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and Multivalued Magnetic Scalar Potential:Master Overunity Mechanisms

Copyright 1996 by T.E. Bearden


This is a flash release of information on the operational principles of three overunity electromagnetic engines that are in the successful prototype stage or advanced engineering development. My purpose is to provide an explanation of the master overunity mechanisms utilized by these devices, and to alert researchers and experimenters that the mechanisms are well-established in the conventional scientific literature, though still but little known to the majority of electrical engineers.
My series of articles[1] on overunity engines and mechanisms, for The Virtual Times, Internet node www.hsv.com, covers these three engines, the master regauging mechanism, the multivalued potential, and several other overunity mechanisms or proposed mechanisms. The magazine has just released my latest article over the Internet, entitled "The Master Principle of EM Overunity and the Japanese Overunity engines: A New Pearl Harbor?" The article is heavily referenced and gives a thorough explanation of the three overunity devices: (1) Johnson's nonlinear boosting permanent magnet gate,[2 ,3] (2) the Takahashi engine, and (3) the Kawai engine.

All Three Engines Use Regauging of Magnetic Scalar Potential

All three devices freely asymmetrically regauge (A-regauge) (recharge or discharge, as required) the magnetic scalar potential energy of the device in a selected A-regauging sector.[4 ,5] Johnson uses a multivalued magnetic scalar potential to accomplish this A-regauging completely by means of a nonlinear permanent magnet rotor and nonlinear permanent magnet stator, without any electrical input. Takahashi and Kawai both use external electrical input to create or alter a magnetic scalar potential in the A-regauging section.

Conservative and Nonconservative Fields and Multivalued Potential (MVP)

Normal engine designers work with conservative fields, which require single-valued potentials. (See Figure 1). They consider A-regauging operations, as well as the multivalued potential (MVP), to be nuisances, since A-regauging may immediately involve nonconservative electromagnetic fields (see Figure 2). Most of the favored "engine design" laws and trusted circuit laws "blow up" during A-regauging, whether by electrical injection or the MVP region. So electrical power engineers just design conventional electromagnetic engines to avoid the MVP or eliminate it. On the other hand, if one deliberately evokes and properly uses the free "jump" of stored potential energy that occurs in an MVP-containing sector of an engine, a standard gauge-theoretic analysis will show that one can legitimately have overunity coefficient of performance from that engine. (See Figure 3). I first pointed this out in 1980.[6 ]

 Figure 1 (27k jpeg)  Figure 2 (32k jpeg)  Figure 3 (23k jpeg)


 Figure 1 (27k jpeg)  Figure 2 (32k jpeg)  Figure 3 (23k jpeg)

Multivalued Potential (MVP) Frequently Occurs in Nature

The multivalued potential occurs widely in nature,[7] and particularly in magnetics. In fact, it is quite often the rule rather than the exception. Still, the MVP is usually ignored by conventional engine designers, and many electrical engineers have hardly heard of it. S-regauging [8] of the magnetic potential changes only the magnetic potential; the force fields themselves need not be changed. A-regauging also creates additional force fields, which may be used to assist the system's operation.
It is easiest to A-regauge a magnetic scalar potential on a rotary electromagnetic engine by simply energizing a coil. If the coil is oriented radially, its associated B-field will not perform radial work on the rotor. Any tangential field resulting from creation of the magnetic scalar potential will either be (i) rotor-accelerating, or (ii) rotor decelerating. Obviously one wants the A-regauging of the magnetic scalar potential to either (iii) accelerate the rotor, or (iv) go to zero so as to zero out the back-drag. So one will adjust the polarity and strength of the magnetic scalar potential created by the radial coil accordingly.
For those unfamiliar with modern gauge theory, we point out that this discussion is completely consistent with Maxwell's equations, which formed the first true gauge theory. It is simply a matter of preference by the electrodynamicists, e.g., that the indefinite potentials of the Maxwellian equations are usually just symmetrically regauged. By use of an MVP region and/or an A-regauging region in an engine, however, additional "free" force terms are created and utilized by the engine designer to accomplish COP>1.0.

Regauging is Work-Free, and Can Produce Additional Orthogonal Fields

Work requires the translation of a force through a distance. Since the A-regauging change creates additional forces, the change in the force fields already present can be helpful. Rigorously it does not require extra work to A-regauge the system. However, the regauging is free to create any number of additional force fields at right angles to those already present before the regauging, depending upon the relationships between the regauged potential and various potentials in adjacent locations at right angles nearby. Let us examine that more closely in Figure 4.

