Mathematical modelling of a small waterplane area twin hulled (SWATH) vessel

Presents and investigates mathematical models of SWATH vessels built on physical laws under strip theory. Strip theory represents the three-dimensional underwater hull form by a series of two-dimensional slices or strips. Each strip has associated local hydrodynamic properties such as added mass, damping and stiffness which contribute to the coefficients for the complete hull in the equations of motion. Similarly the wave excitations experienced by the hull are composed of contributions from all the strips. Strip theory assumes that these local hydrodynamic properties are the same as would be experienced if the strip were part of so infinitely long cylinder of the same cross-sectional shape. In other words three-dimensional effects, such as mutual interference between the strips, flow leakage around the ends of the vessel and effects due to changes in the shape of the strip over a small length are ignored. The paper shows how several state space models are derived using strip theory to obtain hydrodynamic coefficients and then validated under simulation. These models are evaluated under worst case conditions, i.e. at encounter frequencies which induce maximum excitations. This paper also shows how the model uncertainty can be defined for variations from these maximum excitation frequencies. Model uncertainty highlights the need for robust control, since in reality all frequencies are present. The models obtained provide a firm foundation to proceed to controller simulation for validation of robustness. This means it is possible to design a controller for a model at one frequency and test the same controller on the same model but at a different frequency.