Magnetic levitation
Overview

Magnetic levitation, maglev, or magnetic suspension is a method by which an object is suspended
Levitation
Levitation is the process by which an object is suspended by a physical force against gravity, in a stable position without solid physical contact...

with no support other than magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

s. Magnetic pressure
Magnetic pressure
Magnetic pressure is an energy density associated with the magnetic field. It is identical to any other physical pressure except that it is carried by the magnetic field rather than kinetic energy of the gas molecules. Interplay between magnetic pressure and ordinary gas pressure is important to...

is used to counteract the effects of the gravitational
Gravitational acceleration
In physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....

and any other accelerations.

Earnshaw's theorem
Earnshaw's theorem
Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. This was first proven by British mathematician Samuel Earnshaw in 1842. It is usually referenced to magnetic...

proves that using only static ferromagnetism it is impossible to stably levitate against gravity, but servomechanism
Servomechanism
thumb|right|200px|Industrial servomotorThe grey/green cylinder is the [[Brush |brush-type]] [[DC motor]]. The black section at the bottom contains the [[Epicyclic gearing|planetary]] [[Reduction drive|reduction gear]], and the black object on top of the motor is the optical [[rotary encoder]] for...

s, the use of diamagnetic materials, superconduction, or systems involving eddy current
Eddy current
Eddy currents are electric currents induced in conductors when a conductor is exposed to a changing magnetic field; due to relative motion of the field source and conductor or due to variations of the field with time. This can cause a circulating flow of electrons, or current, within the body of...

s permit this to occur.

In some cases the lifting force is provided by magnetic levitation, but there is a mechanical support bearing little load that provides stability.
Discussions
Encyclopedia
Magnetic levitation, maglev, or magnetic suspension is a method by which an object is suspended
Levitation
Levitation is the process by which an object is suspended by a physical force against gravity, in a stable position without solid physical contact...

with no support other than magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

s. Magnetic pressure
Magnetic pressure
Magnetic pressure is an energy density associated with the magnetic field. It is identical to any other physical pressure except that it is carried by the magnetic field rather than kinetic energy of the gas molecules. Interplay between magnetic pressure and ordinary gas pressure is important to...

is used to counteract the effects of the gravitational
Gravitational acceleration
In physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....

and any other accelerations.

Earnshaw's theorem
Earnshaw's theorem
Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. This was first proven by British mathematician Samuel Earnshaw in 1842. It is usually referenced to magnetic...

proves that using only static ferromagnetism it is impossible to stably levitate against gravity, but servomechanism
Servomechanism
thumb|right|200px|Industrial servomotorThe grey/green cylinder is the [[Brush |brush-type]] [[DC motor]]. The black section at the bottom contains the [[Epicyclic gearing|planetary]] [[Reduction drive|reduction gear]], and the black object on top of the motor is the optical [[rotary encoder]] for...

s, the use of diamagnetic materials, superconduction, or systems involving eddy current
Eddy current
Eddy currents are electric currents induced in conductors when a conductor is exposed to a changing magnetic field; due to relative motion of the field source and conductor or due to variations of the field with time. This can cause a circulating flow of electrons, or current, within the body of...

s permit this to occur.

In some cases the lifting force is provided by magnetic levitation, but there is a mechanical support bearing little load that provides stability. This is termed pseudo-levitation.

Magnetic levitation is used for maglev train
Maglev train
Maglev , is a system of transportation that uses magnetic levitation to suspend, guide and propel vehicles from magnets rather than using mechanical methods, such as friction-reliant wheels, axles and bearings...

s, 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 and for product display purposes.

## Lift

Magnetic materials and systems are able to attract or press each other apart or together with a force dependent on the magnetic field and the area of the magnets, and a magnetic pressure
Magnetic pressure
Magnetic pressure is an energy density associated with the magnetic field. It is identical to any other physical pressure except that it is carried by the magnetic field rather than kinetic energy of the gas molecules. Interplay between magnetic pressure and ordinary gas pressure is important to...

can then be defined.

The magnetic pressure of a magnetic field on a superconductor can be calculated by:

where is the force per unit area in pascals
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...

