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!

Experiment 4.8:

These results confirm the trend of the previous experiments, as do other experiments I have conducted that are not posted on the blog. The bottom line is this: Once the transient factors vanish, the system displays symmetry in its counter clockwise (CCW) and clockwise (CW) rotations.

The interesting thing about the data, however is the consistently lower number of rotations we obtain for the case where the wheels are spinning(~3)  than for the case where the wheels are NOT spinning(4.5).

Experiment 4.4

These two experiments (4.3/4.4) show us that there is a small amount of transient torque in the system that dissipates over 40-50 seconds. The last cycles of torque produce roughly the same amount of rotation in both directions.

Something else that is also interesting and not yet fully explainable is that the same amount of torque produces less rotation of the system if the wheels are spinning, than if they are not. As can be seen from experiment 4.4's data, when the wheels were not spinning, an application of the sinusoidal torque caused 4.3-4.7 revolutions and with the wheels spinning, an application of the same sinusoidal torque caused only 2.6-3.2 revolutions.This parallels what the Inductive Effect experiments I conducted in Jan 2010 revealed.

Experiment 4.3:

Tensor Model of Impedances

So what's so special about a flywheel suspended inductively? The key is that if infact gyroscopes show inductive behavior that has certain implications in tensor mathematics. This mathematics might be used to understand how the machine may achieve flight analogous to how certain electrical circuits resonate EM waves at certain frequencies or transform voltages and currents up and down etc. In other words tensor mathematics can be used to analyze the machine even as we are still building it and help us in better designing it.

We must assess the nature of impedance (inductance and capacitance are the two kinds of impedance found in nature) in a mathematical way in relation to other physical entities. Tensors offer a way of understanding impedances that sets them naturally apart from other electrical parameters. As we move forward, I have quoted so extensively from Kron in his book Tensors For Circuits that I have found it expedient to italicize his words to keep my train of thought comprehensible to myself.

Wherever in this entry there is reference to voltage, the reader should be aware that it represents also velocity in the analysis of purely mechanical or electro-mechanical systems and current to angular acceleration. See my entry on the analogy between mechanical and electrical behavioral parameters.

Further, as my entry on Grabriel Kron makes it clear, he himself saw all his analysis as being fully applicable to mechanical machines, indeed all and any machine. Thus, although we are flying through Kron's tensor model of electrical rotating machinery, we are also able to trace in the same model, information regarding our own machine. The flywheels suspended the way they are in the new prototype are the live inductors with a pulsating torque going through them at a certain frequency and the rest of the machine that is spinning under the influence of the Y-axis torque is the capacitor being charged up and their combined impedance is related to the velocity and the acceleration of the overal system as velocity = Z*acceleration (analogously to voltage, e = Z*i in the electrical scenario), where the impedance is a term with time units in the mechanical scenario. A single closed network in the electrical model can be envisioned as the mechanically invariant closed system of components capable of expending energy through torque or other methods in a different kind of machine.

Impedances are mathematically reprensentable as tensors of valence 2. The tensor of valence 2 is a collection of 2-way matrices describing a physical entity. A tensor of valence 1 like voltage e or of current i is called a vector.

Impedances thus form their own class of devices of valence 2 whose tensor laws of transformation require two transformation matrices C1 and C2.

Energy is a tensor of valence 0, i.e. a scalar. A vector of valence 1 is a vector such as a voltage or current and they require only one transformation matrix C, power or energy requires no C's. Because of this "chemical" property of a tensor of attracting a different number of C's the expression "tensor of valence n" originated.

Impedances, being of valence 2, would have transformation tensors with 2 C's, C= C1*C2.

Now, if the variables describing a specific impedance have been changed from i to i' by C1, then from i' to i" by C2 , then again from i" to i"' by C3., the successive transformations may be performed in one step with the aid of one transformation tensor C= C1. C2.C3... This important property of C is called a "group property". (Kron, Tensors for circuits, "WHy tensors")

With the help of a group transformation tensor C, one may model an inductor's behavior as follows.

The fact that power, P is a valence 0 tensor means that it does not undergo transformation and doesn't need a C to transform it from the reference frame of one machine to another. Kron uses this property of tensors to first extract information about the behavior of voltage in such a system.


The law of transformation of the voltage vector may be found from the physical fact that in going from one reference frame to another the instantaneous power input e*i (a linear form) remains unchanged or "invariant". That is P= P' or e*i = e'*i'. This relation is the physical link that connects all networks together (for any given machine)
Now let the current change from i to i' by i = C*i'
Substituting, e*C*i' = e'*i'
Cancelling i' e*C = e'
Hence e' = Ct*e
and e = Ct(inverse)*e'
It should be noted that though both e and i are vectors, they are transformed to a new reference frame in a different manner. But both being tensors for valence 1, they require C once only.

Kron then follows this up with a brilliant analysis of the impedance tensor itself.

Tensor analysis requires that if the equation of a system in one reference frame is e= Z*i, it should have the same form in every other frame. This property will give the law of transformation of Z. In the old reference frame let e = Z*i
Express i and e along the new reference frame. That is, replace i by C*i' and e by Ct(inverse)*e'.
Ct(inverse)*e' = Z*C*i'
Multiplying both sides by Ct
e' = Ct*Z*C*i'
If the following definition is introduced as the law of transformation of Z
Ct*Z*C= Z'
then the equation in the new reference frame becomes e' = Z'*i'
The equation of the new system is of the same form s that of the old system...


In summary, Kron proved that, if there is at all an impedance in the system, then an analysis of the system at any and all levels must involve an analysis of the impedance, with the invariant form of the law of impedance, e = Z*i (where e is voltage or velocity depending on the machine and similarly, i is current or angular acceleration depending on the machine).

We can see darkly from this statement, for example the answer to the questions: Why could this prototype fly? or Why does a gyroscope precess?

The answer, Kron's discoveries seem to say, is that tensor theory mandates that e = z*i is a permanent invariant law in any system involving an inductor or a capacitor (sources of impedance). So then we may further propose that
a) the purely capacitive impedance condition is addressed in traditional newtonian rotational dynamics,
b) the purely inductive impedance condition is met by gyroscopes. (This was something Eric Laithwaite partly recognized when he stated that the gyroscopes are like inductors. He also said that gyroscopes do not do any work. They rotate without being able to accomplish any energy transfer on a meaning level. It is clearer now that, that is because the system is purely inductive without any significant capacitance. The gyro rotates in a set of gimbals that isolate the flywheel's spin so that there are no levers connecting it to the external frame.)

c) the LC resonance condition is what is being targeted in the new prototype's tests.

Kron also gives certain guidelines for machine analysis. For example when coils, beams, wheels etc are connected into an engineering structure, the constrained reference axes are ignored.

Using his methods and his modeling techniques, I will attempt an analysis of the prototype in the next few entries. One of Kron's models is a good starting point for that analysis and is given below.

Experiment Update: Repairs complete. Testing begins tomorrow.