Magnetic levitation

Magnetic levitation, maglev, or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields. Magnetic force is used to counteract the effects of the gravitational acceleration and any other accelerations.

The two primary issues involved in magnetic levitation are lifting forces: providing an upward force sufficient to counteract gravity, and stability: ensuring that the system does not spontaneously slide or flip into a configuration where the lift is neutralized.

Magnetic levitation is used for maglev trains, contactless melting, magnetic bearings and for product display purposes.

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. For example, the simplest example of lift would be a simple dipole magnet positioned in the magnetic fields of another dipole magnet, oriented with like poles facing each other, so that the force between magnets repels the two magnets.

Essentially all types of magnets have been used to generate lift for magnetic levitation; permanent magnets, electromagnets, ferromagnetism, diamagnetism, superconducting magnets and magnetism due to induced currents in conductors.

Stability
Earnshaw’s theorem proves that using only paramagnetic materials (such as ferromagnetic iron) it is impossible for a static system to stably levitate against gravity.

For example, the simplest example of lift with two simple dipole magnets repelling is highly unstable, since the top magnet can slide sideways, or flip over, and it turns out that no configuration of magnets can produce stability.

However, servomechanisms, the use of diamagnetic materials, superconduction, or systems involving eddy currents allow stability to be achieved.

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

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

Magnetic fields are conservative forces 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.

Methods
For successful levitation and control of all 6 axes (degrees of freedom; 3 translational 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 stabilized using ferromagnetism.

The primary ones used in maglev trains are servo-stabilized electromagnetic suspension (EMS), electrodynamic suspension (EDS).

Mechanical constraint (pseudo-levitation)
With a small amount of mechanical constraint for stability, achieving pseudo-levitation is a relatively straightforward process.

If two magnets are mechanically constrained along a single 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 where a cylinder is suspended under an attractive magnet, and stabilized by a needle bearing from below.

Servomechanisms

The Transrapid system uses servomechanisms to pull the train up from underneath the track and maintains a constant gap while travelling at high speed

Floating globe. Magnetic levitation with a feedback loop.
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 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.

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 or Hall effect sensor method is used 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.

Induced currents
These schemes work due to repulsion due to Lenz’s law. 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.

These kinds of systems typically show an inherent stability, although extra damping is sometimes required.

Relative motion between conductors and magnets
If one moves a base made of a very good electrical conductor such as copper, aluminium or silver close to a magnet, an (eddy) 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). At a sufficiently high rate of movement, a suspended magnet will levitate on the metal, or vice versa with suspended metal. Litz wire made of wire thinner than the skin depth for the frequencies seen by the metal works much more efficiently than solid conductors. Figure 8 coils can be used to keep something aligned.

An especially technologically interesting case of this comes when one uses a Halbach array 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 gyroscopes and electric motor and generator spindles.

Oscillating electromagnetic fields
A conductor can be levitated above an electromagnet (or vice versa) with an alternating current flowing through it. This causes any regular conductor to behave like a diamagnet, due to the eddy currents 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. This can be used to levitate as well as provide propulsion.

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

Diamagnetically stabilized levitation
Permanent magnet stably levitated between fingertips
Earnshaw’s theorem does not apply to diamagnets. These behave in the opposite manner to normal magnets owing to their relative permeability of μr < 1 (i.e. negative magnetic susceptibility). Diamagnetic levitation can be inherently stable.

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.

Diamagnetic levitation

Diamagnetic levitation of pyrolytic carbon
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 the material to be repelled by magnetic fields. Diamagnetic materials cause lines of magnetic flux to curve away from the material. 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.

Direct diamagnetic levitation

A live frog levitates inside a 32 mm diameter vertical bore of a Bitter solenoid in a magnetic field of about 16 teslas
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 stronger will be repelled by a magnet.

Diamagnetic levitation can be used to levitate very light pieces of pyrolytic graphite or bismuth above a moderately strong permanent magnet. As water 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 teslas, and therefore create significant problems if ferromagnetic materials are nearby.

