High Quality Content by WIKIPEDIA articles! In applied mathematics, the Joukowsky transform, named after Nikolai Zhukovsky, is a conformal map historically used to understand some principles of airfoil design. In aerodynamics, the transform is used to solve for the two-dimensional potential flow around a class of airfoils known as Joukowsky airfoils. A Joukowsky airfoil is generated in the z plane by applying the Joukowsky transform to a circle in the ? plane. The coordinates of the centre of the circle are variables, and varying them modifies the shape of the resulting airfoil. The circle encloses the origin (where the conformal map has a singularity) and intersects the point z = 1. This can be achieved for any allowable centre position by varying the radius of the circle. A closely related transform is the Karman–Trefftz transform, as used to specify the Karman–Trefftz airfoil, another class of airfoils. The trailing edge of the Karman–Trefftz airfoil does not have the cusp which the Joukowsky airfoil has.

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