A Quasi-Linear and Linear Theory for Non-Separated and Separated Two-Dimensional, Incompressible Irrotational Flow about Lifting Bodies

A general theory is developed for calculating lift, form drag, and moment applicable to thin bodies at small angles of attack without separation or with separation at an arbitrary number of given points. The separated flows are related to fully cavitated and partially cavitated flows by making use of the concept of free streamlines. The closure condition of free-streamline theory is replaced by a boundedness condition. Unique solutions are thereby obtained for a large variety of problems. The mathematical solution involves a Riemann-Hilbert mixed boundary value problem in an upper-half plane. The general solution for this problem is given in the Appendix and is applied to various kinds of mixed boundary conditions. The method is exemplified by means of four illustrative calculations. As may be expected when the boundary profile is truly linear, the solution agrees with the classic exact solution.