Flywheel Energy Storage Calculator
Calculates the usable kinetic energy stored in a flywheel between maximum and minimum operating speeds, accounting for system efficiency. Use it when designing energy storage systems or regenerative braking applications.
About this calculator
A flywheel stores kinetic energy in its rotating mass. The total usable energy E is the difference in rotational kinetic energy between the maximum and minimum operating speeds: E = 0.5 × I × (ω_max² − ω_min²) × η, where I is the moment of inertia in kg·m², ω is angular velocity in rad/s, and η is system efficiency as a decimal. Angular velocity is converted from RPM using ω = N × π / 30. The factor of 0.5 comes from the rotational kinetic energy equation, analogous to ½mv² for linear motion. Energy is expressed in kilowatt-hours by dividing by 3,600,000, or in kilojoules by dividing by 1,000. The moment of inertia depends on the flywheel's geometry and mass distribution; a solid disk gives I = 0.5 × m × r², while a thin ring gives I = m × r², making ring-type flywheels more energy-dense for the same mass.
How to use
Suppose a flywheel has a moment of inertia of 50 kg·m², a maximum speed of 3000 RPM, a minimum speed of 1500 RPM, and a system efficiency of 90 %. Convert speeds: ω_max = 3000 × π / 30 ≈ 314.16 rad/s; ω_min = 1500 × π / 30 ≈ 157.08 rad/s. Calculate: E = 0.5 × 50 × (314.16² − 157.08²) × (90/100) / 1000 = 0.5 × 50 × (98,696 − 24,674) × 0.9 / 1000 = 0.5 × 50 × 74,022 × 0.9 / 1000 = 1,665.5 kJ. This is the usable energy delivered to the load during a speed drop from 3000 to 1500 RPM. If discharge time is 60 seconds, average power output ≈ 1,665,500 / 60 ≈ 27.8 kW.
Frequently asked questions
How does moment of inertia affect flywheel energy storage capacity?
Moment of inertia I is the rotational equivalent of mass and measures how the mass is distributed relative to the spin axis. Energy scales linearly with I, so doubling the moment of inertia doubles the stored energy at any given speed. To maximise I without increasing total mass, material should be concentrated at the largest possible radius—this is why high-performance flywheels use a heavy rim supported by light spokes rather than a solid disk. Carbon-fibre composite rims can spin at very high speeds, and because energy also scales with speed squared, even a modest increase in operating speed dramatically increases storage capacity.
What efficiency losses affect flywheel energy storage systems?
The main efficiency losses in a flywheel system are bearing friction, aerodynamic drag on the rotating assembly, and losses in the motor-generator used to charge and discharge the flywheel. Vacuum enclosures eliminate aerodynamic drag and are standard in high-performance systems. Magnetic bearings remove mechanical contact friction but add electrical overhead. The motor-generator introduces copper and iron losses during both charge and discharge cycles. A well-designed modern flywheel system can achieve round-trip efficiencies of 85–95 %, compared to 70–85 % for lithium-ion batteries, making flywheels attractive for applications requiring frequent charge-discharge cycling.
When should I use a flywheel for energy storage instead of a battery?
Flywheels excel in applications requiring very high power delivery or absorption over short durations—typically seconds to a few minutes—with very high cycle counts. They are ideal for uninterruptible power supplies (UPS), regenerative braking in trains and elevators, grid frequency regulation, and bridging power during generator startup. Batteries outperform flywheels for long-duration storage (hours to days) and stationary applications where the physical footprint and gyroscopic effects of a spinning mass are problematic. Flywheels also have a long operational life (20+ years) with minimal degradation, whereas battery capacity fades with cycle count, making lifetime cost comparisons often favour flywheels in high-cycle scenarios.