Superconductors
Superconductors may be considered perfect diamagnets, and completely expel magnetic fields due to the Meissner effect when the superconductivity initially forms; thus superconducting levitation can be considered a particular instance of diamagnetic levitation. In a type-II superconductor, the levitation of the magnet is further stabilized due to flux pinning within the superconductor; this tends to stop the superconductor from moving with respect to the magnetic field, even if the levitated system is inverted.

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

A very strong magnetic field is required to levitate a train. The JR–Maglev trains have superconducting magnetic coils, but the JR–Maglev levitation is not due to the Meissner effect.

Rotational stabilization
The Levitron brand top is an example of spin-stabilized magnetic levitation
Main article: Spin-stabilized magnetic levitation
A magnet or properly assembled array of magnets with a toroidal field can be stably levitated against gravity when gyroscopically stabilized by spinning it in a second toroidal field created by a base ring of magnet(s). However, this only works while the rate of precession is between both upper and lower critical thresholds—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 M. Harrigan, a Vermont inventor who patented a levitation device in 1983 based upon it. Several devices using rotational stabilization (such as the popular Levitron branded levitating top 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.

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 as well.

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 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, as with any other high speed train. Some maglev Hyperloop prototype vehicles are being developed as part of the Hyperloop pod competition in 2015–2016, and are expected to make initial test runs in an evacuated tube later in 2016.

Homopolar generator

Faraday disk, the first homopolar generator

A homopolar generator is a DC electrical generator comprising an electrically conductive disc or cylinder rotating in a plane perpendicular to a uniform static magnetic field. A potential difference is created between the center of the disc and the rim (or ends of the cylinder) with an electrical polarity that depends on the direction of rotation and the orientation of the field. It is also known as a unipolar generator, acyclic generator, disk dynamo, or Faraday disc. The voltage is typically low, on the order of a few volts in the case of small demonstration models, but large research generators can produce hundreds of volts, and some systems have multiple generators in series to produce an even larger voltage. They are unusual in that they can source tremendous electric current, some more than a million amperes, because the homopolar generator can be made to have very low internal resistance.

The Faraday disc

The first homopolar generator was developed by Michael Faraday during his experiments in 1831. It is frequently called the Faraday disc or Faraday wheel in his honor. It was the beginning of modern dynamos — that is, electrical generators which operate using a magnetic field. It was very inefficient and was not used as a practical power source, but it showed the possibility of generating electric power using magnetism, and led the way for commutated direct current dynamos and then alternating current alternators.

The Faraday disc was primarily inefficient due to counterflows of current. While current flow was induced directly underneath the magnet, the current would circulate backwards in regions outside the influence of the magnetic field. This counterflow limits the power output to the pickup wires, and induces waste heating of the copper disc. Later homopolar generators would solve this problem by using an array of magnets arranged around the disc perimeter to maintain a steady field around the circumference, and eliminate areas where counterflow could occur.

Homopolar generator development

Long after the original Faraday disc had been abandoned as a practical generator, a modified version combining the magnet and disc in a single rotating part (the rotor) was developed. Sometimes the name homopolar generator is reserved for this configuration. One of the earliest patents on the general type of homopolar generators was attained by A. F. Delafield, U.S. Patent 278,516. Other early patents for homopolar generators were awarded to S. Z. De Ferranti and C. Batchelor separately. Nikola Tesla was interested in the Faraday disc and conducted work with homopolar generators, and eventually patented an improved version of the device in U.S. Patent 406,968. Tesla’s “Dynamo Electric Machine” patent describes an arrangement of two parallel discs with separate, parallel shafts, joined like pulleys by a metallic belt. Each disc had a field that was the opposite of the other, so that the flow of current was from the one shaft to the disc edge, across the belt to the other disc edge and to the second shaft. This would have greatly reduced the frictional losses caused by sliding contacts by allowing both electrical pickups to interface with the shafts of the two disks rather than at the shaft and a high-speed rim. Later, patents were awarded to C. P. Steinmetz and E. Thomson for their work with homopolar generators. The Forbes dynamo, developed by the Scottish electrical engineer George Forbes, was in widespread use during the beginning of the 20th century. Much of the development done in homopolar generators was patented by J. E. Noeggerath and R. Eickemeyer.

