# 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.