Page 89 - Introduction to Naval Architecture

76 FLOTATION AND STABILITY

for this intermediate waterplane, again allowing for the permeability.
Using subscript rn to denote the values for the intermediate
waterplane:

where x is the centroid of the lost volume from the CF.
The new draughts can be calculated from the sinkage and trim. A
further approximation can be made if either of these is very large, or
the results can be checked from first principles using the Bonjean
curves allowing for the flooding and permeability.
In the lost buoyancy method the position of G remains unaltered
unless the damage has been so severe as to remove structure or
equipment from the ship,

Added weight method
In this method the water entering the damaged compartment is
regarded as an added weight. Permeability would have to be allowed for
in assessing this weight, and allowance must be made for the free
surface of the water that has entered, but all the hydrostatic data used
are those for the intact ship. Initially the calculation can proceed as for
any added weight, but when the new waterline is established allowance
must be made for the extra water that would enter the ship up to that
waterplane. Again a second iteration may be needed and the
calculation is repeated until a sufficiently accurate answer is
obtained.
In the description of both methods it is assumed that the
compartment that has been breached extends above the original and
the final waterlines. If it does not then the actual floodable volumes
must be used, and the assumed waterplane characteristics amended
accordingly. It will be clear that it is highly desirable for the ship to have
reasonable amounts of potential buoyancy above the intact waterplane
as a 'reserve'. This is termed reserve of buoyancy.

Example 4.5
A vessel of constant rectangular cross section is 60m long and
10m wide. It floats at a level keel draught of 3 m and has a centre
of gravity 2.5m above the keel. Determine the fore and aft
draughts if an empty, full width, fore-end compartment 8 m long
is opened to the sea. For simplicity a permeability of 100 per cent
is assumed.