Chapter 3-ST ABILITY AND BUOYANCY 



147.30 

 Figure 3-1.— Three states of stability. 



WATERLINE 



B = G 



147.31 

 Figure 3-2. — Interaction of force of gravity 

 and force of buoyancy. 



water, in order to find what the ship weighs. 

 This relationship may be written as: 



(1) W= V X 



1 



35 



(2) V = 35W 



where 



V = volume of displaced sea water, in 

 cubic feet 



The volume of an underwater body for a given 

 draft line can be measured in the drafting room 

 by 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 are mea- 

 sured vertically and tons of displacement hori- 

 zontally. 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 

 3-4 for a cruiser. 



To use the curve shown in figure 3-4 for 

 finding the displacement when the draft is given, 

 locate the value of the mean draft on the draft 

 scale at left and proceed horizontally across 

 the diagram to the curve. Then drop vertically 

 downward and read the displacement from the 

 scale. For example, if the mean draft is ?4 feet, 

 the displacement found from the curve is ap- 

 proximately 14,700 tons. 



KB VERSUS DRAFT 



As the draft increases, the center of buoyancy 

 (B) rises with respect to the keel (K). Figure 

 3-5 shows how different drafts result in dif- 

 ferent values of KB, the height of the center of 

 buoyancy from the keel (K). A series of values 

 for KB is obtained and these values are plotted 

 on a curve to show KB versus draft. Figure 3-6 

 illustrates a typical KB curve. 



To read KB when the draft is known, start 

 at the proper value of draft on the scale at the 

 left and proceed horizontally to the curve. 

 Then drop vertically downward to the baseline 

 (KB). 



Thus, if a ship were floating at a mean draft 

 of 19 feet, the KB found from the chart would 

 be approximately 10.5 feet. 



W = weight, in tons 



35 = cubic feet of sea water per ton 

 (When dealing with ships, it is cus- 

 tomary to use the long ton of 2240 

 pounds.) 



It is also obvious, then, that displacement 

 will vary with draft. As the draft increases, 

 the displacement increases. This is indicated in 

 figure 3-3 by a series of displacements shown 

 for successive draft lines on the midship section 

 of a cruiser. 



8.45 



Figure 3-3.— Displacement data. 



35 