Homopolar generators underwent a renaissance in the 1950s as a source of pulsed power storage. These devices used heavy disks as a form of flywheel to store mechanical energy that could be quickly dumped into an experimental apparatus. An early example of this sort of device was built by Sir Mark Oliphant at the Research School of Physical Sciences and Engineering, Australian National University. It stored up to 500 megajoules of energy and was used as an extremely high-current source for synchrotron experimentation from 1962 until it was disassembled in 1986. Oliphant’s construction was capable of supplying currents of up to 2 megaamperes (MA).

Similar devices of even larger size are designed and built by Parker Kinetic Designs (formerly OIME Research & Development) of Austin. They have produced devices for a variety of roles, from powering railguns to linear motors (for space launches) to a variety of weapons designs. Industrial designs of 10 MJ were introduced for a variety of roles, including electrical welding.

Disc-type generator

This device consists of a conducting flywheel rotating in a magnetic field with one electrical contact near the axis and the other near the periphery. It has been used for generating very high currents at low voltages in applications such as welding, electrolysis and railgun research. In pulsed energy applications, the angular momentum of the rotor is used to accumulate energy over a long period and then release it in a short time.

In contrast to other types of generators, the output voltage never changes polarity. The charge separation results from the Lorentz force on the free charges in the disk. The motion is azimuthal and the field is axial, so the electromotive force is radial. The electrical contacts are usually made through a “brush” or slip ring, which results in large losses at the low voltages generated. Some of these losses can be reduced by using mercury or other easily liquified metal or alloy (gallium, NaK) as the “brush”, to provide essentially uninterrupted electrical contact.

A recent suggested modification is to use a plasma contact supplied by a negative resistance neon streamer touching the edge of the disk or drum, using specialized low work function carbon in vertical strips. This would have the advantage of very low resistance within a current range possibly up to thousands of Amps without the liquid metal contact.

If the magnetic field is provided by a permanent magnet, the generator works regardless of whether the magnet is fixed to the stator or rotates with the disc. Before the discovery of the electron and the Lorentz force law, the phenomenon was inexplicable and was known as the Faraday paradox.

Drum-type generator

A drum-type homopolar generator has a magnetic field (B) that radiates radially from the center of the drum and induces voltage (V) down the length of the drum. A conducting drum spun from above in the field of a “loudspeaker” type of magnet that has one pole in the center of the drum and the other pole surrounding the drum could use conducting ball bearings at the top and bottom of the drum to pick up the generated current.

Astrophysical unipolar inductors

Unipolar inductors occur in astrophysics where a conductor rotates through a magnetic field, for example, the movement of the highly conductive plasma in a cosmic body’s ionosphere through its magnetic field. In their book, Cosmical Electrodynamics, Hannes Alfvén and Carl-Gunne Fälthammar write:

“Since cosmical clouds of ionized gas are generally magnetized, their motion produces induced electric fields [..] For example the motion of the magnetized interplanetary plasma produces electric fields that are essential for the production of aurora and magnetic storms” [..]

“.. the rotation of a conductor in a magnetic field produces an electric field in the system at rest. This phenomenon is well known from laboratory experiments and is usually called ‘homopolar ‘ or ‘unipolar’ induction.

Unipolar inductors have been associated with the aurorae on Uranus, binary stars, black holes, galaxies, the Jupiter Io system, the Moon, the Solar Wind, sunspots, and in the Venusian magnetic tail.

