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Author Topic: A Figure of Merit for Twirler Spin Time  (Read 53725 times)

Aerobie

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Re: A Figure of Merit for Twirler Spin Time
« Reply #120 on: December 24, 2017, 09:45:11 PM »

Sandpaper Glued to Stem Handle

I glued a strip of 320 grit sandpaper to the carbon fiber stem on this 1.5" diameter, 50 gram top.
This is the nicest grip I've ever tried.   Better than knurls.

Alan
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Iacopo

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Re: A Figure of Merit for Twirler Spin Time
« Reply #121 on: December 25, 2017, 05:13:37 AM »

perhaps there is coupling between spin and wobble (nutation? as Iacopo suggests)

I am not sure about Alan's tops, but what I see in my tops I believe it is indeed nutation;
the following method is a more refined version I used for to recognize nutation from other kinds of wobbling:

some time ago Russpin gave an interesting formula for to know nutation speed;
for very little angles of tilting, the proportion between spin speed and nutation speed is equal to the proportion between transverse moment of inertia and axial moment of inertia.

A practical sample with numbers:

This is my top Nr. 15:
Axial moment of inertia:  kg-m2 0.0000765
Transverse moment of inertia:  kg-m2 0.0000429
Ratio between the two moments of inertia:  0.0000765 : 0.0000429 = 1.78

The transverse moment of inertia has to be measured at the tip. The trifilar pendulum measures it at the center of mass, not at the tip, anyway in this top the tip is really very close to the center of mass, so I didn't apply the parallel axis theorem.



I used the tachometer to know spin speed and nutation speed:

Spin speed:  247 RPM
Nutation speed: 415 RPM
Spin speed, second check: 229 RPM

Average between 247 and 229 is 238;
in the instant when nutation speed was at 415 RPM, spin speed was at about 238 RPM.

Ratio between the two speeds: 
415 : 238 = 1.74
which is very near to the ratio between the two moments of inertia we have seen before, 1.78.
So we can see there is a correspondence.

This helps to make clear what is the kind of wobbling we can see in a top.

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

I have nutation in my tops in three different situations:

- When the top is spun, usually there is at least a bit of nutation.
- When I kick the stem of the top with a finger while it is spinning. In these first two situations, nutation becomes weaker and weaker by the time, until disappearing completely; it takes some seconds up to some minutes for this to happen, depending on the kind of the top and the initial intensity of the nutation.
- When the contact point is large enough, (this happens when the tip is weared, after many hours of spinning, especially with ball tips), and especially if there is no lubricant. In this case the top starts nutating spontaneously at a certain speed, then it stops nutating spontaneously, a few minutes later, while the top continues spinning.
Some sort of "resonance effect" seems to trigger this effect, when the spin speed is favourable.
When the contact point is still larger, (tip badly weared), the top nutates for the whole duration of the spin.

Nutation is the only one reason I know for an intermediate peak wobbling.
« Last Edit: December 25, 2017, 10:47:52 AM by Iacopo »
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Iacopo

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Re: A Figure of Merit for Twirler Spin Time
« Reply #122 on: December 25, 2017, 06:00:54 AM »

I've tried to use your paintbrush on light (50g) tops with problems. 

I past and copy here one of my comments to Bob Gunther:
"This is because your tops are light.  It may help using a brush with a little diameter, (1 mm or so), with long and soft bristles. I would use the tip of the brush (for a softer touch) and not the sides of the bristles as in the video, (the top in the video is relatively heavy so it's a different situation). A correct amount of color in the bristles and a correct dilution of the color also may help; to me it works better when there is a tiny drop of color on the tip of the bristles, so the lightest touch leaves a clear mark. Another trick could be not to hold the brush by hand, but to use a support for it, (I use a glass), placed on the table, so it is easier to control the tiny movements of the brush.
You can try not to touch directly the stem with the brush, go with the brush very very close to it, (I use magnifier glasses here), then wait for the top to barely touch the brush. As soon as you see the first mark, suddenly remove the brush, to avoid the top to receive other marks in different positions, in case the first touch of the brush was hard enough to make the top to move in a disorderly way."
« Last Edit: December 25, 2017, 06:10:51 AM by Iacopo »
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Iacopo

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Re: A Figure of Merit for Twirler Spin Time
« Reply #123 on: December 25, 2017, 10:11:05 AM »

I glued a strip of 320 grit sandpaper to the carbon fiber stem 
This is the nicest grip I've ever tried.   

