Metacenter

metacenter [′med·ə‚sen·tər]

(fluid mechanics)

The intersection of a vertical line through the center of buoyancy of a floating body, slightly displaced from its equilibrium position, with a line connecting the center of gravity and the equilibrium center of buoyancy; the floating body is stable if the metacenter lies above the center of gravity.

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Metacenter 

the point whose position determines the stability (stability of equilibrium) of a floating body. A floating body in equilibrium is acted upon by a buoyancy force A whose line of action passes through the center of buoyancy CB (the center of gravity of the mass of liquid in the immersed part of the body) and by the force of gravity P, which is applied at the center of gravity (CG) of the body (see Figure 1). In the case of greatest practical importance, when the floating body has a longitudinal plane of symmetry, the point of intersection of this plane with the line of action of the buoyancy force is called the metacenter (A/); When the body is inclined, the position of the metacenter changes. A floating body will be stable if the lowest metacenter (which sometimes is the only metacenter) of the body lies above the center of gravity of the body.

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Figure 1. Position of the metacenter M for stable (a) and unstable (b) equilibrium of a floating body

REFERENCE

Iablonskii, V. S. Kratkii kurs tekhnicheskoi gidromekhaniki. Moscow, 1961. Chapter 4.