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.

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

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.

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

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.

 
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	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.

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

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.