Why is metacentric height most useful for small angles of heel?

In naval architecture, the metacentric height (GM) is defined as the distance between the centre of gravity and the metacentre, which is the point where the buoyant force intersects the ship's midplane.1

The metacentric height is most useful for small angles of heel because it is typically calculated only for the zero-heel condition. As a ship inclines, the geometry of the submerged hull changes, causing the position of the metacentre to shift. Consequently, the metacentric height remains an accurate measure of stability only for small disturbances, generally limited to angles of no more than approximately 10°.12

For larger angles of inclination, the metacentric height is no longer a sufficient indicator of stability. Instead, naval architects use the righting arm, or GZ, to measure stability across the entire range of potential heel angles. If a ship heels to a critical angle where the metacentre falls below the centre of gravity, the metacentric height becomes negative, resulting in a capsizing moment rather than a restoring one.12