Righting moment

The righting moment is the restoring couple that returns a heeled ship toward upright, equal to displacement times the righting arm: RM = Delta * GZ. The couple is formed by the buoyant force acting up through the shifted center of buoyancy and the weight acting down through G, separated by the horizontal lever GZ. At small heel GZ approximates GM * sin(theta), so RM is roughly Delta * GM * sin(theta); at large heel GZ comes from the cross-curves. The righting moment opposes the heeling moment from wind, waves, or cargo, and the ship settles where the two balance. The area under the righting-moment curve is the dynamic stability, the work needed to heel the ship.