An inclining experiment was carried out on a ship of 4000 tonne displacement, when masses of 6 tonne were moved trans- versely through 13.5 m. The deflections of a 7.5 m pendulum were 81, 78, 85, 83, 79, 82, 84 and 80 mm respectively. Calculate the metacentric height.

An inclining experiment was carried out on a ship of 4000 tonne displacement, when masses of 6 tonne were moved trans- versely through 13.5 m. The deflections of a 7.5 m pendulum were 81, 78, 85, 83, 79, 82, 84 and 80 mm respectively. Calculate the metacentric height.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 5.8

 

Solution:

Mean deflection = 81+78+85+83+79+82+84+80/8 = 81.5 mm

GM = m*d/∆ * tanθ

        = m*d*l/∆

        = 6*13.5*7.5/4000*0.0815

        = 1.863 m