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Stability of floating bodies
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Metacentre height determines stability of ships.
A ship is stable if the metacentre (where buoyancy's line of action crosses the centreline when tilted) is above the centre of gravity, giving a restoring torque.
Heavy cargo on deck makes a ship top-heavy.
Wide and low-slung hulls are stabler.
In more detail
A floating body is stable if its centre of buoyancy lies above its centre of gravity, so that tilting produces a restoring torque. Keeping the centre of gravity low improves stability.
Real-world uses
- Ship designers keep cargo low to avoid capsizing.
- Catamarans have wide hulls that maintain stability.
- Naval architects design ships with a low centre of gravity and a suitable metacentre so they will not capsize in waves.
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Frequently asked questions
What is the centre of buoyancy?
The centre of mass of the displaced fluid.
What makes a ship capsize?
When the centre of gravity rises above the centre of buoyancy, a tilt causes a tipping torque.
What is the metacentre?
The point where the buoyant force acts when a floating body is tilted slightly, and its height above the centre of gravity sets stability.
Related topics in Fluids & Elasticity
Archimedes' principle · Floating and sinking · Apparent weight in fluid · Hydrometer · Fluid dynamics · Streamline and turbulent flow