Chapter 3-STABILITY AND BUOYANCY 



To understand what is meant by a virtual 

 rise in G, refer to figure 3-28. This figure 

 shows a compartment in a ship partially filled 

 with water, which has a free surface, fs, with 

 the ship upright. When the ship heels to any 

 small angle, such as e, the free surface shifts 

 to fisi, remaining parallel to the waterline. 

 The result of the inclination is the movement 

 of a wedge of water from fofi to sqsi. Calling 

 %\ the center of gravity of this wedge when 

 the ship was upright, and g2 its center of 

 gravity with the ship inclined, it is evident 

 that a small weight has been moved from 



gl to g2. 



Point G is the center of gravity of the ship 

 when upright, and G would remain at this posi- 



tion if the compartment contained solids rather 

 than a liquid. As the ship heels, however, 

 the shift of a wedge of water along the path 

 g]^g2 causes the center of gravity of the ship 

 to shift from G to G2. This reduces the righting 

 arm, at this angle, from GZ to G2Z2. 



To compute GG2 and the loss of GZ for 

 each angle of heel is a laborious and com- 

 plicated task. However, an equivalent righting 

 arm, G3Z3 (which equals G2Z2), can be ob- 

 tained by extending the line of action of the 

 force of gravity up to intersect the ship's 

 centerline at point G3. Raising the ship's 

 center of gravity from G to G3 would have 

 the same effect on stability at this angle as 

 shifting it from G to G2. 



u. 



H 



O 

 C 



z 



£ 



MINUS (D EQUALS © 

 (3) MINUS © EQUALS (S) 



UNCORRECTED GZS 

 FROM CROSS CURVES'' 



/ 



/ 



/ 



^ © SINE CURVE 



CORRECTED FOR 

 ACTUAL KG, 



10 



20 30 40 50 



ANGLE OF HEEL IN DEGREES 



60 



147.42 



Figure 3-26.— Curve of righting arms corrected for weight addition. 



53 



