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Encyclopedia of Marine and Energy Technology

Metacentric height


The vertical distance between G and M is referred to as the metacentric height. The relative positions of vertical centre of gravity G and the initial metacentre M are extremely important with regard to their effect on the ship’s stability. The ship is in stable equilibrium if G is below M, in neutral equilibrium if VCG and M are coincident and in unstable equilibrium if VCG is above M. If the metacentric height of a ship is small, the righting arms that develop will be small. Such a ship is “tender” and will roll slowly. However, if the metacentric height (GM) of a ship is large, the righting arms that develop, at small angles of heel, will be large. Such a ship is “stiff” and will resist roll.

It is advisable to avoid excessive values of metacentric height, since these might lead to acceleration forces which could be dangerous to the ship, its equipment and cargo. The metacentric height can become negative if the centre of gravity is too high. Even with negative metacentric height, ships with certain forms can still find a position of stable equilibrium at an angle of heel called angle of loll. The angle of loll should be corrected only by lowering the gravity center. The moving masses transversally can endanger the ship.

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