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"Duncan."-405 ft. x 75 ft. x 261 ft. x 14,000 tons; 18,000 I.H.P.,

knots.

Coefficient of fineness =

14,000 × 35

405 x 75.5 x 26.5

= 0.6.

19

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14,100 × 35 Coefficient of fineness 500 x 71 x 26

=

= 0.53.

The following are average values of this coefficient of fineness, viz.—

Battle-ships 06 to 0.65

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As illustrating the importance of the fineness of a ship in connection with the attainment of speed, reference may be made

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to the Formidable and
Duncan. In the former
ship a coefficient of fine-
ness of 0.65 was adopted,
15,000 I.H.P. being in-
tended to realize 18 knots.
In the latter ship, in order
to attain 19 knots without
an excessive expenditure
of I.H.P., a finer form

had to be adopted with a coefficient of fineness of 06.

Difference of Draught of Water when Floating in Salt Water and River Water.-(Salt water 64 lbs., river water 63 lbs. to the cubic foot.) The weight of the ship going from the one to the other remains the same = W tons = W x 2240 lbs.

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=

If T be the tons per inch in salt water and t the difference of draught in inches, the weight of the layer Txt x 2240 lbs., Txt x 2240 64

and the volume of the layer

=

cubic ft.

We have thus found the volume of the layer in two ways, and we can then equate, viz.—

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Thus for a battle-ship 57-2 tons per inch, 15,000 tons displace

15,000

ment, the difference of draught

=

63 × 57.2

= 4 in.

If for W and T we put approximate values, we have

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We can therefore say, roughly speaking, that the difference of draught in inches is one-seventh the draught in feet.

In the general case of a ship passing from water of density d' to water of density d (d' being greater than d), the difference of W

draught is T

d'-d
d

Reserve of Buoyancy and Freeboard.-We have seen that buoyancy is the upward support given by the water to the ship, and this upward force exactly equals the weight of the ship.

Freeboard is the height of the upper deck at side (to top of deck plank if fitted) from the water surface. Reserve of buoyancy is the volume of the ship above the waterplane which can be made watertight. In many ships this will be to the upper deck, but in some ships there are erections, as poop and forecastle, which can be made watertight. The sum of the buoyancy and the

N

reserve of buoyancy is the total floating power of the vessel. Reserve of buoyancy is expressed as a percentage of the buoyancy, and this varies considerably in different types of ship, e.g. in the Devastation, a low freeboard ship, this percentage was about 50 per cent. For modern battle-ships with good freeboard it amounts to about 90 per cent., and for cruisers and destroyers higher values than this are usual.

In merchant vessels sufficient reserve of buoyancy is obtained by specifying the minimum freeboard, this being obtained from tables drawn up by the Board of Trade. All British war-ships have freeboard and reserve of buoyancy considerably in excess of what the Board of Trade would require for merchant vessels of corresponding dimensions. Ships like the torpedo gunboats appear to disadvantage in comparison with merchant vessels of similar size, because of the absence of bulwarks which extend several feet above the upper deck of the latter ships. The presence of the bulwarks, although affording protection from the sea, does not, of course, increase the reserve of buoyancy. Indeed, bulwarks are likely to become a source of danger, if provision is not made for a sufficient number of large clearing ports for the purpose of speedily clearing the deck of water.

The reserve of buoyancy possessed by a ship is important, because this has to be drawn upon if a ship is damaged, and a ship with small reserve could only stand a small amount of damage before being entirely submerged. Freeboard and reserve of buoyancy are also important, however, because of the necessity of providing sufficient stability at large angles of inclination. This will be dealt with in a later chapter.

Sinkage caused by a Central Compartment being open to the Sea. The principles involved will be well illustrated if we take a box-shaped vessel. Such a vessel 100 ft. long, 20 ft. broad, 20 ft. deep floats at a draught of 10 ft. What will be the draught if a central compartment, 20 ft. long, is laid open to the sea (Fig. 159).

The weight of the vessel is the same before and after the bilging, but the buoyancy has been diminished, and the vessel is in a similar condition to one having the watertight side and bottom between the bulkheads replaced by a lattice-work. In consequence of the loss of buoyancy the vessel must draw on the reserve of buoyancy by sinking down to the waterline W'L' to the draught d feet, say

Original volume of displacement = 100 x 20 x 10,

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and seeing that the weight of ship is the same, these two volumes must be the same, so that d = 12.5 ft.

It is important to note that if a compartment is filled with coals, stores, etc., the space thus occupied cannot be taken up by the water, and thus the lost buoyancy is much less. For instance, in the above vessel, if the central compartment were filled with coal from the ends, the vessel floating at the same draught of 10 ft. before bilging, the sinking after bilging would only be 9 in.

If the watertightness of either of the bulkheads in the former example ceased below a height of 12 ft. 6 in., the water would

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not be confined to the central compartment, and the vessel would sink. This illustrates the importance of carrying watertight bulkheads well above the waterline. This is always done with the principal bulkheads in vessels of the Royal Navy (see Figs. 52 and 54).

Watertight flats are important because they serve to confine the results of any damage which may occur. Thus, in the first of the above examples, if a watertight flat were worked 5 ft. from the keel between the bulkheads, if bilging took place

(i.) Below the flat, a sinkage of 1 ft. would result;
(ii.) Above the flat, a sinkage of 14 ft. would result.

The greater sinkage in the latter case is due to the fact that the waterplane area is reduced as well as the buoyancy.

CHAPTER XVII.

INITIAL STABILITY, METACENTRIC HEIGHT, ETC.

Centre of Gravity.-The weight of a body is the sum or resultant of the weights of all the particles composing it, and this resultant

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acts through a definite point however the body is placed. This point is termed the centre of gravity (C.G.), and the body being at rest, we can regard the whole weight as being concentrated at the centre of gravity.

If two weights each of 5 lbs. are placed, as in Fig. 160, 24 in. apart, the C.G. of the system must be midway between them at G, and if the weights were held by a string, it would be immaterial, so far as the

string was concerned, whether the weights are as shown, or the whole 10 lbs. concentrated at G. Again, if the weights are 10 and 5 lbs. respectively, 24 in. apart, we should need to support at the point G, 8 in. from the larger weight, i.e. at the centre of gravity.

The centre of gravity of a ship is the point at which we may regard the whole of the weight to be concentrated.

Centre of Buoyancy. The resultant of the upward buoyancy must have its line of action through the centre of gravity of the displacement. When the water filled the space, before the ship was there, the weight of the water acted through this point, and so the support of the surrounding water, or, as we term it, the buoyancy, must also act through the same point. This point is termed the centre of buoyancy, being the C.G. of the displacement.

The position of the centre of buoyancy (C.B.), relative to the

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