A Study on Mathematical Model for Manoeuvring Motions at Low Speed

Abstract

In recent years, demands for computer prediction of harbour manoeuvring motions are increasing to evaluate ship handling safety under harbour environment. To carry out the task more efficiently, better mathematical model of harbour manoeuvring is necessary. In the present paper, two types of mathematical models were examined for low speed manoeuvring motions, including stopping, backing and large lateral drifting. The first simplified mathematical model dea1s with hydrodynamic characteristics of ships in such low speed conditions, following a conventional procedure. In the second advanced mathematical model, on the other hand, equations of motions for stopping and backing conditions were formulated taking the more detailed hydrodynamic characteristics into account, for example, hull-propeller interaction due to propeller reversing and drag to drifting in low speed condition. Using these two mathematical models, computer simulations were carried out and the results were compared with experimental ones. The obtained results are summarized as follows: (1) For estimation of stopping time only, simplified mathematical model will work fairly well with the effect of reversed propeller thrust. (2) For estimation of yaw and lateral deviations in stopping motions, hull-propeller interaction term due to reversed propeller rotation and drag to drifting in very low speed condition have significant effects. Taking them into consideration, the second mathematical model is found useful for computer simulation of harbour manoeuvring motions of ships.