, is the magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

just above the superconductor in tesla
Tesla (unit)
The tesla is the SI derived unit of magnetic field B . One tesla is equal to one weber per square meter, and it was defined in 1960 in honour of the inventor, physicist, and electrical engineer Nikola Tesla...

s, and = 4π×10−7 N·A−2 is the permeability
Permeability (electromagnetism)
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...

of the vacuum.

## Stability

Static stability means that any small displacement away from a stable equilibrium causes a net force to push it back to the equilibrium point.

Earnshaw's theorem
Earnshaw's theorem
Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. This was first proven by British mathematician Samuel Earnshaw in 1842. It is usually referenced to magnetic...

proved conclusively that it is not possible to levitate stably using only static, macroscopic, paramagnetic fields. The forces acting on any paramagnetic object in any combinations of gravitational
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

, electrostatic, and magnetostatic fields will make the object's position, at best, unstable along at least one axis, and it can be unstable equilibrium along all axes. However, several possibilities exist to make levitation viable, for example, the use of electronic stabilization or diamagnetic materials (since relative magnetic permeability is less than one); it can be shown that diamagnetic materials are stable along at least one axis, and can be stable along all axes. Conductors can have a relative permeability to alternating magnetic fields of below one, so some configurations using simple AC driven electromagnets are self stable.

Dynamic stability occurs when the levitation system is able to damp out any vibration-like motion that may occur.

## Methods

For successful levitation and control of all 6 axes (3 spatial and 3 rotational) a combination of permanent magnets and electromagnets or diamagnets or superconductors as well as attractive and repulsive fields can be used. From Earnshaw's theorem at least one stable axis must be present for the system to levitate successfully, but the other axes can be stabilised using ferromagnetism.

The primary ones used in maglev train
Maglev train
Maglev , is a system of transportation that uses magnetic levitation to suspend, guide and propel vehicles from magnets rather than using mechanical methods, such as friction-reliant wheels, axles and bearings...

s are servo-stabilized electromagnetic suspension (EMS), electrodynamic suspension (EDS), and experimentally, Inductrack
Inductrack
Inductrack is a passive, fail-safe electrodynamic magnetic levitation system, using only unpowered loops of wire in the track and permanent magnets on the vehicle to achieve magnetic levitation. The track can be in one of two configurations, a "ladder track" and a "laminated track"...

.

### Mechanical constraint (pseudo-levitation)

With a small amount of mechanical constraint for stability, pseudo-levitation is relatively straightforwardly achieved.

If two magnet
Magnet
A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, and attracts or repels other magnets.A permanent magnet is an object...

s are mechanically constrained along a single vertical axis, for example, and arranged to repel each other strongly, this will act to levitate one of the magnets above the other.

Another geometry is where the magnets are attracted, but constrained from touching by a tensile member, such as a string or cable.

Another example is the Zippe-type centrifuge
Zippe-type centrifuge
The Zippe-type centrifuge is a device designed to collect Uranium-235. It was developed in the Soviet Union by a team of 60 Austrian and German scientists captured after World War II, working in detention...

where a cylinder is suspended under an attractive magnet, and stabilized by a needle bearing from below.

### Diamagnetism

Diamagnetism is the property of an object which causes it to create a magnetic field in opposition to an externally applied magnetic field, thus causing a repulsive effect. Specifically, an external magnetic field alters the orbital velocity of electrons around their nuclei, thus changing the magnetic dipole moment. According to Lenz's law, this opposes the external field. Diamagnets are materials with a magnetic permeability less than μ0 (a relative permeability less than 1).
Consequently, diamagnetism is a form of magnetism that is only exhibited by a substance in the presence of an externally applied magnetic field. It is generally quite a weak effect in most materials, although superconductors exhibit a strong effect.
Diamagnetic materials cause lines of magnetic flux to curve away from the material, and superconductors can exclude them completely (except for a very thin layer at the surface).

#### Direct diamagnetic levitation

A substance that is diamagnetic repels a magnetic field. All materials have diamagnetic properties, but the effect is very weak, and is usually overcome by the object's paramagnetic or ferromagnetic properties, which act in the opposite manner. Any material in which the diamagnetic component is strongest will be repelled by a magnet.