Physics

Like all dynamos, the Faraday disc converts kinetic energy to electrical energy. This machine can be analysed using Faraday’s own law of electromagnetic induction. This law, in its modern form, states that the full-time derivative of the magnetic flux through a closed circuit induces an electromotive force in the circuit, which in turn drives an electric current. The surface integral that defines the magnetic flux can be rewritten as a line integral around the circuit. Although the integrand of the line integral is time-independent, because the Faraday disc that forms part of the boundary of line integral is moving, the full-time derivative is non-zero and returns the correct value for calculating the electromotive force. Alternatively, the disc can be reduced to a conductive ring along the disc’s circumference with a single metal spoke connecting the ring to the axle.

The Lorentz force law is more easily used to explain the machine’s behaviour. This law, formulated thirty years after Faraday’s death, states that the force on an electron is proportional to the cross product of its velocity and the magnetic flux vector. In geometrical terms, this means that the force is at right-angles to both the velocity (azimuthal) and the magnetic flux (axial), which is therefore in a radial direction. The radial movement of the electrons in the disc produces a charge separation between the center of the disc and its rim, and if the circuit is completed an electric current will be produced.

Free energy & Perpetual motion

Perpetual motion is motion of bodies that continues indefinitely. A perpetual motion machine is a hypothetical machine that can do work indefinitely without an energy source. This kind of machine is impossible, as it would violate the first or second law of thermodynamics.

These laws of thermodynamics apply regardless of the size of the system. For example, the motions and rotations of celestial bodies such as planets may appear perpetual, but are actually subject to many processes that slowly dissipate their kinetic energy, such as solar wind, interstellar medium resistance, gravitational radiation and thermal radiation, so they will not keep moving forever.

Thus, machines that extract energy from finite sources will not operate indefinitely, because they are driven by the energy stored in the source, which will eventually be exhausted. A common example is devices powered by ocean currents, whose energy is ultimately derived from the Sun, which itself will eventually burn out. Machines powered by more obscure sources have been proposed, but are subject to the same inescapable laws, and will eventually wind down.

In 2017 new states of matter, time crystals, were discovered in which on a microscopic scale the component atoms are in continual repetitive motion, thus satisfying the literal definition of “perpetual motion”. However, these do not constitute perpetual motion machines in the traditional sense or violate thermodynamic laws because they are in their quantum ground state, so no energy can be extracted from them; they have “motion without energy”.

The history of perpetual motion machines dates back to the Middle Ages. For millennia, it was not clear whether perpetual motion devices were possible or not, but the development of modern theories of thermodynamics has shown that they are impossible. Despite this, many attempts have been made to construct such machines, continuing into modern times. Modern designers and proponents often use other terms, such as “over unity”, to describe their inventions.

There is a scientific consensus that perpetual motion in an isolated system violates either the first law of thermodynamics, the second law of thermodynamics, or both. The first law of thermodynamics is a version of the law of conservation of energy. The second law can be phrased in several different ways, the most intuitive of which is that heat flows spontaneously from hotter to colder places; relevant here is that the law observes that in every macroscopic process, there is friction or something close to it; another statement is that no heat engine (an engine which produces work while moving heat from a high temperature to a low temperature) can be more efficient than a Carnot heat engine.

In other words:

  1. In any isolated system, one cannot create new energy (law of conservation of energy). As a result, the thermal efficiency—the produced work power divided by the input heating power—cannot be greater than one.
  2. The output work power of heat engines is always smaller than the input heating power. The rest of the heat energy supplied is wasted as heat to the ambient surroundings. The thermal efficiency therefore has a maximum, given by the Carnot efficiency, which is always less than one.
  3. The efficiency of real heat engines is even lower than the Carnot efficiency due to irreversibility arising from the speed of processes, including friction.

Statements 2 and 3 apply to heat engines. Other types of engines which convert e.g. mechanical into electromagnetic energy, cannot operate with 100% efficiency, because it is impossible to design any system that is free of energy dissipation.

