Page 77 - Introduction to Naval Architecture

64 FLOTATION AND STABILITY

Figure 4,27 Cross curves of stability

curves of stability and depend only upon the geometry of the ship and
not upon its loading. They therefore apply to all conditions in which
the ship may operate.

Deriving curves of statical stability from the cross curves
For any desired displacement of the ship, the values of SZ can be read
from the cross curves. Knowing the position of G for the desired
loading enables SZ to be corrected to GZ by adding or subtracting
SG sin <p, when G is below or above S respectively.

Features of the statical stability curve
There are a number of features of the GZ curve which are useful in
describing a ship's stability. It has already been shown that the slope of
the curve at the origin is a measure of the initial stability GM. The
maximum ordinate of the curve multiplied by the displacement equals
the largest steady heeling moment the ship can sustain without
capsizing. Its value and the angle at which it occurs are both important.
The value at which GZ becomes zero, or 'disappears', is the largest
angle from which a ship will return once any disturbing moment is
removed. This angle is called the angle of vanishing stability. The range
of angle over which GZ is positive is termed the range of stability.