Comment on "Analytical Prediction of Vortex Lift"

Abstract

S comments are warranted concerning the paper by J.W. Purvis entitled Analytical Prediction of Vortex Lift, which appears in the April 1981 issue of the Journal of Aircraft. The first comment is relative to the use of singular loadings in the design of mean camber shapes for wings experiencing leading-edge-vortex separated flow. By comparison, Ref. 1 outlines a low-drag, separated-flow design procedure which uses a more appropriate attached-flow initial loading that is nonsingular. There the final solution for the mean camber surface is obtained by iterating to find the shape-yielding minimum separated-flow drag at the required lift coefficient. The second comment is that the section-induced drag, see Eq. (12), does not have an elliptical distribution over the wing as proposed, but only in the Trefftz plane. This is well known (e.g., Ref. 2), and means that for most wings of interest the section-induced drag has to be determined in the near field. The consequence of this wrong assumption leads to an error in Eq. (26) and, hence, in the magnitude of the leading-edge suction force and vortex flow aerodynamics for wings with varying leading-edge sweep. The third comment deals with the missing multiplication by 2 in Eqs. (27), (30), (33), and (34), the missing division by 2 in Eqs. (28) and (37), and the typographical error in Eq. (32). Equation (32) should read