Machines which comply with both laws of thermodynamics by accessing energy from unconventional sources are sometimes referred to as perpetual motion machines, although they do not meet the standard criteria for the name. By way of example, clocks and other low-power machines, such as Cox’s timepiece, have been designed to run on the differences in barometric pressure or temperature between night and day. These machines have a source of energy, albeit one which is not readily apparent so that they only seem to violate the laws of thermodynamics.

Even machines which extract energy from long-lived sources – such as ocean currents – will run down when their energy sources inevitably do. They are not perpetual motion machines because they are consuming energy from an external source and are not isolated systems.

One classification of perpetual motion machines refers to the particular law of thermodynamics the machines purport to violate:

  • A perpetual motion machine of the first kind produces work without the input of energy. It thus violates the first law of thermodynamics: the law of conservation of energy.
  • A perpetual motion machine of the second kind is a machine which spontaneously converts thermal energy into mechanical work. When the thermal energy is equivalent to the work done, this does not violate the law of conservation of energy. However, it does violate the more subtle second law of thermodynamics (see also entropy). The signature of a perpetual motion machine of the second kind is that there is only one heat reservoir involved, which is being spontaneously cooled without involving a transfer of heat to a cooler reservoir. This conversion of heat into useful work, without any side effect, is impossible, according to the second law of thermodynamics.
  • A perpetual motion machine of the third kind is usually (but not always) defined as one that completely eliminates friction and other dissipative forces, to maintain motion forever (due to its mass inertia). (Third in this case refers solely to the position in the above classification scheme, not the third law of thermodynamics.) It is impossible to make such a machine, as dissipation can never be completely eliminated in a mechanical system, no matter how close a system gets to this ideal (see examples in the Low Friction section).

“Epistemic impossibility” describes things which absolutely cannot occur within our current formulation of the physical laws. This interpretation of the word “impossible” is what is intended in discussions of the impossibility of perpetual motion in a closed system.

The conservation laws are particularly robust from a mathematical perspective. Noether’s theorem, which was proven mathematically in 1915, states that any conservation law can be derived from a corresponding continuous symmetry of the action of a physical system. For example, if the true laws of physics remain invariant over time then the conservation of energy follows. On the other hand, if the conservation laws are invalid, then the foundations of physics would need to change.

Scientific investigations as to whether the laws of physics are invariant over time use telescopes to examine the universe in the distant past to discover, to the limits of our measurements, whether ancient stars were identical to stars today. Combining different measurements such as spectroscopy, direct measurement of the speed of light in the past and similar measurements demonstrates that physics has remained substantially the same, if not identical, for all of observable time spanning billions of years.

The principles of thermodynamics are so well established, both theoretically and experimentally, that proposals for perpetual motion machines are universally met with disbelief on the part of physicists. Any proposed perpetual motion design offers a potentially instructive challenge to physicists: one is certain that it cannot work, so one must explain how it fails to work. The difficulty (and the value) of such an exercise depends on the subtlety of the proposal; the best ones tend to arise from physicists’ own thought experiments and often shed light upon certain aspects of physics. So, for example, the thought experiment of a Brownian ratchet as a perpetual motion machine was first discussed by Gabriel Lippmann in 1900 but it was not until 1912 that Marian Smoluchowski gave an adequate explanation for why it cannot work. However, during that twelve-year period scientists did not believe that the machine was possible. They were merely unaware of the exact mechanism by which it would inevitably fail.

The law that entropy always increases, holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations — then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

— Sir Arthur Stanley Eddington, The Nature of the Physical World (1927)

In the mid 19th-century Henry Dircks investigated the history of perpetual motion experiments, writing a vitriolic attack on those who continued to attempt what he believed to be impossible:

“There is something lamentable, degrading, and almost insane in pursuing the visionary schemes of past ages with dogged determination, in paths of learning which have been investigated by superior minds, and with which such adventurous persons are totally unacquainted. The history of Perpetual Motion is a history of the fool-hardiness of either half-learned, or totally ignorant persons.”

