Formula Used
- Angular speed: ω = 2π × rpm / 60, or input directly in rad/s.
- Moment of inertia:
- Solid disk: I = 1/2 m r2
- Thick ring (hollow cylinder): I = 1/2 m (ro2 + ri2)
- Custom inertia: user-provided I
- Stored kinetic energy: E = 1/2 I ω2
- Angular momentum: L = I ω
- Rim speed: v = ω ro
- Average output power (optional): P ≈ (E × η) / t, minus constant losses.
- Stress screening (optional): thin-ring estimate σ ~ ρ v2, so vmax = sqrt(σallow/ρ).
How to Use This Calculator
- Select Solve for to choose what you want to calculate.
- Pick a Rotor model. Use disk/ring for geometry-based inertia, or custom inertia when you already know I.
- Enter speed, mass, and radii as required by your solve mode. Units can be changed anytime.
- For discharge planning, set efficiency and discharge time to estimate average output power.
- Optionally enter density and allowable stress to screen maximum safe rim speed and rpm.
- Press Calculate. Results appear above the form, below the header.
- Use Download CSV or Download PDF to save outputs.
Example Data Table
| Model | Mass (kg) | ro (m) | ri (m) | Speed (rpm) | Energy (kWh) | Rim speed (m/s) |
|---|---|---|---|---|---|---|
| Solid disk | 25 | 0.25 | 0 | 6000 | 0.021 | 157 |
| Thick ring | 40 | 0.30 | 0.12 | 12000 | 0.216 | 377 |
| Custom inertia | — | 0.20 | — | 8000 | 0.043 | 168 |
Example values are illustrative; verify with your design constraints.
Flywheel Energy Storage Guide
1) What a flywheel stores
Flywheel systems store energy as rotational kinetic energy in a spinning rotor. The stored energy scales with the moment of inertia and the square of angular speed, so small speed changes can produce large energy changes. Typical applications include short duration backup power, voltage support, ride-through events, and high cycle buffering.
2) Geometry choices and inertia
A solid disk places mass near the center and has lower inertia for the same mass and outer radius. A ring places more mass near the rim, increasing inertia and stored energy without increasing speed. This calculator supports both models and also accepts a custom inertia when you already have a measured or simulated value.
3) Speed, rim velocity, and scaling
Angular speed is entered as rpm or rad/s. The tool also reports rim speed using v = ωro. Many practical designs are constrained by rim speed because stresses rise rapidly with v. Because energy scales as ω2, doubling speed ideally quadruples stored energy if inertia is unchanged.
4) Stress screening with density
For quick material screening, the calculator uses a thin-ring estimate σ ∼ ρv2. With allowable hoop stress and density, it estimates a maximum rim speed and a corresponding rpm for the chosen outer radius. Treat these results as a first-pass check; real rotors require detailed stress analysis and safety factors, especially for composite rims.
5) Efficiency and usable energy
Round-trip efficiency bundles losses from bearings, motor-generator conversion, power electronics, and windage. When you provide efficiency and a discharge time, the tool estimates average output power from usable energy (E × η) divided by time. You can also enter constant losses to approximate net available power.
6) Power versus energy planning
Energy capacity describes how long the system can supply a load, while power describes how fast energy is delivered. High power can be achieved with short discharge times, but thermal limits, converter ratings, and rotor dynamics may govern. Use the discharge time and losses inputs to explore different operating strategies for the same stored energy.
7) Specific and volumetric metrics
The calculator reports specific energy (J/kg) and energy density (J/m³) when density is provided. These metrics help compare materials and concepts. Higher specific energy is favored by high allowable stress and low density, while higher inertia at the rim improves storage without increasing total mass.
8) Interpreting results for design
Start by selecting a solve mode: compute energy from a proposed design, solve required speed for a target energy, or solve required mass for a target energy at a chosen speed. Then review rim speed, stress-limit rpm, and output power. Export CSV or print to PDF to document assumptions and iterate toward a safe, achievable design.
FAQs
1) Why does energy increase with the square of speed?
E = 1/2 Iω2. If inertia is constant, doubling ω multiplies energy by four. This is why speed is powerful, but it also increases rim stress and containment requirements.
2) When should I choose a ring model instead of a disk?
Rings place more mass near the rim, increasing inertia and energy for the same mass and outer radius. Disks are simpler mechanically, but often store less energy at the same speed.
3) What does “allowable hoop stress” represent?
It is a conservative stress limit for the rotor material, typically including safety factors. The calculator uses it to estimate a maximum rim speed using a thin-ring approximation.
4) Can I use this tool for composite flywheels?
Yes for early estimates. Enter an effective density and allowable stress, then validate with detailed laminate and rotor stress models. Composite rims can behave differently than metal rings.
5) How is output power estimated?
If you provide discharge time, the tool estimates average output power as (E×η)/t. Optional constant losses are subtracted to show a rough net power level.
6) Why might real delivered energy be lower than stored energy?
Systems often avoid very low speeds, so not all kinetic energy is usable. Additional losses occur in bearings, electronics, and the motor-generator. Use efficiency and loss inputs to approximate this.
7) What is the safest way to validate a design?
Use these results for screening, then verify with finite element stress analysis, rotor dynamics, and containment design. Apply appropriate standards, safety factors, and testing protocols for your application.