On Optimum Propulsion by Means of Small Periodic Motions of a Rigid Profile. I. Properties of Optimum Motions

The problem of optimum thrust generation by means of a rigid profile performing small arbitrarily periodic motions in an inviscid incompressible fluid is studied. The motions considered have to generate a prescribed mean value of thrust and must be such that the contribution to this mean thrust by the suction at the leading edge does not exceed a certain given value. Furthermore, the motions are in general subjected to a maximum type constraint on their amplitude. For this infinite dimensional, nonconvex and nonsmooth optimization problem, a generalized Lagrange multiplier rule is derived. In case the constraint on the amplitude is omitted, the optimum motions are calculated analytically; for the general case a number of properties of the solutions are derived from the Lagrange multiplier rule.