Metacenter, abbreviated as \(M\), is a point used to determine the initial stability of a floating body, such as a ship, boat, barge, pontoon, or floating platform. It is defined as the point where the new line of action of the buoyant force, after a small angular displacement or heel, intersects the body's original vertical centerline. The metacenter is therefore a geometric reference associated with the movement of the center of buoyancy when a floating body tilts.
The center of gravity (\(CG\)) is the point through which the body's weight acts downward. When a floating body is upright, the center of gravity and center of buoyancy are generally on the same vertical line. When the body heels, the center of buoyancy moves because the submerged volume changes shape, while the center of gravity generally remains fixed relative to the body. The resulting separation between the lines of action of weight and buoyancy produces a righting moment or an overturning moment, depending on the relative positions of \(CG\) and \(M\).
The vertical distance between the metacenter \(M\) and center of gravity \(CG\) is called the metacentric height \(GM\). For small angular displacements, \(GM > 0\), meaning the metacenter is above the center of gravity, indicates positive initial stability. If \(GM = 0\), the body is neutrally stable with respect to the initial small angle condition. If \(GM < 0\), the metacenter is below the center of gravity and the body has negative initial stability.
