Flywheel Energy Storage Calculator
The flywheel energy storage calculator introduces you to this fantastic technology for energy storage. You are in the right place if you are interested in this kind of device or need help with a particular problem. In this article, we will learn what flywheel energy storage is, how to calculate the capacity of such a system, and learn about future applications of this technology. Let's start spinning!
What is a flywheel?
A flywheel is not a flying wheel, though if things go sideways, it's possible to find flywheels mid-air. Flywheels are devices used to store energy and release it after smoothing eventual oscillations received during the charging process. Flywheels store energy in the form of rotational energy.
A flywheel is, in simple words, a massive rotating element that stores energy by speeding up and maintaining its angular speed. Flywheels have a notable history: humanity, even without a complete understanding of their working principles, started using them in pottery wheels where the rotation of the plate needs to be kept at a constant rate. From there onward, flywheels accompanied humanity, becoming of immense importance with the development of engines, particularly reciprocating steam engines.
For a long time, flywheels had the unique purpose of smoothing the energy output; however, it's intrinsic for this kind of device to store energy. In recent years, flywheels have become an appealing alternative to batteries: with improved manufacturing technologies, it's possible to keep them spinning for long spans of time, storing energy in an alternative form to the classic chemical batteries.
How do you use a flywheel as an energy storage system?
The flywheel energy storage operating principle has many parallels with conventional battery-based energy storage. The flywheel goes through three stages during an operational cycle, like all types of energy storage systems:
- The flywheel speeds up — this is the charging process.
- Charging is interrupted once the flywheel reaches the maximum allowed operating speed. The flywheel energy storage system is now at capacity.
- Connecting the rotating element to any type of shaft, it's possible to draw rotational energy from the flywheel — we are discharging the flywheel.
In recent years, improved fabrication techniques allowed flywheels to reach ever-increasing operating speeds, corresponding to increases in capacity. At the same time, the friction and wear of the components significantly reduced thanks to the introduction, at least in high-end devices, of vacuum vessels and magnetic bearings that theoretically removed any limit on the lifespan of these accumulators.
Though the applications of flywheels are mostly niche for now, the future is bright:
- Spaceflight will likely use this technology to substitute or flank electrochemical batteries. The G2 flywheel of NASA was the first technological demonstrator.
- The power grid already makes limited use of the technology to bridge over relatively short fluctuations. As renewable sources take over the production of energy, the necessity of storage will become more pressing — flywheels are a possible solution!
- Electric vehicles may see a gradual introduction of flywheels as a substitute for traditional lithium batteries. The low cost of modern batteries may hinder this process.
How to calculate the energy storage of a flywheel: capacity of a flywheel battery
The fundamental equation of any flywheel energy storage system is the following:
E = ½ · I · ω²
where:
- E — Energy stored in the flywheel (capacity), in the form of rotational energy (joules);
- I — Moment of inertia of the rotating component of the flywheel (kg·m²); and
- ω — Angular velocity of the rotating component. We measure it in rad/s, which requires us to convert it from the usual unit of revolutions per second with the equation ω[rad/s] = 2 · π · ω[1/s].
The value of I, the moment of inertia, depends on the construction parameters of the flywheel, particularly the shape and mass. Most devices used in energy storage are either solid or hollow disks. The generic formulas for the moment of inertia are:
- Solid disk / cylinder: I = ½ · m · r²
- Thin-rim ring (hollow): I = m · r²
- Thick-walled cylinder (annulus): I = ½ · m · (r₋² + rᵢ²)
where m is the mass, r the outer radius, and rᵢ the inner radius of a hollow flywheel.
How to use our flywheel energy storage calculator
- Choose your unit system: metric (kg, m) or American/imperial (lb, in).
- Select the flywheel shape — solid disk, thin-rim ring, or thick-walled annulus.
- Enter the mass and outer radius of the flywheel (and the inner radius for an annulus).
- Enter the angular velocity and choose its unit (RPM, rad/s, or rev/s).
- Optionally, enter the electricity price and currency to estimate the monetary value of the stored energy.
- The calculator returns the stored energy in joules, kJ, Wh, kWh, kcal, BTU, and ft·lbf, plus the moment of inertia and rim (tip) speed.
FAQs
How do I calculate the energy stored in a flywheel?
Use E = ½ · I · ω², where I is the moment of inertia (kg·m²) and ω the angular velocity in rad/s. For a solid disk, I = ½ · m · r².
How do I convert RPM to rad/s?
Multiply the RPM value by π/30 (≈ 0.10472). For example, 20,000 RPM ≈ 2,094 rad/s.
Why does a heavier or larger flywheel store more energy?
Stored energy grows linearly with the moment of inertia (which increases with mass and the square of the radius) and with the square of the angular velocity. Doubling the speed quadruples the stored energy.
What limits a flywheel's stored energy?
The maximum rim (tip) speed is limited by the tensile strength of the material — beyond it, the flywheel can disintegrate. That is why this calculator also reports the rim speed for your design.