As a double-bottom tank is filled, two effects act on GM:

• The added weight of ballast is low in the ship (deep in the double bottom), so it lowers the centre of gravity, which increases GM (stiffening the ship). This is the dominant effect once the tank is full.
• While the tank is partially full, a free surface exists and produces a free-surface effect that reduces the effective GM. The free-surface correction is rho x i / Delta, where i is the second moment of area of the free surface about its longitudinal axis (i = L B^3/12). For a wide double-bottom tank this can be significant.

Hence during filling, the effective GM first falls (as the free surface develops) and then rises as the tank approaches full and the free surface disappears; when the tank is completely full (pressed up) the free-surface effect is zero and the GM is increased by the low weight. The net effect of a full double-bottom tank is an increase in GM (stiffer ship), but the transient free-surface loss during filling must be watched, especially in a tender ship.

Given: length L = 18 x draught d; breadth B = 2.1 x d; waterplane area coefficient Cw = 0.83; difference between TPC in sea water and TPC in fresh water = 0.7.

TPC = (waterplane area x density)/100. In sea water TPCsw = A x 1.025/100; in fresh water TPCfw = A x 1.000/100.

Difference = A(1.025 - 1.000)/100 = A x 0.025/100 = 0.7.

So A = 0.7 x 100/0.025 = 2800 m2.

Cw = A/(L x B) = 0.83, so L x B = 2800/0.83 = 3373.5 m2.

But L = 18d and B = 2.1d, so L x B = 18d x 2.1d = 37.8 d2 = 3373.5.

d2 = 3373.5/37.8 = 89.25, so d = 9.45 m.

L = 18 x 9.45 = 170.1 m.

TPC in fresh water = A/100 = 2800/100 = 28.0 t/cm.

Answer: length of ship about 170 m; TPC in fresh water = 28.0 t/cm.