Aerodynamic coefficients of a thin elliptic wing in unsteady motion

An analytic solution is presented for the linearized lifting surface problem of a thin wing with an elliptic planform in unsteady incompressible flow. The analysis is based on the expansion of the acceleration potential in an infinite series of ellipsoidal harmonics and extends the steady analysis, recently developed by the authors, to the unsteady flow regime. Explicit expressions are obtained for both the starting lift in the case of impulsive acceleration and for the lift due to constant acceleration. The exact solution thus obtained is valid for the whole range of aspect ratios. The analytic result for the starting lift may thus be regarded as a new generalization of the classical Wagner’s two-dimensional solution for planforms of finite aspect ratio.