The Joukowski conformal mapping w = z + 1/z transforms a cylinder into an airfoil shape, with exact analytic potential flow including lift via Kutta condition.
Joukowski (1910): w = z + c²/z maps the circle |z - a| = r to an airfoil. Lift L = ρV∞Γ (Kutta-Joukowski theorem), Γ = 4πrV∞sin(α + arcsin(a/r)). Conformal mapping preserves Laplace's equation, so potential flow on the circle gives exact flow around the airfoil.