 Figure 4 (25k jpeg)

Rigorously, W = Fds. That is, work is done by a translating force only along the direction of translation. Ancillary force field B2, formed at a right angle to the radial force field B1 in stator coil A, can do tangential work on rotor C without any additional "drain" or effect upon the radial coil other than the normal drain utilized to form the primary B1 field. Simply put, radial forces do not perform work at right angles (tangentially) to their direction. However, at the fixed stator point S1 where radial magnetic force B1 exists, a magnetic scalar potential F1 also exists. At the nextmost tangential stator position S2, a scalar potential F2 exists. If F1-F2 0, then a tangential magnetic field B2 exists between S1 and S2. By adjusting the strength and polarity of F1, magnetic field B2 can be made to assist the rotation of rotor C, in what would otherwise be a "back drag" or decelerating sector. In short, the tangential back-drag force normally existing between F1-F2 in the normally-decelerating sector can be reversed and made to accelerate the rotor C in that sector, without requiring excess work in stator coil A or in stator electromagnet assembly P when the strength and polarity of F1 are regauged. In short, one can A-regauge in the normal back-drag region of the rotation, and reverse what would normally be back-drag into positive acceleration.
Both Johnson and Takahashi do this in their engines. Johnson A-regauges via a complex assembly of stator magnets (see Figure 5) that provides an MVP. Takahashi (see Figure 6) A-regauges by utilizing a radial coil with a weak current through it, where the current is sharply broken by ignition points to provide a "nearly free," momentarily high magnetic scalar potential and thereby perform the regauging nearly "for free."

 Figure 5 (35k jpeg)  Figure 6 (27k jpeg)


Regauging is Free Electrical or Magnetic "Refueling"

A-regauging a sector of a rotary electromagnetic engine is just like refueling a car by putting gas in its gas tank: During the regauging operation, the system is an "open" system receiving an injection of excess potential (stored) energy from the surrounding vacuum -- except in the electromagnetic case the refueling is free. (See Figure 3). The excess stored energy injected into the system from the "refueling" jump due to A-regauging, can then be dissipated in the load during the remainder of the rotary cycle -- just as a refueled automobile can dissipate its additional fuel energy in powering the car, until it is time for refueling again.
By using one or both of these two master principles (i) A-regauging the potential energy of the system, and (ii) use of a multivalued potential for A-regauging, electromagnetic engines can permissibly exhibit COP>1.0, without any violation of the laws of physics, thermodynamics, Maxwell's equations, or advanced electrodynamics. And a totally-permanent-magnet motor can power itself and its load.

The Johnson Force-Producing Magnetic Gate

Figure 5 diagrammatically illustrates the operation of the force-producing magnetic gate in Johnson's permanent magnet motor. As Johnson has shown, by using a multivalued potential in his gates, a rotor magnet is attracted into a highly nonlinear stator gate region where the MVP is located. When it enters the MVP, the rotor encounters a dramatic jump in stator's magnetic scalar potential with a change of polarity. In turn, this produces a sudden accelerating tangential force in the region which would otherwise have been the back-drag region. This accelerating force propels and accelerates the rotor magnet on through the gate and out of it.
Rigorous force meter measurements taken at 0.01 second intervals prove that this occurs as the rotor passes through Johnson's gate. A representative plot of such force meter measurements is shown as the dotted line in Figure 3.
Johnson thus uses a highly nonlinear magnet assembly of special design to create an MVP in his gate. The MVP produces a "magnetic potential jump" and a reversal of the (otherwise) exiting back-drag on the rotor. In short, Johnson causes the system to be automatically "refueled" in the A-regauging sector, so that it can continue to rotate and power a load.

