193. NA August 2022 Q.7(b)

 An inclining experiment was carried out on a ship of 8000 tonne displacement. The inclining ballast was moved transversely through 12 m and the deflections of a pendulum 5.5m long, measured from the centreline, were as follows 

3 tonne port to starboard 64 mm S 

3 Tonne 116 mm S Ballast restored 3 mm S 

3 Tonne starboard to port 54 mm P 

3 tonne starboard to port 113 mm P 

Calculate the metacentric height of the vessel.

Given

Displacement = 8000 t

d = 12 m

l = 5.5 m = 5500 mm

m1 = 3 t and  a1 = 64 mm

m2 = 3 t and a2 = 116 mm 

m3 = 3 t and a3 = 54 mm

m4 = 3 t and a4 = 113 mm

To find 

GM

Solution

Tan θ = a / l

GM = (m x d) / (Δ x Tan θ )

Therefore GM = 0.427 m