Flywheel Energy Storage Systems

Jonathan A. Sobota
October 31, 2007

(Submitted as coursework for Physics 210, Stanford University, Fall 2007)


Flywheel energy storage (FES) is a technology in which a spinning wheel is used as a mechanism for storing energy. Conceptually, this is as straightforward as it sounds, and in fact this technology has been used for hundreds of years; a potter's wheel is a simple example. It may be surprising, then, that FES is an active area of engineering research in industry and academia. The advent of vacuum technology, composite materials, magnetic bearings, and high-temperature superconductors has allowed FES to become a cutting-edge technology, with distinct advantages over traditional energy storage systems such as chemical batteries. The purpose of this article is to review the mechanical principles of FES systems, discuss some of the engineering challenges involved, and provide examples of applications in modern society.

Rotor design considerations

An FES system stores its energy in a spinning rotor. The energy E stored in the rotor is given by

E = 1/2 I &omega2

Where I is the moment of inertia of the rotor, and &omega is its angular frequency. Thus, a convenient feature of FES systems is that the stored energy can be determined simply by measuring &omega, which in practice can be accomplished with great precision. The moment of inertia is given by

I = &int r2 &rho(r) d3r

where r is a vector pointing from the axis of rotation to a volume element of the rotor, and &rho(r) is the density of the rotor at r. Most common rotor designs can be approximated as a hollow cylinder with outer radius ro, inner radius ri, and height h. Assuming constant density &rho, the moment of inertia becomes

I = 1/2 &pi &rho h (ro4 - ri4)

To maximize the moment of inertia, and therefore maximize the energy stored, it seems plausible that the optimal design would consist of a rotor composed of a dense material. This was the approach taken in older designs, in which the rotors were constructed largely out of steel. However, the rotational velocity of these systems was severely limited, since it was found that the steel rotors would self-destruct at high velocities due to the immense stresses present in the material. The stress on the material is proportional to the material's density. Therefore, it makes sense to use materials that are less dense and have higher tensile strength, since a rotor constructed of such a material can safely spin at much higher velocities. Table 1 lists relevant data for common rotor materials, including the maximum energy density that could be obtained by using each material. It can be seen that less dense, but stronger, materials can attain significantly higher energy densities than more conventional materials such as steel, but come at a much higher cost.

Table 1: Properties of materials commonly used to construct flywheel rotors. Data from Ref. 1.
Material Density Tensile strength Max energy density Cost
(kg/m3) (MPa) (J/kg) (Wh/kg) ($/kg)
4340 Steel 7700 1520 0.19 0.05 1
E-glass 2000 100 0.05 0.014 11.0
S2-glass 1920 1470 0.76 0.21 24.6
Carbon T1000 1520 1950 1.28 0.35 101.8
Carbon AS4C 1510 1650 1.1 0.30 31.3

It should be noted that a mechanical failure along the circumferential direction is preferable to a failure along the radial direction, since a failure in the radial direction can produce destructive projectile fragments. Rotors made of fiber composite material are often manufactured so that the fibers are oriented circumferentially, thereby reducing the probability of a radial failure [1]. Furthermore, the rotor must be engineered such that it has no critical resonances within the expected operating range of the FES system, to ensure system stability [2].


In the absence of any losses, an idling FES system will maintain its energy indefinitely. However, any real FES system will contain sources of friction that result in energy loss. The greatest challenge of FES system engineering is identifying and minimizing these sources of friction.

The first source of friction to be considered is windage due to the relative motion of the rotor and the air around it. This problem is easily overcome by encasing the rotor in a vacuum chamber. Typically, the chambers are pumped down to pressures of 10-3 to 10-5 torr. At such low pressures, energy loss due to windage is considered negligible compared to the primary source of friction: the bearings which support the weight of the rotor and allow it to rotate. Indeed, most contemporary FES research is concerned with the development of sophisticated bearings in an ongoing effort to minimize energy loss.

