Chapter S-STABILITY AND BUOYANCY 



ANGLE OF 

 HEEL 



8.55 



Figure 3-11. — (A) Stable condition, G is below 

 M. (B) Unstable condition, G is above M. 



metacentric height is small, the righting arms 

 are also small. Such a ship rolls slowly and is 

 said to be tender . Some GM values for various 

 naval ships are: CLs, 3 to 5 feet; CAs, 4 to 6 

 feet; DDs, 3 to 4 feet; DEs, 3 to 5 feet; and AKs, 

 1 to 6 feet. 



Large GM and large righting arms are de- 

 sirable for resistance to the flooding effects of 



damage. However, a smaller GM is sometimes 

 desirable for the slow, easy roll which makes for 

 more accurate gunfire. Thus the GM value for 

 a naval ship is the result of compromise. 



STABILITY CURVES 



When a series of values for GZ at successive 

 angles of heel are plotted on a graph, the result 

 is a stability curve . The stability curve shown in 

 figure 3-12 is called a curve of static stability . 

 The word static indicates that it is not necessary 

 for the ship to be in motion for the curve to 

 apply; if the ship were momentarily stopped at 

 any angle during its roll, the value of GZ given 

 by the curve would still apply. ^ 



To understand the stability curve, it is neces- 

 sary to consider the following facts: 



1. The ship's center of gravity does not 

 change position as the angle of heel is changed. 



2. The ship's center of buoyancy is always 

 at the center of the ship's underwater hull. 



3. The shape of the ship's underwater hull 

 changes as the angle of heel changes. 



Putting these facts together, we see that the 

 position of G remains constant as the ship heels 

 through various angles, but the position of B 

 changes according to the angle of inclination. 

 Initial stability increases with increasing angle 

 of heel at an almost constant rate; but at large 

 angles the increase in GZ begins to level off and 

 gradually diminishes, becoming zero at very 

 large angles of heel. 



EFFECT OF DRAFT ON RIGHTING ARM 



A change in displacement will result in a 

 change of draft and freeboard; and B will shift 

 to the geometric center of the new underwater 

 body. At any angle of inclination, a change in 

 draft causes B to shift both horizontally and 

 vertically with respect to the waterline. The 

 horizontal shift in B changes the distance be- 

 tween B and G, and thereby changes the length 

 of the righting arm. GZ. Thus, when draft is 

 increased, the righting arms are reduced 

 throughout the entire range of stability. Figure 

 3-13 shows how the righting arm is reduced 



Design engineers usually use GM values as a measure 

 of stability up to about 7 heel. For angles beyond 7°, 

 a stability curve is used. 



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