A Mathematical Model To Simulate Small Boat Behaviour
Browning, Andrew Wilford
The use of mathematical models and associated computer\ud simulation is a well established technique for\ud predicting the behaviour of large marine vessels. For a\ud variety of reasons, mainly related to effects of scale,\ud existing models are unable to adequately predict the\ud manoeuvring characteristics of smaller vessels. The\ud accuracy with which the performance of a boat under\ud autopilot control can be predicted leaves much to be\ud desired. The thesis provides a mathematical model to\ud simulate small boat behaviour and so can assist with the\ud design and testing of marine autopilots.\ud The boat model is presented in six degrees-of-freedom,\ud which, with suitable wave disturbance terms, allows\ud motions such as broaching to be analysed. Instabilities\ud in the performance of an autopilot arising from such sea\ud induced yaw motions can be assessed with a view to\ud improving the control algorithms and methodology.\ud The traditional "regressional" style models used for\ud large ships are not suitable for a small boat model\ud since there exist numerous small boat types and diverse\ud hull shapes. Instead, a modular approach has been\ud adopted where individual forces and moments are\ud categorised in separate sections of the model. This\ud approach is still in its infancy in the field of marine\ud simulation. The modular concept demands a clearer\ud understanding of the physical hydrodynamic processes\ud involved in the boat system, and the formulation of\ud equations which do not rely solely upon approximations\ud to, or multiple regression of, data from sea trials.\ud Although many hydrodynamic coefficients have been\ud introduced into the model, a multi-variable Taylor\ud series expansion of the states about some equilibrium\ud condition has been avoided, since this would infer an\ud approximation to have been made, and the higher order\ud terms rapidly become abstract in their nature and\ud difficult to relate to the real world.\ud The research rectifies the glaring omission of a small\ud boat mathematical model, the framework of which could be\ud expanded to encompass other marine vehicles. Additional\ud forces and moments can be appended to the model in new\ud modules, or existing modules modified to suit new\ud applications. Much more work, covering a greater range\ud and fidelity, is required in order to provide equations\ud which accurately describe the true physical situation.
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