Through the use of a combination of captive tests and some heuristic procedures, Sphaier, Fernandes, Pontes and Correa (1998, 1999, 2000) developed a quadratic model, that have been inherited from the ship maneuvering field, to account for the hydrodynamic lateral force and turn moment. The present paper incorporates some improvements to the model including a heuristic expression to determine the longitudinal force. It is derived from towing tests for different heading angles and takes into account the scale effects through the Reynolds number and the form effect, the viscous pressure resistance, through the Prohaska coefficient k. The process of determining the coefficients depends not only on the tests but also on the knowledge of the added masses. Results from the potential theory (WAMIT, 1995) and from experiments (Clarke, Gedling, and Hine, 1982) are used. Using the maneuvering model a dynamic stability analysis is carried out comparing the behavior of the ship and the model.
In the last forty years an extensive effort has been developed to define mathematical expressions to represent the forces and moments acting on ships traveling on the sea. Beginning with Abkowitz (1964) and Eda and Crane (1965) and followed by Norrbin (1970) and others the so-called maneuvering models for ships in normal speeds have been developed. Although a mathematical model has been used to establish the fundamentals of the theory, it is dependent on experimental tests. With the use of ships as stationary storage units some of these ideas have been imported and, in some case used directly. Using similar tests Wichers (1986), Molin and Bureau (1980), Obokata (1984) and others have developed different models based on the cross-flow model and also used on the maneuvering theory of ship.
