# Inclining Experiment Theory And Explanation

Inclining experiment is conducted by the shipyard to determine the metacentric height(KM), and hence the height of the center of gravity (KG) of the ship. If the height of the center of gravity of the empty ship is known, it is possible to calculate its position for any given condition of loading.

The experiment is conducted on an empty ship ( with minimum personal to conduct experiment). A small mass m is moved across the ship through a distance d. This causes the center of gravity to move from its original position G on the centerline to G1.

If Δ = displacement of ship

Then GG1 = m x d/Δ---- (1)

When the center of buoyancy changes from B to B1, the ship heels to an angle  θ

From the above diagram

GG1 = GM tan θ---- (2)

GM tan θ= m x d/Δ--- from (1) and (2)

GM= m x d/Δ tan θ

In the above equation the only unknown value is θ . To determine the angle of the heel θ, suspend a pendulum. The deflection of the pendulum may be measured when the mass is moved across the deck.

Thus if L = length of pendulum

tan θ = a/L

and GM = m x d x L/(Δ x a)

The height of the transverse metacenter above the keel may be found from the metacentric diagram and hence the height of the center of gravity of the ship may be determined.

KG = KM — GM