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

  1. 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.

  1. 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

We know that :
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.

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