Sunday, February 24, 2013

Experiment 10.8

In this experiment which is a virtual repeat of 10.4, we are analyzing the state of the system at 7 milli-second intervals, looking for the instantaneous current, voltage, torque, power and energy values.

Below are the thin slices of the experiment video and their corresponding current and therefore torque graphs.

Segment 1 / Expt 10.8

Segment 2 /Expt 10.8

Segment 3/Expt 10.8
1. The current graph of the wheel subassembly with the black tape is represented by the orange graph and the corresponding position of its assymetric weight (i.e. the black motor powering the wheel itself) is represented by the blue square. For convenience, I have only plotted the position of the black motor when its only in 3 orientations - up, horizontal or down. 

So take the graph for segment 1 of the video for instance. You will observe that at time index 0.4, there is a blue square up at the top. That means at time index 0.4, the black motor that drives the wheel with the black tape was pointing upward. You will also note that time index 0.4, the orange curve reads ~0.25 Amperes. That means at the time the subassembly motor was pulling 025 Amperes from the power supply.

You will also note that at the same time index, the other wheel subassembly (the one with the redtape) is also  in roughly the same position. You can tell this from the segment 1 graph, because at time index 0.4, the green triangle representing the position of the redtaped wheel subassembly is at the top, and the yellow line representing its current consumption is around 0.4 Amperes.

When the blue square and/or the green triangle are in the bottom position (on the X-axis), it means the corresponding assymetric weight of that subassembly is pointing downward.  When the are in the middle, they are pointing horizontally.

2. Further, in the graph of segment three, you see brown dots at the top of the graph, that indicates that at those time periods, the entire frame was experiencing pivoting or lifting about one of its edges.

In this fashion we are able to understand the inner dynamics of the behavior exhibited by the machine.

Noteworthy Trends:

A) Of the many very interesting things shown by the graphs, perhaps the most interesting is that during segment 3, it seems the wheel subassemblies experience gravitation opposite to what the previous segments experience.

We can deduce this because we can see from the segment 1 and segment 2 graphs that the subassembly motors draw the most current when they are lifting the assymetric weight of the black motors driving the wheels (we'll call them wheel-motors from now on) against gravity, and ponting them up. Correspondingly, it seems that the subassembly motors draw little or no current, when that assymetric weight of the wheel-motors falls in gravity from the top to the bottom, aiding the rotation of the subassembly.

You will note, however, that in the graph for Segment 3, the situation is reversed! The subassemblies draw little or no current when the wheel-motors are being lifted to the top. Further, when the subassembly is falling, the subassembly motors seems to need a lot of current to make the wheel-motors 'fall'.

Could it be that in the active phase, 'up' is 'down' and 'down' is 'up' from the perspective of the spinning wheels?

B) You will note that in the beginning of Segment 2, when the power is switched on, the wheels fight against each other (both drawing high current) till they find a way to orient their spins away from each other. Thereon, they are happy to maintain a constant rotation and draw low currents, keeping their spins opposed to each other, minimizing the net spin exhibited by the machine as a whole. (Following the path of least action it seems - it would rather the wheel- subassemblies spin internal to the machine than the entire machine roll around.)  This seems to be a property of the spin, as physically there is no reason they couldn't rotate in phase. Segment 1 in fact shows very ably that we can physically rotate them in phase when there is no significant spin momentum.

C) During Segment 3, the rules are changed again! The wheels are no longer content to be pointing in opposite directions. Now they want to be at 90 degrees to each other!

And you will notice that the most 'lift' is obtained when they are holding that 90 degree configuration for longer - and the corresponding current graphs keep at high values (indicating high torque and high power consumption).

D) Finally, you will also note that in Segment 1, the currents average no more than 0.4 Amperes while  in Segment 2, the current drawn has gone up to about 1-2 Amperes, only because we have added a single additional parameter - spin of the wheels.

Further, by the time we get to Segment 3, the currents drawn by the wheel subassemblies have spiked to 5 Amperes simply because we chose to rotate the cage as well.

Saturday, February 2, 2013

Experiment 10.4

Let us start by asking a few questions about experiment 10.3. 

Question A) When the two black motors driving the spinning of the wheels are both pointing in the same direction (i.e. up or down or to the left or right etc), the spin momentum of the two wheels 'line up' i.e. they reinforce each other so that the net spin of the entire unit is twice the spin momentum of a single wheel.

When the two black motors are pointing in opposite direction, (i.e., one points up and another points down or one points right and the other point left etc), then the net spin of the entire unit is zero (or nearly so).

So the question is:During the crucial phase of the experiment (i.e. when all the motors are active), why do the motors line up i.e. reinforce each others spin, giving a large net spin, only when they are horizontal?

Further the spins always arrange themselves so they cancel each other (point in opposite directions) when the motors are vertical?

We see that it is possible for them to choose any number of other configurations, for example:

1) They could always line up and reinforce each other.

2) They could always orient themselves so they cancel each other out.

3) They could always orient themselves so they are at 90 degrees to each other.

4) They could always orient themselves so they are 1 degree off from each other.

5) They could always orient themselves so they are 2 degrees off from each other.

etc etc

You get the point.

This question drove me crazy for 2-3 weeks. I repeated the experiment several times to cofirm that this is a pattern. 

