Flywheel
Overview

A flywheel is a rotating mechanical device that is used to store rotational energy
Rotational energy
The rotational energy or angular kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy...

. Flywheels have a significant moment of inertia
Moment of inertia
In classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of inertia of mass, or the angular mass, is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation...

, and thus resist changes in rotational speed. The amount of energy stored in a flywheel is proportional to the square of its rotational speed
Rotational speed
Rotational speed tells how many complete rotations there are per time unit. It is therefore a cyclic frequency, measured in hertz in the SI System...

. Energy is transferred to a flywheel by applying torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

to it, thereby causing its rotational speed, and hence its stored energy, to increase. Conversely, a flywheel releases stored energy by applying torque to a mechanical load, which results in decreased rotational speed.

Flywheels have three predominant uses:
• They provide continuous energy when the energy source is not continuous.
Discussions
Encyclopedia
A flywheel is a rotating mechanical device that is used to store rotational energy
Rotational energy
The rotational energy or angular kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy...

. Flywheels have a significant moment of inertia
Moment of inertia
In classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of inertia of mass, or the angular mass, is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation...

, and thus resist changes in rotational speed. The amount of energy stored in a flywheel is proportional to the square of its rotational speed
Rotational speed
Rotational speed tells how many complete rotations there are per time unit. It is therefore a cyclic frequency, measured in hertz in the SI System...

. Energy is transferred to a flywheel by applying torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

to it, thereby causing its rotational speed, and hence its stored energy, to increase. Conversely, a flywheel releases stored energy by applying torque to a mechanical load, which results in decreased rotational speed.

Flywheels have three predominant uses:
• They provide continuous energy when the energy source is not continuous. For example, flywheels are used in reciprocating engine
Reciprocating engine
A reciprocating engine, also often known as a piston engine, is a heat engine that uses one or more reciprocating pistons to convert pressure into a rotating motion. This article describes the common features of all types...

s because the energy source (torque from the engine) is not continuously available.
• They deliver energy at rates beyond the ability of an energy source. This is achieved by collecting energy in the flywheel over time and then releasing the energy quickly, at rates that exceed the capabilities of the energy source.
• They control the orientation of a mechanical system. In such applications, the angular momentum of a flywheel is purposely transferred to a load when energy is transferred to or from the flywheel.

Flywheels are typically made of steel and rotate on conventional bearings; these are generally limited to a revolution rate of a few thousand RPM. Some modern flywheels are made of carbon fiber materials and employ magnetic bearing
Magnetic bearing
A magnetic bearing is a bearing which supports a load using magnetic levitation. Magnetic bearings support moving machinery without physical contact; for example, they can levitate a rotating shaft and permit relative motion with very low friction and no mechanical wear...

s, enabling them to revolve at speeds up to 60,000 RPM.

## Applications

Flywheels are often used to provide continuous energy in systems where the energy source is not continuous. In such cases, the flywheel stores energy when torque is applied by the energy source, and it releases stored energy when the energy source is not applying torque to it. For example, a flywheel is used to maintain constant angular velocity of the crankshaft
Crankshaft
The crankshaft, sometimes casually abbreviated to crank, is the part of an engine which translates reciprocating linear piston motion into rotation...

in a reciprocating engine. In this case, the flywheel—which is mounted on the crankshaft—stores energy when torque is exerted on it by a firing piston
Piston
A piston is a component of reciprocating engines, reciprocating pumps, gas compressors and pneumatic cylinders, among other similar mechanisms. It is the moving component that is contained by a cylinder and is made gas-tight by piston rings. In an engine, its purpose is to transfer force from...

, and it releases energy to its mechanical loads when no piston is exerting torque on it. Another example of this is friction motors
Friction motors
Friction motors are simple mechanism to propel toy cars. The motor consists of a large flywheel which is connected to the drive wheels of the car via a very low gear ratio. The flywheel's axis is perpendicular to the direction the car is facing. When the car is pushed forward the drive wheels...

, which use flywheel energy to power devices such as toy cars.

