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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 W_{1}L_{1}
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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