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[Iacopo]

"TIP FRICTION AND AIR DRAG MEASUREMENTS"

In this thread I will expose data about tip friction and air drag of different tops.

The aim is to achieve a better understanding of this aspect in spinning tops.  The data can be used for to improve the design of our tops, in the case longer spin times are wanted.
Usually I simply look at the spin time for knowing which top is better, but at times it is not very clear what is the cause of a longer or a shorter spin.  Observing separately the two frictions will help to understand better. 

The method I will use for to know tip friction is to spin the top in absence of air.  Knowing the rotational inertia of the top and its deceleration, tip friction can be calculated.
Subtracting tip friction from total friction, (deduced from the top spinning in normal conditions), we can know air drag.


THE VACUUM SYSTEM:

The first problem I had to solve was to have a vacuum system with sufficiently low ultimate pressure.

If the pressure in the vacuum chamber is not low enough, the top would slow down more rapidly, because of it. 
If I want to measure tip friction alone, there must be no significant residual air drag in the chamber.

I bought this pump.  Declared ultimate vacuum is 0.3 Pa, (about 0.002 mm Hg), which would be perfect.



But this is not an expensive pump, so I wanted to test if the declared ultimate vacuum is true.

I bought a precision gauge, (the black one in the pic below, about 35 times more sensitive than the other gauge on the pump), and connected it to the pump.

Also you can see here the vacuum chamber, which I made with iroko wood, and a robust glass pane.
The wood inside the chamber was covered with some layers of epoxy resin. 
I made the gasket with silicone.  The seal is perfect.



Apart from the precision gauge, I also used a phial filled with refrigerated ethylene glycol in a glass with the same liquid, (it is the same concept of the Torricelli barometer), for to measure the ultimate vacuum in the chamber.
Other liquids do not work because they boil in the vacuum. Even the ethylene glycol, needs to be refrigerated, to avoid bubbles formation.
The difference between the two levels, (indicated by the two arrows in the pic below), is proportional to the absolute pressure in the chamber; 
they are 3.5 mm of ethylene glycol, equivalent to 0.28 mm Hg;  this is the real ultimate pressure I have in the chamber.
The pump works better when it becomes hot, at that point the ultimate pressure becomes about 0.1 mm Hg.
At the start, when the pump is cold, ultimate pressure is about 0.5 mm Hg.



Next problem was to see if  0.1 - 0.5 mm Hg  is a sufficiently low absolute pressure.

I run a

Test for to know residual air drag relevance in the vacuum chamber:

It takes 1'36"2 for my top Nr. 27b to go from 1000 to 900 RPM.
100 RPM lost in 96.2 seconds.

Deceleration is:
100 RPM = 10.47 rad/sec, (lost in 96.2 seconds).
10.47 : 96.2  = 0.109 rad/sec, (lost in 1 second).
Angular deceleration is  0.109 rad/sec².

Torque is:
Moment of inertia x angular deceleration.
The moment of inertia of this top is 0.0000643 kg-m².
0.0000643 x 0.109 = 0.00000701 Newtonmeters = 7.01 millionths of Newtonmeter.

I spun this top in the vacuum chamber and repeated the same timings and calculations.

Results:



At 1.7 mm Hg the torque resulted slightly lower than at 0.8 mm Hg, while the countrary should happen.
This is due to tip friction, which is not stable, but changes continuously a bit.

I added two pieces of scotch tape at the sides of the top and repeated all the timings and calculations:



Because of the scotch tape, the air drag of the top at ambient pressure increased by
73.24 - 7.01 =  66.23 millionths of Newtonmeter.

At the same time, because of the scotch tape, the air drag of the top in the vacuum increased by
1.87 - 1.67 = 0.20 millionths of Newtonmeter, (at 1.7 mm Hg).
1.88 - 1.76 = 0.12 millionths of Newtonmeter, (at 0.8 mm Hg).

So it can be seen that there is still air drag in the vacuum chamber.
Anyway this air drag seems extremely low;

0.20 millionths of Newtonmeter, compared to 66.23, is
0.2/66.23 =  only 1/331, (at 1.7 mm Hg).

And 0.12 millionths of Newtonmeter, compared to 66.23, is
0.12/66.23 = even less, 1/552, (at 0.8 mm Hg).

Even if there is a bit of inaccuracy in this test, because of variability of the tip friction, it seems to me that the residual air drag in the vacuum chamber is practically insignificant. 
Then, also, the timings in the vacuum chamber will be taken at 0.1 - 0.5 mm Hg, which are lower pressures than those of this test.

-----------------------------------------------------------------------------------------------------------------------

This is just the beginning.
In the next days I will start pouring in this thread the data coming out from this project.
 

[ta0]

This is a very important thread and contribution to spinning top science.

We discussed before Professor Emeritus Robert Greenler's presentation about tops (Why Does a Spinning Top Stop). In his autobiographical book, Chasing the Rainbow, after talking about his top collection he wonders about the contributions of tip friction and air drag. He mentions, for example, that air drag should be larger at high rotation rates and that at very low ones tip friction should be larger. He suggests it as a research subject. I'm sure he would love your work.

