The Permanent Magnet Motor

by Howard R. Johnson and William P. Harrison, Jr.

Reprint of 1979 Paper
Now posted for the first time on the Internet

Table of Contents
(links to content below)

All content is now posted and transcribed.  July 19, 2003.

In original copy, all figures came at the end as an appendix.  Here they are inserted within the text where the transcription has been complete.  Pages and Figures not yet transcribed are included at the end of the transcription.  Page numbering on original was added later, and is off a little.  It has been corrected here.  Paper scanned by Douglas Mann.  Transcription by Sterling D. Allan.

Johnson had working model before Harrison composed mathematical model -- Douglas Mann

-- Cover Page --

The Permanent Magnet Motor


Howard R. Johnson

William P. Harrison, Jr.
Engineering Fundamentals Division
Virginia Polytechnic Institute and State University
Blacksburg, VA 24881(?)

To be presented at the UNSTAR Conference on Long-Term Energy Resource, Montreal, Canada, November 26-December 7, 1979

UN Institute for Training & Research

[Johnson's personal address purposely omitted in this reprint]


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The Permanent Magnetic Motor

Howard R. Johnson and William P. Harrison, Jr.

I. Introductory remarks (by Mr. Johnson)

    Today when energy is so expensive, it is not hard to drum up interst for most any avenue that offers a breath of hope or a way of escape, but this was not necessarily so in 1942.  We were somewhat satisfied and convinced that we had the main sources of energy in view.  So it took a pure act of faith to try to develop a new un-named source.
    It took faith to spend time on it.  It took faith to spend money on it.  And it took faith to consider facing the opposition later when I made my work known and faced all the status quo people.
    So, in 1942 using the Bohr model of the atom, and knowing that un-paired electron spins created a permanent magnet dipole, I kept wondering why we couldn't use these fields to drive something.  I was sure that the magnetic effect of the spins was similar enough to the field of a current in a wire to do the same thing.  I had no knowledge of electron spins stopping and knew no method that I could exert to stop them, so I decided to try to work out a method to use them.
    At the same time there were no good hard magnetic materials that I knew of, materials that could be opposed with strong magnetic fields and not be demagnetized enough to damage them.  Not only that, they would not give the thrust that I desired.
    Having a chemical background, I thought it would be nice to use the

-- Page 2 --

best magnetic materials I could find in combination with an interstitial material that was highly diamagnetic to force the electron spin to stay in place.
    The U.S. Navy later made such a compound using bismouth [bismuth] and good magnetic materials, but the internal coercive forces were so great that this strong magnet would fall apart if not encased in glass.  It was also expensive.
    So I kept checking magnetic materials while I worked on designs that I thought should be implemented.  It was a quiet, sometimes lonely job over the years, for I didn't share my plans with my associates.  My self-imposed security would not permit it, and I knew of few people who would be interested anyway.
    In the fifties, as ceramic magnets became better and harder, and long-field metal magnets appeared on the scene, I began to freeze some designs and to have magnets custom made to fit them.
    It was about this time that I mentioned the fact that just as I believed electron spins made permanent magnets, I also believed that they were responsible for the 60 angles in the structure of snowflakes giving the six-spoked wheel, the six-sided spokes, etc.  The dean of the school where I was teaching said, "Maybe so" and ask me if I knew that snowflakes were mentioned in the Bible as being important.  I told him, "No, I didn't know that," but I looked it up.  It said: "Hast thou entered into the treasures of the snow? Or hast thou seen the treasures of the hail?  Which I have reserved against the time of trouble, against the day of battle and war."
    My comment was, "Well, maybe this is more important than I thought."  So I went ahead and worked on it another ten years.

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    I went to the Library of Congress and looked up snowflakes.  I found a wonderful book there by Dr. Bentley of New Hampshire.  He has spend many years making these studies, and he had learned a lot, as well as turning out one of the world's most beautiful books.  He had found that snowflakes have gas pockets oriented on 60 angles and that the gas has a higher percentage of oxygen than air.  That's one reason why snow water rusts so well.  This higher concentration of oxygen also interested me because oxygen is more attracted to a magnetic field than other gases.
    Finally, using the best ceramic magnets I could find and the best metal magnets, I worked out a scheme for a linear motor.  The stator would be laid out as if it were unwound from around a motor.  The parts of the armature would ride just above the stator and have the same beveled angular orientations I have just mentioned.
    Dies were made for the curved armature magnets, and an order was placed for these shapes, despite the objections of magnet manufacturers who said it was a bad design.  They didn't know what it was for, but they were sure it was a bad design.  They wanted to make horseshoe magnets.  They even begged me to content myself with half an order.  I did not agree -- and once again you have that little matter of faith; faith to try to implement a new theory; faith to spend your own limited funds when you have a a family and other financial responsibilities staring you in the face; faith to buck the recognized authorities and manufacturers in the field; faith to believe that your work is good and that some day, despite all the hazards, you will apply for and receive patent rights in your own country and perhaps throughout the rest of the world; and finally, faith that you can resist being smashed into dust by industrial giants and/or being robbed by others who know only how to steal.

