Page 138 - statbility for masters and mates

126 Ship Stability for Masters and Mates
GM KM KG 6:0 5:5 0:5 m Moment of statical stability W GM sin y
4000 0:5 sin 5 Moment of statical stability 174:4 tonnes m
Example 2
When a ship of 12 000 tonnes displacement is heeled 612 degrees the moment of statical stability is 600 tonnes m. Calculate the initial metacentric height.
Moment of statical stability W GM sin y
; GM Moment of statical stability W siny
600 12000sin61
2 GM 0.44 m
The moment of statical stability at a large angle
of heel
At a large angle of heel the force of buoyancy can no longer be considered to act vertically upwards through the initial metacentre (M). This is shown in Figure 14.3, where the ship is heeled to an angle of more than 15 degrees. The centre of buoyancy has moved further out to the low side, and the vertical through B1 no longer passes through (M), the initial metacentre. The righting lever (GZ) is once again the perpendicular distance between the vertical through G and the vertical through B1, and the moment of statical stability is equal to W GZ.
But GZ is no longer equal to GMsiny . Up to the angle at which the
Fig. 14.3