How does a righting moment return a heeled ship toward an upright position?

A ship returns to an upright position through the generation of a righting moment, which is a fundamental concept in naval architecture. This process relies on the interaction between the ship's centre of gravity and its centre of buoyancy.12

When a ship heels (inclines) due to an external force, the shape of the submerged hull changes, causing the centre of buoyancy to shift toward the low side. Because the total buoyancy force continues to act upward through this new centre while the ship's weight acts downward through the centre of gravity, these two forces create a couple.31

As long as the metacentre—the point where the vertical line through the shifted centre of buoyancy intersects the ship's centreline—remains above the centre of gravity, this couple acts as a righting moment that pulls the vessel back toward the upright position. The magnitude of this stability is often measured by the metacentric height, or for larger angles of heel, by the righting arm ($GZ$). If the centre of gravity rises above the metacentre, the righting moment becomes a capsizing moment, leading to instability.1234