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On non-steady motion of slender bodies

Published online by Cambridge University Press:  07 June 2016

John W. Miles
John W. Miles*
Affiliation:
University of California, Los Angeles
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Summary

Following the original work of Munk, Jones, and Ward for steady flow, a solution is given for unsteady, supersonic flow over very slender bodies of revolution and wings. The results are subject to the restriction (M2- l)δ2 loge [(M2- 1)½ δ]«1 where δ is the slenderness ratio, M is the Mach number and, in addition, to the usual restrictions imposed by linearisation. As examples, the lifts and pitching moments on flat wings and bodies of revolution executing pitching motion and the damping moment on a rolling wing are calculated.

It is shown that the order of approximation is consistent with the limitations already imposed by linearisation, at least in supersonic flow, where no Kutta condition is required.

Type
Research Article
Information
Aeronautical Quarterly , Volume 2 , Issue 3 , November 1950 , pp. 183 - 194
Copyright
Copyright © Royal Aeronautical Society. 1950

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References

1. Munk, M. M, (1923). The Aerodynamic Forces on Airship Hulls. N.A.C.A. Report 184, 1923.Google Scholar
2. Jones, R. T. (1946). Properties of Low-Aspect-Ratio Pointed Wings at Speeds Below and Above the Speed of Sound. N.A.C.A. Tech. Note 1032, 1946.Google Scholar
3. Ward, G. N. (1949). Supersonic Flow Past Slender Bodies. Quarterly Journal of Mechanics and Applied Mathematics, 2, 75–97, 1949.Google Scholar
4. Lighthill, M. J. (1945). Supersonic Flow Past Bodies of Revolution. R.& M. 2003, 17–21, 1945.Google Scholar
5. Lighthill, M. J. (1948). Supersonic Flow Past Slender Pointed Bodies of Revolution at Yaw. Quarterly Journal of Mechanics and Applied Mathematics, 1, 76–89, 1948.Google Scholar
6. Lighthill, M. J. (1949). Methods for Predicting Phenomena in High Speed Flow of Gases. Journal Aeronautical Sciences, 16, 69–83, 1949.CrossRefGoogle Scholar
7. Lin, C. C., Reissner, E. and Tsien, H. S. (1949). On Two-Dimensional Non-Steady Motion of a Slender Body in a Compressible Fluid. Journal Mathematics and Physics, 27, 220–231, 1949.Google Scholar
8. Robinson, A. (1948). Rotary Derivatives of a Delta Wing at Supersonic Speeds. Journal Royal Aeronautical Society, 52, 735–752, Nov. 1948.Google Scholar
9. Miles, J. W. (1949). On Damping in Pitch for Delta Wings. Journal Aeronautical Sciences, 16, 574–575, 1949.Google Scholar