Earnshaw's theorem
Earnshaw's theorem
Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. This was first proven by British mathematician Samuel Earnshaw in 1842. It is usually referenced to magnetic...

does not apply to diamagnets. These behave in the opposite manner to normal magnets owing to their relative permeability
Permeability (electromagnetism)
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...

of μr < 1 (i.e. negative magnetic susceptibility
Magnetic susceptibility
In electromagnetism, the magnetic susceptibility \chi_m is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field...

).

Diamagnetic levitation can be used to levitate very light pieces of pyrolytic graphite or bismuth
Bismuth
Bismuth is a chemical element with symbol Bi and atomic number 83. Bismuth, a trivalent poor metal, chemically resembles arsenic and antimony. Elemental bismuth may occur naturally uncombined, although its sulfide and oxide form important commercial ores. The free element is 86% as dense as lead...

above a moderately strong permanent magnet. As water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

is predominantly diamagnetic, this technique has been used to levitate water droplets and even live animals, such as a grasshopper, frog and a mouse. However, the magnetic fields required for this are very high, typically in the range of 16 tesla
Tesla (unit)
The tesla is the SI derived unit of magnetic field B . One tesla is equal to one weber per square meter, and it was defined in 1960 in honour of the inventor, physicist, and electrical engineer Nikola Tesla...

s, and therefore create significant problems if ferromagnetic materials are nearby.

The minimum criterion for diamagnetic levitation is , where:
• is the magnetic susceptibility
Magnetic susceptibility
In electromagnetism, the magnetic susceptibility \chi_m is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field...

• is the density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

of the material
• is the local gravitational acceleration
Gravitational acceleration
In physics, gravitational acceleration is the acceleration on an object caused by gravity. Neglecting friction such as air resistance, all small bodies accelerate in a gravitational field at the same rate relative to the center of mass....

(−9.8 m
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

/s
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....

2 on Earth)
• is the permeability of free space
• is the magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

• is the rate of change of the magnetic field along the vertical axis.

Assuming ideal conditions along the z-direction of solenoid magnet:
• Water
Water
Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

levitates at
• Graphite
Graphite
The mineral graphite is one of the allotropes of carbon. It was named by Abraham Gottlob Werner in 1789 from the Ancient Greek γράφω , "to draw/write", for its use in pencils, where it is commonly called lead . Unlike diamond , graphite is an electrical conductor, a semimetal...

levitates at

#### Diamagnetically-stabilized levitation

A permanent magnet can be stably suspended by various configurations of strong permanent magnets and strong diamagnets. When using superconducting magnets, the levitation of a permanent magnet can even be stabilized by the small diamagnetism of water in human fingers.

### Superconductors

Superconductors may be considered perfect diamagnets (μr = 0), as well as the property they have of completely expelling magnetic fields due to the Meissner effect
Meissner effect
The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin...

when the superconductivity initially forms. The levitation of the magnet is further stabilized due to flux pinning
Flux pinning
Flux pinning is the phenomenon that magnetic flux lines do not move in spite of the Lorentz force acting on them inside a current-carrying...

within the superconductor; this tends to stop the superconductor leaving the magnetic field, even if the levitated system is inverted.

These principles are exploited by EDS (Electrodynamic Suspension), superconducting bearings
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...

, flywheel
Flywheel
A flywheel is a rotating mechanical device that is used to store rotational energy. Flywheels have a significant moment of inertia, and thus resist changes in rotational speed. The amount of energy stored in a flywheel is proportional to the square of its rotational speed...

s, etc.

In trains, a very strong magnetic field is required to levitate a massive train, the JR–Maglev have superconducting magnetic coils. JR–Maglev levitation is not by Meissner effect.

### Rotational stabilization

A magnet can be levitated against gravity when gyroscopically
Gyroscope
A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. In essence, a mechanical gyroscope is a spinning wheel or disk whose axle is free to take any orientation...

stabilized by spinning it in a toroidal field created by a base ring of magnet(s). However, it will only remain stable until the rate 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...

slows below a critical threshold—the region of stability is quite narrow both spatially and in the required rate of precession. The first discovery of this phenomenon was by Roy Harrigan, a Vermont inventor who patented a levitation device in 1983 based upon it. Several devices using rotational stabilization (such as the popular Levitron
Levitron
Levitron is a brand of levitating toys and gifts in science and educational markets marketed by Creative Gifts Inc. and Fascination Toys & Gifts. The Levitron top device is a commercial toy that displays the phenomenon known as spin stabilized magnetic levitation...

toy) have been developed citing this patent. Non-commercial devices have been created for university research laboratories, generally using magnets too powerful for safe public interaction.

