Studies on the Interference of Wings and Propeller Slipstreams

The small disturbance potential flow theory is applied to determine the lift of an airfoil in a nonuniform parallel stream. The given stream is replaced by an equivalent stream with a certain number of velocity discontinuities, and the influence of these discontinuities is obtained by the method of images. Next, this method is extended to the problem of an airfoil in a nonuniform stream of smooth velocity profile. This model allows perturbation velocity potential in a rotational undisturbed stream. A comparison of these results with numerical solutions of Euler equations indicates that, although approximate, the present method provides useful information about the interaction problem while avoiding the need to solve the Euler equations. The assumptions of the classical lifting line theory applied to the wing-slipstream interaction problem are scrutinized. One of the assumptions (uniform velocity in the slipstream) of the classical theory is dropped, and the governing equations are derived for the spanwise lift distribution on a wing in a single axisymmetric slipstream. Spanwise lift and induced drag distributions are obtained for two typical cases, and the effects of nonuniformity in the slipstream velocity profile are examined