Metacentric Height Experiment — Procedure, Formula and Calculations

Aim of the Experiment

To determine the metacentric height of a floating body and to verify the theoretical relationship between the metacentric height and the angle of heel.

Apparatus Required

• Metacentric height apparatus (pontoon with adjustable jockey weight)
• Measuring scale and plumb bob
• Water tank
• Weights (jockey)
• Protractor or angle scale

Theory

The metacentric height (GM) is a measure of the initial static stability of a floating body. When a floating body is tilted through a small angle (θ), the buoyant force acts through the new centre of buoyancy. The point at which the vertical line through the new buoyant force intersects the original vertical axis is called the metacentre (M). GM is the distance from the centre of gravity (G) to the metacentre (M).

Formula: GM = (w × x) / (W × tan θ)

Where: w = jockey weight (N), x = distance of jockey from centre, W = total weight of pontoon + jockey (N), θ = angle of heel.

Procedure

1. Fill the water tank to a sufficient depth to allow the pontoon to float freely.
2. Place the pontoon on water and check that it floats in the upright position.
3. Note the initial position of the plumb bob (zero reading).
4. Place the jockey weight at a known distance x from the centre of the pontoon.
5. Record the angle of heel θ from the plumb bob scale.
6. Repeat for different jockey positions (both sides).
7. Calculate GM using the formula for each reading.
8. Compare experimental GM with the theoretical value: GM = I/V − BG, where I = second moment of area of waterplane, V = volume of displacement, BG = distance between B and G.

Observation Table

Result

The metacentric height (GM) of the floating body = _______ m (experimental). Theoretical GM = _______ m. The experimental and theoretical values are within acceptable limits, confirming the stability characteristics of the floating body.

Precautions

• Ensure the pontoon is floating freely without touching the tank walls.
• Take readings only after the pontoon has reached a stable position.
• Avoid disturbing the water surface during measurement.

Internal Links

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