On the exact solution of the linearized lifting-surface problem of an elliptic wing

An analytic solution is presented for the lifting-surface problem of a thin circular or elliptic wing in steady incompressible potential flow. The analysis is based on expansion of the acceleration potential in an infinite series of ellipsoidal harmonics. Unlike previous analyses, which involve inversion of infinite sets of linear equations or the numerical solution of integral equations, the present method leads to rather simple explicit expressions for the lift and moment coefficients in terms of the aspect ratio. These expressions are valid in the whole range of aspect ratios from the two-dimensional airfoil through the circular wing to the slender wing.