Chapter 3-STABILITY AND BUOYANCY 



where 



RM = W X GZ 



24 FOOT WflTERLINE 

 20 FOOT WATERLINE 

 16 FOOT WATERLINE 



BASE LINE 



8.5 

 Figure 3-5. — Successive centers of buoyancy 

 (B) for different drafts. 



12 



8 9 10 II 12 13 14 15 16 



KB- FEET 



8.51 



Figure 3-6. — KB curve. 



righting moment, the magnitude of which is 

 equal to the magnitude of one of the forces (B 

 or G). times the perpendicular distance (GZ) 

 which separates the lines of action of the forces. 

 The distance GZ is known as the right ing arm 

 of the ship. Mathematically, 



RM = righting moment ( in foot-tons) 



W = displacement (in tons) 

 GZ = righting arm (in feet) 



For example, a ship which displaces 10,000 

 tons and has a 2-foot righting arm at a certain 

 angle of inclination has a righting moment of 

 10,000 tons times 2 feet, or ?0,000 foot-tons. 

 This 20,000 foot-tons represents the moment 

 which in this instance tends to return the ship 

 to an upright position. 



Figure 3-9 shows the development of an up- 

 setting moment resulting from the inclination 

 of an unstable ship. In this case, it is apparent 

 that the high location of G and the new location 

 of B contribute to the development of an up- 

 setting moment rather than a righting moment. 



THE METAC ENTER (M) 



A ship's metacenter is the intersection of 

 two successive lines of action of the force of 

 buoyancy as the ship heels through a very small 

 angle. Figure 3-10 shows two lines of buoyant 

 force. One of these represents the ship on an 

 even keel, the other is for a small angle of 

 heel. The point where they intersect is the 

 initial position of the metacenter. When the 

 angle of heel is greater than the angle used to 

 compute the metacenter, M moves off the cen- 

 terline and the path of movement is a curve. 

 However, it is the initial position of the met- 

 acenter that is most useful in the study of 

 stability. In the discussion which follows, the 



Figure 3-7. — Reserve buoyancy, 

 draft, and depth of hull. 



8.47 

 freeboard, 



37 