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    Believe it or not, my first motor assembly showed about two pounds of thrust.  The little toy car on which I fastened the armature magnets for support ran in both directions over the stator, showing that the focusing and timing of the interactions was not too bad.
    This was the first light at the end of a rather dark tunnel I had been traveling for many years.  I breathed a real sign of relief as my young son played with this "new toy," and was able to operate it as easily as I could.
    After much testing of linear and circular designs, and looking for an attorney for years suited to securing a patent on the new theoretical work, I was led to Dunkan Beaman of Beaman & Beamon in Jackson, Michigan.  It took some time to prepare the patent.  The attorney built some models himself to check certain parameters.  Finally, we entered the case in the patent office expecting a lot of opposition.  We were correct.  We got it.  But again, faith saved the day as we battled for many years to gain a rather complete victory.
    Now the work requires different kinds of faith:  faith in those who have taken cut licenses and who will license; faith to continue the research to replace scarce materials in the magnets; and faith that this work will continue to progress and that it will eventually fulfill its goal.
    For a number of reasons, the permanent magnet motor has not received much consideration.  In fact, nothing too radical has been done since Faraday took some very crude materials and showed the world that it was possible to make a motor.  This work of his largely influenced the thinking of Clerk Maxwell and others who followed.
    Today, the two greatest obstacles to using a permanent magnet motor

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are, first, the belief that it violates the conservation of energy law; and, secondly, that the magnetic fields of attraction and repulsion decrease according to the inverse square law then the air gap is increased.
    In fact, both contentions are quite wrong because they are based on wrong considerations.
    The permanent magnet is a long time energy source.  This has been shown for many years in the rating of magnets as high or low energy sources for many applications over long usage.
    A loudspeaker composed entirely of electromagnets would be unreal in size and energy consumption.  Yet, despite examples of this type, many hesitate to apply the same principles to motors and extend them even further by using permanent magnets for both the stator and armature.
    The elements of all electric and permanent magnet motors are similar.  A field imbalance must be created, the fields must be focused and timed, and magnetic leakage must be controlled.
    In the wound motor, brushes and contact rings give the timing, the size and shape of the wound fields and poles gives the focusing, and the motor case and kind of iron used help to limit the leakage.
    In our permanent magnet motors the timing is built into the motors by the size, shape, and spacing of the magnets in the stator and armature.  The focusing is controlled by the shape of the magnets, pole length, and the width of the air gap.  This air gap, through which magnets oppose and attract each other, is a rare phenomenon.  Usually when a magnetic air gap is increased, the field decreases inversely as the square.
    When the air gap of the permanent magnet motor is increased, a curious but definite change takes place.  There is a large decrease in the reading at south pole of the armature and an increase in the

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reading at the north pole.  Thus, a Hall-effect sensing probe will give a higher gauss reading at the north pole and a decreasing count at the south pole.  This helps explain why the thrust is better with a larger air gap than a smaller one.  The attracting field is minimized and will not produce a locking force, while the repulsion of the crescent magnet is great enough to generate a thrust vector component that will drive the armature.
    As I tried to explain in the patent, I believe that the permanent magnet is the first room temperature super conductor.  In fact, I believe that super conductors are simply large wound magnets.  The current in a super conductor is not initiated by a strong emf, such as a battery, but is instead actually induced into existence by a magnetic field.  Then, in order to determine how much current may be flowing in the super conductor coil, we measure its magnetic field.  This appears to be something like going out the door and coming back in the window.
    Another rather unique feature of super conductors is the fact that their magnetic lines of force experience a change in direction.  No longer do these lines flow at right angles to the conductor, but they now exist parallel to the conductor.  Theoretically, the heavy conductor currents exist in the fine filaments of niobium within each small wire of niobium tin from which such super conductors are made.  Isn't it interesting that the finer the wire the less the resistance until eventually there is no resistance at all?

