Effect of downwash on the induced drag of canard-wing combinations

Abstract

P o = Fourier coefficient in expansion of WT - Fourier coefficient in expansion of K2 = induced drag = biplane gap = circulation = elliptic circulation = induced circulation = lift the lift distribution on each surface is elliptical under the influence of the downwash field of the other, and it is clear that, in order to satisfy such a condition, a lift-dependent twist needs to be imparted to one or both surfaces. In this Note, the induced drag of canard-wing and wing-tail combinations is calculated for the limiting case in which the downstream surface is located in the Trefftz plane (infinite stagger), but based on the assumption that the loading on each surface is elliptical in isolation. It is shown that additional terms associated with induced circulation effects act to reduce the drag over that calculated using the classical theory. This induced thrust component is shown to be very small for the wing-tail configuration, but significant for the canard-wing layout. In addition, given elliptic loading on the upstream surface, an expression is derived for the loading distribution on the downstream surface which is optimum in the sense that the induced thrust component is maximized. The Trefftz plane assumption leads to a simplification of the analysis, since it means that the lift distribution of the downstream surface does not influence the drag of the upstream surface. The case of finite stagger, including the effects of bound vorticity on both surfaces, will be covered in a subsequent paper.