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

Heel Ordinate    SM           Product
0 0.0 1 0
10 0.15 4 0.60
20 0.33 2 0.66
30 0.645 4 2.28
40 0.610 1 0.610
      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

Heel Ordinate SM Product
0 0 1 o
10 0.35 4 1.4
20 0.764 2 1.53
30 1.227 4 4.91
40 1.551 1 1.55
                 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

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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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