Analytical Prediction of Capsizing Probability of a Ship in Beam Wind and Waves

Abstract

This paper presents a set of formulae to evaluate capsizing probability of a ship in both beam wind and waves based on a piece-wise linear approximation of roll restoring moment with and without simplifications as an extension of the work by Belenky (1993). The new simplified formula is also proposed on the basis of sto-chastic properties of roll motion near the angle of vanishing stability. These formulae are applied to a car carrier having a large windage area. As a result, it was pointed out that Belenky's simplified method could overestimate capsizing probability if the apparent roll angle model is used. The capsizing probability in both wind and waves is definitely larger than that in waves on their own. It was remarked that steeper waves or narrower wave spectrum do not always provide larger capsizing probability.