CHAPTERS 



STABILITY AND BUOYANCY 



This chapter deals with the principles of 

 stability, stability curves, the inclining experi- 

 ment, effects of weight shifts and weight changes, 

 effects of loose water, longitudinal stability and 

 effects of trim, and causes of impaired stability. 

 The damage control aspects of stability are 

 discussed in chapter 4 of this text. 



PRINCIPLES OF STABILITY 



A floating body is acted upon by forces of 

 gravity and forces of buoyancy. The algebraic 

 sum of these forces must equal zero if equilib- 

 rium is to exist. 



Any object exists in one of three states of 

 stability: stable, neutral, or unstable. We may 

 illustrate these three states by placing three 

 cones on a table top, as shown in figure 3-1. 

 When cone A is tipped so that its base is off 

 the horizontal plane, it tends, up to a certain 

 angle of inclination, to assume its original 

 position again. Cone A is thus an example of a 

 stable body— that is, one which tries to attain 

 its original position through a specified range 

 of angles of inclination. 



Cone B is an example of neutral stability. 

 When rotated, this cone may come to rest at 

 any point, reaching equilibrium at some angle of 

 inclination. 



Cone C, balanced upon its apex, is an example 

 of an unstable body. Following any slight in- 

 clination by an external force, the body will 

 come to rest in a new position where it will 

 be more stable. 



From Archimedes' law, we know that an 

 object floating on or submerged in a fluid is 

 buoyed up by a force equal to the weight of the 

 fluid it displaces. The weight (displacement) 

 of a ship depends upon the weight of all parts, 

 equipment, stores, and personnel. This total 

 weight represents the effect of gravitational 

 force. When a ship is floated, she sinks into 



the water until the weight of the fluid displaced 

 by her underwater volume is equal to the weight 

 of the ship. At this point, the ship is in equilib- 

 rium—that is, the forces of gravity (G) and 

 the forces of buoyancy (B) are equal, and the 

 algebraic sum of all forces acting upon the ship 

 is equal to zero. This condition is shown in 

 part A of figure 3-2. If the underwater volume 

 of the ship is not sufficient to displace an 

 amount of fluid equal to the weight of the ship, 

 the ship will sink (part B of fig. 3-2) because 

 the forces of gravity are greater than the 

 forces of buoyancy. 



The depth to which a ship will sink when 

 floated in water depends upon the density of 

 the water, since the density affects the weight 

 per unit volume of a fluid. Thus we may expect 

 a ship to have a deeper draft in fresh water 

 than in salt water, since fresh water is less 

 dense (and therefore less buoyant) than salt 

 water. 



Although gravitational forces act everywhere 

 upon the ship, it is not necessary to attempt to 

 consider these forces separately. Instead, we 

 may regard the total force of gravity as a single 

 resultant or composite force which acts verti- 

 cally downward through the ship's center of 

 gravity (G). Similarly, the force of buoyancy 

 may be regarded as a single resultant force 

 which acts vertically upward through the center 

 of buoyancy (B) located at the geometric center 

 of the ship's underwater body. When a ship is 

 at rest in calm water, the center of gravity 

 and the center of buoyancy lie on the same 

 vertical line. 



DISPLACEMENT 



Since weight (W) is equal to the displacement, 

 it is possible to measure the volume of the under- 

 water body (V) in cubic feet and multiply this 

 volume by the weight of a cubic foot of sea 



34 



