Design of warped slender wings with the attachment line along the leading edge

Abstract

This report deals with the design of slender warped wings with unswept trailing edge but otherwise arbitrary planform which have, at the design lift coefficient, zero load along the leading edge and a near planar vortex sheet from the trailing edge. The wing can have an arbitrary chordwise curvature on which a spanwise curvature is superposed so that in any spanwise section the wing is straight over the inner part of the wing and curved over the portion near to the leading edges; the position of this change can vary arbitrarily in the chordwise direction. Formulae and working charts are given for determining the local load coefficient (and with it the streamwise velocity component), the spanwise velocity component, the total lift coefficient and the total drag. Numerical examples, for the gothic planform, are given to illustrate some of the effects of the various parameters on the load distribution, the section shapes and the drag. Slender-wing theory has been applied except for determining the wave drag which has been obtained from an approximate relation derived by the not-so-slender theory of Adams and Sears.