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A problem of minimal induced resistance in unsteady motion

Published online by Cambridge University Press:  04 July 2016

G. Losilevskii
G. Losilevskii*
Affiliation:
Technion, Haifa 32000, Israel
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Abstract

Energy considerations are used to find the spanwise circulatory lift distribution yielding minimal induced resistance for a harmonically oscillating planar wing in a steady incompressible flow. Under the restriction that the time-averaged and oscillatory constituents of the wing's circulatory lift are known, the optimal distribution is such that its time-averaged constituent is elliptical, but the oscillatory one is generally not. The latter varies from elliptical to rectangular as the frequency of the oscillations increases. When the oscillatory part of the lift is not prescribed, present results infer that its reduction — as, for example, by an elastic twist — will typically reduce the drag, even if the twist yields a non-optimal (for that lift) lift distribution.

Type
Research Article
Information
The Aeronautical Journal , Volume 101 , Issue 1002 , February 1997 , pp. 93 - 97
Copyright
Copyright © Royal Aeronautical Society 1997 

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References

1. Munk, M. Isoparametrische Aufgaben aus der Theorie des Fluges, Inaug.-Dissertation, Göttingen, 1919, p 17.Google Scholar
2. Bisplinghoff, R.L., Ashley, H. and Halfman, R.L. Aeroelasticity, Addison-Wesley Publishing Company, 1957, pp 272–281.Google Scholar
3. Ashley, H. and Landahl, M. Aerodynamics of Wings and Bodies, Addison Wesley, 1965, pp 92,135, 136.Google Scholar
4. Sparenberg, J.A. Elements of Hydrodynamic Propulsion, Martinus Nijhoff Publishers, 1984, pp 133 & 156.Google Scholar
5. Gradshteyn, I.S. and Ryzhik, I.M. Table of Integrals, Series, and Products, Academic Press, 1980.Google Scholar
6. von Karman, T. and Burgers, J.M. General aerodynamic theory. Perfect fluids. In: Durand, W.F. (ed.), Aerodynamic Theory, Vol 2, Dover, 1963, pp 100–136.Google Scholar
7. Watson, G.N. A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1966, p 388.Google Scholar
8. Press, W.H., Flannery, B.P., Teukolsky, S. A. and Vetterling, W.T. Numerical Recipes. The Art of Scientific Computing, Cambridge University Press, 1989, p 108.Google Scholar