating flutter characteristics of\nfinite-span swept or unswept wings at subsonic and supersonic speeds .\nthe method is basically a rayleigh type analysis and is illustrated with\n uncoupled vibration modes although coupled modes can be used . the\naerodynamic loadings are based on distributions of section lift-curve\nslope and local aerodynamic center calculated from three-dimensional\nsteady-flow theory . these distributions are used in conjunction with\nthe /effective/ angle-of-attack distribution resulting from each of the\nassumed vibration modes in order to obtain values of section lift and\npitching moment . circulation functions modified on the basis of\nloadings for two-dimensional airfoils oscillating in a compressible flow are\n employed to account for the effects of oscillatory motion on the\nmagnitudes and phase angles of the lift and moment vectors .\nflutter characteristics have been calculated by this method for 12 wings\n of varying sweep angle, aspect ratio, taper ratio, and center-\nof-gravity position at mach numbers from 0 to as high as 1.75 . comparisons\n of the results with experimental flutter data indicate that this method\n gives generally good flutter results for a broad range of wings ."}, {"doc_id": 1340, "text": "method of controlling stiffness properties of a solid-construction\nmodel wing .\na simple method is presented for controlling the bending and torsional\nstiffnesses of a solid-construction model wing . the method consists of\nweakening the wing by drilling holes through the wing normal to the\nchord plane . aerodynamic continuity is maintained by filling the holes\nwith a relatively soft material . the important parameters controlling\nthe stiffnesses are the amount of material removed by drilling, the\nratio of hole diameter to wing thickness, and the plan-form pattern of\nthe holes . data are given which may be used for predicting the\nstiffness of a model wing weakened in this manner ."}, {"doc_id": 1341, "text": "investigation of wing flutter at transonic speeds for six systematically\n varied wing plan forms .\nan investigation of the effects of systematic variations in wing plan\nform on the flutter speed at mach numbers between 0.73 and 1.43 has been\n conducted in the 26-inch langley transonic blowdown tunnel . the angle\nof sweepback was varied from 0degree to 60degree on wings of aspect\nratio 4, and the aspect ratio was varied from 2 to 6 on wings with\nexperimental flutter speed and the reference flutter speed calculated on\n the basis of incompressible two-dimensional flow . this ratio,\ndesignated as the flutter-speed ratio, is plotted as a function of mach\nnumber for the various wings . it is found that the flutter-speed ratio\nincreased rapidly past sonic speed for sweep angles of 45degree and\nless, indicating a favorable effect of mach number . for sweepback of\nmach number range of the tests . reducing the aspect ratio had a\nfavorable effect on the flutter-speed ratio which was of the order of 100\npercent higher for the aspect-ratio-2 wing than for the aspect-ratio-6\nwing . this percentage difference was nearly constant throughout the\nmach number range, indicating that the effect of mach number was about\nthe same for all aspect ratios tested ."}, {"doc_id": 1342, "text": "the calculation of aerodynamic loading on surfaces of any shape .\nthe object of the report is to establish a routine method for the\ncalculation of aerodynamic loads on wings of arbitrary shape . the method\ndeveloped is based on potential theory and uses a general mathematical\nformula for continuous loading on a wing which is equivalent to a double\n fourier series with unknown coefficients . in order to evaluate the\nunknown coefficients the continuous loading is split up into a regular\npattern of horseshoe vortices, the strengths of which are proportional\nto the unknown coefficients and to standard factors which are given in a\n table . the total downwash at chosen pivotal points is obtained by\nsumming the downwashes due to the individual vortices, a process which\nis simplified by the use of specially prepared tables of the properties\nof the horseshoe vortex . by equating the downwash to the slope of the\nwing at each pivotal point, simultaneous equations are obtained, the\nsolution of which defines the unknown coefficients .\nthe first layout involves a total of 76 vortices over the wing, and a\nsecond layout, involving a total of 84, is shown to be of superior\naccuracy . the effect on the solution of the number of pivotal points is\n investigated and it is concluded that by a suitable choice, it is\nunnecessary to use a large number . results for a rectangular wing at\nwith those obtained by other workers and it appears that there may be\nerrors in published results in at least one of these cases . immediate\ndevelopment includes the application to the calculation of the\ncharacteristics of actual sweptback wings, including rotary derivatives, and\n future development includes also applications in wind tunnel design and\n technique ."}, {"doc_id": 1343, "text": "formulas for the supersonic loading, lift and drag\nof flat swept back wings with leading edges behind\nthe mach lines .\n the method of superposition of linearized conical flows has\nbeen applied to the calculation of the aerodynamic properties, in\nsupersonic flight, of thin flat, swept-back wings at an angle of\nattack . the wings are assumed to have rectilinear plan forms,\nwith tips parallel to the stream, and to taper in the conventional\nsense . the investigation covers the moderately supersonic speed\nrange where the mach lines from the leading-edge apex lie ahead\nof the wing . the trailing edge may lie ahead of or behind the\nmach lines from its apex . the case in which the mach cone\nfrom one tip intersects the other tip is not treated .\n formulas are obtained for the load distribution, the total lift,\nand the drag due to lift . for the cases in which the trailing edge\nis outside the mach cone from its apex (supersonic trailing edge),\nthe formulas are complete . for the wing with both leading and\ntrailing edges behind their respective mach lines, a degree of\napproximation is necessary . it has been found possible to give\npractical formulas which permit the total lift and drag to be\ncalculated to within 2 or 3 percent of the accurate\nlinearized-theory value . the local lift can be determined accurately over\nmost of the wing, but the trailing-edge-tip region is treated only\napproximately .\n charts of some of the functions derived are included to\nfacilitate computing, and several examples are worked out in outline ."}, {"doc_id": 1344, "text": "atmospheric entries with vehicle lift-drag ratio modulated\nto limit deceleration and rate of deceleration vehicles\nwith maximum lift-drag ratio of 0. 5.\n an analysis has been made of\natmosphere entries for which the\nvehicle lift-drag ratio was modulated\nto maintain specified maximum\ndecelerations and or maximum deceleration\nrates . the part of the\nvehicle drag polar used during modulation\nwas from maximum lift\ncoefficient to minimum drag coefficient . the\nentries were at parabolic velocity\nand the vehicle maximum lift-drag ratio\nwas 0.5 . two-dimensional\ntrajectory calculations were made for a\nnonrotating, spherical earth with an\nexponential atmosphere . the results\nof the analysis indicate that for a\ngiven initial flight-path angle,\nmodulation generally resulted in a\nreduction of the maximum deceleration\nto 60 percent of the unmodulated value or\na reduction of maximum deceleration\nrate to less than 50 percent of the\nunmodulated rate . these results were\nequivalent, for a maximum\ndeceleration of 10g, to lowering the undershoot\nboundary 24 miles with a resulting\ndecrease in total convective heating to\nthe stagnation point of 22 percent .\nhowever, the maximum convective heating\nrate was increased 18 percent,. the\nmaximum radiative heating rate and total\nradiative heating were each\nincreased about 10 percent ."}, {"doc_id": 1345, "text": "the use of aerodynamic lift during entry into the earth's\natmosphere .\n by employing aerodynamic lift during entry into the earth's\natmosphere at either orbital or /escape/ velocity, the range of\nallowable entry angles for a prescribed peak deceleration is\ngreatly increased, while the total heat energy transferred to the\nvehicle can be held to about the same value as for a nonlifting\nvehicle . only modest lift-drag ratios are required beyond peak g\nto prevent the deceleration from exceeding the peak value, or to\nprevent the vehicle from skipping out of the earth's atmosphere .