Wednesday, July 27, 2011

In Search of a Saturation Speed

Well, a lot has changed since my last post - I found a mistake, I lost my conviction, I had a conversation, I performed more experiments and I found my conviction.

I found a mistake:
The last post I made, (July 17) has a major mistake in it. It happened because I myself did not realize it until after I made the post that I had compiled a table that compared the results of an experiment involving 10 second cycles of torques (for the 0 RPM case) with results of an experiment involving 8 second cycles of torques. When I fixed the mistake and coded the proper videos to get the right data, the chart looked more like this.

The results are much less impressive and I wasn't sure some of this wasn't just a one-off difference and that ultimately there might be nothing different at all. One good result of this mistake is that, I've decided to record more basic data on the online record, not just the aggregated data. I've also decided many more multiples of the same experiment in order to provide crosschecks for data.

One consequence of these results shown by the new prototype was what...

I lost my coviction:
I was pursuing with conviction, the idea that there will be an assymmetry between the clock-wise and the counter-clockwise rotations due the same quantity of torque. Those last three posts showed that such was not the case. At 4900 RPM, the data is showing that there is no assymmetry. After the transient crest, there is no assymetry.

When I had the conversation, I had lost my conviction that this problem was soluble in any non-trivial manner. The symmetrical movement of the wheels laid bare the truth. There was only a fast diminishing amount of lift in the system. When free, the system seemed to be within Newtonian parameters. I thought that perhaps I had seen things in the wrong way. That perhaps a gyroscopic system cannot dissipate any energy afteral.

I had a conversation:

I remembered then that Sandy Kidd had warned me that there was nothing to be had at such high speeds. He was the one who had originally said that spinning wheels can move laterally if rotated about a center located about an axis perpendicular to the spin axis of the wheel. I hadn't really paid attention, but when I built the earlier prototype, there it was. And it remained a problem until I solved it the only way possible - drilling a through-hole and putting a bolt to permanently secure the spinning wheel to the axle on which it was mounted.

So I had an email conversation - with Sandy Kidd. He's a wise old man. He's had his own tussle with this problem and he's still at it. He's been public with his own information already a long time and has personally tried to steer me away from experimenting at high wheel speeds. Something Sandy said in email stuck with me - He said "Consider a typical gyroscope system of the twin opposed gyroscope configuration being rotated at a fixed rotation speed with NO gyroscope rotation. At this point, the system is delivering the maximum angular momentum it can.

By strategically fitting strain gauges to the system and coupling to an oscilloscope or modern equivalent it will be found that angular momentum (or centrifugal force for anyone who is happier with that) diminishes as the gyroscope rotation speed is increased. This loss of angular momentum or centrifugal force begins as soon as the gyroscope starts to rotate and at a point farther up the gyroscope rotation speed range, diminishes to zero at a point I called the "Saturation Point".

No more system rotation speed or gyroscopic rotation speed will affect the system other than increase the gyroscope's upward and inward acceleration, hence saturation (and broken machines)"

I found my conviction:
I think I have a way to test this proposition. If this is infact the way that gyroscopic systems behave, then would it not be true that if I take my current prototype, at run the same experiment (say, 8 seconds per cycle, 4 ampere maximum, 10 cycles of sinusoidal torque) at different fixed speeds of the wheels.I should see that the number of rotations of the system might show interesting variations if there is in fact a phenomenon to study. I'm half way through this, at the moment at it seems a good time to summarize events and release the fresh data.

Consider the following spreadsheet image containing the raw data from 19 experiments over the last few days. I have done multiples of 3 experiments for every unique speed of the wheels to provide verifiability of the results:

Now, it seems from this data that:
1. When the arms are in (i.e., when the wheels are positioned with the motors pointing inwards at the beginning of the experiments and the system therefore having the least moment of inertia in this configuration), the number of rotations received is higher, while when the arms are out, the number of revolutions received for the same torque is lower. This is happening for the same reason that a dancer who is spinning speeds up when she pulls her arms in and slows down when she moves her arms out.

What is not clear however, is why it is that often and especially in the CCW (counterclockwise) direction, we are receiving even fewer rotations than the maximum moment of inertia condition would allow - Somehow the gyroscopes seem to be soaking up the torque, that would be the only way that would be possible. However it seems to be happening only for that particular direction of rotation too...!!

2. When the wheels are NOT spinning, the cage holding the wheels has a significantly larger number of rotations, (almost twice as many) for the first cycle of 4 Ampere worth of torque! You can see from the experimental data that I performed the 0 RPM experiment 5 times. Each time, in the end we see that the number of CW rotations is equal to the number of CCW rotations, thereby indicating to us that the transients have been ironed out of the system. However, with the wheels spinning that is not always the case. In fact the data shows that the lower the wheel speed, the more likely it is that there will be assymmetry in the CCW and CW rotations. So far.

By dropping wheel speed from 4900 RPM to 4500 RPM to 4000 RPM to 3500 RPM to 3000 RPM, we are seeing increasing trend toward assymmetry in the clockwise versus counterclockwise rotations of the cage!

3. Most intriguingly, there seems to be an increase in the 'flightiness' of the machine at lower speeds, especially for on direction of the rotation of the cage and this whatever you want to call it, jumpiness, flightiness - a tendency of the machine to seem to perform a little flightlike manoevor that can look like a mini jump- this is what is responsible for lower rotations for that direction of rotation of the cage! Could it be that it will keep increasing as we keep lowering speed?

4. In addition, even though we dropped the wheel speed drastically from ~5000 RPM to 3000 RPM, we do not see any big change in the number of rotations say, in the number of rotations of the cage during the first cycle of its 4 Ampere phase (stays at around 3.5-4 rotations of the cage during those 8 seconds)! In comparison, the zero RPM condition shows us that during that 1st cycle @ 4 Amperesthe number of rotations go up to 7-8 rotations. Not only that, we have performed dozens of experiments with wheels speeds gradually decreasing from 4900 to 3000 RPM and we do not see a trend of increasing rotations ...yet. 5000 to 3000 RPM is a dramatic drop, so its not clear at what speed of the wheels, the system will start reaching the 7-8 rotations.

In summary, it might yet be that there exists some saturation speed for the system and it might yet be that that speed lies somewhere between 0 RPM and 3000 RPM. It would be that point where those cycles would creep up from 4 to reach 7 or 8.

Thats where we're going right now......! To the Saturation Speed!

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