Karman-Trefftz profile

The Karman-Trefftz profile is a family of analytic 2D airfoil sections from the Karman-Trefftz conformal transform, devised by von Karman and Trefftz in 1918 as a generalization of the Joukowski mapping. Its defining advantage is a finite trailing-edge angle tau, set by the transform exponent n = 2 - tau/pi, where the Joukowski cusp (tau = 0) is the limiting case n = 2. The mapping turns a circle into a realistic cambered, finite-thickness section whose potential-flow solution and lift are known in closed form via the Kutta condition, so the profiles serve as analytic benchmarks for panel methods and rudder-section codes. Section ordinates and the pressure distribution come out exactly, the standard validation cases in foil work.