Mathematical Model for the Manoeuvring Ship Motion in Shallow Water : 2nd Report : Mathematical Model at Slow Forward Speed

Abstract

When a ship proceeds to a berth, a captain or a pilot lets the output of main engine reduce or reverse, and brakes the ship's speed. Then, he adjusts the power of side thrusters or tugs. At a ship-design stage, it is very important to evaluate the manoeuvrability in such shallow water and slow forward speed. In the previous report, the prediction of the manoeuvring ship motion with an adequate main-engine power and forward speed has been presented both in deep and shallow water, using MMG's type mathematical model. However, the behaviour of ship as well as the hydrodynamic forces at the slow forward speed are so much complicated that the conventional MMG's mathematical model can not be applied, because sway and yaw motions sometimes become larger than forward speed by the use of side thrusters or tugs. In this report, steady damping forces and moment acting on hull are mainly investigated, conducting a extreamly large side-slipping and turning CMT. Then the new mathematical model eq. (2) is proposed to describe the ship motion in such slow steaming conditions, by means of simplifying a cross-flow model. From the comparison between simulated ship motion and observed one, it is found that the presented mathematical model can be fairly applied to the prediction of the complicated harbour manoeuvres and also single point mooring systems.