Mechanical bearings are the most primitive, and least preferable, option. These bearings involve moving parts that slide on each other, and are therefore enormous sources of contact friction. This friction can be somewhat reduced by the use of lubricants, but this increases maintenance costs, and can also cause outgassing problems in the low-pressure environment. More sophisticated bearings make use of permanent and electro- magnets to help support the weight of the rotor and substantially reduce the friction. FES systems incorporating these bearings are capable of idling with losses as low as 1% per hour. State of the art FES systems use even more sophisticated bearings that consist of permanent magnets and high-temperature superconductors to actually levitate the rotor. The engineering challenges involved with supporting and stabilizing the rotor are considerable, and the interested reader is advised to consult the references. The result is that the rotor has virtually no mechanical contact with the rest of the world. While it may seem that this implies that there is no friction, there are in fact losses due to complicated electromagnetic interactions between the superconductors and permanent magnets. Nevertheless, energy losses on FES systems with superconducting bearings can be as low as 0.1% per hour. This is particularly impressive because this figure includes the energy cost of maintaining the superconductor below its critical temperature [1,2].


Fig. 1: A simplified gimbal system supporting an FES system. The angular momentum of the flywheel is coaxial with the cylindrical chamber encasing it (yellow). The gimbal system can rotate about two different axes along its pivots (green), effectively isolating the angular momentum of the flywheel from the rest of the environment.

One may wonder why FES systems would ever be utilized when more conventional technologies, such as chemical batteries, are readily available. First of all, FES systems are capable of remarkably high energy and power densities. Recently developed systems have energy capacities on the order of 100 kWh, and can output the energy in bursts up to 1 GW. They can be charged very rapidly; some can charge to full capacity within 15 minutes. Moreover, the maximum capacity of the FES system remains constant during the life of the system, regardless of the type of loads and charge/discharge cycles, whereas chemical batteries are notorious for capacity degradation after extensive use. This means that an FES system can be used for decades with little or no maintenance, while battery systems require frequent replacement. While this is a clear cost advantage, it is also an enormous advantage in terms of environmental impact, since old batteries often end up as chemical waste. Even when an old FES system is retired, it consists of mostly environmentally friendly materials, so its environmental impact is minimal [1,3,4].

Given these advantages, it is not surprising that FES has found applications in systems that require repeated, high-power bursts of energy. A great deal of attention has been given to the use of FES systems to stabilize electric power grids. A sudden disruption to a power grid threatens the integrity of the entire grid, and has the potential to cause a blackout. An FES system could respond to such a disruption within a fraction of a second, stabilize the power supply, and possibly prevent blackouts from happening at all. FES is particularly useful in conjunction with renewable energy sources, such as wind and solar, since these sources are dependent on environment variables, and therefore cannot provide a constant supply of power. Therefore, it is essential to have an energy storage system to compensate during temporary dips in energy production [3,4].

There is also a large amount of interest in using FES systems in vehicles. Vehicles waste an enormous amount of energy by braking. Today's hybrid automobiles reclaim some of this energy by a mechanism known as regenerative braking, in which reclaimed energy is stored in the car's batteries, and then used to power the car's electrical systems. However, these batteries suffer the same shortcomings as all batteries: slow charging times, capacity degradation, and the necessity for eventual disposal. FES systems provide an ideal alternative to batteries, except for one major consideration. Since a charged FES system has a large angular momentum, it will produce enormous gyroscopic effects when placed in a moving vehicle. There are two proposed methods for overcoming this difficulty. One possibility is to compose the FES system out of two rotors spinning in opposite directions at the same frequency. Thus the net angular momentum would be zero, and there would be no external gyroscopic effects. The other possibility is to suspend the FES system in a gimbal system, which effectively isolates the angular momentum of the flywheel from the rest of the system, as illustrated in Fig 1. Due to the space required, FES systems are more practical for large vehicles such as buses and locomotives, but their use in automobiles is also under consideration [3].

It is clear from this discussion that FES systems can find applications almost wherever energy storage is needed. Further examples include: FES to rapidly launch rollercoaster rides, FES as a power source on spacecraft and the International Space Station, and FES to provide pulsed energy in laboratories [2,3,4].

© 2007 Jonathan A. Sobota. The author grants permission to copy, distribute and display this work in unaltered form, with attributation to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] B. Bolund, H. Bernhoff, and M. Leijon. Renewable and Sustainable Energy Reviews 11, 235 (2007).

[2] M. Strasik, et. al. IEEE Trans. Appl. Superconductivity 17, 2133 (2007).

[3] D. Castelvecchi. Science News 171, 312 (2007).

[4] H. Vere. "A Primer of Flywheel Technology," Distributed Energy, May/June 2007.