# Why Maglev

MagLev technology is entirely different from any form of transportation in operation today, but the basic principles that lie at the foundation are not beyond the understanding of the beginning electricity and magnetism student. It is in the application of these principles to design and optimize an actual train that things get hairy. The basic idea has been researched since the mid-sixties, but it is only now that economically feasible prototypes are being built and governments are seriously looking towards magnets to propel us into the next century. Leading the race is Germany. Their design, the Transrapid 07, is ready for commercial production. It utilizes conventional electromagnets and forces of attraction to levitate the train. A good web site to find out more about German plans for their design is http://transrapid.simplenet.com/index-e.htm
The Japanese are investigating an entirely different design involving superconducting magnets to generate huge repulsive forces which levitate the train. However, their MLU002N is still in experimental stages. For more information, check out http://www.rtri.or.jp/rd/maglev_E.html
With a little stretching, the average physics student should be able to comprehend the principles of magnetic levitation and propulsion through synchronous linear motors. To facilitate the process of understanding this complex material, we suggest that the student go through this web site in order. Make sure you understand the basic physics before moving on to the page which applies these principles to magnetically levitated vehicles.
We know from experiment that a moving charge exerts a force on other moving charges; we call this effect magnetism. The magnetic force is a field force, meaning that a moving charge sets up a field which in turn exerts a force on other moving charges. The field set up by a given moving charge is found to be perpendicular to its velocity, and to decay with distance from the charge:
First, we will examine how magnetic fields are created, then we will calculate their magnitude and direction.

Some materials can be said to be natural magnets. These magnets don’t appear to have any moving charge, so how can they set up magnetic fields? The answer is found at the atomic scale:
Electrons circling an atom set up small magnetic fields. In most materials, these fields are aligned in a fairly random manner, so that all of these small fields cancel each other. In a magnet, however, these fields line up to create a net magnetic dipole, so that the object sets up a magnetic field in the surrounding space.

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A current is a moving charge. Moving charges set up magnetic fields. Thus, a current seems the logical way to create a magnetic field. There are two basic setups which can be used for this purpose:
The Biot-Savart Law: in order to find the magnetic field (denoted by the symbol B) produced by a given current distribution, we have to integrate the field at a given test point, P, due to individual current displacements, ids:
The equation for the field integral turns out to be a rather complicated one, known as the Biot-Savart Law:
Ampre’s Law: in cetain situations, this integral can be simplified by symmetry. In these situatins, we can use a more fundamental law, known as Ampre’s Law. This law allows the calculation of the field from the amount of current enclosed by an arbitrary closed loop:
The equation for the magnetic field in such a case turns out to be:
One of the two most commonly used magnetic field equations is that for a long, straight wire. This equation can be determined from Ampre’s Law through the following setup:
The equation is then derived as follows:
A solenoid is a tightly wound coil of wire carrying a uniform current i : The field inside a solenoid is approximately as shown in the following diagram:
We can calculate the field inside a solenoid with n turns per unit length using Ampre’s Law:
We have now examined how magnetic fields are created, and how to calculate their magnitude. Next, we will examine the force felt on moving charges and currents due to magnetic fields.
We know that a moving charge sets up a Magnetic Field. We also know that this field sets up a force on other moving charges. This force is perpendicular both to the magnetic field and to the velocity of the charge:
Next we will determine how to calculate this force, and then examine an example of particular significance to magnetic levitation: repulsion between parallel wires.
For a moving point charge, the magnetic force is proportional to both the magnetic field strength and the velocity of the charge. Furthermore, the direction of this force is perpendicular to both the velocity and the field (direction given by right-hand rule). Thus, the magnetic force is given by:
For a current in a wire, the magnetic force is proportional to the current, the length of the wire, and the magnetic field strength. Direction is perpendicular to current direction and magnetic field.

Thus, the magnetic force equation looks very similar to that for a moving point charge:
The repulsion or attraction between two parallel wires is of particular importance to magnetic levitation. The setup is as follows:
If the currents flow in the same direction (as shown), the wires attract. If the currents flow in opposite directions, the wires repel.

To calculate the force of repulsion, we first calculate the field produced by wire 1:
Next, we use B1 to find the force on wire 2 due to wire 1:
We now know how to determine the force on a moving charge due to a magnetic field, and how to determine the force of attraction or repulsion between two currents. Next, we will examine the phenomenon of induced currents, where a changing magnetic field can produce a current.
In 1831, Michael Faraday and Joseph Henry conducted similar experiments that demonstrated the following phenomena:
In the above illustration, movement of a magnet through a wire loop induces a current in that wire. Reversing the direction in which the magnet travels reverses the current direction.

In this experimental setup, opening or closing switch S induces a momentary current, i. The direction of i when closing the switch is opposite the direction when opening the switch.

