Nonlinear Manoeuvring Models for Ships: A Lagrangian Approach

Abstract

his thesis analyses manoeuvring ships. Good modelling is vital for effective control system design and simulation. Such models are invaluable tools in areas such as training and decision support. This thesis prioritises physical reasoning in the ship model, and contributes with the following:

∙ A physically motivated ship model

∙ A new, compact derivation of the equations of motion with memory effect for ships

The first contribution is a model developed from longstanding analyses in low aspect-ratio aerodynamics. The hull of a ship is treated as an aircraft wing flipped onto its side. An advanced mathematical model structure is then derived. The model copes with the four degrees of freedom of most interest in manoeuvring: surge, sway, roll, and yaw. The effects of sway velocity and yaw rate arrive naturally from these analyses. The goal is to arrive at a model structure, and to enumerate this structure from experiment. That is, the structure is what is sought, and not methods for computing its parameters.

Using experimental data from planar motion mechanism tests, this model is verified and validated. It matches up very closely with what is observed in experiment. Furthermore, the model is compared to a pre-existing commercial model, and shows considerably greater accuracy. The model is additionally verified through full-scale tests on a modern trimaran design.

The Lagrangian formulation in this field dates back many decades. This thesis contains the derivation for the nonlinear equations of motion for a ship manoeuvring through waves. The equations arise from applying Kirchhoff's equations to a convolution integral formulation of the added mass.