BUOYANCY AND STABILITY OF TROOP TRANSPORTS. 151 



is the moment of inertia of the free surface of water in the flooded compartment, s 

 is a factor of permeability, and V is the volume of displacement of the ship. "VVe 

 have, therefore, in a transversely subdivided ship — 



MM, = BB, - ^. 



When a ship is in the light condition, BBi is relatively small, because the water 



does not rise to a great height inside the ship, but — — , which represents the effect 



of the free surface of water in the compartment, will have approximately its full 

 value. The loss in metacentric height is, therefore, a maximum and, hence, the ship 

 is in this condition most liable to take a great list. In the full-load condition, on the 



other hand, BB, is very great, while —pr has about the same value as in the light 



condition, so that MMi is either negative and relatively small or, in some cases, 

 even positive. Hence, after flooding, the metacentric height in the full-load condi- 

 tion is practically the same as when the ship is intact and, provided there are no 

 longitudinal bulkheads, the ship will remain upright with ample stiffness; but, as 

 shown above, in this condition the danger of foundering by bodily sinkage or of 

 going down by the bow or stern is at its maximum. 



Calculations made for a great number of transports showed that the loss in 

 metacentric height by flooding two of the largest compartments in two-compartment 

 ships when in the light condition varied from i to 2 feet, being ordinarily about i>^ 

 feet. In most vessels flooding of the forward boiler-room, together with the ad- 

 joining forehold — generally used as a reserve bunker — gave the greatest loss in 

 stability. 



Having calculated the probable loss in metacentric height in a given ship, it 

 remains to estimate what the residual metacentric height ought to be after bilging, 

 whereupon the appropriate value of this element in the intact condition can be de- 

 termined. Evidently the residual metacentric height must be estimated with due 

 regard to the size of the ship and her liability to take a list. 



Ships that are subdivided on the purely transverse system will remain upright 

 so long as there is any stability left and no external forces tend to heel them over. 

 They will be safe, therefore, with a very small metacentric height, say from j4 foot 

 in vessels of about 500 feet in length to about i foot in vessels of the largest size. 

 Assuming a loss by bilging of i^^ feet, the initial metacentric height should there- 

 fore be not less than from 2 to 2j4 feet in the light condition while the ship is yet 

 intact: If the calculated loss is greater than here estimated, these figures must be 

 correspondingly increased. This requirement being satisfied in the light condition, 

 there will generally be ample stability in the full-load condition. 



Ships with longitudinal bulkheads, whether watertight or not, should have a 

 greater residual metacentric height in damaged condition than required for ships 

 with only transverse bulkheads. The residual metacentric height should be so cal- 

 culated that under the stipulated conditions of damage the list shall not prevent the 



