STABILITY OF SHIPS UNIT-III
UNIT III - CALCULATION OF AREA, VOLUME, FIRST AND SECOND MOMENTS
1. What is meant by “Stiff” and “Tender” ship?
2. What is longitudinal meta centric height?
3. Write down the formula of Simpson’s first and second rule to find the area of a waterplane?
4. What is meant by Displacement of a Ship? Define Displacement.
5. State Simpson’s 1st rule for ‘N’ ordinates.
6. State Simpson’s 2nd rule for ‘N’ ordinates.
7. What is Centre of Gravity of an object? / What do you mean by centre of gravity (G or COG) of a
ship?
8. What is the Simpson’s Rule application in ship stability?
9. Explain the outcome of addition and movement of mass in the ship with respect to Centre of gravity
of the ship. / What is the effect of movement of mass on centre of gravity?
10. How does the added mass effects ship’s stability?
11. Due to addition of mass onboard ship, list the changes takes place in stability data.
12. State the use of intermediate ordinate rule. / Write the use of introducing intermediate ordinates.
13. Mention the effect on C.G. due to movement of suspended mass.
14. What is the position of the Centre of gravity of a suspended mass relative to the ship?
15. What is meant by the term Wall sided ship?
16. What is the effect of movement of mass on centre of gravity?
E1 The equally-spaced half ordinates of a watertight flat 27 m long are 1.1, 2.7, 4.0, 5.1, 6.1, 12Marks
(2017)
6.9 and 7.7 m respectively. Calculate the area of the flat.
E2 The immersed cross-sectional areas through a ship 180 m long, at equal intervals, are 5, 13Marks
(2019)
118, 233, 291, 303, 304,304, 302, 283, 171, and 0 m2 respectively. Calculate the 12Marks
displacement of the ship in sea water of1.025tonne/m3. (2016)
E3 The TPC values for a ship at 1.2 m intervals of draught commencing at the keel are 8.2, 12Marks
(2016)
16.5, 18.7, 19.4, 20.0,20.5 and 21.1 respectively. Calculate the displacement at 7.2 m
draught
E4 The half ordinates of a cross-section through a ship are as follows: 13Marks
(2018)
WL keel 0.25 0.50 0.75 1.0 1.5 2.0 2.5 3.0 4.0 5.0 6.0 7.0 m 16Marks
½ ord 2.9 5.0 5.7 6.2 6.6 6.9 7.2 7.4 7.6 7.8 8.1 8.4 8.7 m (2016)
16Marks
Calculate the area of the cross-section to the 7 m waterline.
(2008)
E5 The half ordinates of a waterplane 180 m long are as follows: 16Marks
(2015)
Section AP ½ 1 2 3 4 5 6 7 8 9 9½ FP 16Marks
½ord 0 5.08.0 10.5 12.5 13.5 13.5 12.5 11.07.5 3.0 1.0 0m (2008)
Calculate:
(a) area of waterplane
(b) distance of centroid from midships
(C) Second moment of area of waterplane about a transverse axis through the centroid.
Prepared by MANIVANNAN.S, Assistant Professor / Marine Engineering Page1|4
STABILITY OF SHIPS UNIT-III
E6 The half ordinates of a waterplane 180 m long are as follows: 13Marks
(2019)
Section AP ½ 1 2 3 4 5 6 7 8 9 9½ FP
½ord 0 5.0 8.0 10.5 12.5 13.5 13.5 12.5 11.07.5 3.0 1.00m
Calculate the second moment of area of the waterplane about the centreline.
E7 A double bottom tank extends from the centerline to the ship side. The widths of the tank
surface, at regular intervals of h, are y1, y2, y3, y4 and y5.
Calculate the second moment of area of the tank surface about a longitudinal axis through
its centroid. It is necessary in this calculation to determine the area, centroid from the
centreline and the second moment of area.
E8 16Marks
A double bottom tank 21 m long has a watertight centre girder. The widths of the tank top (2015)
measured from the centreline to the ship's side are 10.0, 9.5, 9.0, 8.0, 6.5, 4.0 and 1.0 m
respectively. Calculate the second moment of area of the tank surface about a longitudinal
axis through its centroid, for one side of the ship only.
