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of the underwater portion of the hull. For example, if the ship rolls to the starboard side,
then the center of buoyancy shiwfts out toward the starboard side. When this happens,
the lines of action of the weight of the ship and the buoyant force are no longer in line,
which results in a moment (torque) that acts on the ship. This torque is equal to the
perpendicular distance between the lines of action of the forces times the weight of the
ship.
Now here's where we get to the floating upright part that we mentioned earlier. When
a ship rolls, for example, you don't want it to keep rolling until it capsizes. Instead, you
want it to gently return itself to the upright position after whatever force caused it to
roll—the wind, for example—has been removed. In short, you want the ship to be stable.
For a ship to be stable, the line of action of the buoyant force must cross the vessel's
centerline at a point, called the metacenter , above the center of gravity. When this hap‐
pens, the moment developed when the ship rolls tends to restore the ship to the upright
position. If the metacenter is located below the center of gravity, then the moment
developed would tend to capsize the ship. The distance between the center of gravity
and the metacenter is called GM . This is also known as the stability index , as a positive
value means the floating body is stable and a negative GM means the body is unstable.
Figure 16-2 illustrates these two scenarios.
Figure 16-2. Ship stability
 
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