Analytical formulae for predicting the surf-riding threshold for a ship in following seas |
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| Authors: | Atsuo Maki Naoya Umeda Martin Renilson Tetsushi Ueta |
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| Institution: | (1) Graduate School of Maritime Sciences, Kobe University, 5-1-1 Fukae-Minami, Higashinada, Kobe 658-0022, Japan;(2) Department of Naval Architecture and Ocean Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita Osaka, 565-0971, Japan;(3) Australian Maritime College, Maritime Way, Newnham, TAS, 7248, Australia;(4) Centre for Advanced Information Technology, Tokushima University, Minami-Josanjima, Tokushima 770-8506, Japan; |
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| Abstract: | Making use of Melnikov’s method, a generalized formula for predicting the surf-riding threshold is developed as an extension
to the applications of Kan and Spyrou. A new analytical formula for calculating the surf-riding threshold of a ship in following
seas is also proposed in light of nonlinear dynamical system theory. By applying a continuous piecewise linear approximation
to the wave-induced surge force, a heteroclinic bifurcation point is obtained analytically with an uncoupled surge equation.
Results calculated using these formulae are presented, and they show good agreement with those obtained utilizing numerical
bifurcation analysis. Further, it was confirmed that the surf-riding threshold obtained using the proposed formulae agrees
reasonably well with that obtained experimentally for an unconventional vessel. |
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