I believe you. 8) 8) 8)
Original, and ingenious !
« Last Edit: December 25, 2017, 02:13:59 PM by Iacopo »
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Iacopo

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Re: A Figure of Merit for Twirler Spin Time
« Reply #124 on: December 25, 2017, 02:12:30 PM »




I'd be happy to go along with that if the red curve labeled "Tip friction" in your last graph were perfectly flat.
But it clearly slopes down to the right, and we need to know why.

If I understand this red curve correctly, it really plots total braking torque (TBT) vs. speed
at your actual ultimate pressure PU, whatever that may be.
If so, the TBT at PU still includes a contribution varying directly with speed.
Could be nothing more than "wet" (lubricated) friction,
but we're not yet in a position to rule out aerodynamic drag.

I recommend repeating the experiment "dry"

Here it is:

I spun the same top, on the same spinning surface, with and without oil.
I tested with air, not in the vacuum.
The top was started at 1250 RPM and toppled down at 195 RPM, in both tests.

RPM minute after minute, with oil:
1250 - 1163 - 1084 - 1014 - 950 - 890 - 836 - 786 - ? - 697 - 656 - 620 - 584 - 552 - 520 - 491 - 463 - 436 - 412 - 388 - 365 - 343 - 323 - 303 - 285 - 267 - 250 - 235 - 219 - 206.
Spinning time:  29'25"

RPM minute after minute, without oil:
1250 - 1154 - 1070 - 992 - 922 - 856 - 795 - 738 - 684 - 634 - 588 - 544 - 503 - ? - ? - 392 - 358 - 327 - ? - 266 - 237 - 211.
Spinning time:  21'30"

This is an efficiency graph, calculated as percentage of retained speed after one minute spinning:
For example, the first minute without oil is:
1154 : 1250 = 0.923 = 92.3 %



The graph makes evident that the top is more efficient with the oil, (obviously), but also it makes evident that the advantage is stronger at low speed.

                                    Spin time      Spin time
                                     with oil       without oil         
From 1250 to 730 RPM      8'15"            7'10"
From  730  to 416 RPM      9'35"            7'10"
From  416  to 195 RPM     11'35"           7'10"

This seems to demonstrate that there is viscous friction in play with the oil, which becomes stronger at higher speed.
So, Jeremy, it seems that you are correct suggesting that the slope at the right in the first graph could be due to "wet" friction.
I can't calculate the torque from these data so I can't be totally sure that there isn't any residual air drag in action,
(in the red line of the first graph), we will see this better in the next weeks.
« Last Edit: December 26, 2017, 02:56:55 PM by Iacopo »
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Jeremy McCreary

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Re: A Figure of Merit for Twirler Spin Time
« Reply #125 on: December 25, 2017, 04:29:54 PM »

some time ago Russpin gave an interesting formula for to know nutation speed; for very little angles of tilting, the proportion between spin speed and nutation speed is equal to the proportion between transverse moment of inertia and axial moment of inertia. ... This helps to make clear what is the kind of wobbling we can see in a top.

You've turned Russpin's formula into an excellent diagnostic test for gyroscopic nutation, Iacopo! A word of caution about its use at low speeds, though: The derivation assumes a so-called "fast top", which by definition has much less gravitational potential energy than it has kinetic energy about the spin axis. In practice, this limits the formula to speeds far above the "critical speed" for stable steady precession or sleep.

Edit: Ratios below were accidentally inverted first time around. Fixed now. Conclusions remain valid.

Importantly, the formula clearly shows that the kind of wobble underlying the paintbrush method can't be gyroscopic nutation in the general case. When the paintbrush method is applied to a fast top spinning much faster than it precesses, the nutation formula reduces to

s / w = I1 / I3,

where s is the pure spin rate, w is the wobble rate, I3 is the AMI, and I1 is the TMI about the tip. Now, for the paint to end up on the same side of the stem every time, s / w must be a whole number (1 or greater) to a high degree of precision -- regardless of the wobble's cause. But for nutation to work, the same must be true of I1 / I3 as well.

Now think of all the tops to which the paintbrush method has been successfully applied. What are the odds that I1 / I3 just happened to be a whole number in each and every case? Zero. Hence, the success of the paintbrush method must rest on a kind of wobble other than gyroscopic nutation -- one that guarantees a whole-number s / w -- regardless of I1 / I3. I know of only one kind of wobble capable of that -- the fundamentally non-gyroscopic wobble engineers call "whirl".

Whirl can result from either unbalance or misalignment, and sharp resonances in whirl amplitude with speed are the rule. Moreover, whirl predicts that as a top spins down through each resonance, the phase angle (in our case, between the heavy spot and the paint mark) will change in just the ways we observe. Whirl can also excite superimposed nutation under the right circumstances.

