Steady Lifting Surface Theory with a Free Surface

摘要

Steady lifting surface theory with a free surface is developed by an integral equation method. The local lift coefficient appears as a solution to an integral equation of the first kind whose kernel, deduced from a Havelock source potential, is expanded in a Fourier series with respect to the azimuth angle. The coefficients of this series are definite integrals. The method of steepest descents gives asymptotic approximations to coefficients of large index terms, and the remainder can be evaluated approximately in all cases. Numerical applications such as the calculation of the lift and drag for a lifting wing, and the hydrodynamic pressures arising from the turn of a ship are given.