Page 75 - Introduction to Naval Architecture

62 FLOTATION AND STABILITY

This equation is satisfied by two values of <p. The first is sin </> = 0, or
if* = 0. This is the case with the ship upright as is to be expected. The
second value is given by:

With both GMand B^M positive there is no solution to this meaning
that the upright position is the only one of equilibrium. This also
applies to the case of zero GM, it being noted that in the upright
position the ship has stable, not neutral, equilibrium due to the term in

When, however, the ship has a negative GM there are two possible
solutions for <p in addition to that of zero, which in this case would be
a position of unstable equilibrium. These other solutions are at <f> either
side of the upright <p being given by:

The ship would show no preference for one side or the other. Such an
angle is known as an angle of loll The ship does not necessarily capsize
although if (p is large enough the vessel may take water on board
through side openings. The GZ curve for a ship lolling is shown in
Figure 4.25.
If the ship has a negative GM of 0.08 m, associated with a B$M of 5 m,
<p, which can be positive or negative, is:

This shows that small negative GMcan lead to significant loll angles. A
ship with a negative GM will loll first to one side and then the other in
response to wave action. When this happens the master should
investigate why the stability is so poor.

Figure 4,25 Angle of loll