Miscelleneous

C L DUBEY – EXERCISE – 11 (Grain Stability)

Q1. A vessel displacing 16500 tonnes has KG, 7.50m. Calculations of grain shift give the following data.
Volumetric heeling moment = 3960m4
Stowage factor = 1.2m3/tone
For the given displacement and KG the vessel has the following values of GZ at the angle of heel given.
Heel
0
15
30
45
60
75
90
GZ
0.00
0.267
0.645
0.571
0.163
-0.454
-1.104m
Verify whether the vessel satisfies intact stability requirements for grains cargo. Angle of flooding is 400.
Solution –

Given VHM = 3960m4
Weight heeling moment = 3960/1.2
= 3300m4
λ0 = 0.2m, λ40 = 0.16m

  • GM = 0.776m

Therefore, condition 1 satisfied

  • Angle of heel = 120 = Marginal.

GS 01

HeelOrdinate   SM           Product
00.010
100.1540.60
200.3320.66
300.64542.28
400.61010.610
   4.45

Area = 10/3 ⨯ 4.45/57.3
= 0.259m radian

Area of triangle = 0.5 ⨯ 12 ⨯ 0.19/57.3
= 0.0199m radian

Area of trapezium = 0.5 ⨯ (0.19 + 0.16) ⨯ 28/57.3
= 0.085 m radian

Residual area = 0.16m radian ˃ 0.075
Therefore, condition 3 satisfied.

Hence, vessel satisfy intact stability requirement for grain cargo or grain loading criteria.
Q2. The values of GZ of a vessel at different angles of heel are as follows:
Heel (0)
0
5
12
20
30
40
60
75
GZ (m)
0.0
0.188
0.449
0.764
1.227
1.551
1.713
1.298
The heeling arm at 00 = 0.275 metres. The angle of flooding is 400 and maximum difference between the righting arm and heeling arm occurs at an angle greater than 400. Verify whether the vessel satisfies the intact stability requirements for a cargo ship carrying grain in bulk.
Solution –

Given λ0 = 0.275, λ40 = 0.22

GS02

HeelOrdinateSMProduct
001o
100.3541.4
200.76421.53
301.22744.91
401.55111.55
               SOP = 9.30

Area of triangle = 0.5 ⨯ 7 ⨯ 0.265/57.3
= 0.016m radian

Area of trapezium = 0.5 ⨯ (0.265 + 0.22) ⨯ 33/57.3
= 0.139m radian

Residual area = 0.397m radian > 0.075m radian
Therefore, condition 3 satisfied

Hence, vessel satisfy intact stability requirement for grain cargo or grain loading criteria.
Q3. The values of GZ vessel for various angles of heel are as follows:
Heel (0)
00
05
12
20
30
40
60
75
GZ (m)
0.000
0.136
0.315
0.472
0.604
0.631
0.562
0.248
The heeling arm at 00 = 0.18m. The angle of flooding is 400 and maximum difference between the righting arm and heeling arm occurs at 430. Verify whether the vessel satisfied the criteria of stability for a cargo ship carrying grain in bulk (Assume the deck edge immerses at 100  heel).
Solution –

Given, λ0 = 0.18m, λ40 = 0.14m

GS03

List OrdinateSMProduct
00.010
100.26341.052
200.47220.944
300.60442.416
400.63110.631
   SOP = 5.043

Area = 10/3 ⨯ 5.043/57.3
= 0.293 m radian

Area of triangle = 0.5 ⨯ 6.5 ⨯ 0.1735/57.3
= 0.010m radian

Area of trapezium = 0.5 ⨯ (0.1735 + 0.14) ⨯ (4.0 – 6.5)/57.3
= 0.191m radian

Residual area = 0.192m > 0.075m radian
Therefore, All condition satisfied.

Hence, vessel satisfy intact stability requirement for grain cargo or grain loading criteria.
 
Q4. A vessel loaded with grain in bulk is at a displacement of 35186t, KG 7.809m, KM 11.30m. The stowage factor of the grain is 1.3m3/t and the total volumetric heeling Moments are 21321 m4. AT the displacement her KN values are as follows:
Heel (0)
5
12
15
30
45
60
GZ (m)
1.00
2.42
2.90
5.60
7.30
8.05
If her angle of flooding exceeds 400, ascertain whether the vessel complies with the intact stability requirements for such vessels.
Solution –

Given, KM = 11.30
KG = 7.809m

GM = (KM – KG)
        = 3.491m > 0.3m

Therefore, Condition 1 satisfied

Now total volumetric heeling moment = 21321
Weight heeling moment = VHM/SF
= 16400.7692

Heeling arm = λ0 = 16400.76923/35186
= 0.466m
λ40 = 0.373m

heel 51215304560
KN1.0020422.905.607.308.05
KG SinӨ0.6801.6232.0213.9045.5226.763
GZ0.3200.7970.8791.6961.7781.287

GS04

HeelOrdinateSMProduct
0010
100.6542.6
201.0522.10
301.69646.784
401.76011.760
  SOP = 13.244

Area = 10/3 ⨯ 13.244/57.3
= 0.770 m radian

Area of triangle = 0.5 ⨯ 7 ⨯ 0.420/57.3
= 0.026 m radian

Area of trapezium = 0.228 m radian
Therefore, Residual area = 0.516 m radian > 0.075
Condition 3 satisfied.

Hence, vessel satisfy intact stability requirement for grain cargo or grain loading criteria.
Q5. The values of GZ vessel for various angles of heel are as follows:
Heel (0)
00
05
12
20
30
40
60
75
GZ (m)
0.000
0.136
0.315
0.472
0.604
0.631
0.562
0.248
The heeling arm at 00 = 0.18m. The angle of flooding is 400 and maximum difference between the righting arm and heeling arm occurs at 430. Verify whether the vessel satisfied the criteria of stability for a cargo ship carrying grain in bulk (Assume the deck edge immerses at 100  heel).
Solution –

λ0 = 0.18, λ40 = 0.144

GS05

ListordinateSMProduct 
0010
100.13540.54
200.47220.944
300.60442.416
400.63110.631
   4.531

Area = 10/3 ⨯ 4.531/57.3
= 0.2637 m radian

Area of triangle = 0.5 ⨯ 17 ⨯ 0.162/57.3
= 0.024 m radian

Area of trapezium = 0.5 ⨯ (0.163 + 0.144) ⨯ 23/57.3
= 0.062 m radian

Residual area = 0.1811m radian
Therefore, Ship doesn’t comply.

Hence, vessel does not satisfy intact stability requirement for grain cargo or grain loading criteria.


manish-mayank

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Manish Mayank

Graduated from M.E.R.I. (Mumbai). A cool, calm, composed and the brain behind the development of the database. The strong will to contribute in maritime education and to present it in completely different and innovative way is his source of inspiration.

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