E9 A fore peak bulkhead is 4.8 m deep and 5.5 m wide at the deck. At regular intervals of 1.2 12Marks
(2017)
m below the deck, the horizontal widths are 5.0, 4.0, 2.5 and 0.5 m respectively. The
bulkhead is flooded to the top edge with sea water on one side only. Calculate:
(a) area of bulkhead
(b) load on bulkhead
(c) position of centre of pressure
E10 A ship of 8500 tonne displacement is composed of masses of 2000, 3000, 1000 , 2000 and 5Marks
(2019)
500 tonne at positions 2, 5, 8, 10, and 14 m above the keel. Determine the height of the 12Marks
centre of gravity of the ship above the keel. (2016)
E11 A ship of 6000 tonne displacement is composed of masses of 300, l200 and 2000 tonne at 13Marks
(2021)
distances 60, 35 and 11 m aft of mdships, and masses of 1000, 1000 and 500 tonne at 12Marks
distances 15, 30 and 50 m forward of midships. Calculate the distance of the centre of (2016)
gravity of the ship from midships.
E12 A ship of 4000 tonne displacement has its centre of gravity 1.5 m aft of midships and 4 m 16Marks
above the keel. 200 tonne of cargo are now added 45 m forward of midships and 12 m (2016)
16Marks
above the keel. Calculate the new position of the centre of gravity. (2015)
E13 A ship of 5000 tonne displacement has a mass of 200 tonne on the fore deck 55 m forward 2Marks
of midships. Calculate the shift in the centre of gravity of the ship if the mass is moved to a (2019)
position 8 m forward of midships.
E14 A ship of 10 000 tonne displacement has a mass of 60 tonne lying on the deck. A derrick, 16
whose head is 7.5 m above the centre of gravity of the mass, is used to place the mass on Marks
(2007)
the tank top 10.5 m below the deck. Calculate the shift in the vessel's centre of gravity 16Marks
when the mass is: (2012)
(a) just dear of the deck
(b) at the derrick head
(c) in its final position.
TE1 A ship 180 m long has ½ widths of waterplane of 1, 7.5, 12, 13.5, 14, 14, 14, 13.5, 12, 7 13Marks
(2018)
and 0 m respectively. Calculate:
(a) waterplane area
(b) TPC
(C) Waterplane area coefficient.
TE2 The waterplane areas of a ship at l .5 m intervals of draught, commencing at the keel, are
865, 1735, 1965, 2040, 2100. 2145 and 2215 m2 respectively. Calculate the displacement
at 9 m draught.
Prepared by MANIVANNAN.S, Assistant Professor / Marine Engineering Page2|4
STABILITY OF SHIPS UNIT-III
TE3 A ship 140 m long and 18 m beam floats at a draught of 9 m. The immersed cross-sectional 13Marks
(2019)
areas at equal intervals are 5, 60, 116, 145, 152, 153, 153, 151, 142, 85 and 0 m2
respectively.
Calculate:
(a) displacement
(b) block coefficient
(c) midship section area coefficient
(d) prismatic coefficient.
TE4 The ½ ordinates of a waterplane 120 m long are as follows:
Section AP 1 1½ 2 3 4 5 6 7 8 8½ 9 9½ FP
½ ord 1.2 3.5 5.3 6.8 8.0 8.3 8.5 8.5 8.5 8.4 8.2 7.9 6.2 3.5 0 m
Calculate:
(a) waterplane area
(b) distance of centroid from midships.
TE5 The TPC values of a ship at 1.5 m intervals of draught, commencing at the keel, are 4.0,
6.1, 7.8, 9.1, 10.3, 1 1.4 and 12.0 m respectively. Calculate at a draught of 9 m:
(a) displacement
(b) KB
TE6 The ½ breadths of the load waterplane of a ship 150 m long, commencing from aft, are 0.3,
3.8, 6.0, 7.7, 8.3, 9.0, 8.4, 7.8, 6.9, 4.7 and 0 m respectively. Calculate:
(a) area of waterplane
(b) distance of centroid from midships
(c) second moment of area about a transverse axis through the centroid
TE7 The displacement of a ship at draughts of 0, l, 2.3 and 4 m are 0, 189, 430, 692 and 977
tonne. Calculate the distance of the centre of buoyancy above the keel when floating at a
draught of 4 m, given:
VCB below waterline =area between displacement curve and draught axis
displacement
TE8 The widths of a deep tank bulkhead at equal intervals .of 1.2 m commencing at the top, are
8.0, 7.5, 6.5, 5.7, 4.7, 3.8 and 3.0 m. Calculate the load on the bulkhead and the position of
the centre of pressure, if the bulkhead is flooded to the top edge with sea water on one side
only.
