Page 65 - Introduction to Naval Architecture

52 FLOTATION AND STABILITY

The effect on the transverse movement of the centre of gravity Is to
reduce GZby the amount GGi as in Figure 4.16(b). That is, there is an
effective reduction in stability. Since GZ= GMsin (p for small angles, the
influence of the shift of G to Gj is equivalent to raising G to G 2 on the
centre line so that GGj = GGg tan <p and the righting moment is given
by:

Thus the effect of the movement of the liquid due to its free surface, is
equivalent to a rise of GG^ of the centre of gravity, the 'loss' of GM
being:

Free surface effect GGg = p f/i/pV

Another way of looking at this is to draw an analogy with the loss of
stability due to the suspended weight. The water in the tank with a free
surface behaves in such a way that its weight force acts through some
point above the centre of the tank and height I\/v above the centroid
of the fluid in the tank, where v is the volume of fluid. In effect the tank
has its own 'rnetacentre' through which its fluid weight acts. The fluid
weight is p fv and the centre of gravity of the ship will be effectively
raised through GG^ where:

This loss is the same whatever the height of the tank in the ship or its
transverse position. If the loss is sufficiently large, the metacentric
height becomes negative and the ship heels over and may even capsize.
It is important that the free surfaces of tanks should be kept to a
minimum. One way of reducing them is to subdivide wide tanks into
two or more narrow ones. In Figure 4.17 a double bottom tank is shown
with a central division fitted.

figure 4.17 Tank subdivision