Stability – I : Chapter 9

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

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 sin8^{0  )}
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.

We can calculate:
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