We can conclude from the previous experiments that a change in the magnetic field through a current loop produces an current in that wire. More scientifically, we say that a change in magnetic flux (field through a given area) induces a current in the loop to oppose the change in flux. Quantitatively, we find that the negative rate of change in flux is equal to the electromotive force (EMF) in the wire:
For a coil of N turns, the induced EMF is the sum of the voltages from each turn:
The direction of these induced currents, according to a principle known as Lenz’ Law, always opposes the change in magnetic flux that produced it.

When a large peice of conducting material moves through a magnetic field in such a way that the magnetic flux through the material changes, currents are induced in the material:
These currents, known as eddy currents , may produce desired or undesired effects, depending on the situation. Of particular interest to magnetic levitation is the magnetic force produced, which opposes motion through the magnetic field:
This induced magnetic force is somewhat analgous to frictional forces: it opposes motion in or out of the magnetic field. In our example of magnetic levitation, this effect becomes significant, as we will see later.
We have now examined most of the basic electro-physics involved in magnetic levitation. In the next section, we will begin applying these physics to the magnetically levitated train.
A maglev train has a system designed to provide the force for levitation. Since the levitation system is separate from the propulsion system, a designer can choose from various propulsion systems. One propulsion system uses Linear Synchronous Motors (abbreviated as LSM’s). Another propulsion system uses Linear Induction Motors (abbreviated as LIM’s). This page focuses on the levitation system that can be used with either type of propulsion system..

This is a cross section of the Magneplane vehicle and its guideway. This setup achieves levitation through repulsion. The propulstion system is not explicity diagrammed in this picture; however, other sources reveal that the Magneplane system uses a LIM. (Image source: page 338, Linear Motion Electromagnetic Systems.)
Now we will move on to develop equations to model a simple repulsive levitation system.

We will model the levitation system using two separate coils. One coil is part of the vehicle, and carries a direct current in the counter-clockwise direction (as viewed from above the coil). The second coil is part of the track, and carries a direct current in the opposite (clockwise) direction. In practice, the currents need to be quite large to produce a force strong enough to counteract the weight of the train. The resistance of the coils is a very important factor when the cost of providing the power is considered. Smaller resistances allow for more current to be generated using less power, making the magnetic field induced stronger. For this reason, it is most efficient for the coils to be superconducting. However, the cost of superconducting coils and magnets is also considerable.
The magnetic field strength at segment AB due the magnetic field created by segment A’B’ is
The force on the upper wire segment AB due the field created by the lower wire segment A’B’:
The picture below illustrates the direction of FAB, which is the green vector on the drawing labeled FB. FB is perpendicular to ray AB, and the vector B. FB is opposite in direction to Fg , and can balance out the force of gravity.

Since there are four straight wires comprising each loop, there are four forces acting on the upper loop.

Note that the currents in the two loops are traveling in the same direction, which provides a repulsive force. This force provides the lift, or levitating force for the vehicle.

From this simple model we have explaned how levitating forces are created. We also can point out a few further considerations:
? This setup only addressed the vertical forces acting on the train and assumed that the train was horizontally stable. In reality, maglev trains need some means of horizontal stabilization to keep the train on the track, in a manner of speaking.
? In many maglev systems, the coil setup isn’t quite the same as our model explained. The train carries one set of coils, and the track contains a flat conducting surface. The train’s coils have a current flowing, but the track’ conducting surface is completely passive. The moving train coils create a moving magnetic field. This changing magnetic field, or flux, induces eddy currents in the track’s conducting surface. These induced currents then act like the track coil in the model we used. With this in mind, our model is still effective for calculations.
? Our model uses several approximations to make the mathematics more concise. One, in our first equation, we assumed that the segment AB was an infinitely long wire. This means that the calculation for B is not exact.
This page deals with the systems involved in a Maglev train that use repulsion as the means for attraction.

This is a cross section the Krauss-Maffei experimental vehicle and guideway.

This setup uses attractiion for levitation and a LIM for propulsion.

(Image source: page 27, Linear Motion Electromagnetic Systems.)
The setup for the attraction system is very similar to to the setup for the repulsion system, except that the direction of current in one of the coils is reversed, resulting in an attractive force between the coils. Also, the coils are located on an extension of the train that wraps under the track.

It is important to notice that as the distance between the two coils decreases, the attractive force increases. Under certain conditions the two coils could get pulled into direct contact, eliminating the air gap between them. This would be very undesirable. Therefore engineers who design attractive levitation system must make use of a secondary system that monitors the air gap distance and can adjust the magnetic field strength appropriately. This secondary system also would make the ride more comfortable for passengers.

