Any boy standing atop a cliff feels an irresistible urge to see how far he can throw a rock from it. When I lived in New Mexico, a land richly endowed with cliffs, I indulged that urge myself many times.
When I threw those rocks, I wondered about just what angle I should be throwing them at to maximize the distance they’d go. If you’re on a flat plane, the launch angle that will maximize distance is 45 degrees (neglecting air resistance). At a steeper angle, the rock goes higher, but it lands closer to you. At a shallower angle, it simply hits the ground sooner.
“What is that optimum angle when you’re throwing a rock from a cliff?” I wondered. I assumed the angle only depended upon how high the cliff is. I set up the problem with the appropriate equations, and tried to solve for the optimum angle in terms of the cliff height. I found an equation all right, but I was confused as to what it meant. But in those days I was in charge of the high school computer lab, so I programmed three Apples to chew over the equation and spit out optimum launch angles for assorted height values, and left them running all night.
The next morning I pored over the data and was surprised to find that the optimum angle depended upon more variables than just the height. As noted, on a flat plain you throw your rock at a 45-degree angle to maximize the distance it will travel downrange. To calculate how far that distance is, you need to know how fast the rock will be going when it leaves your hand and the local value of g (g being the acceleration due to gravity). Plug those values into the equations with a launch angle equal to 45 degrees and out pops the distance. The thing to note is that throwing the rock at 45 degrees is going to maximize the distance and it doesn’t matter how fast you throw the rock, nor whether you throw it on the Moon, Mars, or Mesklin.
But when throwing a rock off a cliff, that distance-maximizing angle not only depends upon how high the cliff is, but now also depends upon how fast you throw it and what the local value of g is. Now it does matter what planet you’re on!
By the time I went to teach my classes that day, I fully understood what the equation I’d found had been trying to tell me. More importantly, I learned the value of seeking out all of the interlocked variables that might be relevant.
Learning that lesson came in handy ten years later when I was trying to figure out the Marinov Motor. I discussed my work on that thing back in a two-part Alternate View, “The Marinov Motor & Me” which appeared in the February 1999 and April 1999 issues respectively. Around the time those articles saw print I also began working for Infinite Energy magazine, continuing my study of the motor and making my mark in the world of weird science.
Weird (or alternate) science has several “holy grails,” among them gravity control, limitless free energy, a faster-than-light drive, and the “unidirectional” or “reactionless” drive. My Marinov Motor research had led me to the conclusion that, though a unidirectional space drive was out of my reach, maybe a unidirectional motor was not. That is to say, if the net push of the stator on the rotor made the shaft rotate, say, counter-clockwise, and the net push of the rotor on the stator was also in the CCW direction, then I should be able to hang the thing from the ceiling on a monofilament line and have the whole unit accelerate in the CCW sense with no mechanical part of it rotating in the other direction.
So why did I think I could do this? I came to believe that the Marinov Motor, and my own version called “The Warlock’s Wheel,” was just a variant of several other odd motors already known to work. The first is the simplest of the unipolar motors, the one-piece Faraday motor. Take a conductive cylindrical rod magnet, arrange things so that it can freely rotate on its N-S axis, put one brush in contact with the outside surface and another in contact near the axis, and it will rotate. The question is: “What is the magnet pushing on to make it rotate?” Some think the magnet pushes on the external circuit. Most believe the magnet reacts with the current flowing through its interior, essentially pushing on itself. Weird, huh?
Another odd motor is the Feynman carousel, discussed in section 17-4 and at the end of section 27-11 of volume II of The Feynman Lectures on Physics. Mixing straight quotes from section 17-4 in with my own descriptive modifications, consider a thin plastic disc supported on a concentric shaft with excellent bearings, able to rotate freely. On the disc is a superconducting coil of wire in the form of a short solenoid concentric with the axis of rotation, in which current is flowing. Near the edge of the disc, spaced uniformly about its circumference, are a number of small metal spheres insulated from each other and from the solenoid by the material of the disc. Each sphere is given an identical electrostatic charge. Everything is stationary; the disc is at rest.
Initially, the angular momentum of this motor is zero, right?
