Fresh Water Allowance (FWA) is the number of millimetres by which the mean draught changes when a ship passes from salt water to fresh water, or vice-versa, when the ship is loaded to the Summer displacement.
The FWA is found by the formula:
TPCSW is the salt-water TPC value for the summer load draught.
Derivation of FWA:
Displacement of a ship may be calculated by = L x B x d x Cb x ρ
Consider the ship shown loaded to the Summer draught floating in:
(i) salt water;
(ii) fresh water.
The displacements will be different but the volumes of displacement will be the same. If a ship is floating at a draught in FW, to find the equivalent SW displacement for the same draught:
DISPLSW = DISPLFW x 1.025
Therefore, for the ship shown:
DISPLFW x 1.025 = DISPLFW + (WPA x FWA x 1.000 t/m3)
Where, FWA is expressed in meters.
DISPLFW x 1.025 = DISPLFW + (WPA x FWA)
1.025 DISPLFW = DISPLFW + (WPA x FWA)
1.025 DISPLFW – DISPLFW = (WPA x FWA)
0.025 DISPLFW = (WPA x FWA) (i)
Consider now the formula for TPC, where the TPCSW is the weight required to sink the ship whilst at the summer displacement by 1 cm:
TPCSW = WPA x 1.025/100
Rearranging this gives:
WPA = TPCSW/100 x 100 (ii)
Where, the WPA is that for the Summer load draught waterline.
Substituting equation (ii) into equation (i):To express FWA in mm then: