Comment on ''Simplification of the Wing-Body Problem"

Abstract

THE formula for the total lift, including interference effects, for a wing mounted on a circular cylindrical body, in terms of the lift which would be experienced by the exposed wing alone, presented as Eq. (4) by Graham and McDowell was apparently first given by Ward in 1949. Ward also surmised that the formula might have much broader application than its origin in slenderbody theory would suggest. The same formula may be inferred from the results obtained by Spreiter, and it has earlier antecedents in the classical work on wing-body combinations of minimum induced drag. Since Spreiter's and Ward's work, a vast literature on the subject of wing-body interference has come into being, including many heuristic and empirical methods built on extensions of slender-body theory results. Ward's formula was presented or utilized in many subsequent papers. For example, it appears in the survey paper by Lawrence and the writer and, explicitly in the interference factor notation used in Ref. 1, in the book by Nielsen. The main purpose of this Comment, however, is not to set forth the historical development of the particular formula presented in Ref. 1. Rather it is, in view of the approach taken in Ref. 1, to point out again that the total forces and moments of aerodynamically interfering wingbody combinations can almost always be more readily obtained in simple closed form than the forces and moments of components. This can be done by a variety of methods, closely related in principle, but differing in convenience for particular applications. These methods include farfield contour integration as used by Ward, direct application of conformal and mapping to the integral expressions for total force as used by Lawrence and the writer, and Bryson's apparent mass methods, which he applied extensively in the determination of stability derivatives. Utilizing these methods, relatively simple closed-form expressions for the total forces and moments on the various wing-body combinations of considerably more general configurations than the one considered in Ref. 1 have been obtained in the cited references and many other papers. The formulas for slender-body theory interference ratios are usually applied to configurations which are not slender enough for the theory to apply with high precision, the aspect-ratio effects being taken into account through the ex-