Page 84 - Introduction to Naval Architecture

FLOTATION AND STABILITY 71

The wind force will be proportional to the square of the wind
velocity, V w, and can be written as:

where k is an empirical constant. The moment will be:

The curve of wind moment can be plotted with the AGZ curve as in
Figure 4,32. If the wind moment builds up or is applied slowly the ship
will heel to an angle represented by A and in this condition the range
of stability will be from A to B. The problem would then be analogous
to that of the shifted weight. On the other hand, if the moment is
applied suddenly, say by a gust of wind, the amount of energy applied
to the ship as it heeled to A would be represented by the area DAGO.
The ship would only absorb energy represented by area OAC and the
remaining energy would carry it beyond A to some angle F such that
area AEF = area DAO. Should F be beyond B the ship will capsize,
assuming the wind is still acting.

Figure 4.32

A severe case for a rolling ship is if it is inclined to its maximum angle
to windward and about to return to the vertical when the gust hits it.
Suppose this position is represented by GH in Figure 4.32. The ship
would already have sufficient energy to carry it to some angle past the
upright, say KL in the figure. Due to damping this would be somewhat
less than the initial windward angle. The energy put into the ship by the
wind up to angle L is now represented by the area GDKLOH. The ship
will continue to heel until this energy is absorbed, perhaps reaching
angle Q.