# Simulation of Manoeuvring Motion in Regular Waves

## Background and Objectives

Simulating ship manoeuvres is typically carried out for calm water conditions. Sea waves may lead to a strong change of the hydrodynamic forces acting on the ship and thus effect the manoeuvring performance.

However, some difficulties are arising by combining manoeuvring theory and seakeeping theory. This is mainly due to the fact that hydrodynamic forces of different natures dominate. In seakeeping, the inertia forces dominate, while manoeuvring forces are dominated by viscosity-related effects.

For first estimations in the design stage of a ship or for the optimisation of the ship motion behaviour, a time efficient computation is necessary. For seakeeping purposes, this can be obtained by potential strip theory in frequency-domain. Simulations in time-domain give the opportunity to extend the motions to large amplitudes and to consider nonlinear forces. The consideration of the instantaneous floating condition, i.e. the instantaneous waterline, allows the investigation of the motions of hull forms with large changes in the hull form near the waterline, such as flared bows, overhanging sterns, etc.

## Computational Approach

A numerical program for time-domain calculations of the manoeuvring behaviour in regular waves is under development. The program is based on frequency-dependent

coefficients, transfered to time-domain by using the impulse response function. Memory effects are included by using the convolution integral. Nonlinear effects are accounted for by adjusting the mass, the damping, and the restoring data to the instantaneous floating condition. The equations of motion are solved in six degrees of freedom. The forces of the manoeuvring motion are calculated with the nonlinear slender-body theory. The resistance, propulsion and rudder forces follow from semi-empirical procedures. For the wave excitation, Froude-Krylov and diffraction forces are regarded. A validation of the described procedure is performed for manoeuvring in calm water (e.g. in Fig. 1) and straight-ahead motion in regular head waves (e.g. in Fig. 2).