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# Metacentric height

Metacentric height. This expression may be explained best by the following figures:

The ship is floating upright in still water

WL= Waterline.

G= Centre of gravity.

B= Centre of buoyancy of water displaced by the ship.

G & B are lying in the same vertical line amidships.

The ship is in equilibrium. The upthrust or buoyancy acting through B is equal to the weight of the ship acting downward through G.

The ship has inclined to one side through external force and has a slight heel.

The position of G has not changed, assuming the cargo has not shifted.

B1= New position of centre of buoyancy. Owing to the change of the immersed part of the ship, the position of B has shifted to the lower side (B1).

G and B are no longer lying to the same vertical plane amidships.

M= Metacentre, being the point of intersection of the perpendicular line drawn from B and the plane amidships.

GM= Metacentric height. GZ = The βarmβ or βleverβ of the βcoupleβ which has been formed.

The forces of upthrust (buoyancy) and downthrust (weight) are so disposed that there is a tendency for the ship to return to the upright when the inclining force is removed. Hence the vessel is βstableβ and GZ is a βrighting leverβ or βrighting armβ.

On an unstable vessel the position of G is higher, which may result from empty double bottom tanks, stowage of cargo on deck, absorption of water in deck cargo, etc. Summarising, the centre of gravity of ship, cargo, water, bunkers, stores and equipment must always be below the metacentre.

The vessel will have:

1. Positive stability if the metacentre is above the centre of gravity.

2. Neutral stability if the metacentre coincides with the centre of gravity in which case there is no righting lever to restore the original position.

3. Negative stability if the metacentre is below the centre of gravity with the risk of capsizing.

If the metacentric height is very large the vessel will be βstiffβ and will roll in bad weather at very short intervals, subjecting the ship to heavy strain, which may cause damage to the shipβs structure, apart from the risk of shifting cargo through excessive rolling. If the vessel is inclined as a result of unsymmetrical distribution of weight within the vessel she is said to have a βlistβ. In this case G will not be in the amidships vertical plane. She may be perfectly stable, but will not remain upright.

On the other hand, if the metacentric height is too small the ship will be βtenderβ. It will roll less violently and may take a long time to return to the upright. This may also cause danger in heavy weather, possibly because the cargo can shift because of the delay in returning to the upright position.

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