Peculiarities of Zigzag Behaviour in Linear Models of Ship Yaw Motion

Abstract

The present survey, as part of larger project, is devoted to properties of pure linear models of yaw motion for directionally stable ships, of the first-and second-order, sometimes referred to as the Nomoto models. In rather exhaustive way, it exactly compares and explains both models in that what is being lost in the zigzag behaviour, if the reduction to the simpler, first-order dynamics (K-T model) is attempted with the very famous [Nomoto et al., 1957] approximation: T = T1  The latter three time constants of the second-order model, more physically sound, are strictly dependent on the hydrodynamic coefficients of an essential part of the background full-mission manoeuvring model. The approximation of real ship behaviour in either of the mentioned linearity orders, and the corresponding complex parameters may facilitate designing and evaluating ship steering, and identifying some regions of advanced nonlinear models, where linearisation is valid. As a novel outcome of the conducted investigation, a huge inadequacy of such a first--order model for zigzag simulation is reported. If this procedure is used for determining steering quality indices, those would be of course inadequate, and the process of utilizing them (e.g. autopilot) inefficient.