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The Wave Drag of Wing-Quasi-Cylinder Combinations at Zero Incidence

Published online by Cambridge University Press:  07 June 2016

L. E. Fraenkel
L. E. Fraenkel*
Affiliation:
Department of Aeronautics, Imperial College
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Summary

This paper is concerned with the drag, at zero lift, of wing-body combinations which are symmetrical about the wing plane. Only two assumptions are made: that surface slopes are sufficiently small for the application of linearised theory, and that it is sufficient to satisfy the body boundary condition on the surface of a circular cylinder.

The configuration is represented entirely by singularities along the body axis, and three drag formulae are derived. The first involves the Laplace transforms of functions representing the strengths of the sources and multisources; the difficult problem of inverting these transforms is thereby avoided. The second involves these strength functions themselves, and is of the form of a series of double integrals of the famous von Kármán type. The third involves functions describing the geometry of a very hypothetical quasi-cylinder which has the same drag as the Whole configuration in question. The convergence of these formulae is established.

These results are then used to make an order-of-magnitude analysis for wing-slender-body combinations: a large number of drag terms are seen to be negligible when the ratio of body radius to wing chord is small, and the dominant terms for smooth bodies are those appearing in Ward's drag formula.

Finally, the geometry of the “ equivalent quasi-cylinder ” is investigated.

Type
Research Article
Information
Aeronautical Quarterly , Volume 9 , Issue 1 , February 1958 , pp. 55 - 70
Copyright
Copyright © Royal Aeronautical Society. 1958

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References

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