Page 57 - statbility for masters and mates

Transverse statical stability 45
Fig. 6.2
below the metacentre, that is, the ship must have positive initial metacentric height. Figure 6.1(a) shows a ship in the upright position having a positive GM. Figure 6.1(b) shows the same ship inclined to a small angle. The position of G remains unaffected by the heel and the force of gravity is considered to act vertically downwards through this point. The centre of buoyancy moves out to the low side from B to B1 to take up the new centre of gravity of the underwater volume, and the force of buoyancy is considered to act vertically upwards through B1 and the metacentre M. If moments are taken about G there is a moment to return the ship to the upright. This moment is referred to as the Moment of Statical Stability and is equal to the product of the force 'W' and the length of the lever GZ. i.e.
Moment of Statical Stability W GZ tonnes-metres.
The lever GZ is referred to as the righting lever and is the perpendicular distance between the centre of gravity and the vertical through the centre of buoyancy.
At a small angle of heel (less than 15 ):
GZ GM sin y and Moment of Statical Stability W GM sin y