On the Theory of a Two-Dimensional Oscillating Wing

Abstract

To study the extraction of energy from wave and current, it seems necessary to construct the theory of an oscillating thin wing more consistently, because existing theories, especially formulas of work-done or thrust, have no neat form owing to the leading edge suction in comparison with the case of wave resistance. In this paper, the theory of an oscillating thin wing in an infinite stream are expanded on the basis of acceleration potential. At first, homogeneous solutions which are the ones for homogeneous boundary condition are introduced. Secondly, two reciprocity theorems corresponding to Hanaoka's theorems are introduced and they enable us to calculate the strength of trailing vortex, leading edge singularity etc. from the said homogeneous solution as the same way as we can for the lift and moment by Munk's theorem. The thrust formula are deduced from the momentum theorem, so that the leading edge suction is included implicitly, and it, also the damping formula, is represented by quadratic form of the above introduced integral of homogeneous solutions. Lastly, under these preparation, the optimum problem, that is, optimum oscillation to obtain maximum thrust and extraction of energy from a uniform flow are solved easily in the most general formulation.