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Moments of statical stability 127
deck edge is immersed, it may be found by using a formula known as the Wall-sided formula. i.e.
GZ GM 12 BMtan2y siny The derivation of this formula is as follows:
ytani
Fig. 14.4
Refer to the ship shown in Figure 14.4. When inclined the wedge WOW1 is transferred to LOL1 such that its centre of gravity shifts from g to g1. This causes the centre of buoyancy to shift from B to B1. The horizontal components of these shifts are hh1 and BB2 respectively, the vertical components being (gh g1h1) and B1B2 respectively.
Let BB2 be `a' units and let B1B2 be `b' units.
Now consider the wedge LOL1:
Area 12 y2tany
Consider an elementary strip longitudinally of length dx as in Figure
14.5(b).
Volume 12 y2tanydx
The total horizontal shift of the wedge (hh1), is 2=3 2y or 4=3 y.
;Momentofshiftingthiswedge 43 y 12 y2tanydx 23 y3tanydx