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FUNDAMENTALS OF BUOYANCY AND TRANSVERSE STABILITY

two basic properties of a ship are to be studied in detail. One of these properties is buoyancy. The other is stability. Buoyancy may be defined as the  ability of a ship to float. Stability is the ability of a ship to stay right-side-up. Separate treatments are to be given transverse and longitudinal stability. 
Why ships float.  Assume that an object of given volume is placed under water. If the weight of this object is greater than the weight of an equal volume of water, the object will sink. It sinks because the force which buoys it up is lessthan its own weight. However, if the weight of the object is less than the weight of an equal volume of water, the object will rise. It rises because the force which buoys it up is greater than its own weight, and it will continue rising until part of it is above the surface of the water. Here it floats at such a depth that the submerged part of the object displaces a volume of water whose weight is equal to the weight of the object. 
For example, the cube of steel in figure is solid, and measures 1 foot by 1 foot by 1 foot. If dropped in water the steel will sink. But hammer it out into a flat plate 8 feet by 8 feet, bend the edges up one foot all around, and the 6 by 6 by 1 box (fig. 3-1B) that you have formed will float. In fact, it will not only float but will, in calm water, carry an additional 1,800 pounds of weight. 
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It is obviously the submerged part of a floating ship which provides the buoyancy. If the ship is at rest the buoyancy, which is the weight of the displaced water, must be just equal to the weight of the ship. For this reason, the weight of a ship is generally referred to as her displacement.

Displacement. Since weight (W) is equal to displacement, it is possible to measure the volume of the underwater body (V) in cubic feet and multiply this volume by the weight of a cubic foot of sea water, in order to find what a ship weighs. This relationship may be written as:

V = 35W.
V = volume of displacement in cubic feet.
W = weight in tons.
35 = cubic feet of sea water per ton.

In dealing with ships it is customary to use the long ton of 2,240 pounds; in this text the word "ton" refers to the long ton exclusively.

Displacement varies with draft. As the draft increases, the displacement increases. This is indicated in figure 3-2 by the series of displacements shown for successive draft lines on the midship section of a cruiser. The volume of the underwater body for a given draft line can be measured in the drafting room, using graphic or mathematical means. This is done for a series of drafts throughout the probable range of displacements in which a ship is likely to operate. The values obtained are plotted on a grid, on which feet of draft is measured vertically, and tons displacement horizontally. A smooth line is faired through the points plotted, providing a curve of displacement versus draft, or a displacement curve, as it is generally called. The result is shown in figure 3-3 for a typical cruiser. It is one of the curves of form which are supplied to every Naval ship under the title displacement and other curves

To find the displacement when the draft is given, locate the value of mean draft on the draft scale at the left of figure 3-3. Then proceed horizontally across the diagram to the curve. From this point proceed vertically downward to the scale of tons, where the displacement can be read from the scale. For example, given a mean draft of 22 feet, the displacement found from the curve is approximately 13,400 tons. The curve also can be used in reverse. If given a displacement of 10,000 tons, the draft would be approximately 17.5 feet.

Reserve buoyancy. The volume of the watertight portion of the ship above the waterline is the ship's reserve buoyancyFreeboard is a rough measure of reserve buoyancy, being the distance in feet from the waterline to the weather deck edge. Unless otherwise stated references normally are to mean or midship freeboard. As shown in figure 3-4, freeboard plus draft always equals the depth of the hull in feet. 

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When weight is added to a ship, draft and displacement increase in the same amount that freeboard and reserve buoyancy decrease. A substantial amount of reserve buoyancy is, of course, essential to the seaworthiness of a ship. Some approximate values of reserve buoyancy in Naval ships of various types are given below:

BB (new)55% of displacement.
CV (large)130% of displacement.
CA, CL100% of displacement.
DD (2,100 ton)100% of displacement.
DD (1,630 ton)75% of displacement.
DEmore than 100% of displacement.

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