A vessel of 10 000 tonne displacement has a second moment of area of waterplane about the centreline of 60 x 10' m4. The centre of buoyancy is 2.75 m above the keel. The following are the disposition of the masses on board the ship. 4000 tonne 6.30 m above the keel 2000 tonne 7.50 m above the keel 4000 tonne 9.15 m above the keel Calculate the metacentric height.

A vessel of 10 000 tonne displacement has a second moment of area of waterplane about the centreline of 60 x 10' m4. The centre of buoyancy is 2.75 m above the keel. The following are the disposition of the masses on board the

ship.

4000 tonne 6.30 m above the keel

2000 tonne 7.50 m above the keel

4000 tonne 9.15 m above the keel

Calculate the metacentric height.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 5.2

 

Solution:

weight	height	Moment
4000	6.3	25200
2000	7.5	15000
4000	9.15	36600

 

KG = moment/∆

      = 25200+15000+36600/10000

      = 7.680 m

 

BM = I/∇

       = 60*10³ * 1.025/10000

       = 6.15

 

GM = KB + BM – KG

       = 2.75 + 6.15 – 7.68

       = 1.22 m