The formula to calculate the Metacenter (M) is:
\[ M = \frac{I}{V_{o} \cdot G} - B \]
Metacenter is the theoretical point where a vertical line through the center of buoyancy and center of gravity intersects the new center of buoyancy when a body is tilted in water. Moment of Inertia is the measure of the resistance of a body to angular acceleration about a given axis. Volume of Object is the volume occupied by a submerged or floating object in a fluid. Centre of gravity of the object is the point through which gravitational force is acting. Centre of Buoyancy is the center of the gravity of the volume of water which a body displaces.
Let's assume the following values:
Using the formula:
\[ M = \frac{1.125}{54 \cdot 0.021} - (-16) \approx 16.9920634920635 \]
The Metacenter is approximately 16.9920634920635.
| Moment of Inertia (Kilogram Square Meter) | Volume of Object (Cubic Meter) | Centre of Gravity | Centre of Buoyancy | Metacenter |
|---|---|---|---|---|
| 1 | 54 | 0.021 | -16 | 16.881834215167547 |
| 1.05 | 54 | 0.021 | -16 | 16.925925925925927 |
| 1.1 | 54 | 0.021 | -16 | 16.970017636684304 |
| 1.15 | 54 | 0.021 | -16 | 17.014109347442680 |