\nthus, the difficult guidance and control problem is greatly\nalleviated,. in particular, for return from the moon or other\nplanets the necessity for multiple-pass drag braking is eliminated ."}, {"doc_id": 1346, "text": "modulated entry .\n the technique of modulation, or variable coefficients, is discussed\nand the analytical formulation is reviewed . representative numerical\nresults of the use of modulation are shown for the lifting and\nnonlifting cases . these results include the effects of modulation on\npeak acceleration, entry corridor, and heat absorption . results are\ngiven for entry at satellite speed and escape speed . the indications\nare that coefficient modulation on a vehicle with good lifting\ncapability offers the possibility of sizable loading reductions or,\nalternatively, wider corridors,. thus, steep entries become practical\nfrom the loading standpoint . the amount of steepness depends on the\nacceptable heating penalty . the price of sizable fractions of the\npossible gains does not appear to be excessive ."}, {"doc_id": 1347, "text": "approximate analysis of atmospheric entry corridors\nand angles .\n a simple closed-form solution\nfor the achievable corridor depths\nand entry angles as a function of\ng-load limit, entry velocity, and\nvehicle aerodynamics and thermodynamics\nis developed for two modes of\nvehicle operation, constant angle\nof attack and modulated angle of attack .\n for constant angle of attack,\noperation at maximum negative lift\ncoefficient on the overshoot bound,\nand at an angle of attack between\nzero and that for maximum lift-drag\nratio on the undershoot bound, gives\nthe deepest corridor . for modulated\nangle of attack, operating at\nmaximum negative lift coefficient on the\novershoot bound and modulating\nthe angle of attack from maximum\npositive lift coefficient to zero on\nthe undershoot bound give the deepest\ncorridor . the modulated angle of\nattack gives corridor depths two to\nfour times larger than the fixed\nangle of attack . for both cases the\ncorridor depth is increased by\nincreasing maximum lift-drag ratio,\nincreasing g limit, and decreasing\nentry velocity .\n consideration of hot-gas radiation\nplaces a limit on the maximum\nangle of attack for either mode of\noperation . if a maximum free-stream\nreynolds number limit must be placed\non the vehicle to ensure a laminar\nboundary layer, the deep atmospheric\npenetrations associated with\nconfigurations with high lift-drag ratio\nmay be ruled out . both of these\nthermodynamic considerations reduce\nthe acceptable corridor depth below\nthe value calculated from aerodynamic\nconsiderations alone ."}, {"doc_id": 1348, "text": "radiative heat transfer during atmosphere entry at\nparabolic velocity .\n stagnation point radiative heating\nrates for manned vehicles entering\nthe earth's atmosphere at parabolic\nvelocity are presented and compared\nwith corresponding laminar convective\nheating rates . the calculations\nwere made for both nonlifting and lifting\nentry trajectories for vehicles\nof varying nose radius, weight-to-area\nratio, and drag . it is concluded\nfrom the results presented that radiative\nheating will be important for\nthe entry conditions considered ."}, {"doc_id": 1349, "text": "effects of simulated rocket jet exhaust on stability\nand control of a research type airplane configuration\nat a mach number of 6. 86 .\n an investigation has been\nundertaken in the langley 11-inch\nhypersonic tunnel at a free-stream\nmach number of 6.86 to determine\nthe jet-interference effects at\nhigh jet-static-pressure ratios on the\nstability and control of a\nresearch-type airplane configuration .\ncompressed-air tests with a jet\nexhausting from the base of the\nfuselage were conducted over a reynolds\nnumber range of 0.57 x 10 to\nand over a jet-static-\npressure-ratio range of 0 to 1460 . the results\nof these tests indicated that\nthe operation of the jet induced a\nsizable separated-flow region over\nthe vertical- and horizontal-tail\nsurfaces which could be approximately\nduplicated at low angles of attack\nby use of metal jet-boundary\nsimulators . the results of force tests,\nduring which these metal\njet-boundary simulators were used,\nindicated that this separated-flow\nregion caused a large reduction in\nthe longitudinal stability and\ncontrol and a smaller reduction in the\nlateral and directional stability\nand control . by extending the\ndivergent section of the nozzle and thus\nreducing the jet-static-pressure\nratio, these losses were diminished ."}, {"doc_id": 1350, "text": "effects of jet billowing on stability of missile-type\nbodies at mach 3. 85 .\n the interference effects of a\nbillowing jet on the forces and\nmoments of two missile-type bodies\nwere investigated in the nasa lewis\n2-by 2-foot mach 3.85 wind tunnel .\nto simulate a rocket jet, pressurized\nnitrogen was exhausted from an\nannular sonic nozzle .\n the results indicate that for\nboth models the stability parameter\nmoment coefficient with angle of\nattack) in the region of zero angle\nof attack was favorably influenced\nby the interference resulting from\nseparation due to jet billowing .\nschlieren photographs are presented\nthat show the separation due to the\njet billowing at various pressure\nratios and angles of attack ."}, {"doc_id": 1351, "text": "exploratory tests of the effects of jet plumes on the\nflow over cone- cylinder flare bodies .\n schlieren photographs have been\ntaken of the flow over\ncone-cylinder-flare bodies to study the\nextent of boundary-layer separation\ndue to the presence of rocket jet\nplumes . tests were made of three\ncone-cylinder-flare configurations in\nthe langley 11-inch hypersonic tunnel at\na mach number of 9.65 and in the\nlangley unitary plan wind tunnel at a\nmach number of 4.65 with two\nadditional configurations . the stream\nreynolds number varied from\napproximately 317,000 to 582,000 based on\nmodel length . the conical flares\nhad half-angles of 7 or 13 and\ncontained one of two test nozzles with\na design mach number of 3.72 or 4.53 .\nthe test nozzles were operated with\ncompressed air and were designed to\nsimulate a solid-propellant rocket\nmotor operating at altitudes between\nto free-stream static-pressure ratio\nvaried from jet off to 1,150 for the\ntest nozzle with a design mach\nnumber of 3.72 and from jet off to\nmach number of 4.53 . for most of\nthe tests the angle-of-attack range\nwas 0 to -4,. some additional tests\nwere made at 2 and 4 .\n measurements taken from flow pictures\nindicated that at zero angle\nof attack on all configurations tested\nwith jet on the boundary layer\nseparates ahead of the flare-cylinder\njuncture and the separation point\nmoves toward the cone-cylinder juncture\nwith an increase in pressure\nratio . increasing angle of attack\nreduced the extent of boundary-layer\nseparation on the windward side as\ndid increasing the stream mach number\nfrom 4.65 to 9.65 . other parameters\nwhich tended to reduce the extent\nof boundary-layer separation were ..\nnumber, (b) decreasing stream reynolds\nnumber, and (c) displacing nozzle\nexit rearward ."}, {"doc_id": 1352, "text": "aerodynamic investigation of a parabolic body of revolution\nat mach number of 1. 92 and some effects of an annular\nsupersonic jet exhausting from the base .\n an aerodynamic investigation\nof a parabolic body of revolution was\nconducted at a mach number of 1.92\nwith and without an annular supersonic\njet exhausting from the base .\nmeasurements with the jet inoperative were\nmade of lift, drag, pitching moment,\nradial and longitudinal pressure\ndistributions, and base pressures .\nwith the jet in operation,\nmeasurements were made of the pressures\nover the rear of the body with the\nprimary variables being angle of attack,\nratio of jet velocity to\nfreestream velocity, and ratio of jet\npressure to stream pressure .\n the results with the jet inoperative\nshowed that the radial\npressures over the body varied appreciably\nfrom the distribution generally\nemployed in most approximate theories .\nthe linearized solutions for lift,\npitching moment, and center of pressure\ngave relatively poor predictions\nof the experimental results . an analysis\nof several theoretical methods\nfor calculating pressure distribution and\nwave drag showed that some\nmethods gave results in considerable\ndisagreement with experimental values .\n maximum effects of the jet were\nobtained at the lower ratio of jet\nvelocity to stream velocity and the\nhighest ratio of jet pressure to\nstream pressure . these effects amounted\nto a slight decrease in\nfore-drag, a reduction in lift, and a shift\nof center of pressure in a\ndestabilizing direction ."