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(i.) With the sides intact M is 25 ft. above keel, and G consequently 22 ft. above keel. In the bunkers five-eighths the space is occupied by the coal, and threeeighths the space is vacant. When the sides are riddled the vessel sinks slightly, and as the moment of inertia of the waterplane is reduced by the admission of water to the space in the bunkers unoccupied by the coal, from its original value of 6,300,000 to 5,540,000. This causes M to drop to 23.2 ft. from keel, and the resulting metacentric height is 1.2 ft. The vessel is therefore stable since M is above G.

(ii.) If now we trim the coal to the lower bunkers, we depress the C.G. (900 × 12) 12,000

= 0.9 ft., so that the GM is 3.9 ft., and G is 21·1 ft. above keel.

On riddling the sides we get a greater sinkage, but the chief effect is the reduction of the moment of inertia of the waterplane to 4,274,000, the area of the waterplane in the bunkers contributing nothing to the moment of inertia. This gives the point M 20-36 ft. above keel, or 0.74 ft. below the C.G. The vessel is thus unstable in the upright condition.

Methods of increasing the Metacentric Height of a Vessel.-1. If we put ballast, either pig-iron or water, into the lower part of the ship, there will be two effects, viz.

(a) Increase of draught, and

(b) Depression of the C.G. of the ship.

The increase of draught, if moderate, will not in general alter the position of the transverse metacentre very much; whether it does so or not will depend on the shape of the metacentric diagram. If w be the added weight, W the weight of the ship before the addition, and d the distance of the added weight below the C.G., then

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Thus the addition of the weight of 20 tons, 10 ft. below the C.G. of a vessel of 1000 tons displacement, will lower the C.G. of

the ship

20 × 10
1020

= 0.2 ft. In general the GM will increase by

this amount, but if the M locus in the metacentric diagram slopes down sharply as the draught increases the increase of GM may be rather less than thus obtained.

In adding water-ballast to the double bottom of a vessel it is essential that each compartment should be completely filled so that the water will act as a solid weight. If a free surface is left the water can shift over to the side to which the ship is heeling, and this tends to counteract the increased GM obtained by the water-ballast. The manholes to double bottoms are always made

with raised coamings, in order to ensure the compartments being completely filled (see Fig. 48). Air escapes are also provided.

There may be cases where it is undesirable to increase the draught of a ship by adding ballast, and yet it is necessary to obtain greater initial stability. In such cases the following method, or No. 3 below, would have to be adopted.

2. If top weight is taken out of a ship there will be two effects, viz. (1) decrease of draught, and (2) depression of the C.G. Thus a ship is of 5000 tons displacement. The effect of removing two military tops weighing 24 tons, originally 70 ft. above the C.G., would be to cause depression of the C.G. (24 × 70) =0·34 ft., and this will be generally the increase (5000- 24) of metacentric height, unless there is something exceptional about the metacentric diagram.

GIRDLING

3. The two previous methods were concerned with lowering the C.G., the present method deals with the metacentre. It will be remembered that the position of the metacentre is directly dependent on the moment of inertia of the waterplane. If we can increase this we raise the metacentre, and so increase the

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SECTION

W

FIG. 178.

PLAN OF
WATERPLANE

initial stability. This can be done by placing a girdling at the waterline, over the midship portion of the length, as Fig. 178. This adds very little to the draught, but considerably to the moment of inertia of the waterplane. This method of increasing the stiffness used to be frequently adopted in the wooden sailing-ships in order to enable them to "stand up" better.

An instance of its adoption in the Royal Navy was in the case of the Sultan. This ship had to undergo an extensive reconstruction, and it was found that the alterations would leave her with insufficient stability. The best way to increase the stability was found to be by adding a wooden girdling over the midship portion of the length, as the addition of any weight on board was undesirable.

Stability when partially Waterborne.—An application of the

principles of the present chapter, of interest and some importance, is seen in the reduction of stability which takes place when a vessel is partially waterborne. This happens when a vessel is being docked or undocked, and also if a vessel is run on to a shelving beach. In Fig. 179, suppose a ship is being docked, and the water level falls from W'L' to W"L". If we suppose a small inclination 0, the support of the displacement of the zone between W'L' and W"L", viz. w, which originally acted through b, the C.G. of the zone, now acts at the keel, and the buoyancy W - w acts in

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the line B1M1, where M1 is the metacentre corresponding to the waterline W"L".

The original moment righting the ship was W × GM × sin 0, but the moment now righting the ship is

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since the influence of w is to upset the ship.

It may be shown that the reduction of metacentric height thus

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In the case of a ship being docked, the critical point is reached when the keel is just taking the blocks all fore and aft, and the time until this happens is longer in the case of a ship trimming a great deal by the stern than in a ship on a more even keel. In such a ship, therefore, the support w may reach a considerable amount before the ship takes the blocks, after which the shores can be set up. Just before the shores are set up, there is, therefore, a reduction of stability which may be sufficient to render a

ship unstable. It is necessary, therefore, when docking and undocking to keep the ship well under control to prevent any transverse inclinations while any of the weight is taken by the blocks.

For ordinary ships the loss of metacentric height thus caused will not be sufficient to reduce the GM enough to cause instability, but it is possible in a ship having large trim and small metacentric height when being docked.

It is important to note in connection with the docking of ships that a ship with small GM should never be undocked, if, while in dry dock, any alteration of the weights on board is made which tends to reduce the metacentric height, unless other weights are added to compensate. For example, a merchant ship when light may require water-ballast to keep her upright. If docked in this condition the ballast must not be removed while in dock (unless compensation is made), or else it would be found that when the ship was again afloat she would be unstable.

CHAPTER XVIII.

TRIM, MOMENT TO CHANGE TRIM ONE INCH, ETC.

We have now to deal with inclinations in a fore-and-aft or longitudinal direction. As the stability of a ship is a minimum for transverse inclinations, so the stability is a maximum for longitudinal inclinations. We do not need, therefore, to study the

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longitudinal stability of a ship to ascertain whether she is safe or not, as we do the transverse stability, but in order to deal with. questions of trim or forward and after draughts.

If a ship, Fig. 180, is floating originally at a waterline WL,

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