Mathematical modelling of the ship transfer from a turn of a given radius to a straight line

This paper describes a mathematical model of unsteady curvilinear motion of a vessel on a river bend. The main components of the model are dimensionless angular and linear velocities, drift angle at the vessel's centre of mass, heading, advance and transfer of the vessel's centre of mass and roll angle. The proposed mathematical model in combination with the control algorithm allows to obtain the following parameters: the rudder angle of the steady circulation (turn), the angle of manoeuvre commencement anticipation, the rudder angle to the side opposite to the turn, if necessary, the time of rudder delay and the angle of checking helm. These parameters are necessary for transferring the vessel from a curvilinear path of a given radius to a straight line. Before commencement of calculations using the proposed model and control algorithm, the parameters of the vessel motion on the steady circulation (turn) are calculated. These parameters include dimensionless angular and linear velocities, control shifting angle, drift angle, roll angle. The results obtained from the calculations can be incorporated into the control system of fully autonomous vessel, as well as into ship simulators.