Thus, if the ship in the example is in a seaway and rolls to, say, 70 degrees, she will come back to the
upright. But if the extreme angle of a roll exceeds 71 degrees, the ship will capsize, because she develops upsetting
moments beyond this angle.
METACENTRIC HEIGHT. The distance GM between the center of gravity and the metacenter is called the
This distance is a measure of how much B moves when the ship inclines through an angle of heel, Θ. In
the triangle GZM, FIGURE 5-1, the righting arm GZ will always be proportional to GM. This holds true as long as M
remains on the ship's centerline; i.e., from 0to about 7 Therefore, GM is a measure of initial stability for any given
displacement, W. Unless otherwise specified, further reference to metacentric height will refer to initial GM.
The point M does not come into being until the ship heels, but any slight inclination produces a movement
of B and consequently a metacenter is established. Note that the GM produced by a slight heel in an upright position is a
definite value which remains relatively constant up to about 7of heel.
Since at small angles of heel large values of GM indicate large righting arms, ships with large GM are stiff
and resist roll. Small values of GM reflect slowly developed righting arms, and these ships are tender and roll slowly.
Ships with very small GM are apt to hang at the extreme angle of a roll before starting back.
A study of FIGURE 5-3 will indicate that when G is below M, GM is positive and righting arms develop,
whereas when G is above M, GM is negative and upsetting arms develop. Thus, GM is an indicator of whether initial
stability is positive or negative.
Figure 5-3. GM Indicating Initial Stability, Positive/Negative.