}, {"doc_id": 1353, "text": "investigation of a two-step nozzle in the langley 11in .\n hypersonic tunnel .\n flow surveys have been made in\nthe first of several nozzles to be\ninvestigated in the langley 11-inch\nhypersonic tunnel . the nozzle was\ndesigned by the method of characteristics\nfor a mach number of 6.98 . two\nstep expanded the air in the\nhorizontal plane to a mach number of 4.36\nand the second in the vertical\nplane to a mach number of 6.98 .\n the test results showed that, although\na maximum mach number of\nabout 6.5 was obtained, the flow in the\ntest section was not sufficiently\nuniform for quantitative wind-tunnel test\npurposes . deviations from the\ndesign flow were traced to the presence\nof a thick boundary layer which\ndeveloped in the first step along the\nparallel walls ."}, {"doc_id": 1354, "text": "investigation of the flow through a single stage two\ndimensional nozzle in the langley 11in . hypersonic\ntunnel .\n flow surveys have been made in\nthe second of several nozzles to be\ninvestigated in the langley 11-inch\nhypersonic tunnel . the single-stage,\ntwo-dimensional nozzle was designed\nby the method of characteristics for\na mach number of 7.08 without\nboundary-layer corrections .\n the test results show that\nreasonably uniform flow at an average\nmach number of about 6.86 was\nobtained in a central region of the stream\nat the test section . this region\nhad a cross section nearly 5 inches\nsquare and had a deviation from\nuniform flow of less than 1 percent in\nmach number and 0.3 in flow angle .\nan increase in mach number of\nabout 3 percent occurred during test\nruns of about 60 seconds duration\nbecause of distortions of the boundaries\nat the first minimum due to\nnonuniform heating of the nozzle blocks\nduring the tests ."}, {"doc_id": 1355, "text": "boundary layer displacement effects in air at mach\nnumbers of 6. 8 and 9. 6.\n measurements are presented for pressure\ngradients induced by a laminar boundary layer on a\nflat plate in air at a mach number of 9.6 and for the\ndrag of thin wings at a mach number of about 6.8\nand zero angle of attack . the pressure\nmeasurements at a mach number of 9.6 were made in the\npresence of substantial heat transfer from the\nboundary layer to the plate surface . the measured\npressure distribution on the surface of the plate was\npredicted with good accuracy by a modification to\ninsulated-plate displacement theory which allows\nfor the effect of the heat transfer and temperature\ngradient along the surface on the boundary-layer\ndisplacement thickness .\n the total drag of thin wings with square and delta\nplan forms was measured at a nominal mach number\nof 6.8 over a reasonably wide range of reynolds\nnumbers . the total drag was found to be greater\nthan can be explained by adding a classical value of\nlaminar skin friction to the estimated pressure drag .\nthe difference is, in general, explained by the\nincrease in skin friction (20 to 40 percent) caused by\nthe boundary-layer-induced pressures ."}, {"doc_id": 1356, "text": "secondary flow fields embedded in hypersonic shock\nlayers .\n when a ramp or other compression\nsurface is located in a locally\nsupersonic region behind a hypersonic\nbow shock wave, it generates a\nsecondary shock wave . the ramp flow\ndisturbance may be viewed as an\nembedded newtonian impact flow if the\nembedded shock layer is thin .\nexamination of the applicability of newtonian\nflow theory to cones and wedges\nin uniform streams suggests that this\ntheory can be expected to give a\nuseful approximation to the surface\npressures .\n a pressure equation based on this\nconcept predicts a number of\ninteresting things .. first, pressures\ncan differ from simple newtonian\ntheory by factors of 1 5 to 3,. for\nexample, on flare stabilizers on\nblunt-nosed bodies of revolution, pressures\nare lower than newtonian and diminish\nwith increasing flight speed in the\nhypersonic speed range . the calculated\npressures vary over the flare surface\nas a result of the nonuniformity of\nits incident stream, and depend on the\naxial location of the flare . in\nthe case of a flap mounted on a\nlarge-angled blunt-nosed cone, the pressure\ncoefficients vary from 1 to 5 through\nthe variable entropy layer . a\npressure coefficient of 5 greater than\nthe maximum possible in newtonian\nflow can occur because the compression\nprocess is more efficient than a\nsingle shock wave process . on areas\nof the flap that protrude through\nthe main bow wave, the pressure\ncoefficient should revert to the simple\nnewtonian value .\n equations are developed for the\ninitial slopes of the normal-force\nand pitching-moment curves of a flare\nstabilizer . in the simplest case\nthese differ from conventional newtonian\ntheory by the ratio of local\ndynamic pressure to free-stream dynamic\npressure . this ratio takes values\nas low as 0.1 in some of the examples considered ."}, {"doc_id": 1357, "text": "compressive buckling of simply supplorted plates with\nlongitudinal stiffeners .\n charts are presented for the analysis of the stability under\ncompression of simply supported rectangular plates with one, two, three,\nand an infinite number of identical equally spaced longitudinal\nstiffeners that have zero torsional stiffness ."}, {"doc_id": 1358, "text": "compressive buckling of simply supported plates with\ntransverse stiffeners .\n charts are presented for the analysis of the stability under\nlongitudinal compression of simply supported rectangular plates with\nseveral equally spaced transverse stiffeners that have both torsional\nand flexural rigidity ."}, {"doc_id": 1359, "text": "compression tests on circular cylinders stiffened longitudinally\nby closely spaced z-section stringers .\n six circular cylinders stiffened longitudinally by closely spaced\nz-section stringers were loaded to failure in compression . the results\nobtained are presented and compared with available theoretical results\nfor the buckling of orthotropic cylinders . the results indicate that\nthe large disparity that exists between theory and experiment for\nunstiffened compression cylinders may be significantly smaller for\nstiffened cylinders ."}, {"doc_id": 1360, "text": "simplified analysis of general instability of stiffened\nshells in pure bending .\n although much work has been done to develop a theory for\nthe failure of shells by general instability, there is at present no\nsimple method by which the size of the frames may be determined\nfor any given diameter, bending moment,.and frame spacing .\nsuch a method is needed in determining the optimum design for\nstiffened shells, to be used as a basis for weight analysis of\nfuselages, and other shell structures . in an extension of the work\ndone for the rand corporation, a simple coefficient has been\ndetermined for this purpose . since it appears that this method\nmay also be useful in design calculations, a brief description is\npresented below ."}, {"doc_id": 1361, "text": "large deflections of structures subjected to heating\nand external loads .\n the method of direct formulation of the stiffness matrix is\nextended to include the effects of nonuniform heating and large\ndeflections . the purpose is to develop an analytical tool for the\ntreatment of actual structures .\n in the solution of aeroelastic problems the relations between\nforces and deflections must be determined . the usual stiffness\nmatrix formulation of this relationship is limited to small\ntemperature changes and small deflections . for large temperature\nchanges additional terms are required . also the problem\nbecomes geometrically nonlinear when large deflections are\ninvolved . to overcome the inherent difficulties of the nonlinear\nproblem for practical structures either an iterative or a step-\nby-step procedure must be used . the force-deformation relations\nnecessary for this step-by-step or iterative approach are derived\nfor an axially loaded member and for a plate element including\nthe effects of thermal strains ."}, {"doc_id": 1362, "text": "non-linear analysis of heated, cambered wings by the matrix force\nmethod .\nvarious extensions of the matrix force method for complex structure\nanalysis are presented and illustrated with the objective of expanding\nits range to handle the problems likely to be encountered in advanced\nvehicle wing design . methods are covered in detail for (1) determining\nthe change in flexibility that occurs when thermal stresses are present,\nand also how large these stresses must be to cause buckling, (2)\nincluding the non-linear effect of large deflections by an iterative\nprocedure, and (3) analyzing a wing that is initially slightly cambered\nand warped with either or both of the aforementioned effects present .