Ship Forms of Minimum Wave Resistance with Bulbs

Abstract

A ship form of minimum wave resistance with bulbs is obtained by an application of the minimum wave resistance theory to the ship form with bulbs. The ship is assumed to be wall-sided except the vicinity of both ends and represented by a combination of doublet distribution on the center plane and point singularities such as doublet, source and sink at fore and aft ends.
The optimum density of doublet distribution and the optimum intensity of point singularities at both ends are determined by means of calculus of variations. The solution corresponds to the optimum sectional area curve and the optimum size of bulbs at both ends.
The numerical study indicates that the optimum ship form with bulbs has considerably less wave resistance than the optimum ship form without bulbs. This theoretical prediction is verified by experiments.