A general solution for the rectangular airfoil in supersonic flow
Author:
John W. Miles
Journal:
Quart. Appl. Math. 11 (1953), 1-8
MSC:
Primary 76.1X
DOI:
https://doi.org/10.1090/qam/53715
MathSciNet review:
53715
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Abstract: The potential on a rectangular airfoil due to an arbitrarily prescribed motion at its surface is obtained by an operational solution of the linearized equations and subsequent comparison with the known solution in steady flow. It is shown that the result can be extended to more general planforms with the aid of the Lorentz transformation. Other methods of solution are noted.
- Theodore R. Goodman, The quarter-infinite wing oscillating at supersonic speeds, Quart. Appl. Math. 10 (1952), 189–192. MR 51093, DOI https://doi.org/10.1090/S0033-569X-1952-51093-8
- Theodore R. Goodman, Aerodynamics of a supersonic rectangular wing striking a sharp-edged gust, J. Aeronaut. Sci. 18 (1951), 519–526. MR 43662
- John W. Miles, The oscillating rectangular airfoil at supersonic speeds, Quart. Appl. Math. 9 (1951), 47–65. MR 40138, DOI https://doi.org/10.1090/S0033-569X-1951-40138-6
- John W. Miles, Transient loading of supersonic rectangular airfoils, J. Aeronaut. Sci. 17 (1950), 647–652. MR 38196
- N. Rott, On the unsteady motion of a thin rectangular wing in supersonic flow, J. Aeronaut. Sci. 18 (1951), 775–776. MR 47466
- K. Stewartson, On the linearized potential theory of unsteady supersonic motion, Quart. J. Mech. Appl. Math. 3 (1950), 182–199. MR 38792, DOI https://doi.org/10.1093/qjmam/3.2.182
- H. J. Stewart and Ting-Yi Li, Periodic motions of a rectangular wing moving at supersonic speed, J. Aeronaut. Sci. 17 (1950), 529–539. MR 38793
Li, T. Y., Purely rolling oscillations of a rectangular wing in supersonic flow, J. Aero. Sci. 18, 191–198 (1951).
- H. J. Stewart and Ting-Yi Li, Source-superposition method of solution of a periodically oscillating wing at supersonic speeds, Quart. Appl. Math. 9 (1951), 31–45. MR 42272, DOI https://doi.org/10.1090/S0033-569X-1951-42272-8
A review of ref. 9, Math. Rev. 13, 86 (1951).
Kussner, H. G., Algemeine Tragflachentheorie, Luftfahrtforschung 17, 337–378 (1940).
- John C. Evvard, Distribution of wave drag and lift in the vicinity of wing tips at supersonic speeds, Tech. Notes Nat. Adv. Comm. Aeronaut. 1947 (1947), no. 1382, 28 pp. (5 plates). MR 0020900
- Wilhelm Magnus and Fritz Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics, Chelsea Publishing Company, New York, N.Y., 1949. Translated by John Wermer. MR 0029000
- L. A. Galin, A wing of rectangular plan form in supersonic flow, Headquarters Air Materiel Command, Wright-Patterson Air Force Base, Dayton, Ohio., 1949. Tech. Rep. no. F-TS-1217-IA (GDAM A9-T-36). MR 0032280
- John W. Miles, On the reduction of unsteady supersonic flow problems to steady flow problems, J. Aeronaut. Sci. 17 (1950), 64. MR 33695
- Robert T. Jones, Thin oblique airfoils at supersonic speed, Tech. Notes Nat. Adv. Comm. Aeronaut. 1107 (1946), 21. MR 0017094
Hayes, W. D., Linearized supersonic flow, Thesis, Calif. Inst. of Tech., Pasadena (1947).
- H. Behrbohm and K. Oswatitsch, Flache kegelige Körper in Überschallströmung, Ing.-Arch. 18 (1950), 370–377 (German). MR 42266
Baker, B. and Copson, E. T., Huygens’ principle, Oxford U. Press, 2d Ed. (1950).
- H. Bateman, Partial Differential Equations of Mathematical Physics, Dover Publications, New York, N.Y., 1944. MR 0010909
Davis, H., Diffraction of a sound pulse by a semi-infinite plane, Thesis, Univ. of Calif., Los Angeles (1950).
Harkevič, A. A., Akad. Nauk. SSSR, Z̆urnal Tehn. Fiz. 19, 828–832, 833–838 (1949); see Math. Rev. 12, 370 (1951).
