 Explain what is meant by “buoyancy”

 Define the force of buoyancy as an upward force on a floating object

created by the pressure of liquid on the object
 Describe that the buoyancy force is equal to the displacement of a
floating object
 Explain what is meant by “reserve buoyancy”
 Explain how freeboard is related to reserve buoyancy
 Calculate the reserve buoyancy of a box shape V/L whose
dimensions and displacement is known
 Explain the terms “Fresh Water Allowance” & “Dock Water
Allowance”
 Explain why the draught of a ship decreases when it is
 passes from fresh water to seawater and vice versa
 Describe that when loading in fresh water before proceeding into
seawater, a ship is allowed a deeper maximum draught
 Describe that the additional draught is called the Fresh
 Water Allowance (FWA)
 Given the FWA and TPC for fresh water, calculate the amount which
can be loaded after reaching the summer load line when loading in
fresh water before sailing into seawater
 Uses a hydrometer to find the density of water
 Given the density of dock water and TPC for sea water, calculate the
TPC for dock water
 Given the density of dock water and FWA, calculates the amount by
which the appropriate load line may be submerged
 Given the present draught amidships and the density of dock water,
calculate the amount to load to bring the ship to the appropriate
load line in sea water
 Use tank sounding booklet to obtain volume of water KG of water, in
the tank for given sounding or ullage
 Calculate weight of water in the tank
 Describe why WNA mark is situated 50mm below the winter line for
the V/L less than 100m in length
 Given the summer draft, calculate the distance between the winter &
summer, summer & tropical draft.
 Given the summer draft calculate the quantity of cargo to be
loaded / discharged to reach at desired load line

12.1 Explains what is meant by “buoyancy”

When a body is wholly or partially immersed in a fluid it appears to suffer a
loss in weight equal to the weight of fluid displaced. The actual weight of
the body is not changed. A force exerted by the fluid on the body, acting
BNA 016 – 12 – Buoyancy

vertically upwards, creates this apparent loss of weight. This force is

known as the force of buoyancy and it acts through a point called centre of
buoyancy. The force of buoyancy is an upward force acting on a floating
object created by the pressure of liquid on the object

An object when floating will displace some volume of the fluid equal to the
submerged volume of the floating body. The body will float only when the
body weight equals to the weight of fluid displaced. It is the submerged
portion of body which provides buoyancy. That means, the force of
buoyancy is equal to the displacement of a floating object.

12.4 Explains what is meant by “reserve buoyancy”

When a vessel floats in water, the submerged portion of the vessel
provides buoyancy. The volume of the enclosed spaces above waterline is
not providing buoyancy. This volume is held in reserve. If extra weights are
loaded on the vessel, some of this reserve volume gets submerged
providing extra buoyancy to keep the vessel afloat. The vessel will remain
afloat till the buoyancy provided by this enclosed volume is more than or
equal to the weight of the vessel.
Reserve Buoyancy is defined as the volume of enclosed spaces above the
waterline. It may be expressed as the volume or as a percentage of total
volume of the vessel.

12.5 Explains how freeboard is related to reserve buoyancy

In a ship, freeboard is defined as the vertical distance between the loadline
mark and the deck line. When loaded the waterline touches the loadline
mark. Above the loadline mark, till the deck line the vessel is not
BNA 016 – 12 – Buoyancy

submerged. Generally, a ship has enclosed spaces from the keel to the
deck line. So the volume of the ship, which is above loadline and which
corresponds to freeboard of the vessel, is a reserve on buoyancy, which
will help the vessel remain afloat in case subsequent weights are added on
it. Thus it corresponds to the reserve buoyancy of the vessel.
When determining the position of loadline of a ship, reserve buoyancy
provided by the constructional features of the ship is taken into
consideration and accordingly the freeboard of the vessel is assigned.

12.6 Calculate the reserve buoyancy of a box shape V/L whose

dimensions and displacement is known

A box shaped vessel 105m long, 30 m beam and 20m deep is floating
upright in salt water. If the displacement is 19500 tonnes, find the volume
of the reserve buoyancy.

