When a directionally stable ship deviates slightly from her course owing to some external disturbances she can return to a new state of equilibium without any steering.
But in this case the ship's new track is quite different from her original one. In order to keep her course, the helmsman has to use the rudder continuously. In this respect, it is of much importance to study the course-keeping quality of a ship in steered conditions.
The author has studied the motion of a ship when steered, on the assumption that the rudder angle is given directly proportional to the angle of yaw and the distance of deviation from the original track.
The following results have been obtained:-
(1) When the helmsman gives a rudder angle directly proportional to the angle of yaw, the ship's head may come back again onto her course, but in general it is impossible for her to reach her original track.
(2) When the helmsman gives a rudder angle directly proportional to the distance of deviation from the original track, the ship tends to come back onto her original track, but in this case an initial deviation or yaw increases with a sinuous course.
(3) When a rudder angle is given to follow the two modes of steering above mentioned, the ship may come back again onto her course and keep her original track.
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