Marc T. Thompson, Richard D. Thornton and Anthony Kondoleon

"Scale Model Flux-Canceling EDS Maglev Suspension --- Part I: Design and Modeling"

IEEE Transactions on Magnetics, vol. 35, no. 3, May 1999, pp. 1956-1963

To see an abstract of Part II of this paper, click here.

A full listing of Dr. Thompson's Maglev-related publications is given here.


The design and analysis of a scale-model suspension test facility for MAGLEV is discussed. This work describes techniques for the design, construction, and testing of a prototype electrodynamic (EDS) levitation system. The viability of future high-temperature superconducting magnet designs for MAGLEV have been investigated with regard to their application to active secondary suspensions. In order to test the viability of a new "flux-canceling" EDS suspension, a 1/5-scale suspension magnet and guideway was constructed. The suspension was testing by using a high-speed rotating test wheel facility with linear peripheral speed of up to 84 meters/second (300 km/hour). A set of approximate design tools and scaling laws have been developed in order to evaluate forces and critical velocities in the suspension.

Index Terms ---Control systems, high-temperature superconductors, inductance, levitation, magnetic analysis, magnetic forces, magnetic levitation, MAGLEV, modeling, superconducting coils, superconducting magnets


ElectroDynamic magnetic suspension, called EDS Maglev and referred to as repulsive Maglev because it relies on repulsive magnetic forces, has the capability of allowing high speed transportation with a relatively large gap between the vehicle and guideway. In 1966 Danby and Powell [1]-[3] proposed an EDS system for high-speed transportation using superconducting magnets with a "null flux" suspension. Other designs were later proposed using continuous sheet guideways ([4]-[9], among others). Subsequent researchers in the U.S., Japan, Germany, UK and Canada have developed further innovations (such as the use of a ladder-type guideway for increased lift efficiency), but there are still a number of technical problems that need resolution.

The first recorded proposal for an attractive magnetic suspension was by Graeminger [10] in 1911 with a U-shaped electromagnet carried on a vehicle suspended below an iron rail with feedback maintained by sensing a mechanical or pressure sensor. To date the only commercial Maglev implementations have used the electromagnetic suspension (EMS) in which electromagnets support a vehicle with attractive forces to steel guideways. While EMS may be a preferred option for lower speed designs, it has the fundamental disadvantage of requiring a small gap between the vehicle and guideway, typically less than a centimeter, and requires active control to maintain the gap. The promise of EDS is that this gap can be increased by a factor of 5 or more, and therefore guideway tolerances are relaxed and cost might be reduced.

Another purported advantage of EDS is that it can be inherently stable and not dependent on feedback control to maintain a constant gap. Unfortunately, this advantage is not as real as it appears because all EDS designs are highly underdamped and, in certain cases, even unstable [11]-[18]. Other disadvantages of EDS are higher power requirements for suspension, higher external magnetic fields, and the need for a separate low speed suspension.

The foremost problem for all high speed ground transportation systems is the high cost of guideway construction, but this key issue is not unique to Maglev. Many researchers are now convinced that if Maglev technology were fully developed it would be less expensive than a high speed train if all installation and operating costs are compared. This is particularly true if the Maglev system can provide shorter travel times which in turn attracts more users so that the capital cost per user is reduced. The reason for the EMS preference has been it apparently lower cost because it uses a relatively simpler technology with fewer unknowns. German Maglev developers have shown that EMS can operate successfully at speeds over 400 km/hour, so the problem is to improve EDS to the point that, for high speed travel, it has substantial advantages other than that of a larger gap.

We believe that a successful EDS design must face squarely the following problems:

  • The cost of manufacturing and installing suspension and propulsion components on the guideway must be reduces to an absolute minimum;
  • The suspension system must have a power loss that is comparable to that for EMS;
  • All EDS suspension designs are highly underdamped and it is imperative to find practical means to damp oscillations and provide high ride quality;
  • External magnetic fields associated with onboard superconducting magnets must be reduced, particularly in the passenger compartments;
  • It is highly desirable to eliminate the need for a separate low speed suspension system because this adds to the cost, weight and complexity of both the vehicle and guideway;
  • Any superconducting vehicle magnets must be able to operate reliably in a hostile transportation environment.

