Review of the analytical prediction method of surf-riding threshold in following sea, and its relation to IMO Second-Generation Intact Stability Criteria

High-speed ship operations have a significant risk of the broaching phenomenon when navigating in following/quartering seas. The occurrence of this phenomenon can result in a violent yaw motion, regardless of the steering effort. Centrifugal forces due to the yaw motion could cause large roll motion and even capsizing in some cases. 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 Second-Generation Intact Stability criteria (SGISC) to estimate the surf-riding threshold is based on the authors' method, and in its derivation process, Melnikov's method. is utilized. This paper deals with nonlinear equations describing the surge motions of a ship. However, such equations cannot be directly solved; therefore, prior researchers and authors have proposed various approximate methods to predict the surf-riding threshold, including the methods based on Meknikov's method. In this paper, first, the authors describe the mechanism of the surfing phenomenon. Then, the authors explain in detail the derivation of the estimation methods for the surf-riding phenomenon that have been proposed by the prior researchers and the authors. Finally, the authors show the relationship between the theoretical prediction method of the surf-riding threshold based on Melnikov's method and the IMO SGISC.

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