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The induced downwash and lift on a wing of high aspect ratio in unsteady motion

Published online by Cambridge University Press:  04 July 2016

P. Wilmott
P. Wilmott*
Affiliation:
Mathematical Institute, Oxford
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Summary

An unsteady lifting line theory for a general motion of a wing of high aspect ratio is presented. Our analysis parallels that of Van Dyke (1964) in his solution for the steady lifting line by the method of matched asymptotic expansions but is complicated by the shedding of transverse vortices associated with variation of circulation with time. We find expressions for the downwash due to three-dimensional (finite span) effects and the lift on the wing. Calculations are presented for a wing of elliptic planform following a curved path.

Type
Research Article
Information
The Aeronautical Journal , Volume 90 , Issue 892 , February 1986 , pp. 63 - 72
Copyright
Copyright © Royal Aeronautical Society 1986 

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References

Ahmadi, A. R. and Widnall, S. E. Unsteady Lifting-Line theory as a singular perturbation problem. J Fluid Mech. 1985, 153, 59–81.Google Scholar
Betteridoe, D. S. and Archer, R. D. A study of the mechanics of flapping flight. Aero Quart. 1974, 25, 129.Google Scholar
Crighton, D. G. The Kutta condition in unsteady flow. Ann Rev FM, 1985, 17, 411–445.Google Scholar
Dragos, L. The theory of oscillating thick wings in subsonic flow. Lifting Line theory. Acta Mech. 1985, 54, 221–238.Google Scholar
Isaacs, R. Airfoil theory for flow of variable velocity. J Aero Sci. 1945, 12, 113.Google Scholar
James, E. L. Lifting Line theory for an unsteady wing as a singular perturbation problem. J Fluid Mech. 1975, 70, 753.Google Scholar
Lagerstrom, P. A. and Casten, R. G. Basic concepts underlying singular perturbation techniques. SIAM Rev. 1972, 14, 63–120.Google Scholar
Milne-Thomson, L. M. Theoretical Hydrodynamics. MacMillan, 1938.Google Scholar
Phlips, P. J., East, R. A. and Pratt, N. H. An unsteady lifting line theory of flapping wings with application to forward flight of birds. J Fluid Mech. 1981, 112, 97.Google Scholar
Van Dyke, M. D. Lifting Line theory as a singular perturbation problem. Arch Mech Stos. 1964, 16, 601.Google Scholar
Van Holten, Th. Some notes on unsteady lifting line theory. J Fluid Mech. 1976, 77, 561.Google Scholar
Wilmott, P. Unsteady lifting line theory by the method of matched asymptotic expansions. Submitted to J Fluid Mech, 1985.Google Scholar