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Stability

Fresh Water Allowance

Fresh Water Allowance (FWA)

In the basic principle of why a ship floats it is understood that the weight of the volume of water displaced by a ship is equal to weight of the entire ship.

The volume of the displaced water is again equal to the volume of the underwater volume of the ship.

Now when the weight of this displaced water is calculated we take the product of the volume of the water and the density of the water.

So, if the density of the water changes, then the weight of the displaced water changes, the weight of the ship remaining unchanged.

Thus to keep the ship floating something has to be adjusted and adjustment is in the underwater volume of the ship.

So a ship floating in waters of different densities will do so at different levels.

Let us take the example of a ship with a weight of 10000 MT, let this ship float at a certain level (assume the water level is at the mid level of the ship)

Then the underwater part of the ship would be displacing a volume of water that would be equal to the volume of the underwater part of the ship.

Also the weight of this water would have to be equal to the entire weight of the ship.

So we have,

Displaced water = underwater part (volume) of the ship

Weight of this displaced water = entire weight of ship

We know,

Weight of this displaced water = volume of displaced water x specific gravity of the water

So now if the specific gravity of the water changes, then to keep the weight of the water constant the volume of the displaced water has to change – and this is the reason that the ship either sinks lower or rises up when traversing from FW to SW and vice versa.

Thus to keep the ship floating something has to be adjusted and adjustment is in the underwater volume of the ship.

So a ship floating in waters of different densities will do so at different levels.

So we can replace the word level by the nautical word ‘draft’

Thus we may now define Fresh Water Allowance as the amount in millimetres by which a ships MEAN DRAFT changes when she moves between SALT WATER and FRESH WATER and vice versa

As a ship moves from SW to FW, the weight of the displaced water reduces – RD of SW at 1.025 and FW at 1.000, so additional volume of water is required to float the ship, this means that the underwater volume of the ship has to increase so the ship sinks lower to compensate the above. So the draft increases.

In the same way if a ship moves from FW to SW, the weight of the displaced water would be more than the weight of the ship, so the weight of the water has to be reduced, this may be reduced if the volume of the water is reduced, this again depends on the underwater volume of the ship, so the underwater volume of the ship is reduced.

And so the ship rises a little and the draft of the ship reduces.

FWA (in mm) = Displacement/ 4x ( (water plane area x density of water) / 100)

Or FWA = Displacement / ( 4 x TPC)

Effect of draft on FWA

For box shaped vessel, FWA is the same at all drafts.

For ship shaped vessels, FWA increases with draft. As the draft increases, both the displacement and the TPC increase, but the rate of change of displacement is higher than that of the TPC.

Derivation of the FWA formula

Consider a ship floating in SW at load Summer draft at waterline WL.

Let volume of SW displaced at this draft be ‘V’.

Now let W₁L₁ be the waterline for the ship when displacing the same mass of fresh water.

Let ‘v’ be the extra volume of water displaced in FW.

Total volume of fresh water displaced will be V + v.

Mass = Volume x density

Mass of SW displaced = 1025V

Mass of fresh water displaced = 1000 (V + v)

But mass of FW displaced = Mass of SW displaced.

1000(V + v) = 1025V

v = V/40

Assume that ‘w’ is the mass of SW in volume v and ‘W’ in volume V,

Then, replacing the factor as obtained above we get:

w = W/40

But w is a factor that is a product of the FWA and the TPC

Now since the FWA is in mm and the TPC is in cm, they both have to be converted to metres

Thus:

W = (((FWA mm x 100) cm X TPC cm) / 100) metres

Simplifying we have:

w = (FWA x 100 x TPC) / 100 = W / 40

Or (FWA x TPC) = W / 40

But w = TPC x (FWA/10)

Hence W/40 = TPC (FWA/10) or FWA = W/(4 x TPC).

Where ‘W’ = Loaded SW displacement in tonnes.

Dock Water Allowance (DWA)

As a ship sails the seas the SW density is assumed to be constant at 1.025 gms/cc, however the density of the SW is never the same everywhere, especially in partially enclosed salt water bodies, this does not make much difference since the depth of the water is very substantial.

However when a ship enters a river from the sea the density of the water changes from SW to FW, gradually. The density of the river may never attain pure FW conditions and may be in between.

Thus the need to calculate this intermediate correction for the new density.

Docks (enclosed port areas containing jetties) have water that is intermediate between SW and FW, the water is brackish and may have a density of 1.010 gms/ cc.

Thus Dock Water Allowance is similar to FWA and is the amount in millimetres by which the ships mean draft changes when a vessel moves between a salt water and dock water.

Dock water is the water whose density is neither that of fresh water or salt water but in-between the two. RD between 1.000 and 1.025.

To get the correction in millimetres the formula that may be used is:

(Please note however that the DWA allowed for should be for the minimum density that will be encountered by the ship while proceeding to the dock – this as a safety factor)

DWA = FWA (1025 – density of dock water)

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