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Author Topic: Three experiments with gyroscopes  (Read 1767 times)

ta0

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Re: Three experiments with gyroscopes
« Reply #30 on: October 01, 2019, 12:38:15 PM »

Looking forward to your experimental results, as always.

You could also try different surfaces: a rubber mat vs a glass table.
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #31 on: October 01, 2019, 03:13:14 PM »

This is the result with the teflon ball tip.

I premise that teflon is much more slippery than carbon steel;
this can be easily felt when the top with the teflon tip is spun because it slips sideways very easily, compared to the carbon steel ball tip.

One would think that the top with the teflon tip should spin for a much longer time, having so low friction, but this doesn't happen;
the reason is that teflon is a soft material, it flattens a bit at the contact point, so the contact point of the teflon ball is much larger than those of hard material balls like steel, ruby, ceramic, etc.   So, at parity of angular speed, the periphery of the contact point of the teflon tip goes with a much higher linear speed than that of the hard tips, which have a very little contact point. 
At higher speed there is more friction, because there is wear out, teflon wears out while the top spins.
But when it comes to traslational movements, the sliding linear speed of the teflon ball tip is not amplified by the large contact point area, so, the top with the teflon tip slips sideways much more easily than with other tips.
Even while it spins, if I push its stem sideways, it slips easily.

The top is always the same, but with the teflon tip. 
In these tests there is always a very thin layer of grease on the glass spinning surface, so I can see the track left by the top and measure it.
The top made the examined turn of precession in 10.31 seconds, at the average speed of 2036 RPM, by 349.9 spin revolutions.
The average angle of tilting was 11.5°, (12.0° after 90° of the examined turn of precession and 11.0° after 270°).
The calculated diameter of the precession circle is mm 332
The "diameter" of the observed spiral is mm 301 - 316

Again, there is positive slipping.
       
« Last Edit: October 01, 2019, 04:09:20 PM by Iacopo »
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #32 on: October 01, 2019, 03:23:11 PM »

You could also try different surfaces: a rubber mat vs a glass table.

Thanks for the suggestion.  It's not very easy because the top slows down rapidly on the rubber but I will try.
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #33 on: October 02, 2019, 08:49:29 AM »

With the silicon rubber the circle of the precession is very little, about 50 mm.  It seems like the tip sinks a bit in the soft silicon and tends to stay trapped there, so it walks slowly.

I made another experiment:
I made the top spin very slowly with the stem leaned on a ruler.
So there was not precession, the track left by the top on the glass spinning surface was a simple straight segment.
The top made 17.1 spin revolutions, tilted by 10.96° (average), in maybe 20 seconds, with the 4.76 mm carbon steel ball.
The calculated traveled distance is mm 48.6.
The length of the track is mm 49.6.

I expected a shorter track, about 43 mm, but it seems that in this case the ball tip made all the track without slipping.
The 1 mm difference could be an error of the measured angle of tilting, (which changed randomly from 10.6° to 11.6° to 10.7°).
I made this test because I thought that maybe the rotational sliding friction makes the traction less efficient and for this reason there is slipping.   
« Last Edit: October 04, 2019, 03:13:05 AM by Iacopo »
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #34 on: October 02, 2019, 03:37:12 PM »

I tried with sandpaper, (grit 1500).
The top, with the carbon steel ball, rises very fast.  But I can't say much more than this. The wear out of the ball was too much, and the results are not reliable, for the current tests.

I am wondering whether precession and maybe the centrifugal force of the precession have something to do with the slipping.
I have a 3/4" precision ceramic ball; I will make a flywheel for it, it will be a "top" that goes in straight line, without precessing.
I think it is interesting to see whether this object slips too, or not.
« Last Edit: October 03, 2019, 02:44:13 PM by Iacopo »
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #35 on: October 03, 2019, 03:25:37 PM »

Top very unbalanced, (3/16" carbon steel ball tip off centered by 0.2 mm):

At 2143 RPM (average), angle of tilting 7.6° (average), the top made one turn of precession in 10.26 seconds, by 366 spin revolutions.
Calculated traveled distance mm 231
"Diameter" of the spiral mm 186 - 205
Percentage of slipping: (231 - 195.5) : 231 = 15.4 %

Percentage of slipping of the same top with good balance:  10.4 %
Percentage of slipping of the same top with the 3/16" ball teflon tip:  7.1 %

This is a particular of the track left by the unbalanced top on the glass with a thin layer of grease:
the presence of little closed loops too showes that the top is slipping backwards.


