Page 204 - statbility for masters and mates

Chapter 20
Calculating the effect
of free surface of liquids (FSE)
The effect of free surface of liquids on stability was discussed in general terms in Chapter 7, but the problem will now be studied more closely and the calculations involved will be explained.
When a tank is partially ®lled with a liquid, the ship suffers a virtual loss in metacentric height which can be calculated by using the formula:
i
w r n
the second moment of the free
surface about the centre line, in m4
the ship's displacement, in tonnes
the density of the liquid in the tank, in tonnes/cu. m the number of the longitudinal compartments
into which the tank is subdivided
free surface moment, in tonnes m.
FSE VirtuallossofGM i r 1 metres I W n2
where
i p
The derivation of this formula is as follows:
The ship shown in Figure 20.1(a) has an undivided tank which is partially
®lled with a liquid.
When the ship is inclined, a wedge of the liquid in the tank will shift from the
high side to the low side such that its centre of gravity shifts from g to g1. This will cause the centre of gravity of the ship to shift from G to G1, where
Let and then
GG1 w gg1 W
r1 density of the liquid in the tank
r2 density of the water in which the ship floats
GG1 v r1 gg1 V r2