A PROBLEM OF MINIMAL INDUCED RESISTANCE IN UNSTEADY MOTION

Energy considerations are used to find the spanwise circulatory lift d istribution yielding minimal induced resistance for a harmonically osc illating planar wing in a steady incompressible flow. Under the restri ction that the time-averaged and oscillatory constituents of the wing' s circulatory lift are known, the optimal distribution is such that it s time-averaged constituent is elliptical, but the oscillatory one is generally not. The latter varies from elliptical to rectangular as the frequency of the oscillations increases. When the oscillatory part of the lift is not prescribed, present results infer that its reduction - as, for example, by an elastic twist - will typically reduce the dra g, even if the twist yields a non-optimal (for that lift) lift distrib ution.