How to use the Flywheel Calculator
- 1. Give the energyEnter ΔE, or power, engine type and the coefficient of fluctuation of energy.
- 2. Set the speed limitsMean speed and the allowed total speed fluctuation.
- 3. Size itPick rim or disc, then the diameter or allowable stress.
Flywheel formulas
The key relation is ΔE = I·ω²·Cs, where ΔE is the maximum fluctuation of energy, ω the mean angular speed and Cs = (ωmax − ωmin)/ω the coefficient of fluctuation of speed.
- Work per cycle = P × 60 / (cycles per minute), and ΔE = Ce × work per cycle.
- Rim-type flywheel: I ≈ mR², so m = I/R². Hoop stress = ρv².
- Solid disc: I = mR²/2, and the largest stress at the centre is (3 + ν)/8 · ρv².
- Energy stored at mean speed = ½Iω².
A larger diameter needs less mass, but the rim speed and stress rise. The stress limit sets the largest diameter.
Worked example and exam tips
ΔE = 12 kJ, N = 300 rpm and the speed must stay within ±1% (Cs = 0.02). ω = 31.42 rad/s, so I = 12 000 / (31.42² × 0.02) = 607.9 kg·m². With a 1.5 m mean rim diameter, the rim mass is 607.9 / 0.75² = 1081 kg, the rim speed is 23.6 m/s and the hoop stress is 4.0 MPa for cast iron.
- ±1% speed variation means Cs = 0.02, not 0.01.
- A four-stroke engine has one power stroke every two revolutions, so it makes N/2 cycles per minute.
- Find ΔE from the turning moment diagram as the largest difference between the cumulative energy peaks and troughs.
Frequently asked questions
What is the coefficient of fluctuation of speed?
Cs = (Nmax − Nmin)/N, the total allowed speed variation as a fraction of the mean speed. ±1% gives Cs = 0.02.
Why ignore the hub and arms?
In a rim-type flywheel the rim gives most of the inertia, so textbooks usually take I = mR² for the rim alone. The real flywheel is slightly heavier.
What limits the flywheel diameter?
The rim speed. Hoop stress rises with v², so cast iron flywheels are kept to modest rim speeds.
Is this calculator free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. Every calculation runs in your browser and nothing you type is sent anywhere.