### Servomechanisms

The attraction from a fixed strength magnet decreases with increased distance, and increases at closer distances. This is unstable. For a stable system, the opposite is needed, variations from a stable position should push it back to the target position.

Stable magnetic levitation can be achieved by measuring the position and speed
Speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...

of the object being levitated, and using a feedback loop which continuously adjusts one or more electromagnets to correct the object's motion, thus forming a servomechanism
Servomechanism
thumb|right|200px|Industrial servomotorThe grey/green cylinder is the [[Brush |brush-type]] [[DC motor]]. The black section at the bottom contains the [[Epicyclic gearing|planetary]] [[Reduction drive|reduction gear]], and the black object on top of the motor is the optical [[rotary encoder]] for...

.

Many systems use magnetic attraction pulling upwards against gravity for these kinds of systems as this gives some inherent lateral stability, but some use a combination of magnetic attraction and magnetic repulsion to push upwards.

Either system represents examples of ElectroMagnetic Suspension (EMS). For a very simple example, some tabletop levitation demonstrations use this principle, and the object cuts a beam of light to measure the position of the object. The electromagnet is above the object being levitated; the electromagnet is turned off whenever the object gets too close, and turned back on when it falls further away. Such a simple system is not very robust; far more effective control systems exist, but this illustrates the basic idea.

EMS magnetic levitation trains are based on this kind of levitation: The train wraps around the track, and is pulled upwards from below. The servo
Servomechanism
thumb|right|200px|Industrial servomotorThe grey/green cylinder is the [[Brush |brush-type]] [[DC motor]]. The black section at the bottom contains the [[Epicyclic gearing|planetary]] [[Reduction drive|reduction gear]], and the black object on top of the motor is the optical [[rotary encoder]] for...

controls keep it safely at a constant distance from the track.

### Induced currents

These schemes work due to repulsion due to Lenz's law
Lenz's law
Lenz's law is a common way of understanding how electromagnetic circuits must always obey Newton's third law and The Law of Conservation of Energy...

. When a conductor is presented with a time-varying magnetic field electrical currents in the conductor are set up which create a magnetic field that causes a repulsive effect.

#### Relative motion between conductors and magnets

If one moves a base made of a very good electrical conductor such as copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...

, aluminium
Aluminium
Aluminium or aluminum is a silvery white member of the boron group of chemical elements. It has the symbol Al, and its atomic number is 13. It is not soluble in water under normal circumstances....

or silver
Silver
Silver is a metallic chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal...

close to a magnet, an (eddy
Eddy current
Eddy currents are electric currents induced in conductors when a conductor is exposed to a changing magnetic field; due to relative motion of the field source and conductor or due to variations of the field with time. This can cause a circulating flow of electrons, or current, within the body of...

) current will be induced in the conductor that will oppose the changes in the field and create an opposite field that will repel the magnet (Lenz's law
Lenz's law
Lenz's law is a common way of understanding how electromagnetic circuits must always obey Newton's third law and The Law of Conservation of Energy...

). At a sufficiently high rate of movement, a suspended magnet will levitate on the metal, or vice versa with suspended metal. Litz wire
Litz wire
Litz wire is a type of cable used in electronics to carry alternating current. The wire is designed to reduce the skin effect and proximity effect losses in conductors used at frequencies up to about 1 MHz...

made of wire thinner than the skin depth for the frequencies seen by the metal works much more efficiently than solid conductors.

An especially technologically-interesting case of this comes when one uses a Halbach array
Halbach array
A Halbach array is a special arrangement of permanent magnets that augments the magnetic field on one side of the array while cancelling the field to near zero on the other side...

instead of a single pole permanent magnet, as this almost doubles the field strength, which in turn almost doubles the strength of the eddy currents. The net effect is to more than triple the lift force. Using two opposed Halbach arrays increases the field even further.

