Stability of Ships During Grounding

If a ship runs aground in such a manner that the bottom offers little restraint to heeling as in the figure below, the reaction of the bottom may produce a heeling moment. As the ship touches ground during its forward motion, part of the energy due to the forward motion may be absorbed in lifting the ship, in which case a reaction, R, between the bottom of the ship and the ground would develop. This reaction may be increased later as the tide ebbs.

Under these conditions, the force of buoyancy would be less than the weight of the ship, since the ship would be supported by the combination of buoyancy and the reaction of the bottom. The ship would heel until the moment of buoyancy about the point of contact with the bottom became equal to the moment of ship’s weight about the same point, when (W-R) X a equals W x b.

There is only a remote possibility of a stranded ship capsizing as a result of ebbing tide. For this to occur the ship will have to be grounded on a bottom such that there is no restraint to heeling in one or both directions until a very large angle is reached, as for example, on a peak which is considerably higher than the surrounding bottom. In a case as in the figure, the heel would increase as the tide ebbs. The position of the ship will always be such that the moment of buoyancy equals the moment of weight i.e. W x b will be equal to (W-R) x a.

Capsizing

Before the ship could capsize, reaction R must be reduced to zero. Since W x b = (W-R) x a, when R=0, a and b would be equal, which means that G would be directly above B1. This is the same as the ship heeling to its maximum angle of heel for positive stability. It can therefore be said that the stranded ship will not capsize (in the absence of external forces) until it reaches the angle of heel equivalent to its range of positive stability when afloat.