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Stability in Smooth Water.

A BODY which is free to move, is said to be stable, if, when disturbed from its position of balance or steadiness, it tends to right itself, or return to that position. If, on the other hand, it tends to deviate further from that position, or upset, it is said to be unstable.

A ship is always stable as regards vertical disturbances, that is, rising above or dipping below her position of steady floating; for when she rises out of the water, her displacement is diminished, and there is an excess of the weight over the supporting pressure, tending to bring her down again; and when she dips deeper into the water, her displacement is increased, and there is an excess of the supporting pressure over the weight, tending to make her rise again.

The kind of disturbance of a ship's position which it is of primary importance to consider, is that which consists in heeling, or leaning over to one side. Similar disturbances in a longitudinal plane, known as pitching and scending, have also to be considered, although they are of less importance than heeling. All these are disturbances of angular position, and stability against them all depends on similar principles; so that it will be sufficient for the purposes of the present chapter to explain on what stability against heeling, or transverse stability, depends.

It has already been stated, that in order that a pair of forces applied to one body may balance each other, they must not only be equal in amount and opposite in direction, but directly opposed to each other-that is, they must act in opposite directions along the same straight line. When a pair of equal forces act in opposite directions along parallel, but not identical lines, they no longer balance each other, but constitute what is called a couple, tending to turn the body into a new angular position. When the angular position of such a body as a ship is disturbed, the weight and the supporting pressure, which originally were a pair of directly opposed equal forces, producing balance, become a couple;

and the body is stable or unstable, according as that couple is a righting couple, or an upsetting couple.

It may facilitate the understanding of this subject to give an illustration taken from the mechanics of solid bodies. Figs. 3 and 4 represent two blocks, each with a rounded base, resting on a level platform. Either of those blocks may be balanced on its rounded end, by so placing it that the upward pressure of the platform, exerted against the point of support, may act in a line passing through the centre of gravity of the block. If the block with the sharper curvature at the base, Fig. 3, is disturbed, the weight, W, acting through the centre of gravity, G, and the pressure exerted by the platform at the point of support, C, form an upsetting couple, which makes the block fall over on its side. If the block with the flatter base, Fig 4, is disturbed, the weight acting through G, and the pressure of the platform acting through C, form a righting couple, which makes the block return to its position of balance. The condition of a ship as regards stability is analogous to that of the latter block.

Fig. 5 represents an end view of a ship floating upright in

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smooth water, of which YY is the surface. G is the ship's centre of gravity; C the centre of buoyancy, in the same vertical line ZZ; W represents the weight of the ship, exactly balanced by the equal and opposite resultant pressure P. Fig. 6 represents the same ship, having heeled over through a certain angle towards the right. The weight of the ship, W, continues to act through the same centre of gravity, G, in the same vertical line, ZZ; but in consequence of the new form assumed by the immersed part of the ship, or displacement, the centre of buoyancy shifts into a new position, C'; and in a properly designed ship, that new position lies to the same side of the vertical line, ZZ, as that towards which the ship has heeled; so that the weight, W, and the resultant pressure, P, form a righting couple, tending to bring the ship back to the upright position. Had the new centre of buoyancy, through a faulty design, lain to the other side of ZZ, as at c, the weight and pressure would have formed an upsetting couple.

The moment of a couple is the name given to the magnitude of its tendency to turn the body on which it acts, and is computed by multiplying either of the two equal forces of which the couple consists, by the perpendicular distance between the parallel lines of action of the forces, which distance is called the arm or leverage of the couple. The moment of the righting couple which acts on a ship at some fixed angle of heel, is called her moment of stability at that inclination. For example, in Fig. 6, the moment of stability is the weight of the ship, W, multiplied by the horizontal distance of the new centre of buoyancy, C', from the vertical line, ZZ, traversing the ship's centre of gravity; that is-WX EC'. The moment of stability required for different sorts of vessels has been ascertained by practical experience. An account of the experiments for ascertaining the stability of a ship will be found in Chapter XV. For the present, it may be stated, by way of illustration, that a common value for the moment of stability in large vessels at an angle of heel of fifteen degrees, is the weight of the ship acting with a leverage of one foot. The power of a vessel to carry sail obviously depends mainly on her stability.


Steadiness in Rough Water.

ALTHOUGH a certain amount of stability in a ship is absolutely necessary, an excess of that quality becomes an evil, for the following reasons:

I. A ship of great stability is quick in her rolling motion ; and if the stability be excessive, the rolling may be so quick as to strain and damage her structure and contents.

II. The same form and proportions which make a ship very stable in smooth water, tend also to make her accompany the waves in their motions. This, to a certain extent, is necessary, but if it goes too far, causes inconvenience and danger.



III. It is dangerous for a ship in rolling to keep time with the because in that case each successive wave increases the extent of the ship's rolling; and the best way to avoid that danger is to take care that the ship shall roll more slowly than the The time of a ship's rolling is affected by the distribution of the weight of the ship and lading, as well as by the stability. To distinguish the tendency of a ship to keep upright to the surface of the water, whether level or sloping, from the tendency to keep truly upright in rough water, the former may be called stiffness, and the latter steadiness.

Easy Rolling is insured by avoiding excessive quickness of rolling, as already mentioned; and also by so designing the form of the ship's hull, that when she heels over, the pressure of the water shall tend to make her simply roll back again, and shall not tend at the same time to make her pitch, scend, or rise and fall bodily.


Speed and Resistance. The resistance opposed by the water to the progress of a ship depends on the speed with which the ship moves through the water, and on the figure and dimensions of the vessel, and the smoothness of her immersed surface. far as the resistance depends upon speed, it is well ascertained by experience that for a given vessel, and within the limits of speed to which that vessel is suited, the resistance is sensibly propor

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tional to the square of the speed, being fourfold for a double speed, ninefold for a triple speed, and so on; in other words, it is proportional to the height from which a body must fall to acquire the velocity of the vessel. When the speed of the vessel, however, is urged beyond certain limits depending on her dimensions and figure, the resistance begins to increase sensibly faster than the square of the speed; the reason being, that the wave or swell raised in front of the vessel begins to have a sensible effect in adding to the extent of surface acted upon by the resistance. Our knowledge of the manner in which the resistance is affected by the dimensions and figure of the vessel is still imperfect, although it has of late made much progress. During the last century attempts were made to deduce a theory of the resistance of ships from that of the impulse of jets of water against flat surfaces; but the results arrived at were so utterly inconsistent with those of practical experience that the theory has long ago been abandoned as useless; and indeed this was to have been expected, from the want of resemblance between the circumstances of the two cases compared together. Better success has attended the theory which considers the resistance as being analogous to that met with by a stream in flowing along a channel; that is to say, as depending on a certain degree of viscosity, or stiffness, in the water; and by means of that theory, marine engineers have of late years been enabled in various instances to compute beforehand the engine-power required to drive an intended vessel at a given speed with accuracy sufficient for practical purposes. The viscosity of the water acts in two ways; by producing a direct backward drag, exerted by the particles of water on the skin of the vessel, and by causing a heaping-up of water against the bow of the vessel as compared with the stern. Independently of any knowledge of the particular mode of action of the water in resisting the progress of a vessel, it is obvious, and must always have been obvious to common observation, that the vessel which makes the least commotion in the water is the least resisted. Thus it has been known from remote antiquity that the length of a ship should be greater than her breadth; and that fine ends, both at the bow and stern, causing the particles of water to be displaced and replaced gradually, are favorable to speed. It has been left for correct theoretical views to show conclusively, what had already been only partially and imperfectly known through practical experience, that there are limits beyond which great length

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