This and a companion paper in these Transactions report the latest results of MIT research to develop an improved EDS design that addresses all of these issues.


This section describes the design and modeling of the multiple-loop guideway and development of circuit models to predict behavior of a novel Maglev system based on a high-temperature superconducting coils. This so-called "Flux-Canceling" EDS Maglev suspension achieves high efficiency for suspension and guidance in addition to rapid attenuation of magnetic flux with distance [19],[20] by utilizing an iron core and superconducting octapoles. In order to test these concepts, a 1/5-scale suspension magnet using copper coils and guideway embedded in a high-speed rotating test wheel was constructed. Details of the test fixture design and analysis are given in several papers and a Ph.D. thesis by one of the authors [21]-[24].

A. Flux-Canceling Geometry

The guideway is composed of multiple conductive copper coils arranged vertically, and the train magnets are arranged in a dual-row N-S-N-S arrangement (Fig. 1). When the train is in the vertical null position at z = zo and traveling in the +y direction, there is no net flux through the levitating coils, and no net current induced around the loop. However, if the train's vertical position deviates from equilibrium, the net changing flux through the loop induces currents in the loop. This creates a restoring force, with the magnetic suspension acting as a linear spring with spring constant kz. The suspension has a resulting resonant frequency where kz is the magnetic spring constant and M is the total suspended mass. There is no inherent damping mechanism intrinsic to EDS suspensions other then aerodynamic drag.

Fig. 1. Flux-canceling Maglev topology. Top: train at null position, no induced currents. Middle: train above null position. Currents are induced, creating a restoring force. Bottom: magnetic spring constant

B. Suspension Magnet Design

The suspension magnet in the test facility has a pole pitch p = 0.126 meter. A linearized view of the magnet with copper coils is shown in Fig. 2. The magnet core is constructed with laser-cut laminations of 0.9 millimeter thick M19 transformer steel. Eight copper coils were wound with 18 gauge copper magnet wire on an arbor with the same geometry as the magnet polefaces. The final copper coil design had 550 turns in a winding window of 5 cm x 2 cm. The design limit of the copper coils is 8 amps in still air (with current density J =1000 A/cm2 ) and 20 Amps when operating in the liquid nitrogen bath (J = 2500 A/cm2). The measured resistance of each coil is 3.4 Ohms at 300K and 0.442 Ohms when cooled to 77K, corresponding to a maximum copper power dissipation per coil of 200 Watts.

The magnet is mounted to a multi-axis force sensor which allows real-time measurement of forces and moments. The core laminations were sized by considering the power dissipation per unit length in a section of the core made up of NL laminations (Fig. 2d) is calculated to be [25]:


The power loss may be made arbitrarily small by reducing the thickness of the lamination. With a core design with NL = 40 and expected AC fields of B < 0.5 Tesla at frequencies f < 10 Hz, the power loss in the core is calculated to be less than a Watt.

Fig. 2. Detail of magnet design. (a) Side view of linearized iron-core magnet with copper coils. (b) Rear view of dual-row magnet. (c) Iron-core suspension magnet, mounted to multi-axis force sensor, showing capacitive position sensors. (d) Core laminations

The magnets were designed so that the top row of coils are operated in a North-South-North-South arrangement (Fig. 3a), while the bottom row is offset by one half-cycle. The resultant magnet behaves as a magnetic octapole. A significant advantage of the magnetic octapole is the rapid far-field falloff in the field, which reduces the shielding required to maintain a low magnetic field in the passenger cabin [20].

Finite element analyses were run on the non-linear iron core design (Fig. 3b). The flux density normal to the guideway (Bx) was calculated at a distance x = 1 cm from the poleface of the magnet, which is the nominal setpoint for guideway-to-poleface setting. This analysis was checked against measurements taken with a Gaussmeter on the magnet operating with copper coils. The measured value at the center of the poleface was Bx = 0.069 Tesla, which matches the calculated value to within a few percent. The finite element analysis was also used to optimize the thickness of the magnet back-iron, so that the weight of the magnet was minimized while insuring that the iron does not saturate for normal operating levels.