A flywheel may also be used to supply unsustained pulses of energy at energy transfer rates that exceed the capabilities of its energy source, or when such pulses would disrupt the energy supply (e.g., public electric network). This is achieved by accumulating stored energy in the flywheel over a period of time, at a rate that is compatible with the energy source, and then releasing that energy at a much higher rate over a relatively short time. For example, flywheels are used in punching
Punching
Punching is a metal forming process that uses a punch press to force a tool, called a punch, through the workpiece to create a hole via shearing. The punch often passes through the work into a die. A scrap slug from the hole is deposited into the die in the process. Depending on the material being...

machines and riveting machines, where they store energy from the motor and release it during the punching or riveting operation.
The phenomenon of precession
Precession
Precession is a change in the orientation of the rotation axis of a rotating body. It can be defined as a change in direction of the rotation axis in which the second Euler angle is constant...

has to be considered when using flywheels in vehicles. 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. This effect is leveraged in momentum wheel
Momentum wheel
A reaction wheel is a type of flywheel used primarily by spacecraft for attitude control without using fuel for rockets or other reaction devices....

s, a type of flywheel employed in satellites in which the flywheel is used to orient the satellite's instruments without thruster rockets.

## History

The principle of the flywheel is found in the Neolithic
Neolithic
The Neolithic Age, Era, or Period, or New Stone Age, was a period in the development of human technology, beginning about 9500 BC in some parts of the Middle East, and later in other parts of the world. It is traditionally considered as the last part of the Stone Age...

spindle
Spindle (tool)
In machine tools, a spindle is a rotating axis of the machine, which often has a shaft at its heart. The shaft itself is called a spindle, but also, in shop-floor practice, the word often is used metonymically to refer to the entire rotary unit, including not only the shaft itself, but its bearings...

and the potter's wheel
Potter's wheel
In pottery, a potter's wheel is a machine used in asma of round ceramic ware. The wheel may also be used during process of trimming the excess body from dried ware and for applying incised decoration or rings of color...

.

The Andalusian
Al-Andalus
Al-Andalus was the Arabic name given to a nation and territorial region also commonly referred to as Moorish Iberia. The name describes parts of the Iberian Peninsula and Septimania governed by Muslims , at various times in the period between 711 and 1492, although the territorial boundaries...

agronomist
Agronomist
An agronomist is a scientist who specializes in agronomy, which is the science of utilizing plants for food, fuel, feed, and fiber. An agronomist is an expert in agricultural and allied sciences, with the exception veterinary sciences.Agronomists deal with interactions between plants, soils, and...

Ibn Bassal
Ibn Bassal
Ibn Bassal was a Moor botanist in Toledo and Seville, Spain who wrote about cultivation. Basal wrote the treatise The Classification of Soils which divided soil fertility into ten classifications...

(fl
Floruit
Floruit , abbreviated fl. , is a Latin verb meaning "flourished", denoting the period of time during which something was active...

1038–1075), in his Kitab al-Filaha, describes the flywheel effect employed in a water wheel
Water wheel
A water wheel is a machine for converting the energy of free-flowing or falling water into useful forms of power. A water wheel consists of a large wooden or metal wheel, with a number of blades or buckets arranged on the outside rim forming the driving surface...

machine, the saqiya
Sakia
A sakia , tympanum or tablia is a water wheel, somewhat similar to a noria, and used primarily in Egypt. It is a large hollow wheel, normally made of galvanized sheet steel, with scoops or buckets at the periphery...

.

The flywheel as a general mechanical device for equalizing the speed of rotation is, according to the American medievalist Lynn White, recorded in the De diversibus artibus (On various arts) of the German artisan Theophilus Presbyter
Theophilus Presbyter
Theophilus Presbyter is the pseudonymous author or compiler ofa Latin text containing detailed descriptions of various medieval arts, a text commonly known as the Schedula diversarum artium or De diversis artibus , probably first compiled between 1100 and 1120...

(ca. 1070–1125) who records applying the device in several of his machines.

In the Industrial Revolution
Industrial Revolution
The Industrial Revolution was a period from the 18th to the 19th century where major changes in agriculture, manufacturing, mining, transportation, and technology had a profound effect on the social, economic and cultural conditions of the times...

, James Watt
James Watt
James Watt, FRS, FRSE was a Scottish inventor and mechanical engineer whose improvements to the Newcomen steam engine were fundamental to the changes brought by the Industrial Revolution in both his native Great Britain and the rest of the world.While working as an instrument maker at the...

contributed to the development of the flywheel in the steam engine
Steam engine
A steam engine is a heat engine that performs mechanical work using steam as its working fluid.Steam engines are external combustion engines, where the working fluid is separate from the combustion products. Non-combustion heat sources such as solar power, nuclear power or geothermal energy may be...

