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TOMI, et al       by Evan Callicoat

I've been doing some research into PMMs based on the TOMI and similar theories, and I ran across your page. I wanted to share some information with you regarding my design, simulation, construction and experimentation with a linear PMM configuration that is incredibly simple to repeat, as well as an explanation regarding the principle involved, as I get the distinct impression that much of the material on your site (and many others) is shaky on a few points, especially concerning the non-linear flux paths of the TOMI track, triangle gate and Johnson motor.

To begin with, I think it's well known (or at least somewhat obvious) that the key to a PMM -- just as in the common electromagnetic motor (EMM) -- lies in maintaining a field imbalance between a statically mounted and dynamically mounted source of magnetic flux, such as to cause the dynamic source to move in a specified manner. In the case of the EMM, the imbalance is achieved by electromechanical commutation or alternation (of current, such as in an AC induction motor), where the properties of the mechanics and electricity are used to this effect. Our goal in a PMM is to maintain this imbalance without resorting to electricity or its properties; now proceeds that discussion.

If you take two bar magnets of equal size and strength, then you will observe they have straightforward, obvious properties. When the like polar ends are aligned opposite each other, they repel directly. When the unlike polar ends are aligned opposite, they attract directly. Furthermore, if the polar end of one magnet is directed perpendicularly to the side of the other magnet, it will experience a torque about that end, attempting to align it parallel with the other magnet. The direction of the torque depends on the polar configuration of each magnet. This torque at right angles is one half of a very important aspect to observe. The other half is that the polar end also experiences a force vector both towards the magnet side, and along it, the direction again depending on the polar configuration of each magnet. The vector component along the magnet and the torque about the end point are what we're interested in. To be complete, though, you will observe one further, obvious property; if the magnets are placed parallel but askew, such that the ends do not align, yet are still within each others' fields, each will experience a force vector both towards the other and along it, the latter opposite for each magnet to the other, such that the overall effect is to align their ends in parallel.

Now, the parallel arrangements are stable in that they do not attempt to alter basic field alignments, but the perpendicular arrangement is unstable because of the torque, which does. This torque is summarized in the magnetic component of the Lorentz Force Law, F = qv x B, where F, v and B are vectors, q is a 'point charge' (a source of an electric field) and v is the velocity of q. The magnitude of the force is given by F = qvB sin t, where t is the angle (< 180 degrees) between v and B (the motion of the charge and the magnetic field). The magnetic field is considered where N and S are differentiated by + and - values for B. Furthermore, magnetic fields are also considered as varying densities of moving charges (dipole moments), constituting the 'lines of force' (flux). The part of this that we're interested in here is the corollary of the magnitude equation, which is that the force is 0 when the angle between v and B is 0 (or 180), and highest when the angle is 90. Thus, the perpendicular arrangement experiences the highest torque; the maximum instability.

The torque itself is undesirable, but the edgewise -- along the edge -- component of the force vector the 90 degree arrangement provides is the key to directed motion, as there is no material obstruction in its path, whereas the edge-on component of the force vector -- towards the edge -- will be stopped by the edge of the magnet when reached. Counteracting the torque effect can be done mechanically, but it can also be done magnetically while also increasing the force vector edgewise, and reducing it edge-on. This is accomplished by placing another bar magnet parallel to the edge one, opposite the perpendicular magnet, placing it between the two. The polarity of this third magnet is opposite the first one to which it is parallel -- together, these form a track, with the central magnet as a vehicle on that track. Both poles of the vehicle now experience equal, but opposite torques from the track magnets; they also experience equal but opposite forces edge-on towards each track magnet. Interestingly enough, however, the edgewise force is the same along each edge! This is due to the fact that the relationship of vehicle pole to edge pole direction remains the same on each side. Thus, inbetween the track magnets, the vehicle experiences constant thrust in a specific direction.

However, the situation becomes more complex at the ends of the magnet along which edge the other is moving. Without diving into too much complexity, the basic problem is that when approaching the track, the vehicle is interacting with the track poles at an angle far closer to 0 than to 90, during which time it is heavily repelled. Further, at the opposite end, after experiencing the thrust between the track, it passes from 90 towards 180, during which time it is heavily attracted back towards the track, countering the previous thrust.

Obviously, if one could build very long track magnets, then the vehicle would accelerate from just inside one end to just inside the other. As this is impractical or impossible, one can instead simply divide the track magnets into rectangular sections, magnetized across their width, connected directly together in a stack, as long as the track requires. That leaves the 'end' problem, which is not a problem, per se, for uses such as trains or railguns or other such devices which limit their operation to the inner portion of a rail-like path. It is, however, a problem for motors and other devices which 'close the loop' on a track. That's the goal of a PMM: a rotary configuration, which I will explain more about in a moment.

