Dynamic Instability in Quartering Seas—Part II: Analysis of Ship Roll and Capsize for Broaching

Abstract

In earlier studies we have analyzed the phenomena which can generate loss of ship controllability in astern seas. In this paper we examine how the yaw instability associated with broaching can lead to roll instability and ship capsize. The dynamic effects responsible for capsize during the forced turn of broaching do not have their origin in the customary roll equation but are the result of interactions with other motions of the ship. Stability studies based solely on the roll equation are thus clearly inappropriate for this case where a multidimensional approach is deemed necessary. After presenting the theoretical background we set out a multi-degree method of global analysis which is based on transient maps. We apply this method to clarify how capsize occurs during the escape from surf-riding and also during transients from arbitrary initial condition of the ship. Our study establishes the connection between speed, heading, automatic control parameters and capsize. The proposed method can be useful in the context of a design methodology for minimizing the risk of ship capsize in astern seas.