Flywheel Inertia, Energy and Speed Fluctuation Calculator
Moment of inertia, stored kinetic energy and speed fluctuation for a solid disc or a rimmed flywheel, from its dimensions and material density. The energy released over a speed swing, the inertia needed to hold a permitted fluctuation, the rim speed and the free ring hoop stress are all reported, along with the comparison against a solid disc of the same size.
How to use this calculator
- Enter the outer diameter, the bore or inner diameter and the thickness. Leave the bore at 0 for a solid disc.
- Enter the material density, which sets both the mass and the rim stress at a given speed.
- Enter the running speed and the lowest speed reached during an energy draw, plus the speed fluctuation the machine may tolerate.
- Read the inertia, stored energy, the energy given up over the swing, the inertia that would be needed for the permitted fluctuation, and the rim speed and hoop stress.
Frequently asked questions
Why is it better to put the mass at the rim rather than in a solid disc?
Inertia goes with the square of the radius, so material near the axis contributes almost nothing while still costing weight and material. Boring a solid disc out to half its outer diameter removes about a quarter of the mass and only about six percent of the inertia. The energy per kilogram is therefore much better with the metal at the rim, which is why flywheels look like rims on spokes rather than like plates.
What does GD squared mean?
It is an older way of stating inertia, still common on motor and coupling datasheets and in crane and hoist work. GD squared is four times the moment of inertia, where G is the weight rather than the mass. The two figures are the same physical quantity in different units, so always check which one a datasheet is quoting before using it in a torque calculation.
How much can a flywheel speed vary?
It depends on the duty. Punch presses and reciprocating compressors tolerate 2 to 5 percent. Engine flywheels are often held to 1 or 2 percent. Alternator sets driving a grid tie need under about 0.5 percent to keep the frequency within tolerance, because frequency error is directly a speed error. Tighter limits need a heavier flywheel, since the inertia needed is inversely proportional to the permitted fluctuation.
What limits how fast a flywheel can spin?
The hoop stress in the rim, which is density times the square of the rim speed for a free ring, so it depends on the material and the speed and not at all on the size. That is why a scaled up flywheel cannot simply be run at the same speed as a small one. Cast iron is usually held under 30 to 40 m/s because the failure is brittle and sudden, and the fragments travel a long way, so containment and the burst case need designing alongside the running case.