-- Page 7 --

II.  THEORETICAL ANALYSIS [by William P. Harrison, Jr.]

1.  Introduction

    Despite the fact that the linear version of the permanent magnet motor (Johnson, 1979) may appear conceptually simple (see Fig. 1), the complex interactions of the fields alone place it in a class with other quite sophisticated motive systems. 

Figure 1. Partial front and plan views of a linear model of the Howard Johnson permanent magnet motor.

Many parameters play an important part in making possible the successful design of a permanent magnet motor.  A number of these variables relate directly to the geometry of the system and its components.  Mathematical models for both the linear and circular versions of Mr. Johnson's motors are presently under development, and include such controllable parameters as stator-to-armature air gap, stator element air gap spacing, armature pole length, stator magnet dimensions, magnet material variations, magnetic permeability and geometry of backing metals, and multiple armature couplings, to mention only a few.  However, much of the early work involved quit simple mathematical investigations, and even at this level some remarkable revelations resulted.  Also, as often is true with simple models, considerable insight into the mechanisms that might prove predominant was gained.  Therefore, it is our intention to share with you some of those early analytical investigations and findings.
    Even though Coulomb's Law, embodying the inverse square relationship as it does, may yet prove suspect, it nevertheless provides an exceedingly simple yet viable form upon which to base an elementary model of the linear version of the permanent magnet motor.  Describing the interaction between two magnetic monopoles, Coulomb's Law in vector form is recalled as



-- Page 8 --

where M and M' are the pole strengths (positive if north, negative if south), u [mu] is the permeability of the medium in which the poles are located, r is the straight-line separation distance between the two poles, and f [with line over top] is the vector of force (see Fig. 2) acting at each pole (positive in magnitude for repulsion and negative for attraction).

Figure 2. Coulomb's Law

    The vector nature of Eq. (1), the fact that f's line of action is colinear with the straight-line distance r between poles, its superposition properties when applied to multiple poles, and its restriction to static systems fixes in space are all well known conditions on Eq. (1).  We will use the superposition property of Eq. (1) to extend its application to a spatial domain containing many more poles than the two shown in Fig. 2.  However, Eq. (1) will first be resolved into scalar components so that analytical expressiors [sic] can be more easily developed.
    Our analysis will be two-dimensional and coplanar, restricted to the vertical x-y plane.  It should be noted that the horizontal stator "track" of H.R. Johnson's linear model comprises a plurality of flat magnets, rectangular in cross section, each having an aspect ratio (length-to-thickness ratio) of 16.  This high value contributes to the two-dimensional nature of the model and helps to minimize and effects in the z direction.  Thus there is some justification for a two-dimensional analysis, at least in the case of the linear model we are considering here.
    As shown in Fig. 3, we consider first a north pole of strength M located at coordinates (E [epsilon], n [nu]) with a second north pole of strength M', located on the x-axis at (x,0). 

Figure 3. Positional locations of two opposing north monopoles in x-y space.

Force f, acting on the monopole at (E,n), when resolved into its horizontal and vertical components yields, respectively,

-- Page 9 --








2.  The Attractive Sheet

    To illustrate some of the assumptions and extensions of Coulomb's Law that will be made, the simple example of a magnetic sheet lying along the x-axis will be considered first (see Fig. 4).

Figure 4. Spatial orientation of thin, magnetized sheet having high aspect ratio and with south face up.

The sheet, of finite length L, is a permanent magnet magnetized across its y-direction thickness and having high aspect ration (to eliminate z-direction edge effects).  The south-pole face will be oriented up, with north facing downward on the underside of the sheet.  Underside effects will be ignored as though the sheet represented a continuous distribution of only south monopoles along the x-axis.  To incorporate such distributions into Eq. (1) we replace M' with the differential dM' and introduce the function B(x) so that


dM' = B(x) dx.


Then the magnitude of the total force vector, F [with line over top], acting on an isolated north monopole of strength M situated somewhere within the upper half of the x-y plane, becomes



-- Page 10 --

where x [chi] is the ratio x/L.  Assuming that the magnetic density along the sheet can be represented by the southern constant - B [beta(?)], and neglecting end effects at x = 0 and x = L, Equation (5) reduces to






the strength parameter M' having been determined by integrating Eq. (4) over the sheet length L, and p [rho] is the ratio r/L.
    If the north monopole is placed directly above the center of the sheet, at coordinate (E[epsilon], n[eta]), with E[epsilon] = L/2 and the vertical air-gap separation distance n (eta) taken as arbitrary, the symmetrical distribution of incremental force vectors acting at (E,n) will appear as shown in Fig. 5. 

