what are factors affecting ship's static and dynamic stability ?

Answer 1

While comparing center of gravity vs center of buoyancy will tell you the instantaneous forces acting on a ship to (hopefully) right it, a ship's static roll stability is more a question of the righting tendency across the range of roll angles that a ship may encounter. That is, how vigorously does the ship try to turn itself upright once perturbed, across it's entire operating range?

Not to make it sound overly simple, but the main factors affecting static stability are: 1) the height of the ships center of gravity (CG) and 2) the shape of the hull.

Height of CG is reasonably self-explanatory. The shape of the hull takes a little more consideration. As a ship tilts to one side, the shape of the submerged volume changes. In a very narrow ship, it doesn't change a whole lot-- think of a kayak-- and thus the center of buoyancy doesn't shift outboard very much. Thus the buoyant force doesn't have a large leverage arm to couple with the ship's weight, acting down through the CG. And so the ship rolls easily.

Conversely when a wide, shallow barge tips to the side, now the submerged portion (cross-section) quickly starts to look like a triangle rather than a rectangle. The center of buoyancy shifts outboard rapidly and now there is a large leverage arm tending to right the ship. Therefore our wide barge is difficult to roll, and has "greater static stability" than our skinny kayak.

Dynamic stability concerns 1) shifts in the ships CG as the ship heels over and 2) the effect of wave action on the center of buoyancy.

CG can shift due to loose cargo or other moveable weights, or especially the "free surface effect" of liquid in partially filled tanks that sloshes around while the ship rolls.

Center of buoyancy changes dynamically when, for example, the ship heels over into the trough of a wave... the submerged volume toward the heeling side is less than it would be in calm flat water. As the ship struggles to right itself the wave passes on to its peak, and suddenly you have a surplus of bouyancy on the heeling side which (again hopefully) will snap you upright. That anaylsis gets more complicated still when you get into harmonics, i.e. the ship has some momentum when returning to the upright position, so if you hit waves at just the wrong time you'll get no reserve buoyancy to counteract that momentum. You can go as deep into that subject as you like, including statistical analysis of wave spectra and so on.

Answer 2

The center of mass location of the ship and the center of mass location of the water displaced.