Page 205 - statbility for masters and mates

or
GG1 GGv y V r2
GGv v gg1 r1 V y r2
Calculating the effect of free surface of liquids (FSE) 193
Fig. 20.1(a)
Had there been no free surface when the ship inclined, the righting lever would have been GZ. But, due to the liquid shifting, the righting lever is reduced to G1Z1 or GvZv. The virtual reduction of GM is therefore GGv.
For a small angle of heel:
; GGv y v gg1 r1
From the proof of BM I/V, I y v gg1
Let i the second moment of the free surface about the centre line.
Then
GGv i r1 V r2
This is the formula to ®nd the virtual loss of GM due to the free surface effect in an undivided tank.
Now assume that the tank is subdivided longitudinally into `n' compart- ments of equal width as shown in Figure 20.1(b).
Let
l length of the tank, and b breadth of the tank.
The breadth of the free surface in each compartment is thus b/n, and the
second moment of each free surface is given by l (b/n)3 12