The magnetic field strength at segment AB due the magnetic field created by segment A’B’ is
The force on the lower wire segment AB due the field created by the upper wire segment A’B’:
The picture below illustrates the direction of FAB, which is the green vector on the drawing labeled FB. FB is perpendicular to ray AB, and the vector B. FB is opposite in direction to Fg , and can balance out the force of gravity.

Since there are four straight wires comprising each loop, there are four forces acting on the upper loop.

This attractive force provides the lift, or levitating force for the vehicle.

Note that the equations are exactly the same, provided that the setups are different. (That is, in the repulsive case, the vehicle coil was above the track coil. In the attractive case presented on this page, the vehicle coil is below the track coil.)
Linear motors are analogous to conventional (rotary) motors. A Linear Induction Motor, or LIM, can be visualized by ‘unrolling’ a conventional induction motor until it is flat. This presentation will explain the qualitative nature of the LIM, without going into the complicated mathematical and physical derivations. We will focus on a three-phase LIM.

A LIM consists of two parts, a stator, and a rotor. The stator and rotor consist of magnetically permeable material such as iron. Within the stator, three wires are embedded. Each wire weaves through the stator in a special periodic pattern. In the diagram below, the wires are perpendicular to the plane of the computer screen.

Each wire is connected to a sinusoidal current source. The three currents are each 120 degrees out of phase with each other. This setup is called a three-phase current source.

The pattern used with a three phase current source is this: —A C’ B A’ C B’— Each letter represents a wire. A and A’ represent the wire that carries current Ia. A and A’ carry the same current, but point in opposite directions. The same conventions apply to B, B’ and C, C’.

This configuration is very useful because it allows the stator to create a moving magnetic field.

This moving magnetic field induces currents in the rotor. These induced currents, at any instaneous time, oppose the change in the magnetic field, in accordance with Faraday’s Law.

These induced currents then interact with the moving magnetic field, resulting in a force that moves the rotor along with the moving magnetic field in the stator.

LIM’s have the ability to move the rotor relative to the stator without any physical contact. This drastically reduces wear and tear on the parts involved and eliminates frictional forces that cause inefficiency.

LIM’s have the ability to accelerate the rotor from rest up to the speed of the moving magnetic field.

LSM’s are structurally very similar to LIM’s except for one change. The behavior of the two types of linear motors is changed significantly.

Both LIM’s and LSM’s consist of a stator and rotor. Both have three phase currents weaving through the stator. How LSM’s differ is that their rotor has two closely spaced direct current wires spaced regularly as the diagram below shows.

The moving magnetic field is setup, but the induced currents setup are much smaller than in the LIM case. One reason is that the composition of the rotor may be different: it may be laminated or consist of a material of high electrical resistance. The DC currents are the important factor in LSM’s. Look at the diagram below. (Note that the position of the rotor and stator are reversed. Also note the pattern of wires in the stator is A C’ B A’ C B’ )
From Applied Electromagnetism, page 578.

The force acting on the rotor DC currents due to the track flux tends to to move the rotor to the right. (This can be shown using the right hand rule involving the vertical track flux lines. The horizonal track flux lines do not contribute to the propulsion.)
The position of the DC rotor currents is very important. In the diagram above, the rotor currents coming out of the paper are aligned with the leftmost stator wire that is also coming out of the page. This produces the maximum force on the rotor. Now consider what will happen after the diagram’s time frame:
1. the rotor will move (in relation to its acceleration and velocity)
2. the stator’s magnetic field will move (in relation to the frequency of the three phase currents)
Now, after a small time interal, let’s examine the relative positions of the rotor and stator. If the alignment is not the same as the figure, then the force on the rotor will not be the maximum. It should be clear that the Linear Synchronous Motor operates best at its sychronous speed.
Indeed, if the rotor isn’t moving close to the synchronous speed, then the LSM will not move the stator at all!
If the rotor is close enough to the synchronous speed, then the LSM will be able to accelerate the rotor up to the synchronous speed.

Note: the synchronous speed of a LSM can be altered in two main ways:
1. by varying the frequency of the three phase currents
2. by varying the number of wires per unit length in the stator and rotor.
LSM’s, like LIM’s, have the ability to move the rotor relative to the stator without any physical contact. This drastically reduces mechanical wear.

