The centre of buoyancy (B) is the centre of gravity of the displaced volume of water, i.e. the point through which the resultant of the buoyancy forces acts. For a floating ship it lies on the vertical through the centre of gravity when the ship is upright. When the ship is heeled by an external force, the shape of the displaced volume changes and the centre of buoyancy moves to the low side. The buoyancy force acts vertically upwards through the new centre of buoyancy, while the weight acts vertically downwards through the centre of gravity. If the centre of buoyancy moves such that the buoyancy force acts on the high side of the centre of gravity, a righting couple (Delta x GZ) is produced that returns the ship to the upright. Sketch: the ship heeled, with the centre of gravity G and the new centre of buoyancy B', the buoyancy force acting vertically through B' and the weight through G, producing a righting moment that returns the ship to the upright. The ship is stable if the metacentre M is above G (GM positive).

An oil tanker of 17,000 t displacement has its centre of gravity 1 m aft of midships and has 250 t of oil fuel in its forward deep tank 75 m from midships. This fuel is transferred to the after oil fuel bunker whose centre is 50 m from midships. 200 t of fuel from the after bunker is now burned. Calculate the new position of the centre of gravity (a) after the oil has been transferred, (b) after the oil has been used.

Take aft as positive. Initial CG = +1 m (1 m aft of midships). Forward deep tank at -75 m (75 m forward), after bunker at +50 m.

The shift of the CG = w x (change in position)/Delta = 250 x (50 - (-75))/17000 = 250 x 125/17000 = 31,250/17,000 = 1.838 m aft.

New CG = 1 + 1.838 = 2.838 m aft of midships.

Removing 200 t from +50 m shifts the CG forward. The new displacement = 17,000 - 200 = 16,800 t.

New CG = (17,000 x 2.838 - 200 x 50)/16,800 = (48,246 - 10,000)/16,800 = 38,246/16,800 = 2.277 m aft of midships.

Answer: (a) CG is 2.84 m aft of midships after transfer; (b) CG is 2.28 m aft of midships after burning 200 t.