Modelling cyclic reverse movements of the vessel using modified Lammeren's curves of screw action
In our national practice, the screw action curves are traditionally used either for positive values of the screw speed n and the vessel's velocity v, or when one of these characteristics of the movement is negative. Consequently, the used curves of the screw action do not allow to create computer simulators for testing specific maneuvering tasks with reversible moves. The purpose of the work is to study the opportunities of mathematical modelling of the vessel's reverse movements, when the propeller advance of the fixed pitch screw is constantly changing. In foreign sources, really universal Lammeren's curves of screw action can be found. The specificity of these curves is that the introduction to them is performed not due to the pitch ratio itself, but due to the angle b of the direction incident to the propeller blade. This angle is determined by using tangent tg(b) = v /(0.7 π nD ), and it is sensitive to the change of sign of both the ship's velocity v and the revolution speed n. Therefore, these curves are presented as functions of the angle b in the range of angles 0°-360°. These curves are obtained and described by Lammeren as the results of processing experimental data concerning the thrust and the screw torque and are approximated by Fourier series, in which 20 terms are kept. These curves can be used as universal ones. This allows to integrate a system of two equations: the motion of the vessel and the rotation of the screw with arbitrary signs of these movements' direction by means of MathCad. By setting the law regulating the speed of the ship engine, it is possible to simulate arbitrary maneuvers of the vessel with any change of direction. The considered approach to modeling has been tested in the paper and implemented in the interface control for vessel maneuvering within the computer simulator.