« Last Edit: October 04, 2019, 03:13:34 AM by Iacopo »
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ta0

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Re: Three experiments with gyroscopes
« Reply #36 on: October 03, 2019, 05:32:46 PM »

Just by eyeballing, I would say the arcs could add 15% to the distance traveled, so it might not be slipping.
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #37 on: October 04, 2019, 03:36:20 AM »

Just by eyeballing, I would say the arcs could add 15% to the distance traveled, so it might not be slipping.

At this high speed, over 2000 RPM, the top tends to move as it was a balanced top, without wobbling.
It is the tip that wobbles, (being off centered), slipping on the glass surface, what produces the waves.
The direction of the traction doesn't wave, is always tangent to the circle of the precession, so I believe there is still positive slipping.
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #38 on: October 04, 2019, 03:59:19 PM »

This is how the unbalanced top moves; 
the top tends to spin about its center of mass, which is shifted from the geometrical axis of the top because of the added weight on a side of the flywheel. 
Because of inertia, the center of mass tends not to wobble, and tends to make its spiral trajectory without waving. 
The tip too would want not to wave, driven by the spinning surface.
 
But since the ball tip and the center of mass are not on the same axis, at least one of the two is constrained to spin around the other one.
At high speed inertia wins and the tip is constrained to wobble, slipping on the glass surface and tracing the waves.
At low speed the friction of the tip wins and it is the center of mass that wobbles, while the tip tends to trace a linear track, without waves.

https://www.youtube.com/watch?v=1yomsrBnf-c

At high speed there is also back and forth slipping of the tip along the precession trajectory.
The center of mass, and the spin axis of the top, which passes through it, in fact tends to move at constant speed, (the equidistant vertical dotted lines in the drawing below).
The traslational speed of the off centered tip instead is variable;
it is faster between B and D and slower between D and F.
So the tip slips braking the precession between B and D, and slips between D and F accelerating the precession.
There is a rapid sequence of alternate braking and accelerations.

The resultant traslational speed of the tip could be not a simple average of the maximum and minimum speeds;

the center of mass, because of the off centered tip and the tilted position of the top, goes up and down, while the top spins.
I projected the center of mass, (orange dots), on the plane of the contact line of the ball, (yellow dotted line);
the center of mass is accelerated upwards between B and D, and downwards between D and F.
With enough speed and sufficient off centering of the tip, the top could even jump and stay in mid air between D and F.
In my test the track was continuous, so the top didn't jump, but, in any case, its apparent weight is lower between D and F, and higher between B and D;
consequently, the top has more grip between B and D, and slips more easily between D and F instead.
So, the braking phases are more efficient than the acceleration phases.
For this reason, the top goes at a lower traslational speed than expected.

This seems to me a plausible explanation of the increased percentage of "positive" slipping in the unbalanced top, (15 instead of 10%).

I am not sure that positive slipping is the most correct term here, because this extra "positive" slipping does not produce a traslational acceleration of the top, nor rising torque, (in fact in my tests, unbalanced tops do not rise faster than balanced tops).



Side view of the ball tip of a top spinning. The top is spinning counterclockwise, and going towards the right. 
The yellow dotted line is the contact line of the ball, its upper part is towards you, its lower part is towards the inside of the screen.
« Last Edit: October 04, 2019, 04:38:01 PM by Iacopo »
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Jeremy McCreary

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Re: Three experiments with gyroscopes
« Reply #39 on: October 04, 2019, 05:31:32 PM »

...I believe there is still positive slipping.

Could you summarize your current take on how slip evolves during a typical run with your test top? And how it might affect self-righting tendency?
« Last Edit: October 04, 2019, 06:19:08 PM by Jeremy McCreary »
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Playing with the physical world through LEGO

Jeremy McCreary

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Re: Three experiments with gyroscopes
« Reply #40 on: October 04, 2019, 06:11:38 PM »

I can't figure out which forces exactly could cause a forced precession.

Me, neither. Simple sliding friction and not-so-simple rolling resistance could be only part of the self-righting story in real tops. And not just in your tops, but in general.

I've come to the conclusion that we're even more in the dark about tip resistance than we are about air resistance. And that puts a full understanding of self-righting a long way off. But mapping out slip in a real Simonelli top is a valuable contribution.