Allow the temperature of the solenoid to rise above the critical point until it is no longer a superconductor. While the current was flowing, there was a magnetic flux through the solenoid more or less parallel to the axis of the disc. Now with the current flow interrupted, the flux must go to zero, and an electric field is induced which will circulate around in circles centered on the axis. This field exerts a force on the charged spheres, tangential to the perimeter of the disk, and all in the same sense. This results in a net torque on the disk and it starts rotating. Since no one pushed the carousel to set it spinning, we conclude that angular momentum now apparent was stored in the magnetic field.
That’s pretty cool if you think about it. Suppose you started current flowing in the solenoid somewhere else, and only later inserted it into the plastic disc with the charged spheres. Angular momentum stored in a magnetic field is just as portable and real as it is in a spinning gyroscope.
The Warlock’s Wheel is also simple. I describe it better and with a diagram in my April 1999 Alternate View, but I’ll briefly describe it here. Take two very strong rectangular cross-section neodymium-iron-boron (NIB) rod magnets and put them side-by-side so that the north pole of one adjoins with the south pole of the other, top and bottom. (If you’re using the right magnets, they’ll do this all by themselves once you bring them near each other, so watch out!) Put this magnet pair on an axle oriented vertically so that it’s free to rotate on its long axis. Around the pair suspend a copper ring, inner diameter twice the width of the magnet pair, outer diameter half an inch more, coaxial with the magnets and centered horizontally between the top and bottom. The magnets and the ring are free to rotate independently of each other.
To demonstrate the peculiarity of the motor, start with the unit at rest. The brush contact points on the left and right sides of the exterior ring rim are collinear with the axis and the center points of the magnets. When current is introduced through the brushes, it enters on one side of the ring, splits in two, and rejoins and exits on the other side. The magnet pair will begin to rotate in one direction, and the ring will begin rotating in the opposite sense. Now reset the motor to the initial state, but make the brushes touch the ring on the interior rim. Turn on the current and both the magnet pair and the ring will begin to rotate in the same direction.
The first time I did this experiment I was so shocked I just went outside and cut the grass. At the time I wrote my two-part article, I didn’t understand how the motor worked, but I figured it out later. I concluded my motor was much like Feynman’s carousel, only with strong permanent magnets and switchable electric currents.
I became convinced that a unidirectional motor could be built, but what I didn’t know was whether I could build one. I did fashion a crude version of such a motor out of NIB magnets and wire wrapped on a six-ounce disposable coffee cup and it did seem to exhibit the expected unidirectional behavior. But it was so crude it was hardly ready for a formal presentation and its performance was erratic enough that, had someone else built it, even I would not have found it a convincing demonstration of a unidirectional motor. (I described a souped-up version of this motor in my story “Nova Terra,” which appeared in the January/February 2004 Analog.)
How to improve it? Since my first attempt had “sorta worked,” this told me two things. The first was that I was on the right track; the second, that there must be many ways to make a model that “sorta works.” I didn’t want to build a dozen more prototypes with no certainty that the next one would work any better than the previous one. I did a great deal of hard thinking about how to make the next version, but I kept finding myself up against that interlocking variables problem.
For instance, with my first model, I found it desirable to replace the ring with a complex winding consisting of ten turns of copper wire. You might think that if ten turns works a little, maybe twenty will do twice as well. But it doesn’t work that way. I knew before I built the first one that the fewer windings I could get by with, the better. But when I tried to figure out “What is the ideal number of windings?” I discovered that the question had no simple answer. To answer it, I needed to know how strong the magnets were, what all of the dimensions of the motor were going to be, what the wire diameter would be, how much current was going to flow, what the drag of the brushes on the commutator would be . . . It was the rock thrown from a cliff problem all over again, only worse. A hopeless morass of interlocking variables, and this time I lacked the computer skills to even begin to write a simulation to help me out.
When I left Infinite Energy magazine I stopped working on the Warlock’s Wheel, but I’m starting to again. I don’t expect to make anything practical, although I would like to get a journal article out of the research. Perhaps something suitable for The Physics Teacher or even the American Journal of Physics. But mostly I’m going to work on it because my son Joshua has begun to show an interest in physics, engineering, and electronics. If you want your child to behave a certain way, at the very least you must model that behavior yourself. I want my son to grow up with memories of his dad doing interesting experiments in a basement lab, and hopefully of helping me, too.
That’s a variable I can control.
