On Lifting-Line Theory in Unsteady Aerodynamics.

This paper presents a linear theory of a high-aspect-ratio planar wing with a curved center line undergoing unsteady motion in an incompressible flow with a uniform freestream. Five distinct frequency ranges are identified. Except in the low-frequency range where the wave length is comparable to the wing span, matched inner and exterior solutions are obtained. The significance of the induced upwash due to sweep, and the usefulness of the center-line curvature in mitigating this upwash effect, are explained. The theory provides a basic framework wherein the lunate-tail problem in aquatic animal propulsion can be studied.