Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-09T08:50:22.585Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Ward, G. N. The Drag of Source Distributions in Linearized Supersonic Flow. College of Aeronautics Report 88, 1955.Google Scholar
2. Lance, G. N. The Drag of Slender Pointed Bodies in Supersonic Flow. Quarterly Journal of Mechanics and Applied Mathematics, Vol. 5, pp. 165–177, 1952.CrossRefGoogle Scholar
3. Nielsen, J. N. Supersonic Wing-Body Interference. Thesis, California Institute of Technology, 1951.Google Scholar
4. Randall, D. G. Supersonic Flow past Quasi-Cylindrical Bodies of Almost Circular Cross-Section. R.A.E. Tech. Note Aero. 2404, 1955.Google Scholar
5. Van der Pol, B. and Bremmer, H. Operational Calculus. Cambridge University Press, 1955.Google Scholar
6. Watson, G. N. Theory of Bessel Functions. Cambridge University Press, 1944.Google Scholar
7. Hayes, W. D. Linearized Supersonic Flow. Thesis, California Institute of Technology, North American Aviation Rep. AL-222, 1947.Google Scholar
8. Heaslet, M. A.; Lomax, H. and Spreiter, J. R. Linearized Compressible-Flow Theory for Sonic Flight Speeds. N.A.C.A. Report 956, 1950.Google Scholar
9. Ward, G. N. Linearized Theory of Steady High-Speed Flow. Cambridge University Press, 1955.Google Scholar
10. Byrd, P. F. and Friedman, M. D. Handbook of Elliptic Integrals for Engineers and Physicists. Springer, Berlin, 1954.CrossRefGoogle Scholar
11. Nielsen, J. N. and Pitts, W. C. General Theory of Wave-Drag Reduction for Combinations Employing Quasi-Cylindrical Bodies with an Application to Swept-Wing and Body Combination. N.A.C.A. T.N. 3722, 1956.Google Scholar
12. Lomax, H. and Heaslet, M. A. Recent Developments in the Theory of Wing-Body Wave Drag. Journal of the Aeronautical Sciences, Vol. 23, pp. 1061–1074, 1956.CrossRefGoogle Scholar