University of Tasmania

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Analytical formulae for predicting the surf-riding threshold for a ship in following seas

journal contribution
posted on 2023-05-17, 04:27 authored by Maki, A, Umeda, N, Martin RenilsonMartin Renilson, Ueta, T
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.


Publication title

Journal of Marine Science and Technology








Australian Maritime College


Springer-Verlag Tokyo

Place of publication

3-3-13, Hongo, Bunkyo-Ku, Tokyo, Japan, 113-0033

Rights statement

The final publication is available at

Repository Status

  • Restricted

Socio-economic Objectives

Water transport not elsewhere classified