A numerical solution for the minimum induced drag of nonplanar wings.

A procedure has been developed for the accurate computation of the minimum induced drag of nonplanar wings with pylonlike panels, provided the wing front view consists of straight line segments. As is well known, the induced drag may be expressed as an integral in an auxiliary mapping plane. Previously, the main computational difficulty had been the determination of the Schwarz-Christoffel mapping between the real and the auxiliary planes. By means of the electrostatic analogy to potential flow, the constants of the mapping are determined with a small experimental error by using an analog field plotter. The mapping is then integrated by numerical techniques, and the constants are adjusted until the desired geometry is achieved to any order of accuracy. The induced drag is determined by quadrature and is shown by comparison with known test cases to be accurate to 10~ 4. Comparison of results with earlier approximate solutions (Mangier, Cone) shows that some of the earlier approximate solutions give more favorable predictions (less drag) than the solution derived here. The discrepancies in the earlier work are shown to be due to improper boundary conditions, and some suggestions are made to minimize these effects. The results show a potential reduction of minimum induced drag of less than 1% for a current subsonic jet transport when the pylons are properly loaded.