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 
http://freeenergynews.com/Directory/Howard_Johnson_Motor/1979Paper/index.html#REFERENCES
Johnson's Magnetic Motor (Main Page)
http://www.apfn.org/apfn/Magnetic_motor.htm
EMail: apfn@apfn.org