Review of the analytical prediction method of surf-riding threshold in following sea, and its relation to IMO second-generation intact stability criteria

In high-speed maritime operations, the broaching phenomenon can pose a significant risk when navigating in following/quartering seas. The occurrence of this phenomenon can result in a violent yaw motion, regardless of the steering effort, which, in turn, cause the resulting centrifugal force to capsize a vessel. A necessary condition for the occurrence of broaching is the surf-riding phenomenon. Therefore, the International Maritime Organization (IMO) has set up criteria to include theoretical formulas for estimating the occurrence of surf-riding phenomena. The theoretical equation used in the IMO's second-generation intact stability criteria (SGISC) to estimate the surf-riding threshold is based on Melnikov's method. This paper presents nonlinear equations describing the forward and backward motions of a ship. However, such equations cannot be directly solved; therefore, we proposed the use of and explain various approximate solution methods, including Meknikov's method. Subsequently, the relationship between the theoretical prediction method of the surf-riding threshold rooted in Melnikov's method and the IMO's SGISC is determined.