The preceeding has been a detailed summary of the steps that most inventors and theorists have taken in pursuing PMMs, but around this point is where most diverge and (I feel) have great difficulty. In the case of the Johnson motor, TOMI track and the triangle gate, including the many derivatives, there's this constant theme of spacers and unmagnetized flux paths in an attempt to make the flux response non-linear, in hopes (I presume) of imbalancing the system mechanically. I believe it's fairly obvious that the 90 degree field angle is the reason behind any imbalance, and thus the core of maintaining imbalance for motion. Considering such devices, I think they get closer to the core by making the flux path non-linear than by not, but I think they approach it from the wrong idea in the first place, even though all of them must involve some aspect of maintaining a field angle 45 > x > 135 to produce any results.

Now, I'm not attempting to discount any good ideas, designs or attempts on the part of anyone working on this unique challenge. I myself have learned a lot from the ideas and designs of others, much of which contributed to my discerning the principles involved. Instead, I commend all of them! Bravo for at least having the interest and guts to spend precious moments (sometimes an awful lot of them!) of your life on an endeavour that respectable, intelligent men say can't be done because you can see how it ought to work, in one way or another. I hope that the preceding serves as a firm foundation for a truly scientific theory of magnetic instability, as my simple-yet-obvious explanation has shown various linear applications that literally anyone can build with a handful of magnets and simple frameworks. On to the PMM...

Let me start by saying what 99% of everyone else out there says at this point: I don't have a working device which I can sell you, show you or tell you how to build. But. Let me also say that I do know how to make one work, and why most designs that ought to do not, as well as why most linear designs do not work in rotary configurations. Here follows that discussion.

Given the track described above, the first step in a rotary configuration would be, of course, to curve it. Using rectangular stator poles ('track magnets' in a PMM; hereafter 'stator poles', which comprise the 'stator'), we end up with wedge-shaped spaces on the outside of the curve, which is a flux loss and loss of efficiency in coupling. Using the same rectangles for the inner stator and the rotor ('vehicle'), we also have spaces there, another loss. Most importantly, however, it doesn't work. The most obvious difference between the linear and rotary configurations are the gaps and segmented-curve surfaces. At this point, we can insert steel wedges, curve the magnets (pineapple wedge shapes), or both, or various other elaborations. Still, it doesn't work right.

What's going on here? The linear configuration is obvious and straightforward. Are there 'end points' in our rotary setup? Not with wedges of steel or magnets. The flux path is constant; the magnetic edge 'smooth'. What else is different?

As you can see, the angle of field interaction is very, very important for continuous instability. The crucial difference between the two configurations in these examples (and why an electromagnetic coil works when our ring does not) is that the direction of magnetization is not curved. That's it. We've curved the magnets, but left their B vectors linear, then stuck them together, coupled by air or steel or simply edge-on, but their internal flux paths are not curved such that the fields remain in a 90 degree alignment. It is extremely common to produce wedge-shaped stator magnets which are magnetized along the vector normal to the curved surface; it is not common at all (if even done? I'm not entirely sure about what use this would be industrially) to magnetize wedges such that the vector curves along with the wedge shape. Perhaps custom magnets can be ordered in this way, with the right machinery, but it's a safe bet to say that few if any PMM designers have gone this route. Johnson is one of the few I know of to order custom magnets, and I'd be willing to bet that any success on his part is only due to getting the actuators magnetized along their curvature. Another possibility is to use a very thin rectangles and/or more trapezoidal shapes with standard magnetizations to construct the stators, such that the flux paths more closely approximate a curve.

Using standard rectangles for rotor and stator, and magnetic wedges for the gaps, my simulations show approximately a 60%/40% thrust/drag ratio, pretty consistently over all points, which, while being better than 50%/50% at all points, is still vastly inferior to what the linear configuration suggests, being 100%/0% within the edge-on field. My next goal is to model and simulate the suggestion I made above, using very thin magnets with a gentler curve, to see how much more closely the results match the linear configuration.

Lastly, I offer a suggestion (which I plan to construct and test) for how to build a continuous motor of the linear configuration. It is vastly inferior in many ways to the rotary configuration, if it can be achieved, but it still provides continuous motion, albeit with more wear on the parts.

First, construct a framework with two elevated portions, with axles in each. The axles are to be mounted parallel to each other, across the framework. Support on the axles two drums or grooved wheels, for a belt (or chain, etc). On the belt, mount the track magnets with gaps between them, such that when the belt goes around the wheels, the magnets can bend away from and back towards each other without any snapping or breakage. The separation reduces the efficiency of the thrust, but low tolerances will still be sufficient. Then, mount the actuator magnet ('vehicle') below -- and above, if desired -- the belt track. The track portion which is in the actuator's field will always act like the edge of a continuous magnet, and thus the track will continuously rotate.

This is for you and your site, Eric. I would like for you to post it so that others may read it and gain whatever they can from it, until and perhaps in lieu of my own investigations are complete and I have constructed a device to implement the principles I've clarified.

Illustrations:
The first two files are the flux line/density map of a short track and the impulse (force profile) for that track, left to right. The next two files are the flux density map (in greyscale) with much higher resolution of a very long track, and the FEMM file for this track. As you can easily see in the greyscale map, there is a constant, localized difference in flux density behind and in front of the center magnet, which illustrates the imbalance. Also notice that the track pole edges do not distort the fields passing through them -- therefore, this effect must occur at any point along the track and only changes at the ends.