Rolling of Ships

Pitching and Heaving.

The laws governing pitching are identical with those for rolling but there are important numerical differences, the principal of which are due to the fact that the longitudinal stability is very large and period consequently short and that the resistance is relatively great. To keep decks dry it is important that the ship should pitch with the wave instead of re maining level and thus shipping water. In a large number of ves sels the period for pitching is approximately one-half of that for rolling but the maximum angles are considerably less. An ex haustive series of experiments on mercantile ship models in waves has been carried out at the N.P.L., see Trans. I.N.A. 1922. Reference can be made to this paper for details.

When a ship is in still water her natural period of oscillation in a vertical direction known as dipping oscillation is given by the expression 27f I2 where W is the displacement in tons and T" the tons per inch immersion. When the ship is amongst waves these dipping oscillations may synchronize with the waves and set up considerable vertical oscillations known as heaving and defined as the aotual rise and fall produced in a seaway. Heaving motions are favourable to seaworthiness since waves are less likely to break on board.

Dipping oscillations are frequently caused by pitching or roll ing giving rise to uneasy motion. This action may be of im portance in ships whose sides near the waterline have a con siderable slope to the vertical since any rolling motion is then accompanied by vertical oscillations of the centre of gravity. Uneasy rolling of a peculiar character also results from inter ference between the rolling and pitching movements of a ship. This takes place when the centres of gravity of the wedges of immersion and emersion for moderate angles of heel are sepa rated by a considerable distance longitudinally.

A ship is propelled by the thrust on the propellers; and when the ship is in steady motion the thrust on the propellers must equal the resistance of the ship. It is convenient to consider first the resistance of the ship assuming the propeller to be removed and the ship to be towed at uniform speed through undisturbed water. The power thus expended in towing the ship is termed the effective horse power. This power is considerably less than the power exerted by the propelling machinery at the same speed; and the relation between the two—known as the propulsive co efficient—and the effect of the propellers on the resistance of the ship will be discussed below under Propulsion.

Resistance.

In an incompressible perfect fluid it can be shown that a body of "fair" form moving uniformly at a con siderable depth below the surface does not experience any resist ance to motion. For purposes of investigation it is convenient to impress upon the whole system a velocity equal and opposite to that of the body, which then becomes motionless in a uniform stream of the fluid. The motion is then termed steady. The particles of fluid move along paths termed "stream lines," and the surface formed by all the stream lines passing through a small closed contour is termed a "stream tube." The motion of the fluid in a stream tube is such that the flow along the tube is constant, and that Bernoulli's energy equation is satisfied. The other conditions affecting the flow and determining the forms of the stream lines are purely geometrical and depend on the form of the body. The motion in a perfect fluid flowing past bodies of a few simple mathematical forms can be investigated analytically but in the general case the forms of the stream lines can only be obtained by approximate methods.

Components of Resistance.

In actual practice the motion of a ship on the surface of the sea is subject to resistance through various causes. Frictional resistance results from the rubbing of the water past the surface of the hull and in the great majority of ships is responsible for a large proportion of the total resistance. Eddy resistances are caused by abrupt changes of shape and any local discontinuities such as shaft brackets. Resistance due to wind is experienced on the hull and upper works. Also, the stream line motion causes a diminution in the relative velocity of the water at the ends of the ship; this decrease of velocity is, in accordance with the energy equation, accompanied by an increase in pressure resulting in an elevation of the surface of the water at those places. Thus a wave is formed at the bow and stern, which requires an expenditure of energy for its maintenance and adds to the resistance. Eddying is caused by abrupt beginnings or endings, particularly the latter, in the water lines and under water fittings. The resistance from this cause is usually small except with full forms when it may become relatively large.