Page 47 - statbility for masters and mates

Effect of density on draft and displacement 35
The effect on ship-shaped vessels
It has already been shown that when the density of the water in which a vessel ¯oats is changed the draft will change, but the mass of water in kg or tonnes displaced will be unchanged. i.e.
New displacement Old displacement
New volume new density Old volume old density
; New volume Old density Old volume New density
With ship-shapes this formula should not be simpli®ed further as it was in the case of a box-shape because the underwater volume is not rectangular. To ®nd the change in draft of a ship-shape due to change of density a quantity known as the `Fresh Water Allowance' must be known.
The Fresh Water Allowance is the number of millimetres by which the mean draft changes when a ship passes from salt water to fresh water, or vice versa, whilst ¯oating at the loaded draft. It is found by the formula:
FWA (in mm) Displacement (in tonnes) 4 TPC
The proof of this formula is as follows:
To show that FWA (in mm) Displacement (in tonnes)
4 TPC
or
Fig. 5.2
Consider the ship shown in Figure 5.2 to be ¯oating at the load Summer draft in salt water at the waterline WL. Let V be the volume of salt water displaced at this draft.
Now let W1L1 be the waterline for the ship when displacing the same mass of fresh water. Also, let `v' be the extra volume of water displaced in fresh water.