Integral Relations in the Linearized Theory of Wing-Body Interference

Abstract

The reverse-flow theorem is extended to the case of a wing mounted on a cylindrical body of any cross-sectional shape. Also, two TrefTtz-plane theorems relating the total lift and rolling moment on such a body to the corresponding values for the wings are derived. Based on these results, some further general relationships between integrated lifts and moments on the wing, the body, and the combination are obtained. I t is shown that the lift distribution on the wing-body combination in reverse flow is the influence function for lift of the combination. Further, it is shown that the influence function for rolling moment is the lift distribution over the combination rolling at constant angular velocity in reverse flow. I t is also shown tha t the lift induced on the wings by a unit body angle of attack is equal to the lift induced on the body by a unit wing angle of attack in reverse flow. In lifting-line theory, slender-body theory, or for any wings having a span wise axis of symmetry (such as rectangular or diamond wings), the need for consideration of reverse flow is eliminated, and the results assume a particularly simple form. The results are valid for subsonic or supersonic flow within the limitations of linearized theory.