\nformulas are given for calculating the input matrix terms as are the\nmatrix equations and supporting theoretical discussion . an example\nillustrates the nature and magnitude of the effects being examined ."}, {"doc_id": 1363, "text": "a characteristic type of instability in the large deflections\nof elastic plates .\n part 1. from a general equation governing\nthe bending of thin elastic plates into certain\ntypes of surfaces of revolution are derived\nexpressions for the behaviour of rectangular plates\nwith initial curvatures, subjected to pure\nbending about one axis . it is found that such\nplates exhibit the type of instability characteristic\nof thin-walled structures which depend\nfor their stiffness on curvature . curves are\ndrawn showing the deformation suffered by\nsuch plates, and an expression for the critical\nbending moment at which instability occurs is\nobtained . experimental results show satisfactory\nagreement .\n part 2. the analysis of part 1 is extended to deal\nwith the case of flat square or rectangular\nplates loaded by distributed bending moments\napplied to all four edges . curves are drawn\nto describe their behaviour, and they are found\nto exhibit the characteristic instability\ndisplayed by thin-walled curved structures .\nexperimental verification is satisfactory ."}, {"doc_id": 1364, "text": "an experimental investigation of the interaction between shock waves and\n boundary layers .\nan account is given of an investigation into the interaction between the\n boundary layer on a flat plate and a shock wave produced either\nexternally, by a wedge in the supersonic mainstream, or from within the\nboundary layer, by a wedge held in contact with the plate . a wide range\n of free-stream mach numbers, boundary-layer reynolds numbers, and shock\n strengths has been covered, shock strength being defined as the ratio\nof the static pressure downstream of the shock to the static pressure\nupstream of it . variations in these parameters can have large effects\non the interaction, and there are also large differences between cases\nwith externally generated shocks and cases where the shock is generated\nfrom within the boundary layer . the investigation has thrown light on\nthe physical mechanisms involved . it is found that many of the major\nfeatures of the interaction arise because the boundary layer separates\nfrom the surface ahead of the shock wave . the conditions under which\nseparation occurs and the behaviour of the separated boundary layer thus\n have important effects, in terms of which, for example, the differences\n between the interactions observed with laminar and with turbulent\nboundary layers may be explained ."}, {"doc_id": 1365, "text": "approximate calculation of the laminar boundary layer .\n after analyzing a large class of boundary-layer\nvelocity-profiles, the author discovered that the functions l(m) and\nh(m) for all such cases differ only slightly from each other\nover the whole range of positive and negative pressure\ngradients . here l, m and h are defined by\nbeing the\nvelocity-component in the x direction and u the value of u at the\nedge of the boundary-layer and and the displacement\nand momentum thickness, respectively . based on this\ndiscovery, an approximate method is proposed by constructing\ntwo universal curves l(m) and h(m) for all conceivable\nboundary-layer flows found in practice . once these are\nchosen, karman's momentum-integral can be written in the\nform, v being the kinematic\nviscosity coefficient, and can be integrated numerically . as\nexamples, both howarth's and hartree's\ntained is considered good for practical purposes ."}, {"doc_id": 1366, "text": "the compressible laminar boundary layer with heat transfer\nand arbitrary pressure gradient .\n an approximate method for the calculation of the\ncompressible laminar boundary layer with heat transfer and\narbitrary pressure gradient, based on thwaites' correlation\nconcept, is presented . the method results from the application\nof stewartson's transformation to prandtl's equations, which\nyeilds a nonlinear set of two first-order differential equations .\nthese equations are then expressed in terms of dimensionless\nparameters related to the wall shear, the surface heat transfer,\nand the transformed free-stream velocity . thwaites' concept\nof the unique interdependence of these parameters is assumed .\nthe evaluation of these quantities is then carried out by utilizing\nexact solutions recently obtained .\n with the resulting relations, methods are derived for the\ncalculation of the two-dimensional and axially symmetric\nlaminar boundary layer with arbitrary free-stream velocity\ndistribution . mach number, and surface temperature level .\n the combined effect of heat transfer and pressure gradient\nis demonstrated by applying the method to calculate the\ncharacteristics of the boundary layer on thin supersonic surfaces\nand in a highly cooled, convergent-divergent, axially symmetric\nrocket nozzle ."}, {"doc_id": 1367, "text": "a theoretical investigation of the effects of mach number, reynolds\nnumber, wall temperature and surface curvature on laminar separation in\nsupersonic flow .\nlaminar separation in supersonic flow is investigated by an extension of\n stratford's method . it is assumed that separation is of the usual\npractical type, taking place upstream of the shock wave or other agency\nprovoking it . the results of the analysis agree well in most respects\nwith experiment ."}, {"doc_id": 1368, "text": "three dimensional viscous wakes .\nthe velocity fields of three-dimensional\nviscous wakes are examined with the\nuse of the boundary-layer approximations,\nosoen's linearization of the convective\nterms, and the assumption of constant\nfluid properties . transform methods\nyield solutions for general types of initial\nconditions . as an illustration, the\naxial velocity distribution of a wake whose\ninitial isovels (lines of constant\nvelocity) are of elliptic shape and their decay\nto axial symmetry are demonstrated .\nboth laminar and turbulent flows are considered ."}, {"doc_id": 1369, "text": "steady motion of a sphere., oseens's criticism and solution .\nthe formula of stokes for the resistance experienced slowly\nmoving sphere has been employed in physical researches of fundamental\nimportance, as a means of estimating the size of minute globules of\nwater, and thence the number of globules contained in a cloud of\ngiven mass . consequently the conditions of its validity has been much\ndiscussed both from the experimental and from the theoretical side ."}, {"doc_id": 1370, "text": "some remarks on the flat plate boundary layer .\n the authors discuss the solutions for the flow of a viscous\nincompressible fluid near the leading edge of a semi-infinite\nflat plate without pressure gradient . the oseen\nlinearization is employed which approximates the equations of motion\nand continuity by\nwhere are the coordinate directions, the\ncorresponding velocity components and the uniform free stream\nvelocity which is parallel to the plate . defining a\nperturbation stream function by\nthe differential\nequation to be solved is with boundary\nconditions far from the plate and\nwhen y=0 and . the authors discuss the\nproblem by applying the two-dimensional fourier\ntransform and obtain an explicit solution for the velocity gradient\nat the plate which is in disagreement\nwith the result of the blasius solution . from this\nthe authors conclude that it would be more appropriate to\nuse a velocity other than in the linearization of the\nequations of motion and suggest replacing by where .\nthis choice does not affect the solution far from\nthe plate but gives on the plate and in\ncomparison with blasius solution indicates that c=0.35 .\nthe solution of the modified oseen equation with this value\nof c then seems acceptable as the approximate solution in\nthe region intermediate between the stokes flow and the\nfree stream . on the basis of these considerations, the authors\nsuggest an iteration procedure for obtaining the exact\nsolution for the above problem as well as a solution for the plate\nof finite length ."}, {"doc_id": 1371, "text": "axisymmetric free mixing with swirl .