Halbach arrays are also well-suited to magnetic levitation and stabilisation of gyroscope
Gyroscope
A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. In essence, a mechanical gyroscope is a spinning wheel or disk whose axle is free to take any orientation...

s and electric motor
Electric motor
An electric motor converts electrical energy into mechanical energy.Most electric motors operate through the interaction of magnetic fields and current-carrying conductors to generate force...

and generator
Electrical generator
In electricity generation, an electric generator is a device that converts mechanical energy to electrical energy. A generator forces electric charge to flow through an external electrical circuit. It is analogous to a water pump, which causes water to flow...

spindles.

#### Oscillating electromagnetic fields

A conductor
Electrical conductor
In physics and electrical engineering, a conductor is a material which contains movable electric charges. In metallic conductors such as copper or aluminum, the movable charged particles are electrons...

can be levitated above an electromagnet (or vice versa) with an alternating current
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....

flowing through it. This causes any regular conductor to behave like a diamagnet, due to the eddy current
Eddy current
Eddy currents are electric currents induced in conductors when a conductor is exposed to a changing magnetic field; due to relative motion of the field source and conductor or due to variations of the field with time. This can cause a circulating flow of electrons, or current, within the body of...

s generated in the conductor. Since the eddy currents create their own fields which oppose the magnetic field, the conductive object is repelled from the electromagnet, and most of the field lines of the magnetic field will no longer penetrate the conductive object.

This effect requires non-ferromagnetic but highly conductive materials like aluminium or copper, as the ferromagnetic ones are also strongly attracted to the electromagnet (although at high frequencies the field can still be expelled) and tend to have a higher resistivity giving lower eddy currents. Again, litz wire gives the best results.

The effect can be used for stunts such as levitating a telephone book by concealing an aluminium plate within it.

At high frequencies (a few tens of kilohertz or so) and kilowatt powers small quantities of metals can be levitated and melted using levitation melting without the risk of the metal being contaminated by the crucible.

One source of oscillating magnetic field that is used is the linear induction motor
Linear induction motor
A linear induction motor is an AC asynchronous linear motor that works by the same general principles as other induction motors but which has been designed to directly produce motion in a straight line....

. This can be used to levitate as well as provide propulsion.

### Strong focusing

Earnshaw's theory strictly only applies to static fields. Alternating magnetic fields, even purely alternating attractive fields, can induce stability and confine a trajectory through a magnetic field to give a levitation effect.

This is used in particle accelerators to confine and lift charged particles, and has been proposed for maglev trains also.

## Dynamic stability

Magnetic fields are conservative force
Conservative force
A conservative force is a force with the property that the work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the net work done by a conservative force is zero.It is possible to define a numerical value of...

s and therefore in principle have no built-in damping, and in practice many of the levitation schemes are under-damped and in some cases negatively damped. This can permit vibration modes to exist that can cause the item to leave the stable region.

Damping of motion is done in a number of ways:
• external mechanical damping (in the support), such as dashpot
Dashpot
A dashpot is a mechanical device, a damper which resists motion via viscous friction. The resulting force is proportional to the velocity, but acts in the opposite direction, slowing the motion and absorbing energy. It is commonly used in conjunction with a spring...

s, air drag etc.
• eddy current damping (conductive metal influenced by field)
• tuned mass damper
Tuned mass damper
A tuned mass damper, also known as an active mass damper or harmonic absorber, is a device mounted in structures to reduce the amplitude of mechanical vibrations. Their application can prevent discomfort, damage, or outright structural failure...

s in the levitated object
• electromagnets controlled by electronics

## Difficulties

Most of the levitation techniques have various complexities.
• The power requirements of electromagnets increase rapidly with load-bearing capacity, which also necessitates relative increases in conductor and cooling equipment mass and volume.
• Superconductors require very low temperatures to operate, often helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

cooling is employed.

### Maglev transportation

Maglev, or magnetic levitation, is a system of transportation that suspends, guides and propels vehicles, predominantly trains, using magnetic levitation from a very large number of magnets for lift and propulsion. This method has the potential to be faster, quieter and smoother than wheeled mass transit systems. The technology has the potential to exceed 6,400 km/h (4,000 mi/h) if deployed in an evacuated
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

tunnel. If not deployed in an evacuated tube the power needed for levitation is usually not a particularly large percentage and most of the power needed is used to overcome air drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...

, as with any other high speed train.

