Flywheel Energy Storage
Benjamin Wheeler
October 24, 2010
Submitted as coursework for Physics 240,
Stanford University, Fall 2010
There are many renewable energies currently utilized
and in development around the world. Some of these methods include
harnessing solar, wind, hydro, and thermal energies. The only problem is
there are no efficient methods of storage. To be able to convert and use
renewable energy as electricity there needs to be a process for storing
it. The focus of this report is on the feasibility of using flywheels to
store rotational energy and convert it to electric energy when
necessary. I have chosen to approach this from a small vehicle
perspective, rather than determine if flywheels can store the energy
needed to supply a city or country. If flywheels are capable of the
energy density to power a vehicle effectively for the average citizen's
needs then a huge portion of the demand for oil and the pollution of the
environment can be lifted.
To simplify calculations, the capabilities and
outputs of the Tesla Roadster will be used to judge what a flywheel
should be capable of. A majority of drivers here in the US would be more
than satisfied with the 200 mile range of the Roadster's 450 kg, 53 kWh
Li-ion battery pack. [1] Thus we will determine if a flywheel of similar
mass can store energy equivalent to this battery. The following
equations can be found in most physics textbooks and flywheel books.
First, determine the expression for the energy of a
rotational system. Our flywheel will be a hollow cylinder, which gives
us Mr2 for moment of inertia. E-energy. I-inertia. M-mass.
r-radius. w-angular velocity.
Second, determine the limits to angular velocity due
to material used: ρ = density, r = radius, ω = angular
velocity, σ = tensile stress (maximum before breaking).
Third, substitute the maximum angular velocity into
energy equation.
| Material |
M (kg) |
σ (pascals) |
ρ (kg/m3 |
Emax (joules) |
Emax (kWh) |
Emax/M (J/kg) |
| Titanium |
450 |
8.8 x 108 |
4506 |
4.4 x 107 |
12 |
9.8 x 104 |
| Carbon Fiber |
450 |
4.0 x 109 |
1799 |
5.0 x 108 |
139 |
1.1 x 106 |
| Steel |
450 |
6.9 x 108 |
8050 |
1.9 x 107 |
5 |
4.3 x 104 |
| Aluminum |
450 |
5.0 x 108 |
2700 |
4.2 x 107 |
12 |
9.2 x 104 |
|
| Table 1: Maximum flywheel energy storage of
various materials. (Material properties produced from
commercial material suppliers. [3-5]) |
These calculations do not account for frictional
losses or efficiency in transforming electric to kinetic energy and
back. Even if a carbon fiber flywheel is only 50% efficient it has the
ability to store and provide more energy than Tesla's Li-ion battery
with comparable mass. There would also be additional mass needed to
house the flywheel and mechanisms, but these should be small compared to
the maximum limit of energy storage. While metal flywheels do not
perform to standards, a carbon fiber flywheel is a viable option for
storing electricity for vehicles and many other applications such as
back up grid power.
© Benjamin Wheeler. The author grants permission
to copy, distribute and display this work in unaltered form, with the
attribution to the author, for noncommercial purposes only. All other
rights, including commercial rights, are reserved to the author.
References
[1] G. Berdichevsky et al,
"The
Tesla Roadster Battery System," Tesla Motors, August 2006.
[2] Books LLC, Tesla Motors Vehicles: Tesla Roadster (Books
LLC, 2010), pp. 1-40.
[3] James Zerbe, Practical Mechanics for Boys
(M.A. Donohue & Company, 1914), Ch. 17.
[4] J. M. Corum et al., "Basic Properties of
Reference Crossply Carbon Fiber Composite," Oak Ridge National
Laboratory, ORNL/TM-2000/29,
February 2000.
[4] C. Chung, Carbon Fiber Composites
(Butterworth-Heinemann, 1994), pp. 65-66, 102, 164.