\n viscous laminar axially-symmetric\nfree-mixing with small, moderate,\nand large swirl is investigated by a\nboundary layer type of analysis with\nintegral methods . moderate and small\nswirls are formally the same,\ndiffering only in the order of their associated\nradial pressure gradients . neither\ninduces significant axial pressure gradients,.\nconsequently their effect on the\naxial flow is negligible . for moderate and\nsmall swirl an interesting feature\nis the swirl decay . in both compressible\nand incompressible flow, it is\nshown that jet swirl decays more rapidly\nthan wake swirl whereas both swirls\ndecay more rapidly than the non-uniformity\nin axial velocity . large swirl\ngenerates axial pressure gradients as well\nas large radial pressure gradients,\nand therefore alters the streamwise flow .\nexamples calculated for\nincompressible flow, show that the wake is\nlengthened by large swirl . it is\nexpected that this effect will be diminished\nin the presence of higher free-stream\nmach numbers which lead to decreased\ndensities, due to decreased\ncentrifugal effects, decreased radial pressure\ngradients, and decreased axial\npressure gradients ."}, {"doc_id": 1372, "text": "on axially symmetric, turbulent, compressible mixing in the presence\nof initial boundary layer .\nrecent experimental results have shown that the\nmixing of heterogeneous gases having an initial velocity\nratio close to unity occurs faster than is predicted by classical\neddy-viscosity theory . the theoretical analysis of two uniform\nstreams of different gases but of nearly equal velocity,\nperformed with the usual assumptions for eddy viscosity and\nprandtl number equal to a constant, shows that mixing will\ntake place very slowly, i.e., at the rate corresponding to\nlaminar diffusion . it has been suggested that the difference\nbetween analysis and experiment could be attributed to the\npresence of a boundary layer in the experiments . it is the\npurpose of this note to show that the use of the classical\neddy-viscosity law, admitting the existence of a boundary layer,\nis not sufficient to explain the rapid mixing that is observed\nphysically . instead, it is shown that rapid mixing can be\nexplained on the basis of a different eddy-viscosity law, as\nwas suggested in ref. 1 . these conclusions are obtained\nthrough application of the analysis presented briefly below ."}, {"doc_id": 1373, "text": "nose drag in free-molecule flow and its minimization .\n the superaerodynamic nose drag of a body in a free-molecule\nflow involves two parameters .. the speed ratio s between\nordered and random molecular motions (modified mach\nnumber), and the temperature ratio between the solid surface\nand undisturbed gas . simplifications of the drag formula are\nobtained at hypersonic as well as low-subsonic extremes . to\nminimize the drag on a nose of specified length and base radius,\nthe ordinary method of calculus of variation was found\ninadequate . a generalized approach has, accordingly, been developed,\nand the specification of end conditions is discussed at length .\n results of the present investigation indicate that in all cases\nan optimum nose requires a flat tip . the optimum nose curve\nfor the hypersonic extreme does not depend on the temperature\nratio, but that for the low-subsonic extreme varies in the\nfollowing manner .. for a hot body the curve is convex,. for a cold body,\nconcave . an optimum solution exists in a restricted range of\nspecification only . with prescribed tip and base radii the\nadmissible nose length is bounded below for the cases of hypersonic\nand low-subsonic hot body and bounded above for the case of\nlow-subsonic cold body . a vanishing tip radius leads to an\ninfinitely long nose in the former and a vanishing nose in the latter\ncase .\n optimum nose curves for several temperature ratios at the\nlow-subsonic extreme, as well as the one for hypersonic extreme, are\npresented . it is observed that at the low-subsonic extreme, with,\nthe hot-body solution asymptotically approaches\nthe hypersonic solution--i.e., a slender conventional warhead\nwith a flat tip,. whereas with, the cold-body solution\nasymptotically approaches the minimal-surface solution--i.e.,\ntip radius, a flat disc ."}, {"doc_id": 1374, "text": "theoretical analysis of turbulent mixing of reactive\ngases with application to supersonic combustion of\nhydrogen .\n the turbulent mixing of an axisymmetric jet of a\nreactive gas is considered . by assuming a\nconvenient model for the compressible eddy viscosity,\nthe momentum equation is reduced to a form\namenable to approximate solution . the resulting\nvelocity distribution in both incompressible and\ncompressible flows is in reasonable agreement with\nexperiment . the usual assumptions with\nrespect to chemical behavior, namely either frozen or\nequilibrium flow, and to unity lewis numbers\nand prandtl number are employed . the theoretical\nresults for chemical equilibrium are shown\nto be in reasonable agreement with experimental data\nfrom low speed hydrogen flames . a\nnumerical example of interest in connection with a hypersonic,\nair breathing vehicle is carried out in detail ."}, {"doc_id": 1375, "text": "an approximate solution for the axisymmetric jet of a laminar\ncompressible fluid .\nan extension of the modified-oseen method of carrier, based on the\nlinearization of the viscous term of the von mises transformation,\nis presented . the method is employed to determine the velocity field\nassociated with the laminar axisymmetric jet flow of a compressible\ngas with an arbitrary but constant external flow . the approximate\nsolution is shown to be in good agreement with the exact numerical\ncalculation of pai .\nin many boundary layer problems it is not possible to make the\nassumption of flow similarity . the solution in these cases can be\nobtained either by laborious finite difference techniques or by\nresort to approximate solutions . carrier and lewis (1), and more\nrecently carrier (2), have suggested a method of obtaining approximate\nsolutions to problems involving convection and diffusion . this\nmethod, termed by carrier /the modified-oseen method/, overcomes an\nessential difficulty of integral methods, namely, the generation of\nreasonable profiles . it is well known that the integral method gives\naccurate results only if the analytical profiles represent closely\nthe true profiles . according to the modified-oseen method the\nconvective operator in the original partial differential equation\nis replaced by a linear one . the resulting equation for the\nboundary layer problem is the heat conduction equation which can be\ntreated by well-known techniques .\nit is the purpose of this paper to indicate a modification of this\nprocedure and to demonstrate its simplicity and accuracy by treating the\naxisymmetric laminar flow of a compressible gas with arbitrary but\nconstant external flow . the modification is based on the use of the\nvon mises transformation with a subsequent linearization of the viscous\nterm, rather than the linearization of the convective term . pai's\nproblem (3), originally treated by a finite difference technique,\nis considered to illustrate the effectiveness of this method ."}, {"doc_id": 1376, "text": "some applications in physics of the p-function .\n the mathematical background and typical applications\nin physics are presented for a recently tabulated\nfunction . because of its properties, the p function should\nprove to be a useful aid in the solution of certain\nproblems in applied mathematics involving surface\nintegrations in cylindrical coordinates . a tabulation of\nthe function in its normalized form is appended .\nparticular attention is paid to the application of the p\nfunction to multiple scattering problems involving\ncircular symmetry ."}, {"doc_id": 1377, "text": "theoretical investigation of the flow field about blunt\nnosed bodies in supersonic flight .\n a numerical method ofr obtaining the solution to the inverse\nproblem of the flow behind a given detached shock to any desired\naccuracy is presented . the cases of zero and small incidence\nare considered . the combination of sets of such solutions\nsatisfying prescribed boundary conditions (body shapes) is described .\nparticular attention is devoted to the analysis of the sonic and\nsubsonic region of the flow field . convergence and stability of\nthe stepwise integration from the shock in the elliptic region are\ndiscussed . numerical examples are also included ."}, {"doc_id": 1378, "text": "blunt-cone pressure distributions at hypersonic mach numbers .