I have nutation in my tops in three different situations:
- When the top is spun, usually there is at least a bit of nutation.
- When I kick the stem of the top with a finger while it is spinning. In these first two situations, nutation becomes weaker and weaker by the time, until disappearing completely; it takes some seconds up to some minutes for this to happen, depending on the kind of the top and the initial intensity of the nutation.

Agree that the wobble in these cases is likely to be mostly nutation -- especially if the tops were already balanced and aligned. Far above critical speed, small forced nutations can die out from gyroscopic damping alone.

- When the contact point is large enough, (this happens when the tip is weared, after many hours of spinning, especially with ball tips), and especially if there is no lubricant. In this case the top starts nutating spontaneously at a certain speed, then it stops nutating spontaneously, a few minutes later, while the top continues spinning.

Not convinced that the wobble in this case is purely nutation. This would be a good one to test with your nutation diagnostic.

Some sort of "resonance effect" seems to trigger this effect, when the spin speed is favourable.
When the contact point is still larger, (tip badly weared), the top nutates for the whole duration of the spin.

I also find that tips with large radii of curvature tend to promote wobble of some kind. Still not sure why.

Nutation is the only one reason I know for an intermediate peak wobbling.

Here we disagree. IMO, a wobble that behaves like this is much more likely to be whirl than nutation. Below are some free online PDFs with good introductions to whirl...

Swanson, E., et al., 2005, A Practical Review of Rotating Machinery Critical Speeds and Modes

Nelson, F., 2007, Rotor Dynamics without equations

Freese, T.D., and Grazier, P.E., 2004, Balance this!

If you read only one, make it Swanson. For something more mathematical, and with discussions of rotating machines closer to spinning tops, try

Nelson, H.D., and Talbert, P.B., 2003, Rotordynamic considerations (chapter 10 of unknown book)
« Last Edit: December 25, 2017, 07:00:40 PM by Jeremy McCreary »
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the Earl of Whirl

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Re: A Figure of Merit for Twirler Spin Time
« Reply #126 on: December 25, 2017, 11:37:10 PM »

You guys are amazing.  And you did all that on Christmas Day?
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Jeremy McCreary

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Re: A Figure of Merit for Twirler Spin Time
« Reply #127 on: December 26, 2017, 12:29:25 AM »

You guys are amazing.  And you did all that on Christmas Day?

Well, the writing, maybe, but we've been working up to this stuff for a long time. Kinda like that day you juggled bowling balls on a unicycle. Now, that was amazing!
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Iacopo

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Re: A Figure of Merit for Twirler Spin Time
« Reply #128 on: December 26, 2017, 06:27:18 AM »

You've turned Russpin's formula into an excellent diagnostic test for gyroscopic nutation, Iacopo! A word of caution about its use at low speeds, though: The derivation assumes a so-called "fast top", which by definition has much less gravitational potential energy than it has kinetic energy about the spin axis. In practice, this limits the formula to speeds far above the "critical speed" for stable steady precession or sleep.

I think your reasoning is valid for tops with the tip at some distance from the center of mass;
in the case of the top I tested, (Nr. 15), the tip, recessed, is so near to the center of mass that the top is free to nutate without any significant influence from gravity.
As a matter of fact, in the test, the ratio between the two moments of inertia and the ratio between the two speeds were very similar, so Russpin's formula seems essentially still valid here. 

Importantly, the formula clearly shows that the kind of wobble underlying the paintbrush method can't be gyroscopic nutation in the general case. 
..for the paint to end up on the same side of the stem every time, s / w must be a whole number (1 or greater) to a high degree of precision -- regardless of the wobble's cause.
I know of only one kind of wobble capable of that -- the fundamentally non-gyroscopic wobble engineers call "whirl".

Obviously nutation is not related to what I call "unbalance wobbling", they are two totally different and independent kinds of wobbling.
For detecting unbalance, the paint brush method has to be used with "unbalance wobbling", not with nutation.
It doesn't make sense to check for unbalance marking a stem which is undergoing nutation;  in this case the marks would appear randomly distributed around the stem, (which is another simple way for distinguishing nutation from "unbalance wobbling").
I think we agree, until here.

We have different ideas about the nature of this "unbalance wobbling", you see it as "whirl", but I don't think so;
tops have only one pivot, the tip, there is freedom of tilting, then generally tops are rigid;  I can't imagine whirl to happen here.
My explanation is that, in tops like the ones I and Alan make, unbalance shows as the top spinning with the heavier side of its flywheel at a lower height, because of gravity. The lighter side stays at an higher height. A bit like the arms of a scale, where the one with more weight sinks down.  So the stem of the top stays always leaned towards the heavy side of the top.  At whatever speed, the top stays always leaned exactly towards its heavy side, and this makes the paint brush technique reliable, the marks on the stem are always in the direction of the heavy side of the top.
If something different happens, it is because there are other movements superposed to "unbalance wobbling".
Or maybe even it is not "unbalance wobbling" but another movement, nutation or precession.