LSM’s do NOT have the ability to accelerate the rotor from rest up to the speed of a quickly moving magnetic field. This means that Maglev trains that use LSM must either make the synchronous speed start very slowly and increase slowly or use a secondary propulsion system for acceleration.

from Linear Motion Electromagnetic Systems, page 26.
The basic physics of magnetic lift and electrical propulsion are the essentials behind Maglev’s energy efficiency. For example, Maglev consumes per trip about one seventh of the energy used by a Boeing 737-300 for a 125-620 mile trip. In addition, Maglev operation is not dependent upon petroleum for its energy; the electrical power can be derived from other sources. The energy efficiency is due to the mechanical efficiency resulting from drastically reduced friction and less enegry lost as heat in the operation of the vehicle.
High speed is an inherent characteristic of maglev. Because the operation of the vehicle occurs without physical contact, high speeds are within technological limits. Speeds up to 500 miles per hour are possible, with top speeds usually limited not by physical constraints, but rather by economic considerations. Commercial rail today usually travels at only 200 miles per hour, while Maglev promises at minimum a 300 mile per hour top speed. For short trips, Maglev is competitive with short airplane flights of up to 500 miles!
Maglev could be used to effect a fully automated transport system, with goods arriving within seconds of their scheduled time. Combining the reliability and speed advantages, this looks to be a promising possibility.
Because lift and guidance forces are distributed over a large area, contact stresses are at a minima. The Linear Motor allows noncontact propulsion and braking, in contrast to conventional rail where severe stresses occur from wheel/rail contact and by power transfer. A low cost maintenance program is a certain advantage associated with this technology.
Drag Forces: Magnetic and Aerodynamic
When a conductor moves through a magnetic field, the changing flux induces electric currents as reviewed in the induction page of the Basic Physics section.

These eddy currents then react with the magnetic field in such a way as to brake motion through the field. Due to of this phenomenon, a part of the propulsion energy is spent counteracting the drag force. As the table from Linear Motion Magnetic Systems shows, the drag force increases as the speed increases, for the most part. As a maglev gains speed, it requires more and more energy just to remain at cruising speed.

In addition to the magnetic drag force, conventional aerodynamic drag is present. Although both forms of drag are undesirable in many ways, there are some ways of utlizing them to our advantage. The drag forces can help brake a maglev train quite efficiently. In the introduction, there is a photograph of a Maglev train with aerodynamic brakes extended.

Technical Problems – A Study in the Feasibility of the SCM
The major technical barrier to the mass adoption of Maglev as a new transportation system lies in problems with the superconducting magnets (hereafter SCM) used to levitate and power the trains.

To date most Maglev trains have utilized an SCM made of NbTi. The SCM develops extremely high temperatures during operation, during which it must be cooled down to four degrees Kelvin to maintain its properties. Liquid helium is usually used for this purpose. The heat side effects are unavoidable, and thus engineers have focused on the efficacy of the cooling systems rather than designing a “cooler” SCM.

Severe difficulties lie in the storage of the helium vapor, and the reliquification of the vapor once it has absorbed the tremendous heat of the SCM. Currently, this has been the slowest front for progress in Maglev technology.

The current thought is that using cryorefrigeration techniques which constantly cool the magnet without flashing the helium prove to be the most promising. By winding the coolant through tubes surrounding the magnet, an even, constant cooling process will be effected.

This maglev diagram known as the LM-500-01, also from Linear Motion Magnetic Systems, page 338, shows many of the onboard systems relating to refrigerating the superconducting magnets.
These techniques, available today, is limited only by its tremendous expense, which points toward a bottom line for Maglev technology.

Economical considerations have historically been a huge hurdle to otherwise very promising technological advances. This certainly rings true with the SCM and Maglev. The superconducting magnets themselves cost millions, and the cooling system technologies associated with the SCM’s cost millions more. While in the lab the technologies have been very interesting, the conventional systems have so far won out, merely because of costs.
Essentially, we must look at the opportunity costs involved to fully come to a conclusion with regards to the efficacy of this technology. Adopting the Maglev system worldwide would have severe costs, but with a tangible payoff over the next 20 years. We would see a definite reduction in operating costs and a great leap in efficiency, but only after the initial investment in the new technology. SCM’s and cooling system R&D have already cost us millions even billions of dollars, yet we are not as yet ready to commit to the Maglev system. Feasibility studies conducted by the US Department of Transportation have shown a great need for the technology, yet no group ready to invest because of the shear number of R&D dollars still needed with no real examples of Maglev success in this country.
Judging from the progress of other countries, it is our recommendation that the United States take steps toward a greater use of Maglev to reduce its long term public transportation problems and take advantage of the low cost operation, reliability, and energy efficiency associated with Maglev.

We’ve stood on the shoulders of giants, and now it’s time to enumerate them . . .
Bibliography:
References
We’ve stood on the shoulders of giants, and now it’s time to enumerate them . . .
Books
1. D. Halliday, R. Resnik & K. Krane, Physics, vol. 2, 4th ed. John Wiley & Sons Inc., 1992.
2. Liang Chi Shen and Jin Au Kong, Applied Electromagnetism, 3rd ed. PWS Publishing Company, 1995.
3. I. Boldea and S.A. Nasar, Linear Motion and Electromagnetic Systems. John Wiley & Sons Inc., 1995.
Web Sites 