Fig. 3. Flux-canceling Maglev electrical wiring. (a) Magnet wiring for flux-canceling Maglev. (b) Results of finite element analysis, NI = 2200 Ampere-turns per coil

C. Guideway Coil and Test Wheel Mechanical Design

A novel multiple-loop guideway was designed which allows simple and inexpensive manufacturing. The guideway conductor pattern was constructed from 0.093" thick sheets of 1/2 hard #110 copper. The repeating conductor pattern was cut with a high-pressure numerically-controlled water jet cutter, from 35"x12" sections of copper (Fig. 4a) in a 60o arc. In a full-scale system the guideway would probably be constructed from sheets of aluminum, but copper was easier to use for the initial prototype.

After the individual guideway sections were cut, the inner face of the copper conductor pattern was painted with an electrically-insulating paint. The conductor pattern was brazed on the inner and outer radii to ensure good electrical joints and high mechanical strength. After brazing, the eccentricity of the copper ring was measured, and found to be true within 1/16 of an inch. A precision mold was constructed, and a composite disk of fiberglass cloth and epoxy 5/8" thick was constructed over the copper conductors with the conductors near one surface of the disk.

The finished test wheel was mounted to an aluminum hub with a 3" diameter shaft, shown mounted and ready for operation in Fig. 4b. A 10-HP motor and computer control allows adjustment of the wheel speed from 0 - 1000 RPM, with a linear peripheral test speed of 0-84 meters/second (0 - 300 km/hour). A transparent coating of epoxy was used on the front face of the wheel so that the copper conductor pattern is visible.



Fig. 4. Steps in Maglev test wheel construction. (a) Prototype guideway section showing two copper layers bolted and brazed along the edge. (b) Completed test wheel mounted and ready for high-speed operation.


Simple models were developed to demonstrate the effects of mutual coupling between guideway loops on the lift and drag forces and drag peak velocity. The goal of our modeling process was to provide useful models without relying on significant finite-element analyses, and to generate approximate answers and scaling laws useful for engineering design.

A. Loop-Loop Interactions

A very simplified view of an infinite linear ladder guideway (given for illustrative purposes only) is a 3-coil model (Fig. 5b). The relationship between loop currents and induced loop voltage in the sinusoidal steady state is:


where ( is radian frequency of the excitation caused by the moving superconductor coils. The self inductance of each loop is L and the loop-loop mutual inductance Mij = kijL where kij is the loop coupling coefficient which is less than 1. The effects of mutual resistance are modeled by the off-diagonal term rij. The natural frequencies and mode shapes of this structure can be found by assuming single-frequency excitation (i.e. by modeling the effects of the moving suspension coil as a sinusoidal excitation) and by solving the resultant Eigenvalue problem.

For the purposes of calculating guideway coil self and mutual inductances to fill the inductance matrix, approximate models were developed for this guideway structure. Although the inductances can be calculated by finite element analysis, this method gives little insight into scaling laws. Therefore, several simple approximations were developed which were used as a practical design tool.

Fig. 5. Guideway geometry and modeling. (a) Linearized geometry of guideway coils. (b) Broken up into individual coils (exploded view). (c) Rim

B. Approximate Inductance Matrix

Known solutions exist for the calculation of the inductance of geometries such as disk coils and filamentary loops. A realizable geometry for which tabulated results exist is the round loop with rectangular cross section, with mean radius a, axial length b, and width c (Fig. 6a). The self-inductance of this loop may be calculated using techniques outlined in the work by F. Grover [26, pp. 94], where the inductance is found to be:


For this calculation, a is in meters, L is in  Henries and P is a function of the coil normalized radial thickness c/2a. For a coil of zero axial thickness (i.e. for b = 0), the factor F = 1. For b << c and c <<a (coils resembling thin disks) the factor F = 1, an important limiting case. Therefore, for a thin disk coil with double the mean radius, there will be a corresponding doubling of the inductance.

Fig. 6. Inductance modeling of circular coil with rectangular cross section; top view of disk coil.

