OTHER STABILITY KNOWLEDGE

Stability Information
Stability definitions
Stability Formula
Stability Sum Made Easier

Equilibrium

RESERVE BUOYANCY

Reserve Buoyancy may be defined as the volume of the enclosed spaces above the waterline. It may be expressed as a volume or as percentage of the total volume of the vessel.

sample 1:

A box shaped vessel 105m x 30m x 20m is floating upright in fresh water. if the displacement is 19500 tonnes, find the volume of reserve buoyancy.

Volume of water displaced = Mass/Density = 19500/1.000 = 19500 m3

Volume of vessel                 = 105 x 30 x 20 = 63000 m3

Reserve buoyancy               = Volume of vessel - volume of water displaced

                                         = 63000 m3 - 19500 m3 = 43500 m3

DENSITY AND SPECIFIC GRAVITY

Density is define as "mass per unit volume".

FW = 1000 kg per m3 or 1.000 ton/m3
SW = 1025 kg per m3 or 1.025 ton/m3

Density in kg/m3 = 1000 x SG

sample 1:
When double bottom tank is full of fresh water it holds 120 tonnes. Find how many tonnes of oil of relative density 0.84 it will hold.

Relative density = Mass of Oil / Mass of FW
Mass of Oil = Mass of FW x relative density
                    = 120 x 0.84 tonnes
                    = 100.8 tonnes of oil

sample 2:
A tank measures 20m x 24m x 10.5m and contains oil of relative density 0.84. Find the mass of oil it contains when the ullage is 2.5m. Ullage is the distance from the liquid surface in the tank to the top of the tank.

Volume of oil  = L x B x D
                        = 20 x 24 x 8

Density of oil  = SG x 1000
                        = 840 kg/m3 or 0.84 t/m3

Mass of oil      = Volume x density
                         = 20 x 24 x 8 x 0.84
                         = 3225.6 tonnes


Specific Gravity of some liquids
Salt water = 1.025                   Oil fuel = 0.950            Lubricating fuel = 0.900
Fresh water = 1.000                Diesel fuel = 0.900

the mass of each above is 1 ton with various volumes

Effect of change of density when the displacement is constant

When a ship moves from water of one density to water of another density, without there being a change in her mass, the draft will change.

Mass = Volume x Density

The effect on box-shaped vessels 

New Volume  =  Old  density         or     New draft   =   Old density
Old Volume        New density                 Old draft         New density

sample 1:
A box-shaped vessel floats at mean draft of 2.1 metres, in dock water of density 1020 kg/m3. Find the mean draft for tha same mass displacement in salt water of density 1025 kg/m3.

answer: New draft = 2.09 metres (you can try the above formula)

sample 2:
A box-shaped vessel float upright on an even keel as shown in fresh water of density 1000 kg/m3 and the CoB is 0.50 m above the keel. Find the height of the CoB above the keel when the vessel is floating in salt water of density 1025 kg/m3.

CoB of Box shaped vessel :  KB = 0.5 draft

Answer:
In fresh water:   KB=0.5m and since KB = 0.5draft, then draft = 1 m

In salt water :  New draft     =   Old draft x (Old density / New density)
                                              =   1 x 1000/1025
                                              =    0.976 m
                        New KB        =   0.5 new draft
                                              =   0.488 ~0.49 m

 The effect on box-shaped vessels 

 New displacement  =  Old Displacement

New volume x New density  =   Old volume x Old density

New volume  =  Old density

   Old volume       New density

FWA (Fresh Water Allowance) = number of millimeters by which the mean draft changes when a ship passes from salt water to fresh water or vice versa, whilst floating at the loaded draft.

FWA (in mm) = Displacement (W in tonnes) / (4 x TPC)

Dock Water Allowance = FWA (1025 - density of Dock Water) /25

sample 3:A ship is loading in dock water of density 1010 kg/m3 FWA=150 mm. Find the change in draft on entering salt water.

answer:

Let x = the change in draft in mm, then:

x / FWA = (1025 - 1010) / 25

           x  = 150 x (15/25)

           x  =  90 mm

Draft will decrease by 90 mm, i.e. 9 cm