Far above critical speed, small forced nutations can die out from gyroscopic damping alone.

This also depends very much on the distance between the tip and the center of mass. 
When the tip is at the center of mass, nutation can last for minutes, but when the tip is far from it, nutation disappears rapidly.

- When the contact point is large enough, (this happens when the tip is weared, after many hours of spinning, especially with ball tips), and especially if there is no lubricant. In this case the top starts nutating spontaneously at a certain speed, then it stops nutating spontaneously, a few minutes later, while the top continues spinning.
Not convinced that the wobble in this case is purely nutation. This would be a good one to test with your nutation diagnostic.

I haven't tested it with the "nutation diagnostic", (I will try), but it seems very much nutation to me.
Anyway I still don't understand the mechanism that triggers it, I only see that it is related to a large contact point/lack of lubrication.
« Last Edit: December 26, 2017, 06:34:47 AM by Iacopo »
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Russpin

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Re: A Figure of Merit for Twirler Spin Time
« Reply #129 on: December 26, 2017, 10:49:25 AM »

As a matter of fact, in the test, the ratio between the two moments of inertia and the ratio between the two speeds were very similar, so Russpin's formula seems essentially still valid here. 

It's very clever of you Iacopo to apply the free precession formula to your top. As you point out the key assumptions for the formula are:

1) No external torques are applied to the system.
2) A small angle between the angular velocity vector and the symmetry axis.

Given these two conditions the formula is valid for any spin rate.

Great work on the vacuum spin down measurements. I think you are breaking new ground here!
« Last Edit: December 26, 2017, 10:57:55 AM by Russpin »
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Jeremy McCreary

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Re: A Figure of Merit for Twirler Spin Time
« Reply #130 on: December 26, 2017, 01:21:09 PM »

Obviously nutation is not related to what I call "unbalance wobbling", they are two totally different and independent kinds of wobbling. For detecting unbalance, the paint brush method has to be used with "unbalance wobbling", not with nutation. It doesn't make sense to check for unbalance marking a stem which is undergoing nutation;  in this case the marks would appear randomly distributed around the stem, (which is another simple way for distinguishing nutation from "unbalance wobbling").
I think we agree, until here.

Completely.

We have different ideas about the nature of this "unbalance wobbling", you see it as "whirl", but I don't think so;
tops have only one pivot, the tip, there is freedom of tilting, then generally tops are rigid;  I can't imagine whirl to happen here.

Some of the reasons I like whirl as at least a qualitative analogy for your "unbalance wobbling"...
1. We know a lot about whirl from an engineering standpoint.
2. Unbalance is the simplest cause of whirl and generates all of its essential behaviors.
3. Whirl's lowest-speed "rigid body modes" involve no bending whatsoever. They require only "soft bearings" with some slop. These are the modes I see as applicable to tops.
4. Rigid-body whirl from unbalance captures all the behaviors we see in unbalance wobbling.
5. The stem of a spinning top isn't completely free to tilt. It's constrained by gyroscopic torques acting mainly on the rotor. These torques are to some extent analogous to soft bearing forces acting on the stem.
6. Rigid-body whirl also occurs in overhung rotors with one free end.
7. Whirl is an inertial phenomenon seen with both horizontal and vertical spin axes. It may be modified by gravity somewhat, but its essential behaviors don't depend on gravity.

My explanation is that, in tops like the ones I and Alan make, unbalance shows as the top spinning with the heavier side of its flywheel at a lower height, because of gravity. The lighter side stays at an higher height. A bit like the arms of a scale, where the one with more weight sinks down.  So the stem of the top stays always leaned towards the heavy side of the top.  At whatever speed, the top stays always leaned exactly towards its heavy side, and this makes the paint brush technique reliable, the marks on the stem are always in the direction of the heavy side of the top.
If something different happens, it is because there are other movements superposed to "unbalance wobbling".
Or maybe even it is not "unbalance wobbling" but another movement, nutation or precession.

When paint marks fall consistently on the heavy side of the rotor, let's call that a "phase angle" of 0°.  You've reported tops with phase angles of 180°, and I've seen that in some of my tops as well. You suggested that CM height might control phase angle, and I think you're onto something there. Russpin even replicated that behavior in his computer simulations.