The goal of this exercise is to approximate the complicated guideway loop geometry by a geometry where analytic expressions are available. Use of the calculation for the circular disk coil with rectangular cross section was applied to a single loop of the guideway. Shown in Fig. 7a is the actual geometry of one guideway loop coil which spans one pole pitch p = 12.6 cm. The procedure for finding an approximate equivalent disk coil (Fig. 7b) is as follows:

Calculate the circumference of the actual coil, using the mean distance to each coil element from the center

ltotal = 36.1 cm

Find the mean radius of a circular coil which has the same perimeter

a = 5.75 cm

Calculate the mean radial thickness of the coil

c = 0.39 cm

Find P as a function of c/2a = 0.0337, interpolating from Grover Table 26, pp. 113

P = 53.87

Find F as a function of c/2a and b/c = 0.6082, using Grover Table 24, pp. 108

F = 0.9182

This methodology is designed to match the self-inductance of the actual guideway coil with a circular coil. Results (Table 1) show good agreement between measurements made using an actual coil, finite element analysis on the coil, and the approximate calculation. This result shows the weak dependence of inductance on actual loop shape. The measured inductance (at 10 kHz) was done with a single loop and an impedance analyzer. The measured inductance is lower than the finite-element analysis value due to the skin effect.

Fig. 7. Coil model, showing primative coil section and disk coil used for approximate modeling. (a) Actual linearized geometry of one pole-pitch wide primitive guideway loop. (b) Approximate model, using disk coil enclosing same perimeter

Table 1. Comparison of calculations on coil geometries

Measured inductance @ 10 kHz

259 nH

Grover Calculation (using circular disk coil)

276 nH

Finite Element Analysis (using actual guideway coil geometry)

280 nH

In order to calculate the mutual inductance between coils, further approximations were made by modeling the circular disk coil considered previously by a thin filament near the center of the cross-section of the disk. An approximate formula for the calculation of the self-inductance of a wire loop was first given by J.C. Maxwell [27, pp. 345], where:


where a is the radius of the loop in meters and r is the radius of the wire. A paper by T. R. Lyle in 1913 [28] shows that the filament approximation will give the self-inductance of any circular coil with rectangular cross section to any degree of accuracy when the mean coil radius is substituted for a and the geometric mean distance (G.M.D.) is substituted for r. The values of mean radius and G.M.D. are adjusted depending on the mean radius and the cross-section profile of the coil. The same reasoning can be applied to find the mutual inductance between filamentary loops, as in the early papers by S. Butterworth and A. Campbell [29]-[31].

Using these approximation methods, the resultant self and mutual inductances were found (Fig. 8) and used to fill a 15x15 inductance matrix. The self and mutual resistances for the 15 loops was calculated and the resistance matrix was filled. This simplified calculation is compared to measurements made with actual discrete guideway coils. These matrices were used to calculated forces, dominant time constants, and the drag peak velocity with results described later in a companion paper in these Transactions.

Once the inductance and resistance matrices are found and solved, the vectors corresponding to loop currents are used to calculate lift and drag forces. Lift force is found by:


where l is a length scale associated with the horizontal length of the coil, ij is the induced current in the jth coil, and Bj is the average field acting on the induced current. The drag force is found by evaluating the power dissipated in the guideway coils, or:


where v is linear velocity and R is the loop resistance.

Fig. 8. Comparison of calculated (solid line) to measured guideway coil-coil mutual inductance.  Mutual inductance calculation based on approximations in Butterworth


The design and modeling process of a 1/5-scale "flux-canceling" Maglev suspension has been described in this paper. The rotating test wheel facility has been used to measure EDS forces at various train speeds with test wheel operating speed up to 300 km/hour. A set of simple techniques and models for analysis of the guideway geometry has been developed. Using approximate techniques, these models are used to predict accurately the resultant MAGLEV lift and drag forces as a function of train speed. Test results are given in a companion paper in these Transactions.


The authors gratefully acknowledge the support of the Laboratory for Electromagnetic and Electronic Systems and the Center for Transportation Studies at the Massachusetts Institute of Technology, the U.S. Department of Transportation under the Federal Railway Administration, and the Charles Stark Draper Laboratory, who provided research support.