\nthe static pressure distributions on the surface of a\nblunted 7.5 degree-half-angle cone have recently been experimentally\ndetermined in the cal 48 inch hypersonic shock tunnel . this\nfacility and the associated instrumentation are described in detail\nin ref. 1 . these tests covered a mach number range of 8 to 18\nat a reynolds number per foot of approximately 1 times 10 to the 5th\npower., the models included one flat-faced cone and two hemispherically\nblunted cones ."}, {"doc_id": 1379, "text": "hypersonic flight and the re-entry problem .\npaper reviews the possibilities and some of the main problems of three\ntypes of long-range vehicle, the ballistic, the glide, and the skip\nrocket . performance assessments are made on the basis of an ingenious,\nif debatable, conversion of the vehicle characteristics to the breguet\nformula . the problems of aerodynamic heating, aerodynamic loads and\nstability are briefly discussed, and other aspects of hypersonic flight\nfree molecule flow-dash are touched upon . the results on the whole\nfavor the glide vehicle for manned flight . the subsequent discussion\non the paper includes references to multistaging and the use of\nhigh-energy fuels ."}, {"doc_id": 1380, "text": "the problem of obtaining high lift-drag ratios at supersonic speeds .\nthe importance of the lift to drag ratio is well\nknown to all aircraft designers since it gives, to a\ngreat extent, the aerodynamic efficiency of the airplane .\naerodynamic efficiency, however, is only one\ncomponent of the grand compromise that a completed\nairplane represents . at subsonic speeds, lift-drag\nratios of well over 200 have been measured in wind\ntunnels on airfoil sections., but few powered aircraft\nhave attained (lift to drag ratio) value of 20 . it is invariably true\nthat the requirements of stability and control, structure,\nand flight operation all contribute to reducing the\ndesign (lift to drag ratio) considerably below those exotic values\nwhich can be predicted from unrestricted aerodynamic\ntheory . if, however, a certain range or operating\nefficiency is required, there is most certainly a minimum\nif we examine the range equation we see that range is\nproportional to the lift-drag ratio, the thermopropulsive\nefficiency, and the logarithm of the initial to final\nweight ratio . the appearance of the lift-drag ratio as a\nlinear factor in the range equation indicates that every\nattempt should be made to increase (lift to drag ratio)., however,\nthe search for higher (lift to drag ratio) may lead to strange\nand unorthodox configurations . most frequently, such\nconfigurations are ruled out by the adverse effects of\ntheir geometry on the weight ratios . in the present\npaper, we will deal with the maximum lift-drag ratio\nproblem for conventional configurations having a wing\nand a body in close proximity to each other . no attempt\nwill be made to select a particular configuration\nas being the best . however, the promising direction\nto go from the aerodynamic view will be stressed with\nthe understanding that the other factors may outweight\nthe aerodynamics ."}, {"doc_id": 1381, "text": "effect of mach number on boundary layer transition\nin the presence of pressure rise and surface roughness\non an ogive-cylinder body with cold wall conditions .\n the effect of mach number variation\nfrom 1.8 to 7.4 on boundary-layer\ntransition was investigated on a slender\nfin-stabilized ogive-cylinder\nbody in free flight at a constant length\nreynolds number of 13.8 million .\nthe wall to free-stream temperature ratio\nwas constant at a value of 1.0\nbelow mach number 4.5 and at a value of\nof the test showed that increasing mach\nnumber had a very favorable effect\nof increasing the extent of the laminar\nboundary layer for a given surface\nroughness . the transition data, when\nplotted as a function of a factor\nindicative of heat transfer, showed that\nheat transfer was possibly\nresponsible for a good deal of the increase in\ntransition reynolds number with\nmach number .\n transition was found to occur\nfarther forward on the sheltered side\nof the body than on the windward side\nfor angles of attack as low as 0.4\nand for all mach numbers . the pressure\nrise along sheltered-side\nstream-lines was examined and it was found\nthat the pressure-rise coefficient\nat the transition point, showed no\nvariation with mach number . data from\nother sources for different test\nconditions, when reduced to values of\npressure-rise coefficient, were also\nfound to correlate well with that of\nthe present investigation with the\nexception of data at low subsonic mach\nnumbers . these present results also\nshow that mach number, surface\nroughness, pressure rise, and length reynolds\nnumber all affected boundary-layer\ntransition in the region of theoretical\ninfinite laminar stability to\nsmall two-dimensional disturbances as\ncalculated for a flat plate with\nzero pressure gradient ."}, {"doc_id": 1382, "text": "the solution of the equations of the laminar boundary\nlayer for schubauer's observed pressure distribution\nfor an elliptic cylinder .\n the solution of the equations of the laminar\nboundary layer has been carried out for the pressure\ndistribution for an elliptic cylinder of axial ratio 2.96 .. 1 with\nits major axis in the direction of the incident stream .\nthe solution has been obtained by the method of hartree and\nwomersley . in applying this method the derivatives\nparallel to the boundary are replaced by finite differences, so\nthat the partial differential equation of the boundary\nlayer is replaced by an ordinary equation relating the velocity\ndistribution through the boundary layer at one section\nto that at another, at an interval upstream . by two independent\nintegrations covering the same range by finite intervals\nof different sizes, it is possible to estimate the errors\ninvolved in replacing the derivatives by finite differences,\nand so to correct for these errors .\n the process of solution requires the values of the pressure\ngradient along the solid boundary, and there is a certain\ntolerance in the derivation of the pressure gradient distribution\nfrom a limited number of observed values of pressure .\nan analysis of schubauer's pressure distribution is outlined, and\nthe results were used for the main solution calculated .\nit is found that the solution, for the distribution of pressure gradient\nso derived, does not give separation of the boundary\nlayer from the solid boundary, whereas the actual flow does separate .\n it is found that the calculated solution is very sensitive to\nthe pressure distribution, and a comparatively small\nmodification of the pressure distribution gives a solution which\ndoes indicate separation close to the point at which\nseparation is observed to occur . the solution with this pressure\ndistribution also gives very good agreement with the\nobserved velocity distribution through the boundary layer at\npoints upstream from separation ."}, {"doc_id": 1383, "text": "on the theory of laminar boundary layer involving separation .\n the paper presents a mathematical discussion of the\nlaminar boundary layer, which was developed with a view\nof facilitating the investigation of those boundary layers\nin particular for which the phenomenon of separation\noccurs . the treatment starts with a slight modification of\nthe form of the boundary layer equation first published by\nvon mises . two approximate solutions of this equation\nare found, one of which is exact at the outer edge of the\nboundary layer while the other is exact at the wall . the\nfinal solution is obtained by joining these two solutions\nat the inflection points of the velocity profiles . the final\nsolution is given in terms of a series of universal functions\nfor a fairly broad class of potential velocity distributions\noutside of the boundary layer . detailed calculations of\nthe boundary layer characteristics are worked out for the\ncase in which the potential velocity is a linear function of\nthe distance from the upstream stagnation point . finally\nthe complete separation point characteristics are\ndetermined for the boundary layer associated with a potential\nvelocity distribution made up of two linear functions of\nthe distance from the stagnation point . it appears that\nextensions of the detailed calculations to more complex\npotential flows can be fairly easily carried out by using\nthe explicit formulae given in the paper ."}, {"doc_id": 1384, "text": "a theoretical calculation of the laminar boundary layer\naround an elliptic cylinder and its comparison with\nexperiment .