- J. W. Miles, On the diffraction of an electromagnetic pulse by a wedge, Proc. Roy. Soc. London Ser. A 212 (1952), 547–551. MR 53760, DOI https://doi.org/10.1098/rspa.1952.0101
- F. G. Friedlander, On the half-plane diffraction problem, Quart. J. Mech. Appl. Math. 4 (1951), 344–357. MR 44348, DOI https://doi.org/10.1093/qjmam/4.3.344
- John W. Miles, On the general solution for unsteady motion of a rectangular wing in supersonic flow, J. Aeronaut. Sci. 19 (1952), 421–422. MR 49747
Goodman, T. R., The quarter infinite wing oscillating at supersonic speeds, Cornell Aero. Lab. Rep. No. 36 (1951).
Goodman, T. R., Aerodynamics of a supersonic rectangular wing striking a sharp edged gust, J. Aero. Sci. 18, 519–526 (1951).
Miles, J. W., The oscillating rectangular airfoil at supersonic speeds, Q. Appl. Math. 9, 47-65 (1951); see also J. Aero. Sci. 16, 381 (1949) and U. S. Navord Rep. 1170, NOTS 226 (1949).
Miles, J. W., Transient loading of supersonic rectangular airfoils, J. Aero. Sci. 17, 647–652 (1950).
Rott, N., On the unsteady motion of a thin rectangular airfoil in supersonic flow, J. Aero. Sci. 18, 775–776 (1951).
Stewartson, K., On the linearized potential theory of unsteady supersonic motion, Q. J. Mech. and Appl. Math. 3, 182–199 (1950).
Stewart, H. J. and Li, T. Y., Periodic motions of a rectangular wing moving at supersonic speed, J. Aero Sci. 17, 529–539 (1950).
Li, T. Y., Purely rolling oscillations of a rectangular wing in supersonic flow, J. Aero. Sci. 18, 191–198 (1951).
Stewart, H. J. and Li, T. Y., Source-superposition method of solution of a periodically oscillating wing at supersonic speeds, Q. Appl. Math. 9, 31–45 (1951).
A review of ref. 9, Math. Rev. 13, 86 (1951).
Kussner, H. G., Algemeine Tragflachentheorie, Luftfahrtforschung 17, 337–378 (1940).
Evvard, J. C., Distribution of wave drag and lift in the vicinity of wing tips at supersonic speeds, NACA T. N. 1382 (1947); see also NACA T. N. 1484 (1947).
Magnus, W. and Oberhettinger, F., Special functions of mathmetical physics, Chelsea Publ. Co., New York, (1949).
Galin, L. A., A wing of rectangular plan form in supersonic flow, (transl. from Russian) A. M. C. F-T S—1217-IA, Wright Field, Dayton, Ohio (1949).
Miles J. W., On the reduction of unsteady supersonic flow problems to steady flow problems, J. Aero. Sci. 17, 64 (1950).
Jones, R. T., Thin oblique airfoils in supersonic flow, NACA T. N. 1107 (1946).
Hayes, W. D., Linearized supersonic flow, Thesis, Calif. Inst. of Tech., Pasadena (1947).
Behrbohm, H. and Oswatitsch, K., Flache kegelige Korper in Uberschallströmung, Ing. Arch. 18, 370–377 (1950).
Baker, B. and Copson, E. T., Huygens’ principle, Oxford U. Press, 2d Ed. (1950).
Bateman, H., Partial differential equations, Dover Publ., New York, N. Y. (1944), 384, 487.
Davis, H., Diffraction of a sound pulse by a semi-infinite plane, Thesis, Univ. of Calif., Los Angeles (1950).
Harkevič, A. A., Akad. Nauk. SSSR, Z̆urnal Tehn. Fiz. 19, 828–832, 833–838 (1949); see Math. Rev. 12, 370 (1951).
Miles, J. W., On the diffraction of an electromagnetic pulse by a wedge, Proc. Roy. Soc. Lon. (A) 212, 547–551 (1952).
Friedlander, F. G., On the half plane diffraction problem, Q. J. Mech. and Appl. Math. 4, 344–357 (1951).
Miles, J. W., On the general solution for unsteady motion of a rectangular wing in supersonic flow, J. Aero. Sci. 19, 421–422 (1952); the result (5.4) of the present paper is stated therein without proof.
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Article copyright:
© Copyright 1953
American Mathematical Society