The highest recorded speed of a maglev train is 581 kilometers per hour (361 mph), achieved in Japan in 2003, 6 km/h faster than the conventional TGV
TGV
The TGV is France's high-speed rail service, currently operated by SNCF Voyages, the long-distance rail branch of SNCF, the French national rail operator....

speed record. This is slower than many aircraft, since aircraft can fly at far higher altitudes where air drag is lower, thus high speeds are more readily attained.

### Magnetic bearings

• Magnetic bearings
• Flywheel
Flywheel
A flywheel is a rotating mechanical device that is used to store rotational energy. Flywheels have a significant moment of inertia, and thus resist changes in rotational speed. The amount of energy stored in a flywheel is proportional to the square of its rotational speed...

s
• Centrifuge
Centrifuge
A centrifuge is a piece of equipment, generally driven by an electric motor , that puts an object in rotation around a fixed axis, applying a force perpendicular to the axis...

s
• Magnetic ring spinning
Magnetic ring spinning
Magnetic Ring Spinning, magnetic spinning, or innovative spinning is a ring spinning technology for making yarn based on magnetic levitation. This technique functions without a traveler sliding over the ring, enabling much higher spinning rates....

### Levitation melting

Electromagnetic levitation (EML), patented by Muck in 1923 , is one of the oldest levitation techniques used for containerless experiments. The technique enables the levitation
Levitation
Levitation is the process by which an object is suspended by a physical force against gravity, in a stable position without solid physical contact...

of an object using electromagnet
Electromagnet
An electromagnet is a type of magnet in which the magnetic field is produced by the flow of electric current. The magnetic field disappears when the current is turned off...

s. A typical EML coil has reversed winding of upper and lower sections energized by a radio frequency
Radio frequency is a rate of oscillation in the range of about 3 kHz to 300 GHz, which corresponds to the frequency of radio waves, and the alternating currents which carry radio signals...

power supply.

## History

• 1839 Earnshaw's theorem showed electrostatic levitation was impossible, later theorem was extended to magnetostatic levitation by others
• 1912 Emile Bachelet awarded a patent in March 1912 for his “levitating transmitting apparatus” (patent no. 1,020,942) for electromagnetic suspension system
• 1933 Superdiamagnetism Walter Meissner and Robert Ochsenfeld
Robert Ochsenfeld
Robert Ochsenfeld was a German physicist born on May 18, 1901 in Hilchenbach . In 1933 he discovered with Walter Meissner the Meißner-Ochsenfeld effect.He died on December 5, 1993 in Hilchenbach....

(the Meissner effect
Meissner effect
The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin...

)
• 1934 Hermann Kemper “monorail vehicle with no wheels attached.” Reich Patent number 643316
• 1939 Braunbeck’s extension showed that magnetic levitation is possible with diamagnetic materials
• 1939 Bedford, Peer, and Tonks aluminum plate placed on two concentric cylindrical coils shows 6-axis stable levitation.
• 1961 James R. Powell
James R. Powell
James R. Powell is an American physicist notable — together with Dr. Gordon Danby — for his work on superconducting Maglev, for which he shared the Franklin Institute "Medal 2000 for Engineering"....

and BNL colleague Gordon Danby
Gordon Danby
Gordon T. Danby is an American physicist notable for his work on superconducting Maglev, for which he shared the Franklin Institute 'Medal 2000 for Engineering'.-References:...

electrodynamic levitation using superconducting magnets
• 1970s Spin stabilized magnetic levitation
Spin stabilized magnetic levitation
Spin-stabilized magnetic levitation is a phenomenon of magnetic levitation where a magnet is levitated via magnetic forces above another magnet or array of magnets, and stabilised by gyroscopic effect due to a spin that is neither too fast, nor too slow....

Roy M. Harrigan
• 1974 Magnetic river
Magnetic river
Magnetic river is an electrodynamic suspension magnetic levitation system designed by Eastham and Eric Laithwaite in 1974.It consists of a thin conductive plate on an AC linear induction motor...

