PRINCIPLES OF NAVAL ENGINEERING 



m DIRECTION OF 



RIGHTING MOMENT 



8.52 



Figure 3-8. — Development of righting mo- 

 ment when a stable ship inclines. 



is exaggerated in the drawing), establishing a 

 metacenter at M. The ship's righting arm GZ 

 is one side of the triangle GZM. In this triangle 

 GZM, the angle of heel is at M. The side GM 

 is perpendicular to the waterline at even keel, 

 and ZM is perpendicular to the waterline when 

 the ship is inclined. 



It is evident that for any angle of heel not 

 greater than 7°, there will be a definite rela- 

 tionship between GM and GZ because GZ = GM 

 sin . Thus, GM acts as a measure of GZ, the 

 righting arm. 



GM is also an indication of whether the ship 

 is stable or unstable at small angles of inclina- 

 tion. If M is above G, the metacentric height 

 is positive, the moments which develop when 

 the ship is inclined are righting moments, and 

 the ship is stable (part A of fig. 3-11). But if 

 M is below G, the metacentric height is negative, 

 the moments which develop are upsetting mo- 

 ments, and the ship is unstable (part B of fig. 

 3-11). 



FORCE OF BUOYANCY 



DIRECTION OF 



UPSETTING 



MOMENT 



8.53 

 Figure 3-9.— Development of upsetting mo- 

 ment when unstable ship inclines. 



initial position is referred to as M. The distance 

 from the center of buoyancy (B) to the meta- 

 center (M) when the ship is on even keel is the 

 metacentric radius. 



METACENTRIC HEIGHT (GM) 



The distance from the center of gravity (G) 

 to the metacenter is known as the ship's met- 

 acentric height (GM). Figure 3-11 shows a 

 ship heeled through a small angle (the angle 



INFLUENCE OF METACENTRIC HEIGHT 



When the metacentric height of a ship is 

 large, the righting arms that develop at small 

 angles of heel are also large. Such a ship re- 

 sists roll and is said to be stiff. When the 



8.54 



Figure 3-10.— The metacenter. 



38 