Volume of water displaced = Mass / Density = 19500 / 1.025 = 19024.39

m3
Total Volume of vessel = 105 X 30 X 20 = 63000 m3
Reserve Buoyancy = Total Volume of vessel – Submerged Volume of
vessel
= Total Volume of vessel – Volume of water displaced
= 63000 – 19024.39
= 43975.61 cubic metres.

12.7 Explain the terms “Fresh Water Allowance” & “Dock Water
Allowance”
12.8 Explains why the draught of a ship decreases when it is
passes from fresh water to seawater and vice versa
12.9 States that when loading in fresh water before proceeding
into seawater, a ship is allowed a deeper maximum draught.
12.10 States that the additional draught is called the Fresh Water
Allowance (FWA)

Fresh Water Allowance (FWA) is the change in draft when a ship goes from
Salt water to Fresh Water. This change in draft is a result of the differences
in densities of fresh water and salt water.
BNA 016 – 12 – Buoyancy

When a ship is floating in water, the buoyancy provided water is equal to

the product of submerged volume of the ship and the density of water.
This product is equal to the weight of the ship which remains constant.
Mathematically, W = V x δ
where W = weight of ship
V = Submerged volume of ship,
δ = Density of water

Now in the above expression W is constant, so any change in δ will be

compensated by change in V.
i.e. When the ship floats in SW of density 1.025 t/m 3, if volume submerged
is V,
When the ship will come to fresh water of density 1.000 t/m 3, the
submerged volume will increase and will be more than V.
This increase in volume will reflect as increase in draft of the ship and is
termed as Fresh Water Allowance.
Similar to fresh water allowance, a change in draft is observed when a
vessel goes from salt water to water of different density as is in the case of
water inside docks. In this reference, the change is draft is termed as dock
water allowance.

The FWA for the summer load condition is called the FWA of the ship and is
given by the formula
FWA = W / 40 TPC
Where W is the displacement of the ship in salt water, expressed in tonnes
TPC is the tonnes per centimetre immersion in salt water.
FWA is the fresh water allowance in centimeters.

The FWA for the ship at the level of all load lines is considered constant.
When a ship loads in fresh water, she can immerse her loadline by the
FWA of the ship so that when she goes to SW she would rise to her
appropriate loadline.

The FWA does not remain the same for all drafts as W and TPC vary with
the draft. So, if it is intended to calculate the FW draft of the ship, when
she is loaded to any draft other than the loadlines, her FWA can be
calculated using the above formula. The values of TPC and W can be
obtained from the hydrostatic tables of the vessel.

Dock Water Allowance (DWA) is the change in draft of the ship when it
goes from Salt Water to Water inside a dock having different density. Here
the principle for change in draft is same as that of FWA, only difference
being the water inside the dock is neither salt water nor fresh water. The
density of water is different from 1.025 and 1.000. When loading in a dock
a ship can immerse her loadlines by the DWA so that when she comes to
sea, she would rise to her appropriate loadline.

DWA is given by the formula

BNA 016 – 12 – Buoyancy

DWA = (Change of relative density X FWA) / 0.025

12.11 Given the FWA and TPC for fresh water, calculates the
amount which can be loaded after reaching the summer load line
when loading in fresh water before sailing into seawater

Q. A vessel loading in fresh water in summer zone has her summer

loadline at the water level. Her TPC for summer draft is 20 and her FWA is
200 mm. Calculate the amount of cargo that she can further load so that
when she goes to sea her summer load line is at the water level.

FWA = 200mm = 20 cm
TPC = 20
Amount of cargo that can be loaded = 20 x 20 = 400 tonnes.

12.12 Uses a hydrometer to find the density of water

To measure the density of water, the following procedure is to be adopted.