\nthe author, in conjunction with th. von karman,\nhas recently given a new method of approximate\nintegration of the prandtl boundary layer equations,\nwhich was developed in order to treat cases in which\nseparation of a laminar boundary layer might be\nexpected . the method was developed because some doubt\nwas felt as to the accuracy with which the well-known\npohlhausen analysis would describe conditions in the\nneighborhood of such a separation point . numerical\ncalculations were carried out for certain cases involving\ntheoretical simplifications, and very considerable\ndiscrepancies were found between the results of the new\nand pohlhausen methods . the method was also used\nin developing a theory for the maximum lift coefficient\nof certain classes of airfoils . this theory gave\nsatisfactory agreement with experiment but no direct\nexperimental check on the boundary layer analysis itself has\nbeen given up to the present ."}, {"doc_id": 1385, "text": "air flow in a separating laminar boundary layer .\n the speed distribution in a laminar boundary layer on\nthe surface of an elliptic cylinder, of major and minor\naxes 11.78 and 3.98 inches, respectively, has been\ndetermined by means of a hot-wire anemometer . the direction\nof the impinging air stream was parallel to the major axis .\nspecial attention was given to the speed distribution in\nthe region of separation and to the exact location of the\npoint of separation . an approximate method, developed\nby k. pohlhausen for computing the speed distribution,\nthe thickness of the layer, and the point of separation, is\ndescribed in detail,. and speed-distribution curves\ncalculated by this method are presented for comparison with\nexperiment . good agreement is obtained along the\nforward part of the cylinder, but pohlhausen's method fails\nshortly before the separation point is reached and\nconsequently cannot be used to locate this point .\n the work was carried out at the national bureau of\nstandards with the cooperation and financial assistance\nof the national advisory committee for aeronautics ."}, {"doc_id": 1386, "text": "analysis and calculation by integral methods of laminar\ncompressible boundary layer with heat transfer and\nwith and without pressure gradient .\n a survey of integral methods in laminar-boundary-layer\nanalysis is first given . a simple and sufficiently accurate\nmethod for practical purposes of calculating the properties\nlayer in an axial pressure gradient with heat transfer at the\nwall is then presented . for flow over a flat plate, the method\nis applicable for an arbitrarily prescribed distribution of\ntemperature along the surface and for any given constant\nprandtl number close to unity . for flow in a pressure gradient,\nthe method is based on a prandtl number of unity and a uniform\nwall temperature . a simple and accurate method of\ndetermining the separation point in a compressible flow with an adverse\npressure gradient over a surface at a given uniform wall\ntemperature is developed . the analysis is based on an extension of\nthe karman-pohlhausen method to the momentum and thermal\nenergy equations in conjunction with fourth- and especially\nhigher degree velocity and stagnation-enthalpy profiles . from\nthe equations derived here, conclusions regarding the effect of\npressure gradient, mach number, and wall temperature on the\nboundary-layer characteristics are derived and illustrated . in\nparticular the effects on skin-friction, heat-transfer coefficient,\nseparation point in an adverse pressure gradient, and stability\nof the laminar boundary layer are analyzed ."}, {"doc_id": 1387, "text": "the buckling of a square panel under shear, when one\npair of opposite edges is clamped and the other pair\nis simply supported .\n reasons for investigation.--for an efficient design\nof spar with thin sheet web it is important to know\nthe load which will just cause the web to buckle . as stiffeners\ndivide the web into panels, it is required to find the\nbuckling stress of rectangular panels bounded on two sides by\nspar flanges and on the other two sides by stiffeners .\nboundary conditions which represent closely this type of edge\nfixing are clamping (along the flanges) and simple support\ncritical shear stress for a square panel held in this way .\n conclusions and further development.--it is found that the\nvalue of the critical shear stress is almost midway between\nits values when all four edges are clamped and all four edges\nare simply supported .\n the method of solution developed in this report is of very\ngeneral application, and can be used to investigate the\nstability of rectangular panels when the loading is any combination\nof shear and compression or tension, and the edges\nare clamped or simply supported, and not necessarily all clamped\nor all simply supported . by an easy extension the\nmethod of solution can also be used to find the periods of transverse\nvibration of rectangular panels for the same types\nof loading and edge fixing ."}, {"doc_id": 1388, "text": "a process for the step-by-step integration of differential\nequations in an automatic digital computing machine .\n it is advantageous in automatic\ncomputers to employ methods of integration\nwhich do not require preceding function values\nto be known . from a general theory given by\nkutta, one such process is chosen giving\nfourth-order accuracy and requiring the minimum\nnumber of storage registers . it is developed into\na form which gives the highest attainable\naccuracy and can be carried out by comparatively\nfew instructions . the errors are studied and\na simple example is given ."}, {"doc_id": 1389, "text": "numerical construction of detached shock waves .\n this article proposes a new method for solving the problem\nof the detached shock wave . if the shock wave is assumed\nknown, a cauchy problem for a system of partial differential\nequations arises . this has been solved by several authors\nin the region where the system is elliptic (near the peak of\nthe shock wave) . considering the plane stationary case, the\nauthor seeks an analytic continuation of the propagation\nfunction (x,y) in the complex plane y = y1 + y2, x real .\nin the plane (x, y2) the propagation function satisfies a\nhyperbolic equation (near the peak of the shock wave) . a\nnew cauchy problem is solved and the solution of the original\nproblem obtained by analytic continuation . a numerical\nexample is treated with many details ."}, {"doc_id": 1390, "text": "on the numerical calculation of detached bow shock\nwaves in hypersonic flow .\n a method is described for calculating examples of hypersonic\nflow with a detached bow shock wave past a bluff axially\nsymmetric body . the form of the shock wave is assumed, and the\nanalysis is based on a cauchy problem for the stream function\nin the subsonic region, where the motion is governed by a\npartial differential equation of elliptic type . through analytic\ncontinuation into the complex domain, the cauchy problem is\nreformulated in such a manner that it becomes properly set in the\nsubsonic region . this leads to a stable scheme for computation\nof the flow by finite differences . numerical examples at\nfreestream mach number 5.8 are presented in which the flow is\ndetermined throughout the subsonic region, and, in particular, the\ndetachment distance, the location of the sonic line, and the\npressure distribution along the body are calculated . these results are\nin excellent agreement with experimental data obtained at the\ncalifornia institute of technology ."}, {"doc_id": 1391, "text": "shock wave and flow field development in hypersonic re-entry .\na study is made of when and how a shock wave and continuum-type flow\nfield develop in the nose region of a highly cooled blunt body re-\nentering the atmosphere at hypersonic speed and in a free molecular flow\nregime . the various types of flow regimes encountered down to low\naltitude conditions are delineated, and the nature of the flow field and\nbehavior of some of the aerodynamic characteristics are discussed . it\nis shown that for a highly cooled body, free molecule flow conditions\noccur at a higher altitude than previously indicated . based on\navailable evidence, it is suggested that kinetic theory solutions, which are\nessentially modified free molecule results, along with the navier-stokes\n equations with no surface slip, serve to define all of the flow regimes\n except for a narrow transitional layer regime which has a height of\nless than one factor of 10 in free stream density change . it is also\nsuggested that the appearance of a definable shock wave occurs very\nrapidly in terms of density change near the beginning of the\ntransitional layer regime, and that its location, as in continuum flow, is\ngoverned principally by the body geometry, whereas its thickness is\ndetermined by a local mean free path ."