[Iacopo]

Professor Emeritus Robert Greenler... wonders about the contributions of tip friction and air drag. He mentions, for example, that air drag should be larger at high rotation rates and that at very low ones tip friction should be larger. He suggests it as a research subject. I'm sure he would love your work.

We will know this better in the next weeks but I think he was right.
I liked his video "Why Does a Spinning Top Stop".

[Aerobie]

Congratulations of your beautiful science.  Leonardo was an artisan and scientist.  Now we have Iacopo!

Alan

[Iacopo]

TIP FRICTION VARIABILITY WITHOUT LUBRICANT

I spun this top in the vacuum chamber, without any lubricant in the spinning surface, (Jeremy asked me to do so):



This has been its tip friction during the spins:



Tip friction is not stable but changes continuously.

This partly could depend on the fact that, at microscopical level, the shapes of the contact points change continuously while the top spins, because there is a bit of wear.
For example, this is how a carbide spinning surface becomes, after a top with a spiked carbide tip spinned on it for some tens of hours, (at the microscope):




Between 1250 and 1000 RPM there were large and unpredictable changes of tip friction;
this was not due to precession because I always started the top at a higher speed and the top was always already in sleeping position, without wobbling nor precessing, when I started timing it, at 1250 RPM.
Probably, at this higher speed, the top was still walking a bit on the spinning surface, so the friction changed depending on which spot of the spinning surface, (which is not homogeneous at microscopical level), the top spinned on.

Between about 950 and 450 RPM there is a gradual decrease of the tip friction, in all the spins.
I suppose that at about 950 RPM the top stopped walking and settled durably on a spot of the spinning surface.
I don't know the reason of this decrease of the friction. 
Theorically tip friction should remain constant; there was no lubricant between the contact points, and there was not enough air drag in the vacuum chamber, to cause a so evident decreasing friction.

Between 400 and 250 RPM there are again unpredictable changes in tip friction, due to the top starting to wobble before to topple down; the wobbling makes the tip to move in different spots of the spinning surface, and the contact surface of the tip itself is changing, because the top spins in a more and more tilted position during the wobbling.


The changes of friction can be dramatic. Here three samples. Still there are similarities with the spins shown above.
The top is always the same, and, as above, no lube was used.

[Iacopo]

Congratulations of your beautiful science.  Leonardo was an artisan and scientist.  Now we have Iacopo!

Alan

You are too good. Thank you, Alan.

[ta0]

Between 800 and 400 there is a decrease of friction that is consistent between all the curves, so it's likely real. Although without error bars we cannot tell for sure. How often did you measure (or how many data points are there?). Anyway, the decrease is not dramatic and to a first approximation you could say it's constant for that range of values. Friction is a very complex phenomena and perhaps the usual assumption is itself just an approximation.

I finally wrote to Bob Greenler (I hadn't found his email address previously). This is part of what he answered:

I did videotape a few different tops as they went from from spinning fast to falling over. With numbered frames I thought I could get the plot of rotational speed versus time. For fast-enough rotation I expected air drag to dominate and as the top slowed down go to the region where tip friction would dominate. For the higher speeds the drag would depend on speed; for the lower speeds the frictional torque should be independent of speed. I even built a vacuum chamber, with a window for photographing the top, which would enable me to run the same top under the same conditions--with and without significant air drag.

Alas, I didn’t get to analyzing the data until I found out that the Physics Department camera I used was obsolete and had been discarded. I didn’t follow up in trying to locate a used camera. and… and…and sometime during the ordeal of cleaning out my lab and office for retirement, I must have discarded the data videotape. That is one of the (many) projects in my life that remained unfinished—to my regret. I have quite a number of different kinds of tops and thought of writing a paper for the American Scientist, that could give something of a history of tops as well as the answer to the question “Why Does a Spinning Top Stop?”. I think it would have made a nice paper.

[Aerobie]

I too notice variable tip friction.  My observations are with a thin layer of forehead oil.   I wipe the mirror before starting, then tip the mirror slightly about once per minute, moving the ball tip to fresh lube.

As I've previously mentioned, I've made some tops with large balls which don't topple.   Running one just today (2.25" diameter, 131g,  0.50" ball) I observed the following:

9-10% RPM decay per minute between 500 and 200 RPM.  Then decay smoothly increased to about 25% at 100 RPM.  Although not in a vacuum, we can be certain that aero drag was negligible over this speed range.  Sometimes I see decay increase due to wobble, but there was no visible wobble here.

I've seen increased decay at low speed before.  But I haven't determined the cause.

Alan

[Jeremy McCreary]

Iacopo: Many thanks for sharing this tedious but very important work! Your coming data will greatly advance top engineering -- especially for tops started by means other than throwing. Will study your initial results tomorrow.