Figure 5. North monopole symmetrically above the center of a magnetized, attracting sheet.

Note that a shift of the north monopole to the left results in a force imbalance which tends to pull the pole back to the right, as shown in Fig. 6. 

Figure 6. Force imbalance acting on a north monopole above a magnetized sheet tending to restore the pole to sheet center.

So considering now only the x-component of F[line over top], similar to Equation (2) we write



where X and Y are the dimensionless ratios






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For any fixed position (X,Y) of the north monopole in the upper half plane, Eq. (8) can be integrated to give



This ratio is shown in Fig. 7 as a continuous function of X locations with Y treated parametrically.

Figure 7. X-direction distribution of the X-components of attractive force exerted on a north monopole by a thin, magnetized sheet.

The Y = 1 curve represents the field influence on the north monopole situated at a constant air-gap separation (n[eta] = L) quite some vertical distance above the sheet; whereas at Y = 0.1 the monopole is located much closer to the x axis.  Reversal of the force component through its zero value at mid-sheet (X - 1/2) is clearly shown.
    In order to trace some trajectories through this field, we now observe that the y-component of force F[line above] will be



This function is show in Fig. 8 with a Y value of 0.20.

[figure 8 is omitted (unless it is the last, unlabeled figure)]

    In dimensionless form the equations of motion for trajectory paths of the monopole above the sheet in planar X - Y space become







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In these expressions t is real time and T is simply a time constant chosen arbitrarily.  As previously noted on page 9, L is the length of the sheet; whereas, g is the gravitational acceleration constant and W is the downward weight force of the moving monopole above the sheet.  For the magnetic force terms (T[Gamma]X)mag and (TY)magwe substitute directly Eqs. (11) and (12), respectively.
    Several of the trajectories resulting from the integration of Eqs. (13) and (14) are shown in Fig. 9. 

Figure 9. Trajectories of a north monopole in an attractive field generated by the thin, magnetized sheet lying in the X-interval 0-1.

They all exhibit the expected behavior.  As already implied in the discussion of Fig. 7, the function (T[Gamma]X)mag given by Eq. (11) has a stable point of equilibrium at X = 1/2 and therefore drives the free-falling monopole towards sheet center, regardless of the initial drop-point location.  The function (TY)mag from Eq. (12) is equally persuasive in pulling the monopole down towards the sheet itself, and manifests that attraction quite pervasively through the integration of Eq. (14), even when the G term may be omitted (as it was in the trajectories of Fig. 9).  Actually, the computer integration procedure will not carry the monopole all the way to surface contact with the sheet at Y = 0 because of the infinite condition which exists there as reflected by Eq. (12).  Thus, tailings of these trajectories (Fig. 9) have been completed by manually overriding the plotter.

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    As we would anticipate in working with this type of central field, where B in Eq. 4 is a simple constant, the field is conservative with curl of F[line over top] vanishing.  Also, the reverse symmetry of (TX)mag about X = 1/2, as seen in Fig. 7, confirms that the energy integral for this function will vanish within any appropriate limit pairs of X.

3.  The Repulsive Sheet

    By substituting +B[beta] for B in Eq. (4), the sheet of length L lying along the x-axis becomes repulsive, with its northern face directed upward, opposing the north monople above it at location (E[xi],n[eta]).  Of course the sign in Eq. (6) becomes positive and the functions (TX)mag and (TY)mag reverse their behavior accordingly, as illustrated in Fig. 10.

Figure 10. X-direction distributions of (rX)mag and (rY)mag for the repulsive field of a thin, magnetized sheet acting on a moving north monopole.

Again (TX)mag will have an equilibrium point at X = 1/2, but now it is destabilizing.  As a consequence, resulting trajectories for the north monopole are much more interesting in this case than they were with the attractive sheet.  Several paths are shown in Fig. 11 with different values used for the W/F ratio in Eq. (17). 

Figure 11. Trajectories of a north monopole in a repulsive field generated by a thin, magnetized sheet lying in the X-interval 0-1.

Parameter G was included, and in each example the trajectories commenced at (0.9, 0.2) with zero initial velocity.
    The attractive and repulsive sheet results are easily demonstrated since "rubberized" flexible sheet magnets are commercially available, such as those sold by the Permag Corporation of Jamaica, New York.  It may also be interesting to note that with slight modifications this first simple analytical sheet model can be used to gain some insight into operation of the so-called "magnetic Wankel" motor reported on by Scott (1979).

