Flywheel Energy Calculator

How is flywheel energy calculated?

The kinetic energy of a rotating body is half its moment of inertia times the square of its angular velocity: E = ½ × I × ω², with ω = 2 × π × n / 60 from the rotational speed. Doubling the speed gives four times the energy.

A solid disc has I = m × D² / 8 and a hollow rim has I = m × (D² + d²) / 8. Putting the mass at the rim stores more energy for the same weight, which is why flywheels usually have a heavy rim.

What does a flywheel do?

A flywheel stores energy as it speeds up and gives it back as it slows down. On a mechanical press a small motor keeps speeding the flywheel up, and at the moment of cutting the flywheel delivers a large amount of energy in a short time while dropping a few hundred rpm. The energy delivered is the difference between the two speeds: ΔE = ½ × I × (ω₁² − ω₂²).

Example

A solid disc flywheel of 50 kg and 500 mm diameter has a moment of inertia of 50 × 0.5² / 8 = 1.5625 kg·m². At 1500 rpm it holds 19.3 kJ. Slowing to 1200 rpm releases 6.94 kJ. So a 20 percent drop in speed uses 36 percent of the energy.

Limits and safety

This tool calculates energy, not strength. Centrifugal stress in a flywheel rises with the square of rim speed, and an overspeeding flywheel can burst. Take the maximum permitted speed from manufacturer data or from a separate strength calculation.