**Q1. A vessel displacing 16500 tonnes has KG, 7.50m. Calculations of grain shift give the following data.**

** Volumetric heeling moment = 3960m**^{4}

** Stowage factor = 1.2m**^{3}/tone

**Q1. A vessel displacing 16500 tonnes has KG, 7.50m. Calculations of grain shift give the following data.**

**Volumetric heeling moment = 3960m**

^{4}**Stowage factor = 1.2m**

^{3}/tone**For the given displacement and KG the vessel has the following values of GZ at the angle of heel given.**

**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 40**^{0}.

**Verify whether the vessel satisfies intact stability requirements for grains cargo. Angle of flooding is 40**

^{0}.**Solution –**

**Solution –**

**Given VHM = 3960m ^{4}**

**Weight heeling moment = 3960/1.2**

**= 3300m**^{4}

**λ**_{0 }= 0.2m, λ_{40}= 0.16m**GM = 0.776m**

**Therefore, condition 1 satisfied**

**Angle of heel = 12**^{0}= Marginal.

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.**

**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:**

**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 0**^{0} = 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.

**The heeling arm at 0**

^{0}= 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 –**

**Solution –**

**Given λ _{0} = 0.275, λ_{40} = 0.22**

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**

**Hence, vessel satisfy intact stability requirement for grain cargo or grain loading criteria.**

**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:**

**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 0**^{0} = 0.18m. The angle of flooding is 40^{0} and maximum difference between the righting arm and heeling arm occurs at 43^{0}. Verify whether the vessel satisfied the criteria of stability for a cargo ship carrying grain in bulk (Assume the deck edge immerses at 10^{0 } heel).

**The heeling arm at 0**

^{0}= 0.18m. The angle of flooding is 40^{0}and maximum difference between the righting arm and heeling arm occurs at 43^{0}. Verify whether the vessel satisfied the criteria of stability for a cargo ship carrying grain in bulk (Assume the deck edge immerses at 10^{0 }heel).**Solution –**

**Solution –**

**Given, λ _{0 }= 0.18m, λ_{40} = 0.14m**

List | Ordinate | SM | Product |

0 | 0.0 | 1 | 0 |

10 | 0.263 | 4 | 1.052 |

20 | 0.472 | 2 | 0.944 |

30 | 0.604 | 4 | 2.416 |

40 | 0.631 | 1 | 0.631 |

| | | 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.**

**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 m**^{4}. AT the displacement her KN values are as follows:

**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 m**

^{4}. 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.**

**If her angle of flooding exceeds 400, ascertain whether the vessel complies with the intact stability requirements for such vessels.**

**Solution –**

**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 = λ _{0} = 16400.76923/35186**

**= 0.466m**

**λ**_{40 }= 0.373mheel | 5 | 12 | 15 | 30 | 45 | 60 |

KN | 1.00 | 2042 | 2.90 | 5.60 | 7.30 | 8.05 |

KG SinӨ | 0.680 | 1.623 | 2.021 | 3.904 | 5.522 | 6.763 |

GZ | 0.320 | 0.797 | 0.879 | 1.696 | 1.778 | 1.287 |

Heel | Ordinate | SM | Product |

0 | 0 | 1 | 0 |

10 | 0.65 | 4 | 2.6 |

20 | 1.05 | 2 | 2.10 |

30 | 1.696 | 4 | 6.784 |

40 | 1.760 | 1 | 1.760 |

| | 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.**

**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:**

**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 0**^{0} = 0.18m. The angle of flooding is 40^{0} and maximum difference between the righting arm and heeling arm occurs at 43^{0}. Verify whether the vessel satisfied the criteria of stability for a cargo ship carrying grain in bulk (Assume the deck edge immerses at 10^{0 } heel).

**The heeling arm at 0**

^{0}= 0.18m. The angle of flooding is 40^{0}and maximum difference between the righting arm and heeling arm occurs at 43^{0}. Verify whether the vessel satisfied the criteria of stability for a cargo ship carrying grain in bulk (Assume the deck edge immerses at 10^{0 }heel).**Solution –**

**Solution –**

**λ _{0 }= 0.18_{, }λ_{40} = 0.144**

List | ordinate | SM | Product |

0 | 0 | 1 | 0 |

10 | 0.135 | 4 | 0.54 |

20 | 0.472 | 2 | 0.944 |

30 | 0.604 | 4 | 2.416 |

40 | 0.631 | 1 | 0.631 |

| | | 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.**

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