, and his contemporary James Pickard
James Pickard
James Pickard was an English inventor. He modified the Newcomen engine in a manner that it could deliver a rotary motion. His solution, which he patented in 1780, involved the combined use of a crank and a flywheel....

used a flywheel combined with a crank
Crank (mechanism)
A crank is an arm attached at right angles to a rotating shaft by which reciprocating motion is imparted to or received from the shaft. It is used to change circular into reciprocating motion, or reciprocating into circular motion. The arm may be a bent portion of the shaft, or a separate arm...

to transform reciprocating into rotary motion.

## Physics

A flywheel is a spinning wheel or disc with a fixed axle so that rotation is only about one axis. Energy is stored in the rotor as kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

, or more specifically, rotational energy
Rotational energy
The rotational energy or angular kinetic energy is the kinetic energy due to the rotation of an object and is part of its total kinetic energy...

:

Where:
• is the angular velocity
Angular velocity
In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...

, and
• is the moment of inertia
Moment of inertia
In classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of inertia of mass, or the angular mass, is a measure of an object's resistance to changes to its rotation. It is the inertia of a rotating body with respect to its rotation...

of the mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

about the center of rotation. The moment of inertia is the measure of resistance to torque
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....

applied on a spinning object (i.e. the higher the moment of inertia, the slower it will spin when a given force is applied).

• The moment of inertia for a solid cylinder is ,
• for a thin-walled empty cylinder is ,
• and for a thick-walled empty cylinder is ,

Where m denotes mass, and r denotes a radius.

When calculating with SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

units, the standards would be for mass, kilograms; for radius, meters; and for angular velocity, radians per second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

. The resulting answer would be in joule
Joule
The joule ; symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended in applying a force of one newton through a distance of one metre , or in passing an electric current of one ampere through a resistance of one ohm for one second...

s.

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
Hoop stress
Circumferential stress is a type of mechanical stress of a cylindrically shaped part as a result of internal or external pressure.The classic example of circumferential stress is the tension applied to the iron bands, or hoops, of a wooden barrel...

on the rotor is a major consideration in the design of a flywheel energy storage system.

Where:
• is the tensile stress on the rim of the cylinder
• is the density of the cylinder
• is the radius of the cylinder, and
• is the angular velocity
Angular velocity
In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...

of the cylinder.

## Examples of energy stored in flywheels

object k (varies with shape) mass diameter angular velocity energy stored, [J] energy stored, [Wh]
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 http://www.vyconenergy.com/pq/VDCtech.htm 1/2 600 kg 500 mm 30000 rpm 92 MJ 26 kWh

### High-energy materials

For a given flywheel design, the kinetic energy is proportional to the ratio of the hoop stress to the material density and to the mass:

could be called the specific tensile strength
Specific strength
The specific strength is a material's strength divided by its density. It is also known as the strength-to-weight ratio or strength/weight ratio. In fiber or textile applications, tenacity is the usual measure of specific strength...

. The flywheel material with the highest specific tensile strength will yield the highest energy storage per unit mass. This is one reason why carbon fiber
Carbon fiber
Carbon fiber, alternatively graphite fiber, carbon graphite or CF, is a material consisting of fibers about 5–10 μm in diameter and composed mostly of carbon atoms. The carbon atoms are bonded together in crystals that are more or less aligned parallel to the long axis of the fiber...

is a material of interest.

For a given design the stored energy is proportional to the hoop stress and the volume:

### Rimmed Flywheels

A rimmed flywheel has a rim, a hub, and spokes. The structure of a rimmed flywheel is complex and, consequently, it may be difficult to compute its exact moment of inertia. A rimmed flywheel can be more easily analysed by applying various simplifications. For example:
• Assume the spokes, shaft and hub have zero moments of inertia, and the flywheel's moment of inertia is due to the rim alone.
• The lumped moments of inertia of spokes, hub and shaft may be estimated as a percentage of the flywheel's moment of inertia, with the remainder due to the rim, so that

For example, if the moments of inertia of hub, spokes and shaft are deemed negligible, and the rim's thickness is very small compared to its mean radius (), the radius of rotation of the rim is equal to its mean radius and thus: