Stability – I : Chapter 9

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

We know that Righting moment = (W x GZ )
Where, W = displacement for all of keel, M = Transverse meta centre.
Displacement (W) = 10000t,
 GM = 0.4m, heel = 5degree

We know that
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

We know that :
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.