The Takahashi Engine

Figure 6 diagrammatically shows the scheme of operation of the Takahashi engine. Here a set of permanent magnets, each at an angle to the various radial lines of the device, comprises a slightly widening spiral stator that is "almost" circular but not quite. A circular rotor with a sector magnet is mounted inside this spiral stator. An end gap exists in the stator as shown, so that the stator is not a completely closed ring. The direction of rotation for the rotor is clockwise as shown. For demonstration of the principle, the beginning air gap is 0.1 mm and the ending air gap is 5 mm.
A permanent magnet is mounted along the perimeter of an angular sector of the rotor. It is magnetized, say, with the north pole facing radially outwards, and the south pole facing radially inside. In the stator, the permanent magnet north poles are facing radially in toward the rotor, but at an angle, and the south poles are facing radially outside but at an angle.
Thus tangentially the north pole of the rotor is in a nonlinear magnetic field, and it will experience a clockwise force and acceleration from position 1 (where the air gap is the minimum) to position 2 (where the air gap reaches maximum).
If this were all there was to it, the Takahashi motor would not be overunity because the tangential field is conservative. When the rotor crossed the end gap in the stator between point 2 and point 1, very sharp and dynamic braking work would be done back upon the rotor magnet by the field of the stator magnets at point 1. This braking work would precisely equal the amount of dynamic acceleration work that was done in accelerating the rotor magnet from position 1 to position 2, in accordance with a distortion of Figure 1. For an absolutely frictionless machine with no losses, the coefficient of performance (COP) would be 1.0. Since any real machine will have at least some friction and drag, the actual COP would be less than 1.0.
Let us now utilize the notion of the magnetostatic scalar potential to examine a new situation in the end gap.
Technically, let us regard a single unit north pole in the rotor, going from position 1 to position 2 (the acceleration cycle, where the engine will deliver shaft horsepower against a load), and then from position 2 to position 1 (where the magnetostatic scalar potential must be A-regauged to equal or exceed the potential at position 1, in order for the rotor to continue unabated or even further accelerate. I.e., in the separation gap, a A-regauging operation must be done so that the "stator to inner" potential is increased equal to or exceeding the "stator to inner" potential of position 1.
In normal machines, the A-regauging part of the cycle is conventionally where the design engineer forcibly inputs energy from outside the system to do brute physical work on the machine to forcibly wrestle its energy storage back to initial conditions. In the past engineers have automatically assumed COP<1.0 without exception, since their forcible RESET work was always equal to the maximum theoretical energy output to the load during the motor part of the cycle from point 1 to point 2, plus any losses in the "wrestling" process and in the machine itself.
So we simply must perform the A-regauging or RESET of the system's energy storage, without performing tangential "back-drag" work on the rotor. In other words, we must refuse to engage in the conventional "wrestling match." For that purpose, an electromagnet is utilized to fill the end gap in the stator, arranged so that when it is activated its north pole will face radially inward. A small current activates the coil weakly, through a distributor with breaker points. At the proper timing (i.e., when the rotor is directly opposite the electromagnet polepiece, a set of ignition points is sharply broken in the circuit with the coil of the electromagnet. Momentarily, a very high potential will appear at the end of the coil as the collapsing field is highly amplified and trying to sustain the previous current in its previous direction. The end result is the formation of a strong magnetostatic scalar potential (pole), of north polarity, on the stator polepiece facing the rotor. Note that no radial work can be done on either the stator polepiece or the rotor by gradients of this high potential, because they cannot move radially.
The potential in the end gap is now higher than the potential at position one. Consequently a clockwise tangential force field exists between the end gap potential and the lower potential at position one. This force cannot do "back-drag" work on the fixed stator. It cannot oppose the radial B-field, because it is orthogonal to it. An assisting clockwise tangential force therefore appears upon the rotor, and the rotor is accelerated and "boosted" out of the stator gap and back past point 1. At that point the electromagnet has lost its potential, but the engine has now been A-regauged and again is in the clockwise acceleration field of the rotor-stator permanent magnets.
In short, the rotor perceived the sudden change of magnetostatic scalar potential from the electromagnet in the stator gap as a pseudo-MVP, and the system received a sharp influx of potential energy, without work except for that lost in the electromagnet circuitry. Since that loss can be made quite nominal by conventional electronic practices, the engine permissibly provides COP>1.0. It can therefore be rigged to power itself and a load simultaneously.
Placed in an electric vehicle with necessary switching circuitry and ancillary equipment, a properly designed Takahashi engine and its derivatives should be capable of starting from a single ordinary battery, then powering the vehicle agilely, powering the accessories, and recharging its own battery -- all three simultaneously.

The Kawai Engine

Figure 7 shows eight snapshots of the rotor advance of a typical Kawai engine, taken from Kawai's patent.[9] This is one end rotor/stator side of a two rotor device, where a similar rotor/stator device is on the other end of the central shaft 11. In Figure 7A, polepiece 14 has three outward teeth 14b dispersed equally around the circumference, alternated with three notches. An end magnet 13 provides the source of flux passing through the polepiece. With the electromagnets de-energized, their core materials 16c, 16d, 16g, 16h, and 16k, 16l are shown shaded, by flux from central magnet 13 outwards through teeth 14b.

 Figure 7a (12k jpeg)  Figure 7b (12k jpeg)
 Figure 7c (11k jpeg)  Figure 7d (11k jpeg)
 Figure 7e (10k jpeg)   Figure 7f (12k jpeg)
 Figure 7g (12k jpeg)  Figure 7h (11k jpeg)

