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

PLAN OF
WATERPLANE

SECTION

W

FIG. 178.

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

the line BM1, where M1 is the metacentre corresponding to the waterline W"L".

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

since the influence of w is to upset the ship.

It may be shown that the reduction of metacentric height thus

caused is (ŵ × 0b)·

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

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,

and by some means is made to float at the waterline W'L', the centre of buoyancy must shift, owing to the changed shape of the displacement, from B to B' say. Then the original vertical through B and the new vertical through B' will intersect in the point M, which is the longitudinal metacentre. This point is precisely analogous to the transverse metacentre, the difference consisting in the direction of the inclination. The distance between the C.G. and the longitudinal metacentre is the longitudinal metacentric height.

The point M is determined with reference to the C.B., and the distance BM is given by the equation

where Io is the moment of inertia of the waterplane about a transverse axis through its centre of gravity (this C.G. is termed the centre of flotation), and V is the volume of displacement.

The calculation for Io is somewhat complicated, but it may be approximately written

Io = n'. L3. B (n' being a coefficient)

also Vk. L.B.D ( being the coefficient of fineness)

where L is the length of ship between perpendiculars in feet D is the mean draught in feet

b is a coefficient which does not vary much from 0.075.† This approximate formula shows the great influence of the length in determining the position of the longitudinal metacentre.

Longitudinal shift of Weights already on Board.-The trim of a ship is the difference between the forward and after draughts. Thus H.M.S. Pelorus is designed, under normal load conditions, to float at a draught of 12 ft. forward and 15 ft. aft, giving a trim of 3 ft. by the stern.

Change of trim is the sum of the changes of draught forward

* See the author's "Theoretical Naval Architecture."

In a vessel with full waterplane n' will be large, but k will also be large, the ship being of full form. If n' is small, k also will be small. So that the quotient