Hull form optimization of high-speed displacement ships under imposed design constraints

Reducing wave resistance is an important consideration in the design of high-speed displacement ships. The optimal sectional area curve for minimizing wave resistance has been studied theoretically, but the optimal waterline half-breadth curve at the design draft remains unresolved, and hull forms are often determined empirically. This study presents a rational method for determining the hull forms that minimize the wave resistance under imposed design constraints without prescribing either curve in advance. This is achieved by minimizing the sum of the wave and frictional resistance coefficients. The hull form is represented using a double trigonometric series, which enables systematic optimization by expressing the resistance coefficients as functions of the series coefficients. The optimization is conducted using the Lagrange multiplier method under the imposed constraints. Using this method, we optimized the Series 64 hull form, a high-speed displacement hull form researched by the US Navy. The optimization resulted in a hull form characterized by a U-shaped forebody and V-shaped afterbody. Model tests confirmed reductions in the total and residual resistance coefficients near the speed used for the optimization, demonstrating the effectiveness of the optimization in designing hull forms that reduce the resistance.