  1. J. R. Powell and G. R. Danby, "High Speed Transport by Magnetically Suspended Trains," ASME Publication No. 66 WA/RR5 (December 1966)
  2. J. R. Powell and G. R. Danby, "Magnetically Suspended Trains for Very High Speed Transport," Proceedings of the Fourth Intersociety Energy Conversion Engineering Conference, Sept. 22-26, 1969, Washington, pp. 953-963
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  5. C. A. Guderjahn and S. L. Wipf, "Magnetic Suspension and Guidance for High-Speed Trains by Means of Superconducting Magnets and Eddy Currents," Proceedings of the 1969 Cryogenic Engineering Conference, UCLA, June 16-18, 1969, found in Advances in Cryogenic Engineering, vol. 15, pp. 117-123
  6. C. A. Guderjahn and S. L. Wipf, "Magnetically levitated transportation," Cryogenics, June 1971, pp. 171-178.
  7. H. H. Kolm and R. D. Thornton, "The Magneplane: Guided Electromagnetic Flight," Proceedings of the 1972 Applied Superconductivity Conference, May 1-3, 1972
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  10. B. Graeminger, "Electromagnetic Suspension Devices," U. K. patents #24,499 and 24,541 (1912)
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  12. L. C. Davis and D. F. Wilkie, "Analysis of Motion of Magnetic Levitation Systems: Implications for High-Speed Vehicles," Journal of Applied Physics, vol. 42, no. 12, November 1971, pp. 4779-4793
  13. M. Iwamoto, T. Yamada, and E. Ohno, "Magnetic Damping Force in Electrodynamically Suspended Trains," IEEE Transactions on Magnetics, vol. MAG-10, (1974), pp. 458-461
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  15. F. C. Moon, "Vibration Problems in Magnetic Levitation and Propulsion," Transport Without Wheels, E. Laithwaite Editor, Elek Science, London 1977 pp. 122-161
  16. D. Chu and F. C. Moon, "Dynamic Instabilities in Magnetically Levitated Models," Journal of Applied Physics, vol. 54, no. 3, March 1983, pp. 1619-1625
  17. S. S. Chen, S Zhu, and Y. Cai, "On Unsteady-Motion Theory of Magnetic Forces for Maglev Systems," Journal of Sound and Vibration, vol. 188, no. 4, pp. 529-543, 1995
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  20. R. D. Thornton, D. Perreault, T. Clark, "Linear Synchronous Motors for Maglev," U.S. Dept. of Transportation, Federal Railroad Administration Report DOT/FRA/NMI-92/13, January 1993
  21. M. T. Thompson, "High Temperature Superconducting Magnetic Suspension for Maglev," Ph.D. Thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, May 1997
  22. A. Kondoleon, D. Seltzer, R. D. Thornton, and M. T. Thompson, "Development of a Large Scale High Speed Wheel Test Facility," Proceedings of the Third International Symposium on Magnetic Suspension Technology, NASA Conference Publication 3336, part 2, pp. 523-534, Dec. 13-15, 1995
  23. M. T. Thompson and R. D. Thornton, "Modeling of HTSC Based Iron-Core Flux-Canceling Electrodynamic Suspension for Maglev," Proceedings of the 4th International Symposium on Magnetic Suspension Technology, NASA Conference Publication, 1997
  24. R. D. Thornton and M. T. Thompson, "Magnetically Based Ride Quality Control for an Electrodynamic Maglev Suspension," Proceedings of the 4th International Symposium on Magnetic Suspension Technology, NASA Conference Publication, 1997
  25. M. Zahn, Electromagnetic Field Theory: A Problem Solving Approach, Krieger Publishing Company, Malabar Florida, 1987
  26. F. W. Grover, Inductance Calculations: Working Formulas and Tables, Dover Publications, Inc., New York, 1946
  27. J. C. Maxwell, A Treatise on Electricity and Magnetism, vols. 1 and 2, Dover Publications
  28. T. R. Lyle, "On the Self-Inductance of Circular Coils of Rectangular Section," Philosophical Transactions, vol. 213A, (1913) pp. 421-435
  29. S. Butterworth, "On the Coefficients of Self and Mutual Induction of Coaxial Coils," Philosophical Magazine, vol.29, 1915, pp. 578-592
  30. S. Butterworth, "On the Coefficients of Mutual Induction of Eccentric Coils," Philosophical Magazine, series 6, vol.31, 1916, pp. 443-454.
  31. A. Campbell, "On the Use of Variable Mutual Inductances," Philosophical Magazine, vol. 15, 6th series, 1908, pp. 155-171.


