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these are equal no further increment of rolling can take place.
3. A succession of waves of precisely the same period is a very unlikely occurrence.
It has often been noticed that ships with a great reputation for steadiness at sea occasionally roll heavily. This is doubtless caused by the fact that a succession of waves has been met with having a period approximately synchronizing with the double period of the ship.
In a ship thus rolling heavily a slight alteration of the course would be sufficient to destroy the synchronism, since what affects the ship is the apparent period of the waves, and if the ship's course be taken obliquely to the wave advance, the synchronism is at once destroyed.
The longer the period of a ship the less chance there is of meeting synchronizing waves. A series of waves of 16 seconds period is quite exceptional, so that the battle-ships of the British Navy having 16 seconds for their double period should be very steady, and this is borne out by actual experience. Atlantic storm waves have periods about 10 seconds, and it is only the smaller vessels of the Navy which have their double period as low as this; see above for periods of some typical ships.
Observations of Rolling.1—If a ship is rolling in still water, and a pendulum could be suspended at the centre of oscillation, then the point of suspension of such a pendulum would have no motion, and the pendulum would always remain vertical; the angles indicated would therefore give the angles of oscillation of the ship. If, however, the point of suspension is somewhere else, then as the ship rolls this point has motion and the pendulum does not give the true vertical. If one takes a fishing-rod, for instance, with a few feet of line, it is evident that, if the rod is swayed backwards and forwards, the line does not remain vertical. The same state of things obtains on board a ship; the pendulum does not hang vertically, and the angle it indicates will be in excess or defect of the true angle to which the ship rolls, unless it happens to be suspended at the centre of oscillation. If the point of suspension is above this centre the angle indicated will be in excess, if below, the angle will be in defect. (It is usually assumed that the centre of oscillation is near the C.G. of
1 In Sir W. H. White's "Manual of Naval Architecture" a whole chapter is devoted to this subject.
the ship.) In the above illustration of the fishing-rod, if the line is very long, the motion of the rod does not have any sensible effect on the line, so that for all practical purposes the line will remain vertical. This is the principle which has been effectively employed in instruments for measuring rolling, viz. that a pendulum of very long period is not appreciably affected by the motion of the ship, but will maintain itself practically vertical as the ship rolls.
When a ship is rolling at sea, an ordinary pendulum is still less likely to give correct angles, as in addition to rolling, the ship has a bodily movement among the waves.
Mr. Froude's apparatus for rolling records is most valuable when accurate observations are desired, as it shows automatically the rolling of the ship together with a time record. It is, however, too elaborate an instrument for ordinary use. It primarily depends on a heavy wheel, so weighted that its C.G. is very close to the axis of suspension (Tj,60^ in. below), giving a very long period for a single oscillation,1 viz. 34 seconds.
An instrument, Fig. 197, which is very simple and which has given admirable results has been devised by Mr. Mallock (I.N.A.,
1901). It gives a pendulum of very long period, but the instrument is of small dimensions. A paddle P is supported on delicate pivots and is enclosed in a box containing fluid. The paddle is made of the same density as the fluid, and in this way the friction on the pivots is very small (buoyancy practically equals the weight). Any rotary motion of the outside case is not communicated to the mass of the fluid, and in the interior of the box the fluid is practically at rest when the box is in motion. The paddle is adjusted so that its C.G. is just below the axis. When free it has a complete period of 4 seconds, but when enclosed in the box the complete period is between 30 and 40 seconds. The paddle therefore remains practically vertical, and the box being attached to the ship, the pointer I will show on the paddle the angle of roll.1 This rolling indicator is now issued to ships of the Royal Navy.
1 This is interesting as analogous to the case of a ship with great moment of inertia and small metacentric height, both of which conduce to a long period.
The method of observing angles of roll by the use of battens is very simple. It can, however, only be used when the horizon or some fixed object (as a star) is visible. The battens are arranged so that they can be rigged up on the fore bridge as Fig. 198.
There are two battens on which a scale of angles is painted, the zero corresponding to the horizontal when the ship is upright. A bracket is placed at the middle line (attached to the chart house, say) having a horizontal slit. The horizon or distant object can be sighted through this slit at the extremity of each roll, and the angle can be noted. The time of each roll should also be noted by another observer. Forms are issued to ships of the Royal Navy giving detailed instructions.
1 "Mr. Mullock's instrument is exceedingly simple, it is always in place, it may be put anywhere, it is always measuring the angle of heel and is ready to be observed. I have invariably heard it spoken of very highly by those who have used it."—Mr. Philip Watts, F.E.S. (I.N.A., 1901).
THE TURNING OF SHIPS.
When the rudder of a ship moving ahead is put over, a force is brought into existence causing the ship to (1) heel, (2) turn, (3) to slacken in speed, and (4) to have side movement or drift. The rudder, being placed obliquely to the middle line of the ship, causes the streams of water flowing aft to be deflected, and this causes a force to act upon the rudder, as P, Fig. 199. The value of this normal force depends upon the area of the rudder, the square of the speed of the water meeting the rudder, and the angle to which the rudder is placed. In a sailing-ship the speed of water meeting the rudder is rather less than the speed of the ship, because the friction of the ship's surface causes a layer of water to be dragged along in the direction of the ship's motion. The rudder of such a ship is thus not passing through still water but through water which has a forward motion. The steering of a sailing-ship depends on the motion of the ship, and such a ship loses her power of steering as she loses way. With a screw-steamer, although there is the same frictional ivake, yet the action of the propellers send a stream of water astern, and such a ship has steerage directly the engines are working, before she attains any motion at all. A ship with a very full stern is likely to steer badly, as the water does not get a clean flow past the rudder, which is necessary in order to get the normal pressure required. (See discussion of the steering of Agamemnon, United Service Institution, 1887-88.)
In Fig. 199, let P be the normal pressure acting on the rudder at C. At the C.G. of the ship, G, introduce two equal and opposite forces, P, in a line parallel to the line of action of P. Then we have acting on the ship—
(i.) A couple tending to turn the ship, as shown, of magnitude PxDG; and (ii.) A force, P, acting in the line EG.
This force, P, will have a transverse component, FG, P cos 0, tending to move the ship bodily to starboard, and a fore-and-aft component, EF, P sin 6, tending to stop the ship. The force causing side motion has small effect, since the resistance of the ship to this motion is very great. The fore-and-aft component has, however, a sensible effect in checking the speed when turning.
In a ship with a deadwood there is a side pressure due to the slackening of the stream lines on putting the rudder over. This side pressure on the deadwood has a considerable leverage to turn the ship (see Fig. 192, and note on action of bilge keels, p. 226.)
Heel caused by putting Rudder over.—On first putting a rudder over, the force P has a tendency to cause heeling inwards. This inward heeling is specially felt in vessels like destroyers, in which the rudder area is relatively large. In a full-sized ship, however, this inward heeling tendency is only of short duration, as when the ship gets on the circle the centrifugal force comes into action, and when, as is usually the case,
the C.G. of the ship is above the centre of pressure of the water on the outward side (centre of lateral resistance), there is a couple, as shown in Fig. 200, tending to heel the ship outwards. This heeling tendency is resisted by the stability of the ship, and it can be shown that the vessel will take up an angle of heel 0, given approximately by—