We've also seen reports of 90° phase angles, perhaps most recently from Alan. In its totality, this odd phase angle behavior can't be explained solely with gravity or even with gyroscopic effects. But it's a well-documented and well-understood part of whirl.
« Last Edit: December 26, 2017, 05:05:30 PM by Jeremy McCreary »
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Jeremy McCreary

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Re: A Figure of Merit for Twirler Spin Time
« Reply #131 on: December 26, 2017, 03:10:07 PM »

I glued a strip of 320 grit sandpaper to the carbon fiber stem on this 1.5" diameter, 50 gram top.
This is the nicest grip I've ever tried.   Better than knurls.

Great idea, Alan! LEGO purists will disapprove, but I'll definitely give it a try in one of my highest-AMI tops.

Q: What's the final stem diameter with the sandpaper?
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Iacopo

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Re: A Figure of Merit for Twirler Spin Time
« Reply #132 on: December 26, 2017, 04:49:39 PM »

The stem of a spinning top isn't completely free to tilt. It's constrained by gyroscopic torques acting mainly on the rotor. These torques are to some extent analogous to soft bearing forces acting on the stem.

This analogy sounds a little forced to me...

When paint marks fall consistently on the heavy side of the rotor, let's call that a "phase angle" of 0°.  You've reported tops with phase angles of 180°, and I've seen that in some of my tops as well. You suggested that CM height might control phase angle, and I think you're onto something there.


I tried to keep things simple to avoid a longer explanation, so I said "in tops like the ones I and Alan make", which are generally large and low.

I have made 31 tops, at present.
 
29 tops, out of them, stay always leaned towards their heavy side, when they are unbalanced;
speed has no effect on their direction of leaning, they stay always leaned towards their heavy side, at whatever speed.

Then I have one top, (Nr. 8 ), which behaves differently, because it leans towards its light side, when it is unbalanced: the first time I tried to balance this top I was very confused, because I didn't expect this behaviour, and, at that time, I had no explanation for it.

Some months later I suspected that that behaviour depends on the height of the center of mass, or more precisely on the ratio between AMI and TMI at the tip, because the Nr. 8 was the most tall and narrow top I had made.
So I made a new top, (Nr. 17), with a movable axis, allowing large changes of the height of the center of mass, for to see how the top behaves changing this parameter.

The result was that, with low center of mass, the top, unbalanced, stays always leaned towards its heavy side, at whatever speed.

With high center of mass, the top, unbalanced, stays always leaned towards its light side, at whatever speed.

Then there is an intermediate set up, by which the top, unbalanced, stays leaned not towards the heavy side nor towards the light side, but somewhere in between.
This is the only set up where the direction of leaning of the top depends also on speed.
But, generally, tops rarely behave in this way, because having a tip longer/shorter by just about two millimeters  is sufficient to exit from this intermediate set up.
So the great majority of the existing tops, when unbalanced, stay always leaned towards the same side, (the heavy or the light one), without any influence by speed.



I have an explanation for these behaviours, it would take a long post to explain them barely decently, with my poor language.
It isn't about gravity alone, but its interaction with centrifugal force and inertia.
Gyroscopic torques are not involved here, they are less or more present but they are related to precession and not to "unbalance wobbling".
« Last Edit: December 26, 2017, 05:16:43 PM by Iacopo »
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Aerobie

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Re: A Figure of Merit for Twirler Spin Time
« Reply #133 on: December 26, 2017, 07:33:43 PM »

More on sandpaper stem grip:

I've been using this stem and absolutely love it.

It's a bit tricky to neatly glue a wrap of sandpaper.   So I just ordered some sandpaper sleeves with 1/4" and 3/8" OD and 1/2" and 3/4" length.  They are cheap and available in many grits.

Iacopo will have to lay-out arc-shaped pieces to fit his tapered stems.

Alan
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Aerobie

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Re: A Figure of Merit for Twirler Spin Time
« Reply #134 on: December 26, 2017, 07:46:08 PM »

Variation in tip drag with speed:

First of all, I haven't carefully read this discussion, nor Jeremy's links.  But I'll throw this into the discussion anyway.

Friction creates heat, and the energy which produces the heat reflects back to the top as a torque load.  This process isn't necessarily linear.  For example radiative heat transfer = t^4, where t is absolute scale.

If there is lubricant present, centrifugal force will "hurl" the lube radially outward by the spinning tip.  So there would be less lube at high speed.  That process, and the viscose drag of the lube are also not linear.

I find Iacopo's data quite adequate and am not motivated to fine-tune the details of the vacuum curve.

Alan
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