On the Transverse Inclination of a Ship when the Helm is put over, or in a Similar Case

Abstract

A ship is inclined inwardly toward the centre of a turning circle soon after the rudder is put over, and when she becomes to turn steadily, she inclines in the opposite side. In this paper, the inclinations of those two kinds are considered.The first inward heel is important for the safety of a ship when helmed over abruptly, and consequently for the determination of the time required to put the helm hard over, which is necessary to determine the capacity of the steering gear. Treating dynamically the motion of a ship helmed over, the expression for the maximum inward inclination is obtained as follows:θmax=θ0{1+Ts/πt0|sinπ/Tst0|}where θ0: static l heel angle due to the heeling moment caused by the transverse force on the rudder plate put hard over.Ts: natural period of the ship.T0: the time required to put the helm hard over.A similar motion of a ship occu s in an inclining experiment, and the conditions in order to avoid the free rolling, usually accompanied, are discussed. Additionally, the motion of a pendulum on board used in that experiment is investigated.Lastly, for the outward heeling angle in the stendy turning, the breadth of the ship must be considered, though neglected usually, and the new expression for it is got as follows:tanθ_??_tanθ1/1-b/dtanθ1where θ: the required angle of heel.θ1: the angle of heel which is usually taken, neglecting the effect of breadth.b and d: half breadth and draft of a ship respectively.Studying the effect of a bilge keel on the heeling quality experimentally, it is found that the bilge keel is very injurious to that quality in a turning condition.