Shear Flow Past a Wing of Circular Plan Form

Abstract

The problem of flow past a thin wing of circular plan form when the undisturbed flow is along the x-axis, U(z)=Az+V has been solved.The solutions for potential flow past a wing of circular plan form have been given in terms of spheroidal co-ordinates using the concept of acceleration potential. The solutions can be easily adapted to the case when the undisturbed flow is weakly sheared. In the particular case when the undisturbed velocity U(z) = Az+V, where A and V are constants, the pressure equation can be simplified by a simple substitution and the solution for a thin wing of circular plan form can be easily constructed from the solution for potential flow. If the wings in the two cases develop the same lift, it is found that the wing in shear flow should be slightly cambered (potential wing is un-cambered). The results are shown graphically in Fig. 1.