A ship of 6000 tonne displacement has its centre of gravity 5.9 m above the keel and transverse metacentre 6.8 m above the keel. A rectangular double bottom tank 10.5 m long, 12 m wide and 1.2 m deep is now half-filled with sea water. Calculate the metacentric height.

A ship of 6000 tonne displacement has its centre of gravity 5.9 m above the keel and transverse metacentre 6.8 m above the keel. A rectangular double bottom tank 10.5 m long, 12 m wide and 1.2 m deep is now half-filled with sea water.

Calculate the metacentric height.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 5.11

 

Solution:

Mass of water added = L*B*D*1.025/2

                                    = 10.5*12*1.2*1.025/2

                                    = 77.49 tons

GM = KM – KG = 6.8 – 5.9 = 0.33 m

w	d	moment
6000	5.9	355400
77.49	0.3	23.247

 

New KG = 35400+23.247/6000+77.49

              = 5.829 m

Free surface effect = ρ_f * I/ ρ_w * ∇

                                   = 1/12 * LB³ / ∇

                                   = (1/12 * 10.5 * 12³ )/ (6000/1.025)

                                   = 0.255 m

Virtual KG = 5.829 + 0.255 = 6.084 m

 

GM = KM – KG = 6.8 – 6.084 = 0.716 m