Thin-ship theory and influence of rake and flare

Abstract

The basic computational task of the thin-ship theory of free-surface potential flow about a ship that advances at constant speed along a straight path in calm water, of large depth and lateral extent, is considered. Specifically, a straightforward method for evaluating the pressure and the wave profile at a ship hull (the wave drag, hydrodynamic lift and pitch moment, and sinkage and trim are also considered) in accordance with Michell’s thin-ship theory is given. A main ingredient of this method is a simple analytical approximation to the local-flow component in the expression for the Green function (associated with the classical Michell–Kelvin linearized free-surface boundary condition) of thin-ship theory. This practical Green function is used to evaluate and analyze steady flow about a four-parameter family of ship bows with rake and flare. In particular, the variations of the bow-wave height and location with respect to the draft-based Froude number, the entrance angles at the top and bottom waterlines, and the rake angle are explored via a systematic parametric study. This parametric study provides estimates—immediately useful for design—of the influence of rake and flare on the height and the location of a ship bow wave, and shows that rake and flare effects can be significant, especially at low Froude numbers.