## STABILITY OF A FLOATING BODY BASIC INFORMATION AND TUTORIALS

Have you ever wondered why the passenger basket on a hot air balloon is suspended underneath and not simply strapped to the top of the balloon? After all, most hot air balloons are used for sightseeing and a basket on the top would give much better views.

Consider the balloon shown in the left-hand diagram of below:

The balloon floats because the hot air inside it is less dense than the cold air surrounding it, giving rise to a buoyancy force acting upwards through B. When this force equals the total weight of the balloon and basket, acting through the centre of gravity G, the balloon will float at a constant altitude.

As the wind changes and the occupants of the basket move around, the balloon will rock through a small angle θ. Since the centre of buoyancy is higher than the centre of gravity, any angular displacement produces a turning moment which acts to restore the balloon to an upright position. Such an arrangement is said to be in stable equilibrium.

Now look at the bizarre case in the right-hand diagram. The buoyancy force again equals the weight, but here any angular displacement causes a turning moment which makes the basket topple over. The reason for this is that the centre of buoyancy B is below G. The situation is known as unstable equilibrium.

Something very similar applies to ships, but there are cases where stable equilibrium can be achieved even where the centre of buoyancy is below the centre of gravity. This occurs because the shape of the displaced water alters as the ship rocks and so the centre of buoyancy moves sideways in the same direction as the ship is leaning.

Therefore the line of action of the buoyancy force also moves to the side of the ship which is further down in the water, and the buoyancy force tries to lift the ship back to the upright position. Whether or not the restoring moment is enough to make the ship stable depends on the position of the point where the line of action of the buoyancy force crosses the centreline of the ship, known as the metacentre, M .
The distance between G and M is known as the metacentric height.

If M is above G then the metacentric height is positive and the ship is in stable equilibrium. If G is above M then the metacentric height is negative and the ship is in unstable equilibrium. This is the situation which led to the sinking of King Henry VIII’s flagship, the Mary Rose, off Portsmouth.

This had sailed successfully for a number of years and was just stable as it cast off on its fateful last voyage, even though an unusually large shipment of weapons and soldiers had raised the centre of gravity to danger level.

Finally, when the soldiers crowded up onto deck for a last glimpse of land as the ship put out to sea, the centre of gravity rose so high that the first big wave they encountered away from the shelter of the harbour caused the ship to topple completely over.