The hydrometer should be taken out of the tube, the tube shall be filled
with the liquid, and then the hydrometer is put into the tube. When the
hydrometer quits bobbing up and down, the number off the scale on the
hydrometer is read where the liquid meets it. If the hydrometer tube is
filed with water, it should be very near 1000. (It won't be exactly 1000,
because water will probably have some gases dissolved in it, won't be the
temperature the hydrometer was calibrated for, etc.)
BNA 016 – 12 – Buoyancy

12.13 Given the density of dock water and TPC for sea water,
calculates the TPC for dock water
The TPC in salt water is given as
TPCSW = (1.025 x A) / 100 where A is the waterplane area.
From the above expression, waterplane area can be calculated as
A = (TPCSW x 100)/1.025

For a vessel in dock water of density δ, TPC is given as

TPCDW = δ x A / 100
= (δ x (TPCSW x 100)) / (1.025 x 100)
= (TPCSW x δ) / 1.025

12.14 Given the density of dock water and FWA, calculates the
amount by which the appropriate load line may be submerged

Q. A vessel is in dock water of relative density 1.015. Her FWA is 200mm.

Calculate the amount by which her summer loadline can be submerged so
that when she goes to sea, she floats at her summer draft.

The amount by which her summer loadline can be submerged when

loading in dock water so that when she goes to sea, she floats at her
summer draft =
DWA = (change of densities) x FWA/ 0.025
= (1.025 – 1.015) x 20 /.025
= .010 x 20 / .025
= 8 cm

Q. A vessel loading in dock water of RD 1.015 in summer zone has her

summer loadline at the water level. Her TPC for summer draft is 20 and
her FWA is 200 mm. Calculate the amount of cargo that she can further
load so that when she goes to sea her summer load line is at the water
level.

FWA = 200mm = 20 cm
DWA = (change of densities) x FWA/ 0.025
= (1.025 – 1.015) x 20 /.025
= .010 x 20 / .025
= 8 cm

TPC = 20
Amount of cargo that can be loaded = 20 x 8 = 160 tonnes.

12.15 Given the present draught amidships and the density of

dock water, calculates the amount to load to bring the ship to the
appropriate load line in sea water
BNA 016 – 12 – Buoyancy

Q. A box shaped vessel of dimensions 100m X 20m X 15m floats in dock

water of RD 1.014 at a draft of 7m. If her summer draft is 11.8m calculate
the amount of cargo she can load to bring her to summer draft in sea
water.

Present displacement of ship = length x breadth x present draft x density

of water
= 100 x 20 x 7 x 1.014
= 14196 t
Summer displacement of ship = 100 x 20 x 11.8 x 1.025
= 24190 t
Cargo to be loaded = 24190 – 14196 = 9994 t

12.16 Uses tank sounding booklet to obtain volume of water KG

of water, in the tank for given sounding or ullage

Aboard a ship capacities of various tanks used for carriage of ballast are
mentioned in a tabular form in the tank sounding booklet against the
sounding (height of liquid column in the tank). Also the distance of centre
of gravity of the tank from the keel i.e. KG when the tank is full is also
mentioned.
However in case of a tank with uniform cross-section, the KG can be taken
at a height half of the sounding of water in the tank. It can also be
determined by subtracting the ullage (height of empty space above the
surface of liquid) from the tank height and dividing the remainder by 2.
BNA 016 – 12 – Buoyancy

12.17 Calculates weight of water in the tank

Weight of liquid in a tank can be given as = Volume of liquid in tank X
density of liquid in tank
i.e. W = L x B x D x δ
Where, L = Length of tank
B = Breadth of tank
D = Sounding of liquid in tank
δ = Density of liquid in tank

12.18 Draw to the scale the load lines of a cargo & timber ship
12.19 State that the WNA mark is situated 50mm below the
winter line for the V/L less than 100m in length

Load lines
(1) Except as otherwise provided for in paragraph (3), the load lines shown
in Figure shall consist of horizontal lines of 230 millimetres in length and
25 millimetres in width extending forward or abaft of a vertical line 25
millimetres in width marked 540 millimetres forward of the centre of the
ring of the load line mark and at right angles to that line. The individual
load lines shall be as follows -
(a) the Summer load line, which shall extend forward of the said vertical
line, and shall correspond horizontally with the line passing through the
centre of the ring of the load line mark, and shall be marked S;

(b) the Winter load line, which shall extend forward of the vertical line, and
be marked W;

(c) the Winter North Atlantic load line, which shall extend forward of the
BNA 016 – 12 – Buoyancy

vertical line, and be marked WNA;

(d) the Tropical load line, which shall extend forward of the vertical line,
and be marked T;

(e) the Fresh Water load line, which shall extend abaft the vertical line,
and be marked F; and

(f) the Tropical Fresh Water load line, which shall extend abaft the vertical
line and be marked TF.

