A ship displaces 12 000 tonne, its centre of gravity is 6.50 m above the keel and its centre of buoyancy is 3.60 m above the keel. If the second moment of area of the waterplane about the centreline is 42.5 x 103 m4 find the metacentric height.

A ship displaces 12 000 tonne, its centre of gravity is 6.50 m above the keel and its centre of buoyancy is 3.60 m above the keel. If the second moment of area of the waterplane about the centreline is 42.5 x 10³ m4 find the metacentric height.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 5.1

 

Solution:

Volume Displacement, ∇ = 12000/1.025

BM = I/∇

        = 42.5*10³ * 1.025/12000

        = 3.630 m

 

KM = KG + GM

=> GM = KM – KG

=> GM = KB + BM – KG

=> GM = 3.6 + 3.63 – 6.5

=> GM = 0.73 m