The linearised subsonic flow over the centre-section of a lifting swept wing

Abstract

The linearised equation for the velocity potential of subsonic flow past a semi-infinite plane sector has eigensolutions. These determine the singular behaviour of the loading, according to the linearised theory of subsonic flow, at the leading and trailing edges of the centre-section of a swept wing. The eigensolutions are proportional to a positive power of the distance from the apex of the sector. Values of the exponents of this factor for the first two eigensolutions are calculated as functions of the apex angle, using a finite-difference approximation to the partial differential equation. The first of these corresponds to the strength of the singularity in the loading at the apex of a swept wing and the second, which is compatible with the Kutta-Joukowski condition; describes the rate at which the loading tends to zero as the trailing-edge root is approached.