CHAPTER XXI.

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 wake, 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 PX DG; 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 0, 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.

H.

FIG. 199.

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

FIG. 200.

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—

where d is the distance in feet between the C.G. of ship and

the centre of lateral resistance;

V is speed in knots on the circle;

R is radius of turning circle in feet;

GM is the metacentric height.

The above shows the qualities of a ship which affect the heeling when on the circle, viz.

(i.) It depends directly as the square of the speed;

(ii.) It depends inversely as the radius of the turning circle; and (iii.) It depends inversely as the metacentric height.

Thus a ship of high speed and small GM, turning in a small circle, might possibly heel to a considerable angle, sufficient to prevent the guns being laid horizontal on the inner side.

In the case of Yashima, a Japanese battle-ship, the outward heel at full speed was 840, at 10 knots only 2°. This ship had a very large rudder, and turned in a very small circle. On first putting the rudder over there was an inward heel, but when on the circle the inward heel, due to the pressure on the rudder, was overcome by the outward heel, due to the centrifugal force.

In destroyers, where the distance of the C.G. from the centre of lateral resistance is not great, the outward heeling tendency due to centrifugal force on the circle may be overcome by the inward heeling due to the rudder pressure. If the helm in such a ship were suddenly righted, the inward heeling tendency, due to the rudder, would be suddenly withdrawn, and the ship might give a dangerous lurch outwards. Under these circumstances the rudder should be righted gradually, so that as the rudder pressure is withdrawn the ship may come off the circular path. The above is one of the reasons for giving destroyers a relatively large metacentric height, in order to provide for their safety when manœuvring.

Pivoting Point and Drift Angle.-In a ship turning in a circular arc the centre line of the ship points inside the circle, so that the thrust of the propellers is delivered in a direction oblique to the motion of the ship. This, together with the drag of the rudder, is the reason of the reduction of speed always experienced when turning. If, at any instant, the ship is as shown in Fig. 201, GIGG being the path of the C.G. and O being the centre of the path, then GT being the tangent to the path at G, the angle PGT is the drift angle at the point G. At the point P, where OP is drawn perpendicular to the centre line of the ship, there is no 1 See a paper by Mr. Philip Watts, F.R.S. (I.N.A., 1898).

drift angle, as the tangent to the circle through P is the centre line of the ship.

The motion of any point in the ship is instantaneously in the direction of the tangent to the circle that point is turning in. At the point P this tangent is the centre line of the ship. At the point b, for instance, the motion in the direction be may be resolved into its components, bd in the direction of the keel, and be in an athwartship direction. All points abaft P therefore will, relative to P, move to port, and all points forward of P will move to starboard in Fig. 201. This is why, to an observer on board, the ship appears to be turning about the pivoting point P.

Path of Ship when turning.—When the rudder of a ship is

put over, the ship commences to turn in a spiral path, as Fig. 202. By the time she has gone through eight points the path is approximately circular. The distance from the position at which the helm is put over to the position when she is at right angles to her original course is termed the advance, and the distance from the original course to the position of the ship when she has turned through sixteen points is termed the tactical diameter. The path swept out by the stern will have a greater diameter than this. This must be allowed for when considering the room a ship can turn in.

The features of a ship which influence the turning are

1. Time of putting the helm over.

2. Angle of helm.

3. Size of rudder.

4. Moment of resistance of underwater body of ship to turning.

5. Moment of inertia of the vessel.

1. In modern ships with steam steering gear the time of putting the rudder hard over is a matter of seconds only. The shape of the rudder is of importance in this connection; a rudder that is balanced has the centre of pressure close to the axis, and offers a small resistance only to being put over. Such a rudder can be got over more quickly than one hinged on the fore side (see rudders in Figs. 71 to 76). The more quickly the rudder is put over the sooner its turning effect comes into operation. This is illustrated by the paths on turning of Orlando and Astrea (Fig. 202). Although the former ship has a smaller tactical diameter, yet it is longer in getting into the circle because of the fact that the rudder was not balanced. If there is a difference in the time of getting the rudder over a thigh speeds as compared with low speeds, the tactical diameter at the higher speeds will be greater than at the lower speeds. Usually, however, with steam steering gear, the path on turning is practically constant for all speeds.

2. The usual maximum angle of helm in ships of the Royal Navy is 35°. The tactical diameter will vary approximately inversely as the angle of helm, so that a vessel may be made to turn in a path greater than that with the maximum helm angle by using a smaller helm angle. Ships of different type may thus be made to move through similar arcs by determining the helm angles beforehand by experiment.

3. The size of the rudder has a direct influence on turning, because the pressure P depends directly on the rudder area. This area is expressed as a fraction of the area of the immersed middle line plane of the ship. For large ships in the Navy this ratio is from 4 to 6. Recent battle-ships and cruisers have a ratio of 45, about. The Yashima mentioned above has the ratio. In a typical destroyer the ratio was 35.

1

50'

4. The resistance the ship offers to turning depends on the shape of the underwater body and the position of the "pivoting point." This pivoting point is usually forward of amidships when going ahead; in some ships it is right up at the bow. The