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Minimum Induced Drag of Non-Planar Ground Effect Wings with Small Tip Clearance

Published online by Cambridge University Press:  07 June 2016

T Kida
Affiliation:
University of Osaka Prefecture, Japan
Y Miyai
Affiliation:
University of Osaka Prefecture, Japan
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Summary

This paper treats theoretically the problem of the minimum induced drag of non-planar ground effect wings with both tips very close to the ground, within the limitations of the linearised lifting-line theory. The gap clearance between the wing tip and the ground is assumed to be very small and, using this small parameter, an approximate theory, which yields the minimum induced drag of a non-planar ground effect wing, is formulated by the method of matched asymptotic expansions. As a check on the accuracy of the method, this theory is compared with the exact theory for a semicircular wing. This shows that the present method is accurate within the small gap clearance. Moreover, the present method is applied to other wing configurations, such as semi-elliptic wings and wings with endplates, circular arc wings in a tube and circular arc wings. These computations show the theory to be very effective and it can be easily extended to various spanwise cambers.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1974

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References

1 Tomotika, S, Hasimoto, Z, Urano, K, The forces acting on an aerofoil of approximate Joukowski type in a stream bounded by a plane wall. Quarterly Journal of Mechanics and Applied Mathematics, Vol IV, p 289, 1951.CrossRefGoogle Scholar
2 Ashley, H, Widnall, S, Landahl, M T, New directions in lifting-surface theory. AIAA Journal, Vol 3, p 3, January 1965.Google Scholar
3 Ando, S, An idealised ground effect wing. Aeronautical Quarterly, Vol XVII, p 53, February 1966.Google Scholar
4 Ashill, P R, On the minimum induced drag of ground effect wings. Aeronautical Quarterly, Vol XXI, p 211, August 1970.Google Scholar
5 Mamada, H, Ando, S, Minimum induced drag of a semicircular ground effect wing. To be published in Journal of Aircraft.Google Scholar
6 Van Dyke, M, Perturbation Methods in Fluid Mechanics, p 164, Academic Press, New York, 1964.Google Scholar
7 Barrows, T M, Widnall, S E, Optimum lift-drag ratio for a ram wing tube vehicle. AIAA Journal, Vol 8, p 491, August 1970.Google Scholar
8 Widnall, S E, Barrows, T M, An analytic solution for two- and three-dimensional wings in ground effect. Journal of Fluid Mechanics, Vol 41, p 769, 1970.CrossRefGoogle Scholar
9 Mamada, H, Ando, S, The minimum induced drag of the semi-elliptic ground effect wing. Journal of the Japan Society for Aeronautical and Space Sciences, Vol 21, p 5, 1973 (in Japanese).Google Scholar
10 Tomotika, S, Elliptic Functions. Kyoritu Press, Tokyo, 1958 (in Japanese).Google Scholar
11 Muskhelishvili, N I, Singubr Integral Equations, p 242, Noordhoff, Groningen, 1953.Google Scholar