Mathematical Model of the Manoeuvring Motion of a Ship

There are many kinds of mathematical models that have been proposed to simulate the ship manoeuvring characteristics. The total force model or the simple rudder to yaw response model are useful to do real-time simulation and control. However, each of these models has some limitations. The total force model combined the hull, propeller and rudder forces together. Therefore, if the propeller or rudder is changed in the model, the whole force model needs to be modified. Moreover, the hydrodynamic derivatives for the force terms have less physical meaning to compare. On the other hand, using the rudder to yaw response model, the change in ship velocity or speed drop during manoeuvring cannot be predicted. Considering these facts, this paper describes a widely used mathematical model known as the manoeuvring mathematical group (MMG) or modular model. This model considers not only the hull, rudder and propeller forces separately but also the interactions among them. Each term used in this model has a physical meaning and is constructed as simple as possible. The given model is also verified by the turning tests and speed tests results.