In Figure 7B, electromagnets 16a, 16e, and 16d are energized. The shaded area shows the sharp convergence of the flux from magnet 13 through polepiece 14 and the edge of teeth 14b. Since the electromagnets are magnetized in attracting mode, the rotor will experience a torque tending to widen the flux path from magnet 13 to the activated electromagnets. Thus a clockwise torque exists on the rotor, and it will start to rotate clockwise.[10] Note also that each electromagnet is operating independently of the other two.
As shown in Figure 7C, 7D, 7E, and 7F the rotation of the rotor continues clockwise, widening the connecting flux path to the three activated electromagnets. During this time the torque on the rotor is clockwise.
In Figure 7G, the flux path to the activated electromagnets is fully widened. Also, the leading edges of the three teeth are just beginning to enter the domains of the next electromagnets 16j, 16b, and 16f. This is getting similar to the original position shown in Figure 7B. Consequently, the electromagnets 16i, 16a, and 16e are deactivated, and electromagnets 16j, 16b, and 16f are activated. Asymmetrically, this regauges and resets the engine back to the original starting position in Figure 7B. The action cycle begins anew. As can be seen, in each complete rotation of the shaft, each of the three teeth of the rotor will be A-regauged 12 times. So 36 total A-regaugings/resettings/refuelings are utilized per shaft rotation.
In each stator coil, at energization a tooth is just entering that coil. Energized in attractive mode with respect to the ring magnet around the shaft, the flux in the polepiece "jumps" from fully widened flux (and small or vanishing radial torque on the rotor) to angled and narrowed flux (with full radial clockwise torque on the rotor). As previously explained, the narrowed flux and its angle exert a clockwise accelerating tangential component of force upon the rotor. Each coil is de-energized prior to beginning to exert radial back emf (which it would do if it remained energized as the trailing edge crossed it and again narrowed the flux path). So the Kawai engine uses normal magnetic attraction to accelerate the rotor for a small distance, then A-regauges to zero attraction to eliminate the back-drag portion of the attractive field. It A-regauges to zero as the "RESET" condition.
For appreciable power and smoothness, the Kawai engine uses an extensive number of A-regaugings per axle rotation, being 36 times on each end, or a total of 72 for the two ends. The forcefield of each coil, accompanying its increased magnetostatic scalar potential, is oriented radially inward, so that radial work cannot be done by the coil on the rotor because the rotor does not translate radially. Advantage is taken of the initial clockwise acceleration force initially produced, and A-regauging eliminates the counterclockwise drag or "decelerating" force that would be produced without the A-regauging.
The major benefits of the Kawai arrangement are that (i) a large number of A-regaugings occurs for a single rotation of the rotor assembly, enabling high power-to-weight ratio, (ii) each electromagnet is energized only when positively contributing to the clockwise torque that drives the rotor, and (iii) each coil is de-energized to A-regauge the system during those periods when the coil would otherwise create back-drag (counterclockwise torque) if it remained energized.
So the Kawai engine delivers what it advertises: It dramatically reduces or eliminates the "back drag" fields of the stator electromagnets, because there are no back-drag fields activated in the electromagnets during the back-drag sectors. A conservative field cycle is one in which the back-drag is equal to the forward boost. Eliminating the back-drag portion of the cycle is a form of A-regauging, and makes the net field highly nonconservative. Note that again it was accomplished by a change in the magnetostatic scalar potential, which was reset to zero by the de-energizing coil during the back-drag portion of an otherwise conservative cycle. The Kawai engine therefore uses A-regauging and nonconservative fields in order to legitimately achieve overunity operation.
Because of the numerous A-regaugings and back drag elimination, this engine definitely can provide a COP>1.0. Placed in an electric vehicle with necessary switching circuitry and ancillary equipment, a properly designed Kawai engine and its derivatives should be capable of starting from a single ordinary battery, then powering the vehicle agilely, powering the accessories, and recharging its own battery -- all three simultaneously. And in so doing, it complies with all the laws of physics and thermodynamics.

Closed Loop (Self-Powering) Operation

Both the Kawai and Takahashi engines require input power, at least in the configurations shown to date. However, both engines are technically capable of overunity -- e.g., in his patent Kawai quotes performance measurements indicating 318% efficiency. Obviously, such a system can be close-looped by simply hooking it to a generator, and using positive feedback of a portion of the generator output to run the engine while using the remainder of the output to power a load.
The Johnson engine is inherently already self-powering, since it requires no external power input in the conventional fashion. One accents, of course, that in any such self-powered engine, there is indeed a steady input of power from the vacuum, in the violent virtual photon exchange with the particles and atoms comprising the magnets. A magnet simply acts as a gate in that energy exchange, as indeed does the bipolarity of an electrical power source.


Presently the three inventors mentioned have developed prototype engines which (1) produce COP>1.0, and (2) apply a multivalued potential, pseudo-multivalued potential, or A-regauging, or both. The Johnson engine is already self-powering. Both the Takahashi and Kawai engines are readily convertible to self-powering embodiments.
It would appear that these engines should now move into full development for introduction upon the world market.[11] Together with the Patterson cell,[12] we believe that these engines will usher in a new age of cheap clean energy for everyone.

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