Marc T. Thompson (M '92)1 is an engineering consultant and Adjunct Associate Professor of Electrical Engineering at Worcester Polytechnic Institute. He received the BSEE degree from the Massachusetts Institute of Technology (MIT) in 1985, the MSEE in 1992, the Electrical Engineer's degree in 1994, and the Ph.D. in 1997. Dr. Thompson's doctoral thesis at MIT "High Temperature Superconducting Magnetic Suspension for Maglev" concerned the design and test of high-temperature superconducting suspensions for MAGLEV and the implementation of magnetically-based ride quality control.

Dr. Thompson has worked as a consultant in analog, electromechanics, and magnetics design, and holds 2 patents. His research areas at MIT included other topics such as: analysis of heating effects in magnetic fluids, and electromechanical stability analysis of magnetic structures. Other areas of his research and consulting interest include planar magnetics, power electronics, high speed analog design, induction heating, IC packaging for improved thermal and electrical performance, use of scaling laws for electrical and magnetic design, and high speed laser modulation techniques.

At W.P.I. Dr. Thompson teaches intuitive methods for analog circuit and power electronics design, and currently works as a consultant for Magnemotion, Inc, Polaroid Corporation, and Thornton Associates.

Richard D. Thornton (Fellow, IEEE)2 is Professor of Electrical Engineering and Computer Science at MIT with primary research in magnetic levitation and propulsion and power electronic control systems. In addition, he teaches and is involved in research on modeling and simulation of electronic circuits and microprocessor controlled electromagnetic and electromechanical systems. Starting in 1965 Prof. Thornton worked on various transportation projects in conjunction with the DOT supported MIT Project Transport.. From 1970 to 1975 Dr. Thornton worked with Dr. Henry Kolm and others at MIT on the development of the NSF supported MIT Magneplane. Dr Thornton is author or co-author of 3 international patents on the Magneplane System. He was a member of the Maglev Technical Advisory Committee, reporting to the U. S. Senate Committee on

Since 1987 years the main focus of Dr. Thornton's work has been on maglev suspension, linear motor propulsion and fault tolerant control. He has written several papers and presented many talks on the design of suspension systems and multi-megawatt power electronic control systems. He has worked with members of the electric utility industry to study the proper design of electric power distribution systems for high speed ground transportation, and has also reviewed the research of others in this field. He is a fellow of the IEEE and President of Magnemotion, Inc.

Anthony S. Kondoleon3 received the B.S. in mechanical engineering from Northeastern University in 1972 and the M.S. in mechanical engineering at the Massachusetts institute of technology in 1976. He is currently a Principle Member of the Technical Staff in the Mechanical Design and Analysis Division at Charles Stark Draper Laboratory and is the focal point for electro-magnetic bearing projects in the department.

Mr. Kondoleon has experience in the design and manufacture of inertial instruments, both mechanical and solid state. He had over five years of experience in the design, assembly and computer analysis of precision ball bearing assemblies. He has been the principle leader in adapting automated processing to the production of precision piece part assemblies. He has authored over two dozen papers and articles on this subject over the last 20 year and is holder of one U.S. patent and is a member of A.S.M.E..

1 Formerly from the Laboratory for Electromagnetic and Electronic Systems at the Massachusetts Institute of Technology, the author is an independent consultant at 19 Commonwealth Road, Watertown Massachusetts, 02172; business phone (617) 923-1392; FAX: (617) 923-8762; Email: and and is Adjunct Associate Professor of Electrical Engineering at Worcester Polytechnic Institute, Worcester Massachusetts.

2 Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, Room 10-050, Cambridge Massachusetts, 02139 and Magnemotion, Inc., 142V North Road Sudbury, MA 02776. Email: and

3 Charles Stark Draper Laboratory, Cambridge Massachusetts

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