The broaching of ships in following seas
The two aims of this work were: (1) to develop a theoretical technique for determining the conditions where a broach would occur, and (2) to identify the principal factors affecting the liability of a ship to broach. The first step was to develop a mathematical model based on the conventional manoeuvring equations with coefficients which were functions of the ship's longitudinal position in the wave, but independent of encounter frequency. Next, a theoretical method for calculating the values of some of the coefficients as functions of wave position was developed using a strip theory approach and the results compared with those obtained experimentally. The experimental technique involved using a planar motion mechanism to oscillate a constrained model balanced on a wave created by a wave dozer in a circulating water channel. Although the agreement was poor and experimental scatter high for some of the coefficients, the more important ones were predicted quite well using the theory. Constrained model experiments were also --carried out in calm water in order to determine the approximate value of the roll coupling terms and it was found that, since they were small, the roll equation could be ignored as a first approximation. It was then possible to study the stability of the lateral and longitudinal motions separately for various wavelengths and to determine that the principal factor causing a broach was the large wave induced yaw moment combined with the small restoring moment available from the rudder operating with reduced effectiveness. The lateral and longitudinal equations were then combined using a digital/analogue hybrid simulation permitting the conditions which caused a broach to be determined. When the results from the simulation-were compared with results which had already been carried out by the Admiralty Marine Technology Establishment at Haslar there was fairly good agreement, implying that this method could be used to determine whether a proposed design would meet an acceptable standard. Finally, possible improvements to the simulation were suggested and guidelines for reducing the liability to broach were given both for the operator and the designer.