(Note: I started writing something about this topic in the thread "8 inch guns". Since it has nothing at all to do with such weapons, I expanded it here. I hope it can be of some use)
We will analyse three warship designed by Messrs. von Pastor & Le Pasteur, of the award-winning Germagnano Imperial Yard:"To the naval architect, stability is a measure of the moment of force trying to bring the ship upward from a heeled position." [D. K. Brown]
- the monitor HMS Impossible (shallow draught, extra broad beam)
- the aircraft carrier USS Nevertown (a "midrange" ship)
- the cruiser IJN Everykaze (narrow beam, plus the tallest pagoda tower ever)
each of them has a displacement of 10,000 tons.
Figure 1 shows the three ships (transversal section view) in a flat calm.
G = centre of Gravity. The weight of the ship (W=10,000 tons of iron) acts downward through this point. We will consider G as a fixed point, although in the real world it will slightly change position when the ship is heeled (due to the movement of fuel, and as a rule of anything not bolted to the hull). The yellow area represent the amount of ship above surface.
B = centre of Buoyancy. The buoyancy force (equal to W since, according to Archimedes, it is the weight of the 10,000 cubic meters of water dislocated by the hull) acts upward through this point. This point clearly moves as the ship is heeled. The blue area represent the amount of ship above surface. We will consider the ship as impermeable, although in the real world the sea will actively try to fill the interior of the hull through any opening.
Note that, to show the variations, I tried (being a not simple task!) to make blue areas of same size in all conditions and all ships.