The Permanent Magnet Motorby Howard R. Johnson and William P. Harrison, Jr. Reprint of 1979 Paper


 Cover Page 
by
Howard R. Johnson
and
William P. Harrison, Jr.
Engineering Fundamentals Division
Virginia Polytechnic Institute and State University
Blacksburg, VA 24881(?)
To be presented at the UNSTAR Conference on LongTerm Energy Resource, Montreal, Canada, November 26December 7, 1979
UN Institute for Training & Research
[Johnson's personal address purposely omitted in this reprint]
 Page 1 
by
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 unnamed 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 unpaired 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 selfimposed 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 longfield 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 sixspoked wheel, the sixsided 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.
 Page 3 
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.
 Page 4 
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
 Page 5 
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
 Page 6 
reading at the north pole. Thus, a Halleffect 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
statortoarmature 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
(1) 
 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 straightline 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 straightline 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 twodimensional and coplanar, restricted to the vertical xy
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 (lengthtothickness ratio) of 16. This high value contributes to the
twodimensional nature of the model and helps to minimize and effects in the z direction. Thus
there is some justification for a twodimensional 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 xaxis at
(x,0).
Figure 3. Positional locations of two opposing north monopoles in xy space.
Force f, acting on the monopole at (E,n), when resolved into its horizontal and vertical components yields, respectively,
 Page 9 
(2) 
and
(3) 
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 xaxis 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 ydirection thickness and having high aspect ration (to eliminate zdirection edge effects). The southpole 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 xaxis. 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. 
(4) 
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 xy plane, becomes
(5) 
 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
(6) 
where
(7) 
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 airgap 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 xcomponent of F[line over top], similar to Equation (2) we write
(8) 
where X and Y are the dimensionless ratios
(9) 
and
(10) 
 Page 11 
For any fixed position (X,Y) of the north monopole in the upper half plane, Eq. (8) can be integrated to give
(11) 
This ratio is shown in Fig. 7 as a continuous function of X locations with Y treated parametrically.
Figure 7. Xdirection distribution of the Xcomponents 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
airgap 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 midsheet (X  1/2) is clearly shown.
In order to trace some trajectories through this field, we now observe that the
ycomponent of force F[line above] will be
(12) 
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
(13) 
and
(14) 
where
 Page 12 
(15) 
(16) 
and
(17) 
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 (T_{Y})_{mag}we
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 Xinterval 01.
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 freefalling monopole towards sheet center, regardless of the initial droppoint location. The function (T_{Y})_{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.
 Page 13 
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 (T_{X})_{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.
By substituting +B[beta] for B in Eq. (4), the sheet of length L lying along the xaxis 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 (T_{X})_{mag} and (T_{Y})_{mag} reverse their behavior accordingly, as illustrated in Fig. 10.
Figure 10. Xdirection distributions of (r_{X})_{mag} and (r_{Y})_{mag} for the repulsive field of a thin, magnetized sheet acting on a moving north monopole.
Again (T_{X})_{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 Xinterval 01.
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 socalled "magnetic Wankel" motor reported on by Scott (1979).
 Page 14 
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 Halleffect 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 directreading experimental results suggest that the function
(18) 
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, x_{p} , is double that shown in Fig.
12.
Using (18), the total force magnitude expression (5) becomes
(19) 
 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 Xdirection only. So we need consider only the Xcomponent of F from
Equation (19) which yields
(20) 
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 Xdirection motion over a threeelement 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 Xdirection 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, V_{X}, in Fig. 11, since V_{X} is defined as
(21) 
 Page 16 
It will be noted in Fig. 14 that the north monopole has been allowed to
selfstart its motion at the origin with V_{X} 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 airgap 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 twodimensional 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 x_{p}
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 Xdirection motion shown traversing a linear stator assembly comprised of seven permanent magnet elements.
It was found that through small variations in x_{p} 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.
Figure ??  Plot of tables in magazine article (computer dynamic measurement) [see note regarding 'mystery' figure]
 Page 17 
Mystery Figure in Howard Johnson's 1979 Paper  There is a missing "figure 8" and an unlabeled figure at the end of Howard Johnson's 1979 paper "The Permanent Magnetic Motor." Possible significance. 

Page posted by SDA, July 13, 2003
Last updated March 12, 2013
