On the application of slender body theory to antisymmetric motions

Abstract

The purpose of this paper is to present a new composite expansion of slender body theory, which is more suitable for antisymmetric motions than an ordinary composite expansion.A new composite solution is gained by retaining second order terms in far field solution and in matching of far field and near field solution. This solution has three dimensional correction terms due to antisymmetric flow field component, and an ordinary composite solution has no these three dimensional antisymmetric correction terms.When applying this method to lifting flow problems, order of lateral motion must be small, because slenderness assumption is also necessary for free vortex sheets.In the case of small lateral motion, simple approximate formulas are shown for lateral force distribution, sway force and yaw moment. These formulas are composed of usual slender body approximation formulas and new correction terms.As to non-lifting potential flow problems, even in the case that order of lateral motion is unity, this method can be applied effectively as well as the case that order of lateral motion is small.The effectiveness of this method is shown for a potential flow about a spheroid, by comparing results of analytical method, usual slender body theory and this method.