Analysis of mathematical models of changing the vessel's course when turning - Kalinichenko, Yevgeniy; Burmaka, Igor (Eastern-European Journal of Enterprise Technologies, 2016)
Mathematical models of changing the course of a vessel when turning without taking into account the duration of putting the rudder blade over are presented. All in all, three models of different degree of adequacy to the actual turning process were explored, and the correspondence of mathematical models to the experimental field observations of specific vessels was revealed. Analytical expressions for calculating the duration of both phases of a turn by the method of simple iterations were obtained. An analysis of mathematical models under consideration was conducted for the purpose of identifying the model, most adequate to the actual process of the vessel’s turn. As a result of the imitation simulation of the vessel’s turn to 90°, whose inertial characteristics of turning ability were obtained from the field observations, it was established that when using mathematical model of the first type for the prediction of the curvilinear section, the trajectory error was 150¸200 m, for the second type of the model this value was 35¸40 m, and for the third type – 25¸30 m. The mathematical model of the vessel’s turning ability of the third type proved to be the most acceptable, since along with sufficient simplicity it possesses the required accuracy (maximum divergence of experimental and model trajectories is 25¸30 m. Results of the study can be used in navigation information systems for developing the function of calculation of parameters of the vessel’s turn for the assigned initial data.