TE9 A forward deep tank 12 m long extends from a longitudinal bulkhead to the ship's side.
The widths of the tank surface measured from the longitudinal bulkhead at regular
intervals are 10, 9, 7, 4 and 1 m. Calculate the second moment of area of the tank surface
about a longitudinal axis passing through its centroid.
TE10 A ship 160 m long has ½ ordinates of waterplane of 1.6, 5.7, 8.8, 10.2, 10.5, 10.5, 10.5,
10.0, 8.0, 5.0 and 0 mrespectively. Calculate the second moment of area of thewaterplane
about the centreline.
TE11 The immersed cross-sectional areas of a ship 120 m long, commencing from aft, are 2, 40,
79, 100, 103, 104, 104, 103, 97,58 and 0 m2. Calculate:
(a) displacement
(b) Longitudinal position of the centre of buoyancy.
TE12 A ship of 4000 tonne displacement has its centre of gravity 6 m above the keel. Find the
new displacement and position of the centre of gravity when masses of 1000, 200, 5000
and 3000 tonne are added at positions 0.8, 1.0, 5.0 and 9.5 m above the keel.
TE13 The centre of gravity of a ship of 5000 tonne displacement is 6 m above the keel and 1.5 m
Prepared by MANIVANNAN.S, Assistant Professor / Marine Engineering Page3|4
STABILITY OF SHIPS UNIT-III
forward of midships. Calculate the new position of the centre of gravity if 500 tonne of
cargo are placed in the 'tween decks 10 m above the keel and 36 m aft of midships.
TE14 A ship has 300 tonne of cargo in the hold, 24 m forward of midships. The displacement of 16Marks
(2012)
the vessel is 6000 tonne and its centre of gravity is l .2 m forward of midships. Find the
new position of the centre of gravity if this cargo is moved to an after hold, 40 m from
midships.
TE15 An oil tanker of 17 000 tonne displacement has its centre of gravity 1 m aft of midships 16Marks
(2015)
and has 250 tonne of oil fuel in its forward deep tank 75 m from midships. This fuel is 16Marks
transferred to the after oil fuel bunker whose (2012)
centre is 50 m from midships. 200 tonne of fuel from the after bunker is now burned.
Calculate the new position of the centre of gravity:
(a) after the oil has been transferred
(b) after the oil has been used.
TE16 A ship of 3000 tonne displacement has 500 tonne of cargo on board. This cargo lowered 3 16Marks
(2013)
m and an additional 500 tonne of cargo is taken on board 3 m vertically above the original
position of the centre of gravity. Determine the alteration in position of the centre of
gravity.
TE17 A ship of 10 000 tonne displacement has its centre of gravity 3 m above the keel. Masses 16Marks
(2012)
of 2000, 300 and 50 tonne are removed from positions 1.5, 4.5 and 6 m above the keel.
Find the new displacement and position of the centre of gravity.
TE18 A vessel of 8000 tonne displacement has 75 tonne of cargo on the deck. It is lifted by a 16Marks
(2013)
derrick whose head is 10.5m above the centre of gravity of the cargo, and placed In the 16Marks
lower hold 9 m below the deck and 14 m forward of its original position. Calculate the (2011)
shift in the vessel's centre of gravity from its
original position when the cargo is:
(a) just clear of the deck
(b) at the derrick head
(C) in its final position.
TQ1 Explain the effect of stability (COG) of the ship when the mass is added, shifted, 13Marks
(2017)
suspended and the conclusion. 13Marks
(2018)
TQ2 Derive an expression for a shift in centre of gravity due to added mass. 10Marks
(2007)
Prepared by MANIVANNAN.S, Assistant Professor / Marine Engineering Page4|4
