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 is flywheel energy storage, how to calculate the capacity of such a system, and learn about future applications of this technology.

Let's start spinning!

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 desks 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. In the next section, we will discover how!

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 for now, the applications of flywheels are mostly niche, there is a possibility that in the future, more and more flywheel energy storage systems will become common usage.

Currently, flywheels are operated in research laboratories that require enormous input energies (nuclear fusion facilities, for example), and in a small grade, in the transportation industry. The future is bright:

• Spacefly will likely use this technology to substitute or flank electrochemical batteries. The G2 flywheel of NASA was the first technological demonstrator.

• The power grid makes already limited use of the technology to bridge over relatively short fluctuations. As renewable sources will (hopefully) 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.

Let's dive into the calculations for a flywheel energy storage system.

The fundamental equation of any flywheel energy storage system is the following:

where:

• $E$ — Energy stored in the flywheel (capacity) in the form of rotational energy;

• $I$ — Momentum of inertia of the rotating component of the flywheel; and

• $\omega$ — Angular velocity of the rotating component. We measure it in $\mathrm{rad/s}$, which requires us to convert it from the usual unit revolution per second with the following equation: $\omega [\mathrm{rad/s}] = 2\cdot\pi \cdot \omega [1\mathrm{/s}]$. Our angular velocity calculator and circular motion calculator can help you with this conversion.

The value of $I$, the momentum 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 formula for the momentum of inertia is:

where:

• $k$ — A geometric constant characteristic for each shape;
• $m$ — Mass of the rotating component; and
• $r$ — The reference radius.

The two most common types of flywheel have the following values of $k$:

• Solid disk: $k=0.606$; and
• Hollow disk: $k=0.333$.

Specific energy calculations for flywheel energy storage systems

The ratio between energy and mass returns the specific energy of the flywheel. This quantity is related to another ratio through the geometric constant we mentioned above:

where:

• $\sigma$ — Tensile strength in pascals; and
• $\rho$ — Density of the material.

This equation gives you insight into the flywheel's requirements and expected performance in a more realistic fashion than the previous one.

Our flywheel energy storage calculator allows you to compute all the possible parameters of a flywheel energy storage system.

Select the desired units, and fill in the fields related to the quantities you know: we will immediately compute all the values we can with these inputs.

Let's try an example: the same NASA flywheel we mentioned before. That relatively small machine proved the feasibility of such technology, but how much energy could it store? Let's start with the parameters:

• $r = 12\ \mathrm{in}$;
• $m=250\ \mathrm{lb}$;
• $k=0.333$ (the flywheel has a hollow-disk shape); and
• $\omega = 60,\!000\ \mathrm{RPM}$.

Our calculator will first find the momentum of inertia with the formula:

And then, it plugs the result into the formula for the stored energy:

Enough energy to charge an iPhone 13 more than 1500 times! Admit it; you'd like this kind of charger!