A theoretical and numerical determination of optimal ship forms based on Michell's wave resistance

TL;DR

This paper combines theoretical analysis and numerical simulations to identify the optimal ship hull shape that minimizes total water resistance, including wave and viscous components, for a specified speed.

Contribution

It introduces a new method to determine the optimal hull shape considering both wave and viscous resistance, with proven existence, uniqueness, and smoothness of the solution.

Findings

Optimized hulls significantly reduce water resistance.

Theoretical proofs confirm the existence and uniqueness of the optimal shape.

Numerical results validate the effectiveness of the proposed approach.

Abstract

We determine the parametric hull of a given volume which minimizes the total water resistance for a given speed of the ship. The total resistance is the sum of Michell's wave resistance and of the viscous resistance, approximated by assuming a constant viscous drag coefficient. We prove that the optimized hull exists, is unique, symmetric, smooth and that it depends continuously on the speed. Numerical simulations show the efficiency of the approach, and complete the theoretical results.