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Asymptotic analysis of the classical aircraft stability equations

Published online by Cambridge University Press:  04 July 2016

W. R. Graham
W. R. Graham*
Affiliation:
Department of EngineeringUniversity of CambridgeCambridge, UK
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Abstract

A new approach to deriving analytical approximations for the free modes of motion of an aircraft is presented. Based on an asymptotic analysis, it eliminates the need for a priori assumptions regarding the characteristic motion of each mode, and is thus particularly suitable for an introductory exposition. In its basic form, it yields expressions for natural frequencies, damping factors and time constants which agree, to leading order, with well established results. At a more advanced level, it allows us to assess the validity of these results. In particular, we find that the two degree-of-freedom approximations to the short period oscillation and Dutch roll are asymptotically incorrect. This is unlikely to have a significant effect on the accuracy of the former, but is the reason for the poor damping predictions of the latter.

Type
Research Article
Information
The Aeronautical Journal , Volume 103 , Issue 1020 , February 1999 , pp. 95 - 103
Copyright
Copyright © Royal Aeronautical Society 1999 

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References

1. Duncan, W.J. Control and Stability of Aircraft, Cambridge University Press, Cambridge, 1952.Google Scholar
2. Babister, A.W. Aircraft Stability and Control, Pergamon Press, London, 1961.Google Scholar
3. McRuer, D., Ashkenas, I. and Graham, D. Aircraft Dynamics and Automatic Control, Princeton University Press, Princeton, NJ, 1973.Google Scholar
4. Nelson, R.C. Flight Stability and Automatic Control, McGraw-Hill, London, 1989.Google Scholar
5. McLean, D. Automatic Flight Control Systems, Prentice-Hall, London, 1990.Google Scholar
6. Stevens, B.L. and Lewis, F.L. Aircraft Control and Simulation, Wiley, New York, 1992.Google Scholar
7. Hancock, G.J. An Introduction to the Flight Dynamics of Rigid Aeroplanes, Ellis Horwood, Hemel Hempstead, 1995.Google Scholar
8. Etkin, B. and Reid, L.D. Dynamics of Flight. Wiley, Chichester, 1996.Google Scholar
9. Cook, M.V. Flight Dynamics Principles, Arnold, London, 1997.Google Scholar
10. Olver, F.W.J. Asymptotics and Special Functions, Academic Press, London, 1974.Google Scholar
11. Jane's All The World's Aircraft, 1991–1992, Jane's Information Group, Coulsdon, Surrey.Google Scholar
12. Babister, A.W. Aircraft Dynamic Stability and Response, Pergamon, Oxford, 1980.Google Scholar