The Monoplane as a Lifting Vortex Surface

Abstract

In Prandtl's airfoil theory the monoplane was replaced by a single lifting vortex line and yielded fairly practical results. However, the theory remained restricted to the straight wing. Yawed wings and those curved in flight direction could not be computed with this first approximation; for these the chordwise lift distribution must be taken into consideration. For the two-dimensional problem the transition from the lifting line to the lifting surface has been explained by Birnbaum. In the present report the transition to the three-dimensional problem is undertaken. The first fundamental problem involves the prediction of flow, profile, and drag for prescribed circulation distribution on the straight rectangular wing, the yawed wing for lateral boundaries parallel to the direction of flight, the swept-back wing, and the rectangular wing in slipping, with the necessary series developments for carrying through the calculations, the practical range of convergence of which does not comprise the wing tips or the break point of the swept-back wing. The second problem concerns the calculation of the circulation distribution with given profile for a slipping rectangular monoplane with flat profile and aspect ratio 6, and a rectangular wing with cambered profile and variable aspect ratio-the latter serving as check of the so-called conversion formulas of the airfoil theory.