Eric Laithwaite
Eric Laithwaite
Eric Roberts Laithwaite was a British electrical engineer, known as the "Father of Maglev" for his development of the linear induction motor and maglev rail system.- Biography :...

and others
• 1979 transrapid
Transrapid
Transrapid is a German high-speed monorail train using magnetic levitation. Based on a patent from 1934, planning of the Transrapid system started in 1969. The test facility for the system in Emsland, Germany was completed in 1987...

train carried passengers
• 1984 Low speed maglev shuttle in Birmingham Eric Laithwaite and others
• 1999 Inductrack
Inductrack
Inductrack is a passive, fail-safe electrodynamic magnetic levitation system, using only unpowered loops of wire in the track and permanent magnets on the vehicle to achieve magnetic levitation. The track can be in one of two configurations, a "ladder track" and a "laminated track"...

permanent magnet electrodynamic levitation (General Atomics)
• 2000 Diamagnetically levitated live frog Andre Geim
Andre Geim
Andre Konstantin Geim, FRS is a Dutch-Russian-British physicist working at the University of Manchester. Geim was awarded the 2010 Nobel Prize in Physics jointly with Konstantin Novoselov for his work on graphene...

• Acoustic levitation
Acoustic levitation
Acoustic levitation is a method for suspending matter in a medium by using acoustic radiation pressure from intense sound waves in the medium. Acoustic levitation is possible because of the non-linear effects of intense sound waves....

• Aerodynamic levitation
Aerodynamic levitation
Aerodynamic levitation is the use of gas pressure to levitate materials so that they are no longer in physical contact with any container. In scientific experiments this removes contamination and nucleation issues associated with physical contact with a container.-Overview:The term aerodynamic...

• Electrostatic levitation
Electrostatic levitation
Electrostatic levitation is the process of using an electric field to levitate a charged object and counteract the effects of gravity. It was used, for instance, in Robert Millikan's oil drop experiment and is used to suspend the gyroscopes in Gravity Probe B during launch.Due to Earnshaw's...

• Optical levitation
Optical levitation
Optical levitation is a method developed by Arthur Ashkin whereby a material is levitated against the downward force of gravity by an upward force stemming from photon momentum transfer...

• Cyclotron
Cyclotron
In technology, a cyclotron is a type of particle accelerator. In physics, the cyclotron frequency or gyrofrequency is the frequency of a charged particle moving perpendicularly to the direction of a uniform magnetic field, i.e. a magnetic field of constant magnitude and direction...

s levitate and circulate charged particles in a magnetic field
• Inductrack
Inductrack
Inductrack is a passive, fail-safe electrodynamic magnetic levitation system, using only unpowered loops of wire in the track and permanent magnets on the vehicle to achieve magnetic levitation. The track can be in one of two configurations, a "ladder track" and a "laminated track"...

a particular system based on Halbach arrays and inductive track loops
• Launch loop
Launch loop
A launch loop or Lofstrom loop is a proposed system for launching objects into space orbit using a moving cable-like system attached to the earth at two ends and suspended above the atmosphere in the middle...

• Levitron
Levitron
Levitron is a brand of levitating toys and gifts in science and educational markets marketed by Creative Gifts Inc. and Fascination Toys & Gifts. The Levitron top device is a commercial toy that displays the phenomenon known as spin stabilized magnetic levitation...

• Linear motor
Linear motor
A linear motor is an electric motor that has had its stator and rotor "unrolled" so that instead of producing a torque it produces a linear force along its length...

• Rapid transits using linear motor propulsion
• 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...

• Nagahori Tsurumi-ryokuchi Line
• StarTram
StarTram
StarTram is a proposal for a maglev space launch system. The initial Generation 1 facility would be cargo only, launching from a mountain peak at 3 km to 7 km altitude with an evacuated tube staying at local surface level, raising ≈150,000 tons to orbit annually...

is an extreme proposal for levitation via superconductors over multiple kilometers of distance
• Zippe-type centrifuge
Zippe-type centrifuge
The Zippe-type centrifuge is a device designed to collect Uranium-235. It was developed in the Soviet Union by a team of 60 Austrian and German scientists captured after World War II, working in detention...

uses magnetic lift and a mechanical needle for stability
• Magnetic ring spinning
Magnetic ring spinning
Magnetic Ring Spinning, magnetic spinning, or innovative spinning is a ring spinning technology for making yarn based on magnetic levitation. This technique functions without a traveler sliding over the ring, enabling much higher spinning rates....