The Joukowski transformation

is an analytic function of a complex variable that maps a circle in the

plane to an airfoil shape in the

plane. The mapping is conformal except at critical points of the transformation where

. This occurs at

with image points at

. The sharp trailing edge of the airfoil is obtained by forcing the circle to go through the critical point at

. The trailing edge of the airfoil is located at

, and the leading edge is defined as the point where the airfoil contour crosses the

axis. This point varies with airfoil shape and is computed numerically. The distance from the leading edge to the trailing edge of the airfoil is the chord, which the aerodynamics community uses as the characteristic length for dimensionless measures of lift and pitching moment per unit span. The shape of the airfoil is controlled by a reference triangle in the

plane defined by the origin, the center of the circle at

and the point

.