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# Chapter 9 - Stability Calculation

### 1. A ship of 10000t displacement has a GM of 0.4m. Calculate the moment of statical stability when she is heeled by 5 degree.

Solution:

GZ =Righting lever, GM = Metacentric height

Righting moment = (W x GZ ) Where, W = displacement for all of keel, M = Transverse meta centre. Displacement (W) = 10000t, GM = 0.4m, heel = 5 degree RM ( righting moment or moment of statical stability) = (W x GM x sinθ) = (10000 x 0.4 x sin 50 ) = 348.62tm

### 2. A ship of 12000t displacement is heeled by 6 degree. If her righting lever is then 0.1m, find the moment of statical stability . If her KM is 8.2m , find her KG .

Solution :

Displacement (W) = 12000t, Heel = 6degree GZ = 0.1m & KM = 8.2m GZ = GM sinθ 0.1 = GM sin 60. GM = (0.1 / sin 60) = 0.956m KG = (KM – GM) = (8.2 – 0.956) = 7.44m

RM (righting moment or moment of statical stability) = (W GM sinθ) = (12000 x 0.956 x sin60 ) = 1199.15 tm.

### 3. When a ship of 14000t displacement is heeled by 8 deegre , her moment of statical stability is 400tm . If KG 7.3m, find KM.

Solution :

Displacement (W)= 14000t, Heel = 8degree , RM = 400tm & KG 7.3m

RM (Righting moment or moment of statical stability) = (W x GM x sinθ) 400 = (14000 x GM x sinθ) GM = 400/ (1400 x sin80 ) GM = 2.053m

Now, KM = (KG + GM ) = (7.3 + 2.053 ) = 9.353m.

### 4. A ship of 8000t displacement has KB 3.5m, KM 6.5m, and KG 6m . Find her moment of statical stability at 20 degree heel, assuming that her deck edge remains above water (i.e. she is steel wall side at that angle of heel.

Solution :

Displacement (W) = 8000t, KB = 3.5m & KM = 6.5m , KG = 6m, heel= 20degree. GM = (KM – KG) = (6.5 – 6) = 0.5m

Since, GZ = Sinθ(GM + 1/2 BM tan2θ) GZ = sin 200 (0.5 + 1/2 x 3 x tan2200 ) Again , GZ = 0.239 ,

RM (Righting moment or moment of statical stability) = (W.GZ) = 8000 x 0.239 = 1911.8 tm

### 5. A ship of 4000t displacement has KG 5.1 m, KB 2.1m, KM 5.5m . Find the moment of statical stability when she heels 24 degree , assuming that she is wall- side.

Solution :

Displacement (W) = 4000t, KG = 5.1m ,KB = 2.1m & KM = 5.5m, Heel =24degree GM = (KM – KG) = (5.5 – 5.1) = 0.4m

Similarly, BM = ( KM – KB) = (5.5 – 2.1) = 3.4m

RM can be calculated as : RM (Righting moment or moment of statical stability) = (W.GZ) = W.sinθ ( GM + 1/2 BM tan2θ) = 4000 x sin240(0.4 + 1/2 x 3.4 x tan2240 ) = 1200tm.