— Henry Dircks, Perpetuum Mobile: Or, A History of the Search for Self-motive (1861)

Some common ideas recur repeatedly in perpetual motion machine designs. Many ideas that continue to appear today were stated as early as 1670 by John Wilkins, Bishop of Chester and an official of the Royal Society. He outlined three potential sources of power for a perpetual motion machine, “Chymical [sic] Extractions”, “Magnetical Virtues” and “the Natural Affection of Gravity”.

The seemingly mysterious ability of magnets to influence motion at a distance without any apparent energy source has long appealed to inventors. One of the earliest examples of a magnetic motor was proposed by Wilkins and has been widely copied since: it consists of a ramp with a magnet at the top, which pulled a metal ball up the ramp. Near the magnet was a small hole that was supposed to allow the ball to drop under the ramp and return to the bottom, where a flap allowed it to return to the top again. The device simply could not work. Faced with this problem, more modern versions typically use a series of ramps and magnets, positioned so the ball is to be handed off from one magnet to another as it moves. The problem remains the same.

The “Overbalanced Wheel”.

Gravity also acts at a distance, without an apparent energy source, but to get energy out of a gravitational field (for instance, by dropping a heavy object, producing kinetic energy as it falls) one has to put energy in (for instance, by lifting the object up), and some energy is always dissipated in the process. A typical application of gravity in a perpetual motion machine is Bhaskara’s wheel in the 12th century, whose key idea is itself a recurring theme, often called the overbalanced wheel: moving weights are attached to a wheel in such a way that they fall to a position further from the wheel’s center for one half of the wheel’s rotation, and closer to the center for the other half. Since weights further from the center apply a greater torque, it was thought that the wheel would rotate for ever. However, since the side with weights further from the center has fewer weights than the other side, at that moment, the torque is balanced and perpetual movement is not achieved. The moving weights may be hammers on pivoted arms, or rolling balls, or mercury in tubes; the principle is the same.

Perpetual motion wheels from a drawing of Leonardo da Vinci.

Another theoretical machine involves a frictionless environment for motion. This involves the use of diamagnetic or electromagnetic levitation to float an object. This is done in a vacuum to eliminate air friction and friction from an axle. The levitated object is then free to rotate around its center of gravity without interference. However, this machine has no practical purpose because the rotated object cannot do any work as work requires the levitated object to cause motion in other objects, bringing friction into the problem. Furthermore, a perfect vacuum is an unattainable goal since both the container and the object itself would slowly vaporize, thereby degrading the vacuum.

To extract work from heat, thus producing a perpetual motion machine of the second kind, the most common approach (dating back at least to Maxwell’s demon) is unidirectionality. Only molecules moving fast enough and in the right direction are allowed through the demon’s trap door. In a Brownian ratchet, forces tending to turn the ratchet one way are able to do so while forces in the other direction are not. A diode in a heat bath allows through currents in one direction and not the other. These schemes typically fail in two ways: either maintaining the unidirectionality costs energy (requiring Maxwell’s demon to perform more thermodynamic work to gauge the speed of the molecules than the amount of energy gained by the difference of temperature caused) or the unidirectionality is an illusion and occasional big violations make up for the frequent small non-violations (the Brownian ratchet will be subject to internal Brownian forces and therefore will sometimes turn the wrong way).

The “Float Belt”. The yellow blocks indicate floaters. It was thought that the floaters would rise through the liquid and turn the belt. However, pushing the floaters into the water at the bottom takes as much energy as the floating generates, and some energy is dissipated.

Buoyancy is another frequently misunderstood phenomenon. Some proposed perpetual-motion machines miss the fact that to push a volume of air down in a fluid takes the same work as to raise a corresponding volume of fluid up against gravity. These types of machines may involve two chambers with pistons, and a mechanism to squeeze the air out of the top chamber into the bottom one, which then becomes buoyant and floats to the top. The squeezing mechanism in these designs would not be able to do enough work to move the air down, or would leave no excess work available to be extracted.