}, {"doc_id": 1392, "text": "the solution of small displacement, stability or vibration\nproblems concerning a flat rectangular panel when the\nedges are either clamped or simply supported .\n this report describes an energy method for\nthe exact solution of problems concerning the small\ndisplacements, stability or vibration of a flat rectangular panel\nwhen the edges are either clamped or simply supported .\nthe influence of stiffeners which are parallel to one pair of edges,\nand situated in pairs on opposite sides of the panel\nso that the neutral axis of each stiffener pair lies in the middle\nsurface of the panel, is taken into account . the method\nis not only applicable to isotropic panels but also to aeolotropic\npanels when the material of the panel has two directions\nof elastic symmetry parallel to the edges .\n the final solution of the problems depends on an infinite set of\nlinear equations for small displacement problems or on\nan infinite determinantal equation for stability and vibration\nproblems . the important feature of the analysis given is\nthat it enables a direct approach to be made to these equations\nin any particular problem . it is not in general possible\nto obtain a direct solution of the final equations and it is\nnecessary to approximate and consider a finite set of linear\nequations or a finite determinantal equation derived from the\nmore important terms in the analytical expression for the\ntransverse displacement of the panel . here, physical intuition\nand, if available, experimental data serve as a guide and\nthe accuracy of the final results so obtained is gauged by the\nrate of convergence with the increase in the number of\nterms considered .\n the general method of solution is applied first to the free\nvibration of a square panel when all the edges are clamped,\nand second to the buckling of a square panel under shear when\nthree edges are clamped and one edge is simply supported ."}, {"doc_id": 1393, "text": "heat transfer near the forward stagnation point of\na body of revolution .\nin order to determine the temperature distribution over a\nbody moving through the atmosphere, a knowledge of the\nlocal heat-transfer coefficients is required . for slender\nsharp-nosed bodies, the heat-transfer coefficients are frequently\napproximated by using the comparable flat-plate values .\nhowever, for blunt-nosed bodies, flat-plate solutions are not\napplicable near the forward stagnation point . since the greatest rate\nof heat transfer may occur at the forward stagnation point, its\nvalue should be investigated . in this note a theoretical solution\nis given for the heat transfer near the forward stagnation point of\na body of revolution assuming laminar, incompressible, low-speed\nflow . the comparable solution for two-dimensional flow has\nbeen given by squire . in the case of a blunt-nosed body moving\nwith supersonic velocity, the flow behind the central portion of\nthe bow wave is subsonic, and it is possible that a low-speed\nsolution, using as /free-stream/ conditions those behind the center\nof the bow wave, will apply near the stagnation point ."}, {"doc_id": 1394, "text": "stagnation point heat transfer measurements in hypersonic\nlow density flow .\nin hypersonic, low reynolds number flow around a blunt body,\nthe boundary-layer thickness approaches the shock-layer\nthickness (shock standoff distance) within the region of\ncontinuum flow . in this instance, the customary boundary-layer\napproximations no longer apply . hoshizaki and probstein\nhave obtained solutions to the incompressible navier-stokes\nequations in the stagnation region of a blunt body in this\nhypersonic low reynolds number flow . the results indicate that\nheat-transfer rates are substantially higher than those predicted by\nincompressible boundary-layer theory . probstein indicated that\nthe actual heat-transfer rates would be correspondingly higher\nthan the predictions of fay and riddell . these findings are of\nparticular importance in the atmospheric entry phase of\nrecoverable satellites ."}, {"doc_id": 1395, "text": "low density stagnation point heat transfer measurements\nin the hypersonic shock tunnel .\n presents absolute heat-transfer measurements, using resistance\nthermometer, for hemisphere-cylinder at mach numbers 9.2 to 11.2 .\nresults show vorticity-interaction and viscous-layer effects\nincrease heat transfer above values predicted by boundary-layer\ntheory . data are correlated using cheng's reynolds-number-\ndependent parameter . investigation covers vorticity-interaction to\nincipient-merged-layer regimes (free-stream unit reynolds numbers"}, {"doc_id": 1396, "text": "shear buckling of clamped and simply-supported infinitely\nlong plates reinforced by transverse stiffeners .\n the paper presents a solution to the buckling of infinitely long\nplates clamped along the edges, together with an extension of the\nsolution obtained by stein and fralich for the case when the edges are\nsimply-supported . it is shown that, as a consequence of increasing the\nedge support from that of a simple support to one in which both\ndeflection and rotation are prevented, the rigidity which an\nintermediate transverse stiffener must possess in order to support the\nplate effectively is much reduced . agreement between the theoretical\nrelationships and existing experimental data is good ."}, {"doc_id": 1397, "text": "critical shear stress of an infinitely long simply\nsupported plate with transverse stiffeners .\n a theoretical solution is given for the critical shear stress of\nan infinitely long, simply supported, flat plate with identical, equally\nspaced, transverse stiffeners of zero torsional stiffness . results are\nobtained by means of the lagrangian multiplier method and are presented\nin the form of design charts . experimental results are included and\nare found to be in good agreement with the theoretical results ."}, {"doc_id": 1398, "text": "stability of rectangular plates under shear and bending\nforces .\n the author first discusses the problem of a plane, simply\nsupported rectangular plate loaded by shearing forces in\nthe plane of the plate on all four edges . there are two\nstiffeners attached one third and two thirds of the way\nalong the plate . the critical load is calculated for various\nstiffener rigidities . also, the rigidity necessary to keep\nthe stiffeners straight when the plate buckles is found .\nthis stiffener rigidity is found to be slightly larger than\nthat necessary for a plate with one stiffener and the same\npanel dimensions as the plate with two stiffeners .\n the second problem discussed by the author is that of a\nplane, simply supported rectangular plate loaded by\nuniformly distributed edge shearing forces in the plane of the\nplate and linearly distributed tension and compression in\nthe plane of the plate at the ends . the end forces vary\nfrom tension, at one corner to, at the other corner,\nso that their resultant is a bending moment . the\npresence of the edge shearing forces is found to diminish the\ncritical bending stress in this case . calculations are made\nfor various magnitudes of bending and shearing forces for\nplates of various proportions ."}, {"doc_id": 1399, "text": "buckling of transverse stiffened plates under shear .\n this paper presents an analysis of buckling of simply\nsupported rectangular plates reinforced by any number of\ntransverse stiffeners and subjected to shearing forces\nuniformly distributed along the edges . two cases are\nconsidered .. (a) the case of a plate with a finite length,.\ning stresses in both cases are expressed in similar forms,\nthat is, in equation (13), and\nk in equation (24), respectively . design\ncurves are drawn as shown in figs. 2,3, and 5 ."}, {"doc_id": 1400, "text": "the buckling shear stress of simply-supported infinitely\nlong plates with transverse stiffeners .\n this report is an extension of previous theoretical\ninvestigations of the elastic buckling in shear of flat\nplates reinforced by transverse stiffeners . the plates are treated\nas infinitely long and simply-supported along the long\nsides . stiffeners are spaced at regular intervals, dividing the plate\ninto a number of panels of uniform size . the effect\nob bending and torsional stiffnesses of the stiffener upon the buckling\nshear stress is calculated for the complete range\nof stiffnesses, for panels with ratios of width to stiffener spacing of\ngraphical forms ."}] \ No newline at end of file