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Ship manoeuvrability has been generally predicted based on 3-DOF mathematical model. However, medium-high speed ships such as containerships and passenger ferries make sometimes a large roll motion by the steering, which more or less affects on the ship manoeuvrability. Although a lot of researches have been done about the effect of roll motion, the mathematical models of hydrodynamic forces have been proposed individually putting the additional terms of roll angle into the conventional 3-DOF mathematical model. This makes the difficulty in the prediction of manoeuvrability. In this paper, the captive model tests have been performed with a container ship and a passenger ferry. In order to grasp the characteristics of the effect of roll angle on the conventional 3-DOF mathematical model, CMT(Circular Motion Test) have been carried out with setting a constant roll angles. And then, the effects of roll angle on the hydrodynamic derivatives have been extracted. From this analysis, the suitable 4-DOF mathematical model has been introduced by means of eliminating the less contributing terms of the roll effect. For the validation of the proposed mathematical model, free running model tests were carried out with several GM and ship's speed since the roll angle during a manoeuvring is affected by them. After comparing simulated results by the proposed 4-DOF mathematical model and the results of free running model test, it is found that the effect of GM and ship's speed on turning trajectories or the overshoot of Z-test can be well predicted by the proposed 4-DOF mathematical model.

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