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A flywheel is a mechanical device with significant moment of inertia used as a storage device for rotational energy. Flywheels resist changes in their rotational speed, which helps steady the rotation of the shaft when a fluctuating torque is exerted on it by its power source such as a piston-based (reciprocating) engine, or when the load placed on it is intermittent (such as a piston pump). Flywheels can be used to produce very high power pulses as needed for some experiments, where drawing the power from the public network would produce unacceptable spikes. A small motor can accelerate the flywheel between the pulses. Recently, flywheels have become the subject of extensive research as power storage devices for uses in vehicles; see wikipedia:flywheel energy storage.

## Physics Edit

Energy is stored in the rotor as kinetic energy, or more specifically, rotational energy:

$E_k=\frac{1}{2}\cdot I\cdot \omega^2$

where

$\omega$ is the angular velocity, and
$I$ is the moment of inertia of the mass about the center of rotation.
• The moment of inertia for a solid-cylinder is $I_z = \frac{1}{2} mr^2$,
• for a thin-walled cylinder is $I = m r^2 \,$,
• and for a thick-walled cylinder is $I = \frac{1}{2} m({r_1}^2 + {r_2}^2)$.

where m denotes mass, and r denotes a radius. More information can be found at list of moments of inertia

When calculating with SI units, the standards would be for mass, kilograms; for radius, meters; and for angular velocity, radians per second. The resulting answer would be in Joules

The amount of energy that can safely be stored in the rotor depends on the point at which the rotor will warp or shatter. The hoop stress on the rotor is a major consideration in the design of a flywheel energy storage system.

$\sigma_t = \rho r^2 \omega^2 \$

where

$\sigma_t$ is the tensile stress on the rim of the cylinder
$\rho$ is the density of the cylinder
$r$ is the radius of the cylinder, and
$\omega$ is the angular velocity of the cylinder.

### Examples of energy storedEdit

You can use those equations to do 'back of the napkin' calculations and find the rotational energy stored in various flywheels. $I = k m r^2 \,$, and k is from List of moments of inertia

object k (varies with shape) mass diameter angular velocity energy stored, J energy stored, kWh
bicycle wheel 1 1 kg 700 mm 150 rpm 15 J 0.0000004 kWh
bicycle wheel, double speed 1 1 kg 700 mm 300 rpm 60 J 0.0000016 kWh
bicycle wheel, double mass 1 2 kg 700 mm 150 rpm 30 J 0.0000008 kWh
Flintstones concrete car wheel 1/2 245 kg 500 mm 200 rpm 1680 J 0.00047 kWh
wheel on train @ 60km/h 1/2 942 kg 1 m 318 rpm 65,000 J 0.018 kWh
giant dump truck wheel @ 18mph 1/2 1000 kg 2 m 79 rpm 17,000 J 0.0048 kWh
small flywheel battery 1/2 100 kg 600 mm 20000 rpm 9.8 MJ 2.7 kWh
regenerative braking flywheel for trains 1/2 3000 kg 500 mm 8000 rpm 33 MJ 9.1 kWh
electrical power backup flywheel 1/2 600 kg 500 mm 30000 rpm 92 MJ 26 kWh
the planet earth 2/5 5.97e24 kg 12725 km ~1 per day 2.5e23 J 7e16 kWh

See [6], [7], [8], [9], and Rotational energy

### High energy materialsEdit

For a given flywheel design, it can be derived from the equations above that the kinetic energy is proportional to the ratio of the hoop stress to the material density.

$E_k \varpropto \frac{\sigma_t}{\rho}$

This parameter could be called the specific tensile strength. The flywheel material with the highest specific tensile strength will yield the highest energy storage. This is one reason why carbon fiber is a material of interest.

## Applications Edit

Main article: wikipedia:flywheel energy storage

In application of flywheels in vehicles, the phenomenon of precession has to be considered. A rotating flywheel responds to any momentum that tends to change the direction of its axis of rotation by a resulting precession rotation. A vehicle with a vertical-axis flywheel would experience a lateral momentum when passing the top of a hill or the bottom of a valley (roll momentum in response to a pitch change). Two counter-rotating flywheels may be needed to eliminate this effect. The flywheel has been used since ancient times, the most common traditional example being the potter's wheel. In the Industrial Revolution, James Watt contributed to the development of the flywheel in the steam engine, and his contemporary James Pickard used a flywheel combined with a crank to transform reciprocating motion into rotary motion.

In a more modern application, a 'momentum wheel' is a type of flywheel useful in satellite pointing operations, in which the flywheels are used to point the satellite's instruments in the correct directions without the use of thruster rockets.

Flywheels are used in punching (stamping) machines and riveting machines, where they store energy from the motor and release it during the operation cycle (punching and riveting).

## History Edit

The principle of the flywheel is already found in the Neolithic spindle and the potter's wheel.[1]

The flywheel as a general mechanical device for equalizing the speed of rotation is first described in the Kitab al-Filaha of the Andalusian engineer Ibn Bassal (fl. 1038-1075), who applies the device in a chain pump (saqiya) and noria.[2]

According to the American medievalist Lynn Townsend White, Jr., such a flywheel is also recorded in the De diversibus artibus (On various arts) of the German artisan Theophilus Presbyter (ca. 1070-1125), who records applying the device in several of his machines.[1][3]