Chapter 3-STABILITY AND BUOYANCY 



4 r 



CURVE B 

 CURVE A 

 CURVE C 

 CURVE D 



10 20 30 40 50 60 



ANGLE OF HEEL.IN DEGREES 



Figure 3-30.— Stability curve corrected for effects of added weight, 

 free surface, and free communication. 



8.64 



becomes greater, then the change is said to be 

 by the bow. Conversely, if the draft aft becomes 

 greater, the change of trim is by the stern . 



Changes of trim are produced by shifting 

 weights forward or aft or by adding or subtract- 

 ing weights forward of or abaft of the center of 

 flotation. 



LONGITUDINAL STABILITY 



Longitudinal stability is the tendency of a 

 ship to resist a change intrim. For small angles 

 of inclination, the longitudinal metacentric height 

 multiplied by the displacement is a measure of 

 initial longitudinal stability. The longitudinal 

 metacentric height is designated GM' and is 

 found from 



r= the moment of inertia of the ship's 

 waterline plane about an athwartship 

 axis through the center of flotation 



V = the ship's volume of displacement 



The value of BM' is very large— sometimes 

 more than a hundred times that of BM. The 

 values of BM' for various drafts may be found 

 from the curves of form (fig. 3-25). 



MOMENT TO CHANGE TRIM ONE INCH 



The measure of a ship's ability to resist a 

 change of trim is the moment required to pro- 

 duce a change of trim of a definite amount, such 

 as one inch. The value of the moment to change 

 trim one inch is obtained from 



GM'= KB +BM' - KG 



MTI = 



GM' X W 

 12 L 



where 



where 



KB and KG are the same as for transverse 

 stability BM' (the longitudinal metacentric 

 radius) is equal to 



BM'=- 



where 



GM'= longitudinal metacentric height (feet) 



W = displacement (tons) 



L = length between forward and after 

 perpendiculars (feet) 



57 



