A ship of 12 500 tonne displacement and 15 m beam has a metacentric height of 1.10 m. A mass of 80 tonne is lifted from its position in the centre of the lower hold by one of the ship's derricks, and placed on the quay 2 m from the ship's side. The ship heels to a maximum angle of 3.5° when the mass is being moved.

A ship of 12 500 tonne displacement and 15 m beam has a metacentric height of 1.10 m. A mass of 80 tonne is lifted from its position in the centre of the lower hold by one of the ship's derricks, and placed on the quay 2 m from the ship's side. The ship heels to a maximum angle of 3.5° when the mass is being moved.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 5.13

 

Solution:

D = 15/2 + 2 = 9.5 m

GM = m*d/∆tanθ

        = 80*9.5/ 12500*tan3.5⁰

        = 0.994 m

Thus, the metacentric height is reduced from 1.10 m to 0.994 m. Since the draught doesn’t alter and hence the transverse metacentre remains in the same position, this reduction in GM must be due to rise in COG/KG.

Rise in COG = GM` - GM

                     = 1.1 – 0.994

                     = 0.106 m

Rise in center of gravity = m*h/∆

=> 0.106 = 80*h/12500

=> h = 16.56 m