C L DUBEY – EXERCISE – 11 (Grain Stability)

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