Vertical Motions or a Ship Running in Following and Quartering Seas

Abstract

Heave and pitch motions of a ship model running in following and quartering seas with zero and very low encounter frequency were measured in a seakeeping and manoeuvring basin. Considering that 2D added mass tends to infinity at zero encounter frequency, new formulae to evaluate heave and pitch motions at zero encounter frequency were presented as a limit of a solution set of a strip theory. By comparison of the experiment and some theoretical predictions, it was concluded that, when the ship meets danger for capsizing in following and quartering seas, heave and pitch motions can be approximated by simply tracing their static equilibria. The prediction as the limit of the solution set of the strip theory at zero encounter frequency shows better agreements with the experimental values than the prediction based on the Froude-Krylov assumption. Further, up to the steepness 1/10 the heave and pitch motion with very low encounter frequency can be regarded as linear with respect of wave steepness.