Determination of meta-centre height

DETERMINATION OF META-CENTRE HEIGHT

1. Analytical Method

When the body has undergone small strip of dx at a distance x from the centre O, the depth of immersion can be expressed as z +x tan θ.

Taking moments about a vertical plane at a distance x1 from O, the have For equilibrium position,

2. Experimental Methods for Matacentric Height

Consider a floating in water with its top surface horizontal as shown in figure 1.45. Let a small movable mass of weight w. Weigh can move on the top surface be placed centrally on the top. Let w be the weight of the body including the movable mass.

Now, move the movable mass transversely through a distance x. The vessel gets tilted by an angle θ as shown in figure (b) which can be measured using a plumb line and protractor. In the new equilibrium position the centre of gravity is G1 and centre of buoyancy is B1. They will be in a vertical line with the metacentre M.

Equating the moment due to the change of G and the moment due to change of position of the movable mass, we get,

From the measured value of θ for any displacement x, the metacentric height of the floating body can be calculated using the above equation (1).