On the Application of Slender Body Theory to Antisymmetric Motions

Abstract

In the previous report, a new composite solution in slender body theory was presented. The solution is more suitable than an ordinary solution of slender body theory for antisymmetric motions such as sway and yaw in ship manoeuvring motion.In this report, the method is extended to shallow water problems. The composite solution in shallow water is also composed of two dimensional potential at cross section and three dimensional correction terms like in deep water.As water depth increases, shallowness assumption that far field solution is approximated by horizontal plan flow does not hold good, and antisymmetric component of the solution converges to usual strip method.Consept of equivalent body is used in three dimensional correction terms. As water depth decrease, slenderness ratio of equivalent body increases. Then the restriction to small slenderness ratio becomes more strict than in deep water, but slenderness ratio of usual ship is within this limit.The practical effectiveness of this method is shown for acceleration coefficients of ships by comparing results of model tests, three dimensional calculations and this method.