Deriving the Kutta-Joukowsky Equation and Some of Its Generalizations Using Momentum Balances

Abstract

Momentum balances are used to derive the Kutta-Joukowsky equation for an infinite cascade of aerofoils and an isolated aerofoil. These derivations are simpler than those based on the Blasius theorem or more complex unsteady control volumes, and show the close relationship between a single aerofoil and an infinite cascade. The modification of lift due to the presence of another lifting body is similarly derived for a wing in ground effect, a biplane, and tandem aerofoils. The results are identical to those derived from the vector form of the Kutta-Joukowsky equation.