The Wave Resistance of a Thin Ship with a Rotational Wake

Abstract

An inviscid model for a ship with a viscous wake is developed. The wake is considered as a region of vorticity trailing behind the ship. The problem is systematically linearized by the use of a perturbation parameter representing the beam-to-length ratio. To first order it is found that the complete velocity potential is composed of two parts. The first is identical to the well-known solution for a thin ship without a wake. The second is the result of the specified vorticity distribution in the wake acting in the absence of the ship. The wake potential is determined for a semi-infinite, U-shaped vortex sheet. The wave resistance for a thin ship with a vortex sheet wake is analytically determined. The results clearly indicate the influence of the wake and its interactions with the ship. Numerical computations are presented for a mathematical form. They show that the wake-wave resistance is about 1 0 percent of the ship-wave resistance. The interaction term may be positive or negative depending on the wake attachment point. A comparison with experimental data is made. It is found that the present type of rotational wake model can account for the differences between Michell's integral and experiments for the mathematical form.