The use of conical camber to produce flow attachment at the leading edge of a delta wing and to minimize lift-dependent drag at sonic and supersonic speeds

Abstract

In an attempt to avoid flow separation at the leading edge of a thin delta wing with subsonic leading edges, an attachment line is prescribed there. This is done by requiring the load, as predicted by attached-flow theory, to vanish along the leading edge at the design lift coefficient. For sonic speed, a complete account of this flow is given in terms of slender-wing theory and the load distributions corresponding to arbitrary conical camber are calculated. For supersonic speeds, load distributions arising in the slender-wing theory are considered and the corresponding conical-camber distributions are found by linearized theory. The lift-dependent drag for a given lift is then minimized with respect to the coefficients of a linear combination of these load distributions. It is found that the lift-dependent drag factor for these conically-cambered wings approaches the value it takes for the attached flow (in which leading-edge suction occurs) past the uncambered wing at the same Mach number, as more terms are included in the linear combination. However, when the leading edge is almost sonic an appreciable reduction is predicted. The corresponding load distributions and wing shapes are calculated and drawn. The optimum shapes for a fixed number of terms resemble flat plates drooped downwards near their leading edges, so that the localized leading-edge suction is replaced by a distributed force on a forward-facing surface, producing an effect of similar magnitude.