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4.  The Sinusoidal Model

    The first paper (Harrison, 1979) relating, indirectly, to any mathematical analysis of the permanent magnet motor adopted a cosine function (Fig. 12) to simulate the distribution of influence parameter M' generated by the flat stator track of Mr. Johnson's linear model.

Figure 12. Pole strength influence factor, M', as a cosine function of linear displacement distance, x.


  An experimentally determined distribution, shown in Fig. 13, was obtained by moving a Hall-effect probe (courtesy of F. W. Bell, Incorporated, of Orlando, Florida) over the stator track of one of Mr. Johnson's early linear models having seven flat ceramic magnet elements.

Figure 13. Experimentally determined magnetic flux density, B, along a linear model of the Johnson permanent magnetic motor.

The figure shown was produced by a plotter connected directly to the monitor computer controlling positioning of the Hall probe and processing its output signal.  (Ordinate values on the graph are magnetic flux density in gauss measured relative to a predetermined background value.)  These direct-reading experimental results suggest that the function



substituted into Eq. (4) should prove interesting to pursue as a more challenging test of what might be gleaned from this simple Coulomb model we have been discussing.  It should be noted that one of the important differences between the function (18) and that shown in Fig. 12 is that in (18) the period length parameter, xp , is double that shown in Fig. 12.
    Using (18), the total force magnitude expression (5) becomes



-- Page 15 --

where a total track length distance of L has been used to form the dimensionless ratios
  Also, if Eq. (7) is used for F[flourish] in (19), then in that expression one must substitute the product B[beta]L for M'.
    Now we plan to hold Y constant while investigating linear motion of the monopole along this track in the X-direction only.  So we need consider only the X-component of F from Equation (19) which yields



With this expression substituted into Eq. (13), integration becomes straightforward and yields the typical oscillatory type of trajectory path shown in Fig. 14.

Figure 14. Oscillatory path of a north monopole restrained to X-direction motion over a three-element linear stator assembly.

As Mr. Johnson has brought out, the focusing armature magnet of his linear model will start at either end of the stator track simply by insuring that the north end of this bipoled crescent is leading the south (see Fig. 1).  So, in Fig. 14, we are showing the X-direction motion from right to left instead of from left to right as in our previous examples.  Also, by simply rotating the figure clockwise through ninety degrees, it becomes easy to follow the behavior of dimensionless velocity, VX, in Fig. 11, since VX is defined as



-- Page 16 --

    It will be noted in Fig. 14 that the north monopole has been allowed to self-start its motion at the origin with VX initially zero.
    We now discuss our final adjustment which proved to be an exciting revelation at the time it was first investigated several months ago.  Johnson (1979, col. 5, line 39) states that the horizontal air-gap spacing between the magnet elements which the stator track comprises should vary slightly from nominal in order to smooth out movement of the armature.  Introducing this type of variation into a two-dimensional model, provided the change is nonuniform, would certainly transform the field from conservative to non conservative.  (It should by now be apparent that only a nonconservative model has any chance at all of even partially explaining the phenomenon of the permanent magnet motor.)
    With these thoughts in mind, an attempt was made to drive the armature monopole of Fig. 14 on to the second stator magnet and beyond by varying the horizontal gap parameter xp during the integration process (i.e., during the motion).  The results are shown in Fig. 15.

Figure 15.  Continuous path of a north monopole restrained to X-direction motion shown traversing a linear stator assembly comprised of seven permanent magnet elements.

It was found that through small variations in xp in Eq. (20), as the monopole advanced along its trajectory path from one X position to another, sufficient control over the moving pole could be exercised to carry it over the full length of the stator and beyond.

[click for enlargement]

Figure ?? - Plot of tables in magazine article (computer dynamic measurement) [see note regarding 'mystery' figure]

-- Page 17 --


  • Harrison, William P., Jr., "A Solution for the Optimal Gap of a Monopole Element Moving in a Sinusoidally Distributed Magnetic Field", paper presented to the Engineering Section, Virginia Academy of Science, 57th Annual Meeting, Richmond, Virginia, May 8011, 1979.
  • Johnson, Howard R., United States Patent No. 4,151,431 dated April 24, 1979, entitled "Permanent Magnet Motor."
  • Scott, David, article entitled "Magnetic 'Wankel' for Electric Cars", Popular Science, p. 80, June.  1979.

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