We discussed before Professor Emeritus Robert Greenler's presentation about tops (Why Does a Spinning Top Stop).... He mentions, for example, that air drag should be larger at high rotation rates and that at very low ones tip friction should be larger.

If ABT stands for "aerodynamic braking torque", and FBT for "frictional braking torque", then Greenler's just saying that ABT > FBT at sufficiently high speeds, and that ABT < FBT at sufficiently low speeds. As a statement of theory, I totally agree, but it leaves open some important practical questions in real tops.

High-speed case: I have no doubt that my (generally high-drag) LEGO tops launch in the ABT > FBT regime in room air, and we've seen strong evidence to that effect in low-drag tops like Iacopo's and Alan's as well. So far, so good.

Low-speed case: Tops that come to rest upright clearly reach the ABT < FBT regime before falling, but I have yet to see data proving that other tops can do so on a routine basis -- repeated statements to that effect notwithstanding. Hoping that Iacopo's coming data will shed some light on this empirical question.

[Jeremy McCreary]

I finally wrote to Bob Greenler (I hadn't found his email address previously). This is part of what he answered:

I did videotape a few different tops as they went from from spinning fast to falling over. With numbered frames I thought I could get the plot of rotational speed versus time. For fast-enough rotation I expected air drag to dominate and as the top slowed down go to the region where tip friction would dominate. For the higher speeds the drag would depend on speed; for the lower speeds the frictional torque should be independent of speed. I even built a vacuum chamber, with a window for photographing the top, which would enable me to run the same top under the same conditions--with and without significant air drag.

Alas, I didn’t get to analyzing the data until I found out that the Physics Department camera I used was obsolete and had been discarded. I didn’t follow up in trying to locate a used camera. and… and…and sometime during the ordeal of cleaning out my lab and office for retirement, I must have discarded the data videotape. That is one of the (many) projects in my life that remained unfinished—to my regret. I have quite a number of different kinds of tops and thought of writing a paper for the American Scientist, that could give something of a history of tops as well as the answer to the question “Why Does a Spinning Top Stop?”. I think it would have made a nice paper.

Greenler video physics lecture "Why Does a Spinning Top Stop?" here, date unknown. Alas, he doesn't get to the title question until 53:54 and ends the talk at 57:00. Nothing most of us don't already know about spin-down, but I enjoyed the video anyway and would recommend it to any top fancier.

Strong evidence that folks of all ages still like tops: Most people run from physics lectures as soon and as fast as they can, but Greenler demonstrated this one with many tops from his large international collection. Instead of rushing the doors at the end, most of his audience, young and old, rushed down to see the tops.

[Jeremy McCreary]

Next problem was to see if  0.1 - 0.5 mm Hg  is a sufficiently low absolute pressure.... So it can be seen that there is still air drag in the vacuum chamber.
Anyway this air drag seems extremely low....

This ultimate pressure range corresponds to 13-67 Pa. At room temperature, 13 Pa falls in the transitional regime between viscous and molecular flow. At 67 Pa, you're barely in the viscous flow regime. In both cases, there will be an aerodynamic braking torque (ABT), however small, and this ABT should grow somehow with speed. However, the exact nature of the ABT-speed dependence is unknown and may differ between the 2 flow regimes.

[Iacopo]

Although without error bars we cannot tell for sure. How often did you measure (or how many data points are there?).

There is one point every 50 RPM in the curves, (19 or 20 points for each curve).

Error bars; I am not sure how much accurate are these data. 
There is a bit of uncertainty because of the residual air drag in the vacuum chamber; 
based on the preliminary test I made, I should have no more than 0.01 millionths of Newtonmeter error, at high speed, because of it, and practically no error at slow speed.
Accuracy in timings is limited by the fact that my tachometer makes one reading per second, anyway the timed lapses last about 1 - 6 minutes, so the error here is little.
I will make a more accurate test for knowing the relevance of the residual air drag.

In any case, I feel confident that there is good accuracy in these data, and that the decreasing friction between 800 and 400 RPM is absolutely real.
   

[Iacopo]

I too notice variable tip friction.

I imagine that air drag should decrease gradually with speed, and always with the same values.  If there are irregular changes of the spin decay, these changes should be caused by tip friction variability. 
I too see that these irregular changes can be noticed even without a vacuum chamber, (and not only at the slowest speeds).   

[Iacopo]

Low-speed case: [/b]Tops that come to rest upright clearly reach the ABT < FBT regime before falling, but I have yet to see data proving that other tops can do so on a routine basis -- repeated statements to that effect notwithstanding. Hoping that Iacopo's coming data will shed some light on this empirical question.

Lego tops have generally so high air drag that I would be no surprised if their air drag curve would be permanently above the tip friction curve, never crossing it.

[Jeremy McCreary]

Lego tops have generally so high air drag that I would be no surprised if their air drag curve would be permanently above the tip friction curve, never crossing it.

Totally agree. But we still need to prove that lower-drag tops really do cross over, as is often claimed.