A Theoretical Note on the Lift Distribution of a Non-planar Ground Effect Wing

Abstract

Summary The problem of a non-planar wing of finite span very close to the ground is considered by the method of matched asymptotic expansions. This method is based on the work of Widnall and Barrows, in which a planar wing very close to the ground was examined in detail. A simple analytic solution, to first-order approximation, is obtained for a non-planar wing which is uncambered. Expressions for the lift coefficient, induced angle and induced drag coefficient, which are valid for small ground clearance and moderately small aspect ratio, are derived for the case when the configuration of the wing projected onto a transverse plane normal to the free stream is elliptic. The problem of the optimum lift distribution around the wing and the rolling-moment coefficient for the inclined flat wing are discussed. The distribution of camber and of aerofoil angle of attack is given analytically for an optimally loaded non-planar wing, to first-order approximation. Moreover, it is seen that, to first-order approximation, the aerodynamic forces given for the small aspect ratio are independent of the wing planform and depend only on the wing configuration at the trailing edge projected onto a transverse plane.