The Theory of Stability
As a boat is heeled by an external force, a restoring moment is set up. Refer to the illustration and note that the angle of heel has been labeled 0
Because of the shape of the hull, the athwartship center of buoyancy has moved from its upright position on the centerline to a point outboard of the centerline as shown. Nothing has been done to change the weight of the vessel, of course, and it acts vertically downward through the vessel's center of gravity. The equal and opposite force of buoyancy acts vertically upward from the heeled center of buoyancy. The horizontal distance between the two forces is labeled GZ and is called the righting arm. It should be easy to see that the restoring moment, called the righting moment by small craft designers and termed RM, is equal to the product of the vessel's weight times the righting arm:
RM = DISP x GZ
By definition, the point on the vessel's centerline vertically above the heeled center of buoyancy is the metacenter, labeled M in the illustration. The distance between G and M, measured along the vessel's centerline, is called the metacentric height and is referred to as GM. Look at the drawing and you can see that the righting arm, GZ is directly proportional to the metacentric height, GM. Double GM, and you will double GZ and thereby double the righting moment. The formula for this relationship is:
GZ = GM sin 0
Thus, a boat can be made more stable by lowering G, by raising M, or both; anything that increases the distance (GM) between the two.