Lecture 4:
The Weight Curve
Aim of this lecture:
• To understand the weight distribution curve and the major
contributions to the weight distribution
At the end of the lecture, you should be able to:
• Understand how to model the longitudinal weight
distribution for a ship
• Describe the principal components of a weight curve
• Calculate the area and centroid of a trapezoid and other
common used shapes to represent weight distribution
• We have thought about the equilibrium forces acting on a
ship in still water and when poised on a wave
• We have also thought about the distribution of buoyancy
over the ship length and methods to calculate draft, trim
and LCB for a given LCG and ship weight
• Now we need to think about the other side of the
equilibrium equation – the weight distribution
• What are the important masses on a ship to consider?
• Lightship:
• Steel Structure
• Machinery
• Equipment
• Deadweight:
• Cargo
• Fuel
• Stores
• Water
• Passengers
• Weight distribution is considered LONGITUDINALLY only
• We can subdivide the lightship into:
• Continuous Material
• Concentrated and semi-concentrated material
• In pairs, try to categorise the following items:
• Shell plating
• Longitudinal stiffeners
• Longitudinal bulkheads
• Transverse frames
• Compartment Bulkhead
• Anchor
• Main engine Continuous Semi- Concentrated
• Superstructure concentrated
• Cargo Hatch
• Crane
• Lifeboat and davits
• Anything else?
• We normally treat the longitudinal hull structure as continuous
• Weight/unit length is greater amidships
• Parallel middle body
• It is possible to develop an approximate curve for the weight
of continuous material bearing in mind these characteristics
• A well known approximation was proposed by Sir John H Biles
The Biles approximation assumes
the weight distribution curve as
shown to the right.
• Over the amidships third the weight
distribution curve is assumed to be
constant.
• The weight distribution is then assumed to drop off linearly to
values of a and b at the aft and fore ends respectively.
• The value of the ordinate of the weight curve amidships is
assumed to be 1.2 x the mean ordinate of the curve.
• The ordinates a and b are then calculated so as to give the correct
total weight of of continuous material W and position of centre of
gravity K from amidships.
From this figure we can see
the following relationships:
Total Area
L 1.2h a L 1.2h b L
1.2h ( ) ( ) W
3 2 3 2 3
Or ab
(0.8h )L W
6
Moment of area about amidships:
1.2h a L L 1.2h a L 1.2h b L L 1.2h b L
( ) ( ( )( )) ( ) ( ( )( ) WK
2 3 3 1.2h a 18 2 3 3 1.2h b 18
Or 7 L2
( a b) WK
108
Solving these two simultaneous equations the following values
are obtained:
54WK 54 K 54 K
a 0.6h 2
h ( 0.6 ) b h(0.6 )
7L 7 L 7 L
These values of a and b apply only to the
type of weight distribution considered.
• It is clear these assumptions could not apply to all ships.
– For example the weight per unit length of a large tanker would probably
be constant over a greater proportion of the length than one third.
– Or for a very fine ship with no parallel middle body, the weight will fall
off with the distance from amidships.
• A semi-continuous item has a weight distributed over a short
length, either:
• Uniform weight/length over the length of the item
• Changing weight/length over the length of the item
• If the weight changes appreciably:
• Represent with a trapezoidal distribution
• Calculate ordinates a and b for the correct CofG
• CoG and weight can be calculated:
l ( a b) l ( a b)
x w
6 ( a b) 2
• We can then derive for a and b:
w 6w x w 6w x
a 2 b 2
l l l l
• Judgement is required for semi-continuous items
• Add concentrated and semi-continuous items to the weight
curve
• Treated similar to semi-continuous lightship masses
• Use section area curves for the compartments
• Deadweight is added to the weight curve
• The LCG of the weight diagram will be the LCG of the ship
• The actual weight curve has many discontinuities
• Difficult to integrate / tabulate
• Overcome by dividing the ship into regular intervals and
assuming weight is constant within the interval
• Check total weight and LCG for the stepped diagram
• Use TPC and MCTC formulae to calculate the new draught
and trim of the following ship from a previous iteration:
• Current Displacement (from buoyancy analysis) = 80000 tonnes
• Required Displacement = 81000 tonnes
• Waterplane Area = 6000 m2
• Length bp = 150m , Breadth = 32m
• LCG and LCF are at amidships
• LCB = 0.1m fwd of amidships
• Previous iteration with even keel trim and T = 10m
Aim of this lecture:
• To understand the weight distribution curve and the major
contributions to the weight distribution
At the end of the lecture, you should be able to:
• Understand how to model the longitudinal weight
distribution for a ship
• Describe the principal components of a weight curve
• Calculate the area and centroid of a trapezoid and other
common used shapes to represent weight distribution
