Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T16:02:53.470Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on subsonic aerofoil theory

Published online by Cambridge University Press:  07 June 2016

John W. Miles
John W. Miles*
Affiliation:
Department of Engineering, University of California, Los Angeles
Get access

Summary

A linearised theory for the subsonic, lifting surface problem is formulated in terms of Fourier integral solutions to Laplace’s equation. The symmetric and anti-symmetric problems of the first kind are solved explicitly, while the problems of the second kind depend on the solution of dual integral equations. The antisymmetric problem of the second kind is cast in a variational form, from which certain well-known theorems may be deduced.

Type
Research Article
Information
Aeronautical Quarterly , Volume 2 , Issue 1 , May 1950 , pp. 23 - 33
Copyright
Copyright © Royal Aeronautical Society. 1950

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Miles, J. W. (1948). On Linearized Supersonic Airfoil Theory. North American Aviation Company, Aerophysics Lab. Report AL-801, 1948.Google Scholar
2. Schwinger, J. S. (1944). Seminar on the Theory of Guided Waves. Radiation Laboratory, Massachusetts Institute of Technology, Cambridge, Mass., 1944.Google Scholar
3. Levine, H., and Schwinger, J. (1948). On the Theory of Diffraction by an Aperture in an Infinite Plane Screen, I. Physical Review 74, 958–974, 1948.CrossRefGoogle Scholar
4. Durand, W. F. (1942). Aerodynamic Theory, Part II, Div. E. Durand Reprinting Committee, Pasadena, 1942.Google Scholar
5. Kussner, H. G. (1940). Allgemeine Tragflachentheorie. Luftfahrtforschung, 17, 370–378, 1940; translated in N.A.C.A. Technical Memorandum 979, 1941.Google Scholar
6. Reissner, E. (1944). On the General Theory of Thin Airfoils for Non-Uniform Motion. N.A.C.A. Technical Note 946, 1944.Google Scholar
7. Von karman, TH. (1935). Neue Darstellung der Tragflügeltheorie. Zeitschrift fur Angewandte Mathematikund Mechanik 15, 56–61, 1935.Google Scholar
8. Fuchs, R. (1939). Neue Behandlung der Tragflügeltheorie. Ingenuieur Archiv. 10, 48–63, 1939.Google Scholar
9. Trefftz, E. (1921). Zur Prandtlschen Tragflächentheorie. Math. Annal. 82, 306–319, 1921.Google Scholar
10. Dirac, P. (1935). Quantum Mechanics, Oxford, pp. 21 et seq., 1935,Google Scholar
11. Titchmarsh, E. C. (1937). Theory of Fourier Integrals, Oxford, p. 50 (2.1.2), 1937.Google Scholar
12. Watson, G. N. (1947). Bessel Functions, MacMillan & Co., New York, 1947.Google Scholar
13. Kinner, W. (1937). Die kriesförmige Tragfläche auf potential-theoretischer Grundlage. Ingenieur Archiv. 8, 47–80, 1937.CrossRefGoogle Scholar
14. Krienes, K. (1940). Die elliptische Tragfläche auf potential-theoretischer Grundlage. Zeitschrift für Angewandte Mathematik und Mechanik 20, 65–68, 1940; translated in N.A.C.A. Technical Memorandum 971, 1941.Google Scholar
15. Courant, R., and Hilbert, D. (1937). Methoden der Mathematischen Physik, Julius Springer, Berlin, Vol. II, p. 269 et seq., 1937.Google Scholar