(2) The maximum depth to which a ship may be loaded in relation to a

load line referred to in paragraph (1) shall be the depth indicated by the
upper edge of the appropriate load line.

(3) In the case of a sailing ship -

(a) the Summer load line shall consist of the line passing through the
centre of the ring of the load line mark; and

(b) the Winter North Atlantic load line and Fresh Water load line only shall
be marked on the ship as shown in Figure. The WNA mark is situated
50mm below the winter line for the V/L less than 100m in length.
BNA 016 – 12 – Buoyancy

Timber load lines

(1) Timber load lines shall consist of horizontal lines of the dimensions
specified in respect of such lines as explained in above paragraph,
extending abaft or forward of a vertical line 25 millimetres in width and
marked 540 millimetres abaft the center of the ring of the load line mark
and at right angles to that line as shown in Figure and individual Timber
load lines shall be as follows -
(a) the Summer Timber load line, which shall extend abaft the said vertical
line and be marked LS;

(b) the Winter Timber load line, which shall extend abaft the vertical line
and be marked LW;

(c) the Winter North Atlantic Timber load line, which shall extend abaft the
vertical line and be marked LWNA;

(d) the Tropical Timber load line, which shall extend forward of the vertical
line and be marked LT;

(e) the Fresh Water Timber load line, which shall extend forward of the
vertical line and be marked LF; and

(f) the Tropical Fresh Water Timber load line, which shall extend forward of
the vertical line and be marked LTF.
(2) The maximum depth to which a ship may be loaded in relation to a
Timber load shall be the depth indicated by the upper edge of the
appropriate Timber load line.

Position of load lines

Each load line shall be marked in such a position on each side of the ship
that the distance measured vertically downwards from the upper edge of
the deck-line to the upper edge of the load line is equal to the freeboard
assigned to the ship which is appropriate to that load line.

Method of marking
(1) The appropriate marks shall be marked in such a manner as to be
plainly visible.

(2) If the sides of the ship are of metal the appropriate marks shall be cut
in, centre punched or welded; if the sides of the ship are of wood the
marks shall be cut into the planking to a depth of not less than 3
millimetres; if the sides are of other materials to which the foregoing
methods of marking cannot effectively be applied the marks shall be
permanently affixed by bonding or some other effective method.

(3) The appropriate marks shall be painted in white or yellow if the

background is dark, and in black if the background is light.
BNA 016 – 12 – Buoyancy

(4) Where a ship is assigned special freeboards which are less than those
required by regulation 29 of load line regulations the load line mark shall
comply with the requirements of regulation 17, except that it shall be
painted in red on a contrasting background. If the red marking is in
addition to the load line mark required by regulation 17 it shall be placed
with the centre of the ring 762 mm abaft the load line mark.

12.20 Given the summer draft, calculate the distance between

the winter & summer, summer & tropical draft.

Q. Draw the loadline marks on the port side of a ship of length 95m having
a summer draft of 8m and summer displacement 12000 tonnes. The
moulded depth of ship is 12 m and the waterplane area at summer draft is
2000m2.

Ans:
TPC of ship = A x 1.025/ 100 = 2000 x 1.025 /100 = 20.5 t
FWA = W / 40xTPC = 12000 / 40x20.5 = 14.634 cm
BNA 016 – 12 – Buoyancy

Summer Freeboard = 12 – 8 = 4m
Distance between Summer and Tropical OR Summer mark and Winter
mark = 1x8/48
= 16.667cm
Since the length of ship is 95m (less than 100m) so it will be having WNA
mark.

12.21 Given the summer draft calculate the quantity of cargo to

be loaded / discharged to reach at desired load line

As the distance between the different draft marks can be calculated using
the summer draft, amount of cargo to be loaded or discharged can be can
be calculated by multiplying this depth by the TPC of the vessel.