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On the Low Aspect Ratio Oscillating Rectangular Wing in Supersonic Flow

Published online by Cambridge University Press:  07 June 2016

John W. Miles
John W. Miles*
Affiliation:
University of California
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Summary

The Laplace transform of the lift distribution on an oscillating rectangular wing in a supersonic flow is obtained by separating the linearised equation for the velocity potential in elliptic (cylindrical) co-ordinates. The results for the case of no spanwise distortion are expanded in ascending powers of the aspect ratio in order to compare with the slender body theory, and the longitudinal stability derivatives are calculated. It is found that at either supersonic or transonic speeds single-degree-offreedom instability in pitch is impossible insofar as the fourth power of the aspect ratio is neglected.

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Type
Research Article
Information
Aeronautical Quarterly , Volume 4 , Issue 2 , August 1953, pp. 231 - 244
Copyright
Copyright © Royal Aeronautical Society. 1953

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References

1. Miles, J. W. (1952). On Non-steady Supersonic Flow About Pointed Bodies of Revolution. Journal of the Aeronautical Sciences, Vol. 19, p. 208, March 1952. On Non-Steady Motion of Slender Bodies. Aeronautical Quarterly, Vol. II, Nov. 1950.Google Scholar
2. Stewartson, K. (1950). Supersonic Flow over an Inclined Wing of Zero Aspect Ratio. Proc. Camb. Phil. Soc, Vol. 46 (Pt. 2), p. 307, April 1950.Google Scholar
3. Schwarzschild, K. (1902). Die Beugung und Polarisation des Lichts durch einen Spalt. Math. Ann., Vol. 55, p. 177, 1902.CrossRefGoogle Scholar
4. Gunn, J. C. (1947). Linearised Supersonic Aerofoil Theory. Parts I and II. Phil. Trans. Roy. Soc, A. Vol. 240, p. 327, 1947.Google Scholar
5. Stewartson, K. (1950). On the Linearised Potential Theory of Unsteady Supersonic Motion. Q. J. Mech. and Appl. Math., Vol. 3, p. 182, June 1950.Google Scholar
6. Lamb, H. (1932). Hydrodynamics. Cambridge University Press, 6th ed., 1932.Google Scholar
7. Wien, W. (1906). Uber die partiellen Differentialgleichungen der Physik. Jahresbericht d. Deutsch Math. Verein, Vol. 15, p. 42, 1906.Google Scholar
8. Sieger, B. (1908). Die Beugung einer ebenen elektrischen Welle an einem Schirm von elliptischen Querschnitt. Ann. d. Physik, Vol. 27, p. 626, 1908.CrossRefGoogle Scholar
9. Morse, P. M. and Rubenstein, P. O. (1938). Diffraction of Waves by Ribbons and by Slits. Ph. Rev., Vol. 54, p. 895, December 1938.CrossRefGoogle Scholar
10. McLachlan, N. W. (1947). Theory and Application of Mathieu Functions. Oxford University Press, 1947.Google Scholar
11. Miles, J. W. (1951). On Slender Wing Theory. Journal of the Aeronautical Sciences, Vol. 18, p. 770, November 1951.CrossRefGoogle Scholar
12. Lagerstrom, P. A. and Graham, E. MARTHA (1947). Low Aspect Ratio Rectangular Wings in Supersonic Flow. Douglas Aircraft Rep. SM-13110, Santa Monica, Cal., 1947.Google Scholar
13. Jones, R. T. (1946). Properties of Low Aspect Ratio Pointed Wings at Speeds Below and Above the Speed of Sound. N.A.C.A. Report 835, 1946.Google Scholar
14. Lin, C. C., Reissner, E. and Tsien, H. S. (1949). On Two-Dimensional Non-Steady Motion of a Slender Body in a Compressible Fluid. No. 3. J. Ma. and Ph., Vol. 27, p. 220, 1949.Google Scholar
15. Miles, J. W. (1951). U.S. Naval Ordnance Report 1292. Inyokern, Calif., 1951.Google Scholar