The answer to this question must have to do with gravity. The black motors driving the wheels apply a torque upon the spinning wheels because they try to fall down vertically, in the earth's gravitational field (like everthing else on earth).  The horizontal position gives the most gravitational torque upon the spinning wheels due to the fact that it has the longest torque arm (and torque = force X torque arm). Thus it seems that gyroscopes seek out the maximum torque position, rather than try to avoid torque. 
Thats interesting!!! You might think that the arrangement might try to minimize its interactions however it seems it is maximizing its interactions with external forces. Its like the machine is actively seeking out the maximum force configuration!!!

Question B) The next question is a little more subtle. To understand it easily, I would suggest that we first review one of Eric Laithwaite's experiments - the experiment on the model Eiffel tower. You can observe this experiment by going to this website and downloading and watching experiment 4 in the list.

The relevant portion of the experiment comes somewhat towards the end of the video, from time index 7 mins 10 seconds onwards.

Now, if you've watched the professor's experiment, you know that on the Eiffel tower for example that when a precessing gyro is pushed in the direction of its precession, it rises. Whereas, if its pushed in the opposite direction, it gives way.

In our experiment 10.3 too we see that the entire frame lifts about an edge when the Y-motor pushes along the direction of the precession and the spins line up in the H-plane.

That tallies.

The same Laithwaite's experiment also showed that trying to resist the precession of the gyro caused the gyros to give way.

So we'd expect that engaging the main motor in the  OPPOSITE direction to the one in 10.3 would cause the gyros to give up lifting when they are in the horizontal plane.

The interesting question might be:
Will the spins then orient so they cancel and the whole cage speed up? or will they continue to line up, just not lift, simply speed up the cage rotation and/or speed up/relieve the load on the sub-assembly rotation?)

If the spins orient so they cancel in the horizontal plane, then might we expect that the spins will line up when they are vertical? In which case, since there can be no precession when the imposed rotation is in the same plane as the spin of the wheels, we might expect a continuous speeding up fo the entire cage in a flash??

On the other hand, if the spins still line up in the H-plane, then we might expect that the wheels exprience a tilt up both in the clockwise and cc directions about the horizontal axis, which might  lead to a lift???

So to test this out, I performed another experiment, we can call it  experiment 10.4.  This experiment is essentially identical to experiment 10.3 except that in this experiment, the main motor that is on top rotates in the OPPOSITE direction to experiment 10.3 

(well, the other difference is that I increased the rate of rotation of the subassemblies to 1.5 seconds per revolution, instead of 3 seconds per revolution. I also synchronized the time period of the sinusoidal torque pulses applied on the cage to a 1.5 second waves. The experiment is therefore twice as fast as experiment 1.3, so it also lasts only half as long.)

Here is the sequence of events for experiment 10.4:

Time Index 8 seconds: The wheel motors are started

Time Index 58 seconds: The subassembly motors are started

Time Index 1 minute 50 seconds: The main motor is started

The results were also interesting, and different from the two scenarios I was wondering about. The wheels still behaved the same as 10.3, except instead of lifting the machine about an edge on the far side, they lifted the machine about an edge on the near side to the motors. A simple reversal, akin to the behavior of the gyro in Professor Laithwaite's experiment above.

I realized then that I had not understood the professors experiment properly and that if I had, I could have foreseen this third alternative.

Oh well! We live and learn.

I do have however another question now, one I have yet to test.

Question C) So far, we've synchronized the rotation rate of the subassemblies, and the time period of the sinusoidal torque applied to the cage. That is, in expt 10.3, both the subassemblies rotated at 1 revolution per 3 seconds as well, the time period of the sinusoidal torque applied on the cage had a time period of 3 seconds (remember that we applied 14 strokes of 3 seconds each).

In expt 10.4, we upped the speed of the subassemblies to 1 revolution for every 1.5 seconds and also adjusted the time period of the sinusoidal torque applied on the cage to 1.5 seconds.

What would happen if we changed that ratio? What would happen if for example, we rotated the subassemblies at 1 revolution per 3 seconds, but the cage itself was pushed around with a sinusoidal torque of time period 1.5 seconds? Further what would happen if we made that sinusoidal torque so that we switched its direction from clockwise to counterclockwise every 1.5 seconds?

My analysis says that this might force the spinning wheels to either switch the lifting from the far edge to the near edge as the direction of the sinusoidal torque changes. And if we synchronize this with the overal rotation rate of the cage, can we not make it so that the wheels always the machine about one side of the machine? So that way, instead of the whole machine see-sawing back and forth, would it not experience one consistent lift about one side of the machine???

I feel that my expectation might again be based on some flaw somewhere in my logic. That last experiment has made me more cautious. However, I can see past this proposition right now, so I am going to try that out next.

Note: You will notice that inspite of the addition of the capacitors, the two subassemblies do infact still defy the command to rotate at 1.5 seconds per revolution when their motors are initially engaged. This seems to be because they are encountering a very large load, much large than even the torque of the entire machine about its bottom edge. B.L. and I are currently trying to calculate the load coming on the wheels quantitatively. I will present the results of that as well, soon. There seems to be more than meets the eye there, however you will note that once the subassemblies start rotating at 1.5 seconds per revolution, they do not have any problem sustaining that rotation, unlike in 10.3, where they repeatedly stalled even during the experiment. It seems the start up load is amazingly high, atleast a 100 times what we expected. Curious!!