Metacentric height

Metacentric height is the vertical distance between a vessel’s center of gravity and its metacenter. It indicates initial stability for small angles of heel.

Metacenter: The point where the buoyant force’s vertical line through a slightly heeled vessel intersects its original upright centerline. Metacentric height is measured from the center of gravity to this reference point.
Displacement (ship): The weight of water displaced by a floating vessel, equal to the vessel’s weight in equilibrium. Displacement sets the buoyant force and enters standard metacentric-height calculations.
Ship stability: A vessel’s ability to resist capsizing and return toward equilibrium after being disturbed. Metacentric height is a standard measure of a vessel’s initial transverse stability.
Righting lever: The horizontal separation between a vessel’s weight and buoyancy lines of action at a given heel angle. Unlike metacentric height, it describes the restoring geometry at finite heel angles.
Center of gravity: The point at which an object’s mass can be treated as concentrated for calculating its weight and motion. Its position relative to the metacenter determines the sign and magnitude of metacentric height.
Waterplane area: The area enclosed by a vessel’s waterline where the hull intersects the water surface. Its shape and size affect how far buoyancy shifts during a small heel.
Intact stability: A ship’s stability with its hull and watertight boundaries undamaged. Metacentric height is checked as one part of assessing intact stability.
Dynamic stability: A measure of the work required to heel a vessel through an angle, represented by area under its righting-lever curve. It captures stability over a range of heel angles rather than only the initial response.
Center of buoyancy: The centroid of the displaced fluid volume, through which the resultant buoyant force acts. As a vessel heels, this point shifts and helps establish the metacenter.
Second moment of area: A geometric measure of how area is distributed around an axis, used in bending and stability calculations. The waterplane’s second moment determines the metacentric radius.

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