metacenters

A metacenter is a concept used in naval architecture and stability analysis to determine the initial stability of a floating body. It is defined as the point where the vertical line through the center of buoyancy of a heeled vessel intersects the original vertical line of symmetry of the vessel. This point is crucial for understanding how a vessel will respond to small angles of tilt.

The center of buoyancy is the geometric center of the submerged volume of the floating body. When the body heels, the shape of the submerged volume changes, and consequently, the center of buoyancy shifts. The metacenter's position relative to the center of gravity (the point where the weight of the body is concentrated) dictates the stability of the object.

If the metacenter is above the center of gravity, the vessel is considered initially stable. Any small tilt will create a righting moment that tends to restore the vessel to its upright position. Conversely, if the metacenter is below the center of gravity, the vessel is initially unstable, and any tilt will result in an upsetting moment, causing it to capsize. The distance between the metacenter and the center of gravity is known as the metacentric height, which is a direct measure of the initial stability. A larger metacentric height indicates greater initial stability.