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Gough-Joukowski transform

B1. Naval Architecture

Definition

Conformal mapping used in 2D foil section analysis.

This entry is the Joukowski (Joukowsky) transform, the conformal mapping z = zeta + c^2 / zeta that maps a circle in the zeta-plane to an airfoil or strut section in the z-plane, used in classical 2D foil and rudder-section analysis. With the circle center offset from the origin it produces cambered, finite-thickness shapes whose flow follows from the known circle solution plus the Kutta condition, giving closed-form lift via the Kutta-Joukowski theorem L = rho V Gamma. The Joukowski airfoil ends in a zero-angle cusp; the Karman-Trefftz generalization adds a finite trailing-edge angle. The seed name gough-joukowski is garbled: the prefix gough is spurious and the concept is the Joukowski transform.

Source: Joukowsky (1910) conformal transformation