A real top spinning on a ball tip is a complicated mechanical system. Our understanding will improve as we continue to cycle between the observed kinematics and the modeled dynamics. But usually best to start from a solid kinematic description, as you're building here.

In kinematics, you map out the observed motions in space and time as best you can. It's good to start thinking about causes at this point. Just don't get too attached. In dynamics, you then try to go from the observed kinematics to a plausible model of the forces and torques in play. The kinematic picture often sharpens as you test and tweak the dynamic model.

Slip is a kinematic observation. I sense that it shapes visible top behavior in some common situations. But exactly how and when, I can't yet say. After all, we're still working out kinematic issues as basic as rolling vs. slipping in ball tips.
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #41 on: October 05, 2019, 03:31:01 AM »

Could you summarize your current take on how slip evolves during a typical run with your test top? And how it might affect self-righting tendency?

I have little free time so I am slow with these tests.  I haven't data yet about slip evolution during the same spin.
But Ta0 reported that slipping is more intense at higher speed and with a more tilted position of the top.
This seems interesting because the rise of the top too is more rapid when the top spins faster and in a more tilted position, (at least with the ruby ball tip, because with the teflon tip it seems not to rise faster), and rolling resistance by itself seems not sufficient to explain this behaviour.  So, probably there is something else helping tops to rise. 
But I have no ideas what it could be, and I am still very puzzled about tops slipping.
I will continue with the kinematic observations, maybe something will turn up. 
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Iacopo

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Re: Three experiments with gyroscopes
« Reply #42 on: October 05, 2019, 02:32:46 PM »

The photos below are about some tracks left by the unbalanced top at different speeds with the carbon steel and with the teflon ball tips;

The waves are due to sideways slipping of the tip, which is off centered from the spin axis;
this sideways slipping is present with the teflon tip at all the speeds.
The carbon steel tip instead tends not to slip at slow speed, so the waves tend to disappear.

The test confirms that teflon is more slippery than carbon steel, as for traslational movements. 



The photos are all in the same scale.  Variations in the length of the waves are due to differences in the angle of tilting of the top, (waves are longer when the top is in a more tilted position).  The tracks of the teflon ball are larger because the teflon ball flattens a bit being a softer material.
« Last Edit: October 06, 2019, 02:54:04 AM by Iacopo »
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Jeremy McCreary

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Re: Three experiments with gyroscopes
« Reply #43 on: October 05, 2019, 10:59:25 PM »

I have little free time so I am slow with these tests.  I haven't data yet about slip evolution during the same spin.

No apologies, my friend! Our understanding of top behavior progresses only as fast as hard-won high-quality empirical data comes in -- especially on the kinematic side. And you share a lot more quality data than anyone else on this forum.

I've learned a great deal from your thoughtful experiments, videos, graphs, and numerical data. And that despite the vast differences in our respective design spaces. Thanks!

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Iacopo

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Re: Three experiments with gyroscopes
« Reply #44 on: October 07, 2019, 01:48:30 PM »

I've learned a great deal from your thoughtful experiments, videos, graphs, and numerical data. And that despite the vast differences in our respective design spaces. Thanks!

I too learned a lot, especially from you and Ta0, the appreciation and the gratitude are reciprocal.

I made the brass flywheel for my precision ceramic ball, and tested it.
Also I adapted an electric engine for to spin the top, because it is difficult to spin it with the fingers, since there is not a stem.

With sufficient spin speed, this top goes straight, without precessing.
So the track was a segment, (214.8 mm long).
The diameter of the ceramic ball is mm 19.05, and the angle of tilting was 1.58°
The ball top made 115.5 spin revolutions in 1.51 seconds, (at 4589 RPM).
The calculated traveled distance is mm 190.5
The length of the track is mm 214.8
Percentage of slipping:  - 12.8 %, (negative slipping).

There is a bit of uncertainty about the angle of tilting, I believe that my measurement is not wrong by more than 0.2°,
but out of a so little angle, (1.58°), it means possible inaccuracy up to 12-13 %.
 
Also I want to be surer that the acceleration phase is completed before the top walks in the examined segment.
I checked the video and the top was not accelerating at all in the examined segment.

The negative slipping is even more puzzling than the positive one, because the top is slipping forward, without apparent reasons.
 
I will try again, with less speed and the top more tilted.

https://www.youtube.com/watch?v=sTNllZErbZw
« Last Edit: October 10, 2019, 11:47:00 PM by ta0 »
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