Asymmetric Surging of Ships in Following Seas and its Repercussions for Safety

Abstract

A comprehensive investigation of an asymmetric longitudinal motion of ships displayed in long and steep following waves is presented. The focus is on the strongly nonlinear response, on the verge of the so called surf-riding condition, where a ship could be performing large-amplitude longitudinal oscillations around a mean forward speed. Expressions, in closed form, describing transient surge motion on the phase-plane are derived. For steady-state in particular, is shown that it is possible to determine an explicit analytical solution in the time-domain. Simple prediction formulae for the higher limit of asymmetric surging (threshold of global surf-riding) are derived on the basis of two alternative methods. Also, we investigate the effect of asymmetric surging on a ship's tendency for capsize in the neighborhood of wave crests where restoring capability is often reduced. The paper includes, as an Appendix, a review of types of ship instability and a summary of the historical roots of the field.