ship displacement theory

1. DISPLACEMENT DEFINITIONS AND
FORMULAS

2. Light Displacement : (LDT) is defined as the weight of the ship excluding cargo, fuel, water,
ballast, stores, passengers, crew, but with water in boilers to steaming level.[7]
Dead weight : is the difference between Load displacement and light displacement .
Load Diplacement :Is the weight of the ship including cargo, passengers, fuel, water,
stores, dunnage and such other items necessary for use on a voyage. These bring the ship
down to its "load draft",[7] colloquially known as the "waterline".
Dispalcement :The displacement or displacement tonnage of a ship is its weight, expressed
in tons of water its hull displaces. It is measured indirectly using Archimedes' principle by first
calculating the volume of water displaced by the ship then converting that value into tons.

3. • Density is mass per unit volume and =Mass/ Volume
• Mass = Volume X density
• Weight = Mass X acceleration (9.81 )
• Relative density or Specific gravity is : the ratio of the weight of
substance to the weight of an equal weight of Fresh Water and is
• = Density of substance /density of Fresh water ( 1000 tons/cu.mtr)
• FW RD = 1.000
• SW Rd = 1.025
• Displacement = Volume of displacement X Water density
• W= V X D
• Volume of displacement = length X Breadth X Draft
• V = L XB X d
• Displacement = L X B Xd X D

4. Draught : is the distance
from Keel to the Water
line as measured at the
forward and after ends of
the Vessel and is
expressed in Meters.
1
Freeboard : Is the
distance between the
Water line and the Top of
uppermost continuous
Deck and is expressed in
MMS and is measured
amidships .
2
Hull depth = Draught +
Freeboard .
3

5. Reserve
Buoyancy :
Is the Volume of all enclosed
spaces above water Line

6. Law of Flotation
• Archimedes Principle :
• When a body is wholly or
partially immersed in fluid it
appears to suffer a loss in
Mass equal to the Mass of
water it displaces

8. TPC
• The TPC for any given
draught is the weight
that must be loaded or
discharged to change the
ship’s mean draught by
one centimetre.

9. • A weight of 30 tonnes is loaded on
deck so that the mean draught
increases by 1 cm
Since the ship’s displacement is equal to
the mass of water displaced (Law of
Flotation) it follows that the mass of the
additional ‘slice’ of displaced water is
equal to the added weight of 30 tonnes.
In this instance, 30 tonnes represents the
value of the Tonnes per Centimetre
Immersion (TPC) for the ship at the initial
draught before the weight was loaded.

10. • Derivation of TPC/ how TPC is derived ?
• Consider the previous situation.
• Since: Mass = Volume x Density
• then:
• Mass of additional slice of water = Volume
of the additional slice of water X Density.
• If the WPA is assumed to not significantly
change between the two waterlines, then:
• Volume of the slice = WPA (m2) x 1 cm
• We cannot multiply m2 by cms, therefore:
• Volume of slice = WPA (m2) x 1 (m)/100;
• ∴ Added displacement (t) = WPA (m2) x 1
(m) x density (t/m3)/100;
• Therefore, the formula for TPC is:
•

11. Considering the
TPC formula:
1
It shows that:
2
TPC increases with
WPA and for a
normal ship-shape
the WPA will
increase with
draught.
3
Bodily sinkage
rise(cm ) =
W/TPC
4
TPC increases
with density.
5

12. COEFFICIENTS

13. Coefficient of fineness of waterplane Area ( Cw )
is defined as the ratio of the ship’s water-plane area (WPA) to the area of a rectangle having the same
length (L) and breadth (B) of the ship at the waterline in question.
L = LBP
B= BR.MLD
• Since the ship’s WPA is less in area than the rectangle formed around it, the value of Cw must always be
less than 1.00.

14. Block Coefficient ( Cb )
The block coefficient (CB) of a ship is
the ratio of the underwater volume of
a ship to the volume of the
circumscribing block.
Since the ship’s volume of
displacement is less than the volume
of displacement of the surrounding
block, the value of CB must always be
less than 1.00.

15. MIDSHIPS COEFFICIENT ( Cm )
• The midships coefficient (CM) of a ship at any
draught is the ratio of the underwater transverse
area of the midships section to the product of the
breadth and draught.

16. PRISMATIC COEFFICIENT ( Cp )
• The longitudinal prismatic coefficient (CP)
of a ship at any draught is the ratio of the
underwater volume of the ship to the
volume of the prism formed by the
product of the transverse area of the
midships section and the waterline
length.
• Cb = Cm X Cp

17. Block
Coefficient and
Life Boat
Cb for life Boat is 0.6
V= L X B X D X 0.6
No.of Persons it can carry = V/X
X= 0.283 for LB =or > 7.3 mt. lenght
X= 0.396 for LB 4.9 mt. length .