Why does a ship float?

Eureka! Eureka! cried Archimedes, jumped out of his bath tub and ran naked. Perhaps he found an answer to a long standing problem in his mind! Now we know his answer as the Archimedes principle.

Principle:

A body wholly or partly immersed in a fluid, undergoes a loss in weight equal to the weight of the fluid it displaces.

(For e.g.)
An aluminium cube of 1ft length weighing 168lb (Fig 1a), when immersed in water (1cubic feet of water =62lbs) undergoes a weight loss equal to the weight of the displaced water , now its weight has apparently decreased to 106lb [168 lb-62lb] (fig 1b)

Principle of floating:


If a body, on being immersed in a fluid would displace a volume of fluid whose weight is greater than that of the body concerned, then that body will float on the fluid. In other words a body floats when it sinks to such a depth that the displaced fluid weighs exactly as much as the floating body. Buoyancy (acting upward) is said to be in equilibrium with the weight of the body.

For e.g.

A 1ft wooden cube (fig 2) weighing about 50lb will float in water, when the submerged part of the cube displaces a volume of water weighting 50lb, counter- balancing the weight of the cube.

What’s the case with the ship?

Apart from floating, a ship must additionally be able to reorient itself after being swung to an inclined position by external force such as wind pressure.
Fig 3a shows the ship in normal position. The weight of this ship acts downward at its centre of gravity S. The counter balancing upward force acts at the centre of buoyancy W, which is the centre of gravity of the displaced volume of water. In normal position (Figure 3a) the points S and W are on the same vertical line. When the ship heels over (Figure 3b & 3c) the centre of gravity of the displaced water shifts to a different position W’.

The upward movement acting here strives to rotate the ship around its centre of gravity S. the intersecting point of the upward force A with the ships axis of symmetry ( vertical dotted line) is called the metacentre M. If the metacentre is located above the centre of gravity S (Fig 3b) the ship will float and return to its normal upright position. On the other hand if the metacentre is below the centre of gravity S (Fig 3c) the ship will capsize when it heels over.

Reference:
An illustrated encyclopedia of technology, Heron books. C.Van Amerongen.