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Assignment No 3- Stability at Large Angles of Heel, Docking,Grounding & Damaged Stability 1. Derive the Wall sided formula for large angle of heeling GZ= (GM+BM*Tan 2θ/2)*Sinθ. Hence Derive expression for Angle of Loll. 2. A ship of 5000 tonne displacement has a rectangular double bottom tank 9 m wide and 12 m long, half full of sea water. Calculate the virtual reduction in metacentric height due to free surface. Ans. 0.149 m 3. Prove that for small angle of heel, Metacentric Radius is given by the ratio of Transverse Moment of Inertia of Ship's water plane around its longitudinal axis and Volumetric displacement of the ship. 4. For M.V. MMTI, displacement 5000 t. KN values for different Angles of Heel are given below . Draw the Curve of Righting Lever for KG= 6.1m and find following values from the Graph. a. Range of Stability b. Value of Maximum Righting Lever and angle of Maximum Righting Lever c. Approximate initial GM d. The Moment of Statical Stability at 30 degrees of Heel. e. Angle of Vanishing Stability. Angle of Heel (θ)
0
KN (m)
0
15
30
45
60
75
90
2.65 5.15 6.90 7.55 7.35 6.4 Ans. a. 0-94 degrees, b. 2.58 at 45 degrees, c. 3.25 m, d. 10500 t-m, e. 94 Degrees
5. A ship at displacement 45000t has GM=0.67m. The Cross curves show constant values of GZ for any displacement from 43000t to 45000t inclusive, and for the ship's actual KG, the values of GZ are as follows. A 2000 t of Cargo are discharged from a position 17m below the Center of Gravity of the ship. Draw the GZ curve for the new condition and state information obtained from it. Angle of Heel (θ)
0
3
6
9
12
15
30
45
60
75
GZ(m)
0
0.035
0.07
0.1
0.14
0.22
0.71
1.05
1.02
0.85
90
0.56 Ans. a. GM= -0.2 m, b. Angle of Loll= 14, c. Angle of Vanishing Stability= 77 Degress, d. Range of Stability = 14- 77 degrees, e. Max GZ= 0.51m
6. A ship displacing 5000t has GZ values as follows when KG= 6m. Draw the Statical Stability Curve for this condition and for KG= 5 m. Discuss the effect on Stability of lowering the CG of ship. Angle of Heel (θ)
0
15
30
45
60
75
90
GZ(m)
0
0.14
0.36
0.73
0.67
0
-0.65
7. A ship with 12500t has KG= 6.3m has following particulars. Cargo of 500t at KG= 10.5m is discharged. Due to the discharge of cargo, find the effect on Maximum value of GZ and Range of Stability. Angle of 0 7.5 15 30 45 60 75 Heel (θ) GZ(m)
0
0.05
0.119
0.39
0.55 0.35 -0.21 Ans. New KG of Ship= 6.125 m
8. A ship has the following values of GZ at a displacement of 13473t. Angle of 0 15 30 45 60 Heel (θ) GZ(m)
0
0.53
1.29
1.61
1.03
75 -0.22
No. 1 hold is 118m long and 58m wide and contains cargo with a stowage rate of 58 m3/tonne. Due to rolling in heavy seas, the cargo shifts and its surface is lowered by 3m on one side and raised by 3m on the other side. Calculate a. Permanent List b. The reduction in the range of Stability c. The reduction in the value of maximum GZ. Ansa. Permanent List= 8.3 degrees, b. Reduction in range of Stability= 9.1 Degrees, c. Reduction in Max GZ= 0.17 m 9.
When inclined, a ship of 8000t displacement has the following righting levers
Angle of Heel (θ)
15
30
45
60
GZ(m)
0.2
0.3
0.32
0.24
Calculate the Dynamical stability to 60 degrees of heel.
Ans- 2038.4 t-m
10. A box shaped vessel 65m X 10m X 6m is floating upright on an even keel at 4m draft in salt water. GM=0.6m. Calculate the dynamical stability to 20 degrees of heel. Ans- 107.2 t-m 11. The dimension of a box barge floating in sea water is 75m length *15m breadth *1.0m draft. The KG of light box barge is 2.5m. 6000tonnes of cargo loaded in box barge whose centre of gravity is 4.2m above the keel. Find the GM and draw the statical stability curve. Ans- GM= 2.192m 12. A ship 12000 t displacement has second moment of area about the centerline 72x10 3 m4. If the metacentric height is -0.05. Calculate the Angle of Loll. At one point during Voyage, the above vessel is found to have angle of Loll 130. Calculate the initial Metacentric height. Ans- 7016' -0.164m
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