Mathematical Modeling of Ship Speed-Loss Due to Wind and Seas

The design of an ocean-going vessel and the determination of routes and schedules for the operation of that vessel involves some prediction of the vessel's performance in a given wind and sea state. Theoretical studies and tests in tow-tanks have not been able to model the speed-loss suffered by a vessel in very rough seas. This is partly because a major component of speed-loss is the voluntary reduction in speed to reduce the violence of a ship's motions. A reasonable approach to the modeling problem is to develop a general expression for ship speed-loss incorporating factors for hull-type, propulsion, wave height and relative wind and wave direction. The value of each of the coefficients in the expression can then be determined by analyzing empirical data from actual cruises. A mathematical expression based on nearly 5000 data points from 11 cruises of the bulk cargo carrier Mei Qui Hai is able to match the empirical curves to within a fraction of a knot for sea states ranging from dead calm to wave heights of 9 meters.