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Author Topic: Flywheels and fairings and spokes, oh my!  (Read 7118 times)

Iacopo

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Re: Flywheels and fairings and spokes, oh my!
« Reply #150 on: April 11, 2021, 10:10:41 AM »

Iacopo: Could you instead repeat your tests in Replies #5 and #8 at 1,000 to 500 RPM?

I repeated the test, even between 1000 and 500 RPM, with a flat bottom added to the top, 84 mm, like the your.

ONE MORE GROUND EFFECT TEST

I attached a cardboard disk, (84 mm), to the bottom of the top, with some double sided adhesive tape.
The hole in the center of the disk is for the base to reach the recessed tip into the top.
The hole in the cardboard disk is large enough and it never touches the horn of the base during the spins.
At the right you see the top spinning with this cardboard disk attached to its bottom.



Then I added a CD on top of the base. The hole in the CD is closed by the horn of the base, there are no gaps for the air to pass through.  At the right you see the top with its cardboard disk spinning on the base with the CD.
The clearance between the cardboard disk and the CD is about 5 mm.



Timings, (seconds):

                                        With CD    Without CD   With CD   Without CD   Difference
From 2000 to 1500 RPM        54.7           51.3           55.1          51.7            6.6 %
From 1500 to 1000 RPM        89.8           84.5           89.9          85.3            5.8 %
From 1000 to 500 RPM         190.3         184.3         189.9        183.5            3.4 %


I confirm that there is ground effect and that the top spins longer because of it, (from 6.6% longer at 2000-1500 RPM , to 3.4% longer at 1000-500 RPM).
« Last Edit: April 11, 2021, 10:37:51 AM by Iacopo »
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ortwin

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Re: Flywheels and fairings and spokes, oh my!
« Reply #151 on: April 11, 2021, 02:07:06 PM »

Ground effect - no ground effect
@ Iacopo and Jeremy: I admire the good experimental work both of you present! 
Did you considerprecession or absence of it? You most probably have, I must admit I did not read everything in this topic as carefully as I should have.
Is precession absent in both of your tops in the relevant phase of measurement? Otherwise I can imagine precession stirring up some beneficial equilibrium that leads  to a ground effect.   
Edit: Iacopo, I just saw you have that beautiful video where you visualize the airflow next to a top with smoke. Did you try anything like that here?
« Last Edit: April 11, 2021, 02:27:41 PM by ortwin »
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Iacopo

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Re: Flywheels and fairings and spokes, oh my!
« Reply #152 on: April 11, 2021, 04:02:55 PM »

Ortwin, our tops were not precessing during the tests.
But Jeremy found a tendency of his top to hula hoop above 300 RPM with the ground near the top;
maybe this increased a bit his spin times, hiding the ground effect.
Also, in my latest test, it turned out that at low speed, (1000-500 RPM, the speeds used by Jeremy), the ground effect is weaker, 3.4%.

My top never hula hooped because I have a pointed tip, Jeremy has a ball tip instead.
But I am not sure why the ground makes the top to hula hoop.

I thought for a while to try with the smoke but I give up because it is not so easy to do it in this case with little time.
But I plan to do at least one sequence with smoke, in my future video of my new top, which has removable ground and shroud. 
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ta0

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Re: Flywheels and fairings and spokes, oh my!
« Reply #153 on: April 11, 2021, 05:33:42 PM »

AMI (I3): 8.2e-4 kg m²
This is 0.00082 kg m2 ?
It seems a very high value, my copper top Nr. 22 weighs 656 grams, weight concentrated outwards, diameter 80 mm, and the AMI is 0.00064, less than this your 165 grams/84 mm top.  It doesn't seem possible.
Yes, 8.2e-4 = 0.00082. Agree, my AMI for Top D and yours for Nr. 22 can't both be right.

I'm not so sure they cannot be both right. Maybe the intuition here is failing because the dependence on the square of the radius.
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Jeremy McCreary

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Re: Flywheels and fairings and spokes, oh my!
« Reply #154 on: April 11, 2021, 06:42:06 PM »

Re: Iacopo's latest ground effect findings (Reply #151)...

I confirm that there is ground effect and that the top spins longer because of it, (from 6.6% longer at 2000-1500 RPM , to 3.4% longer at 1000-500 RPM).

Thanks for the new data, Iacopo! With only a 3.4% beneficial ground effect at 1,000 to 500 RPM in your Reply #151, I think we now have to start looking at small differences in our experimental setups.

Relative shroud width: In Replies #135 and #141, my bottom shroud's radius was only 90 mm — just 7% larger than 84 mm. In Reply #151, your bottom shroud (CD) had a radius a good bit larger than 84 mm.

Rotor shape: My flywheel put a sharp edge above the entrance to the air gap beneath Top D. Your rounded flywheel edge made the entrance to your air gap a little less abrupt.

Could these small differences have affected how air flowed into and out of our respective air gaps? Conceivably.

Did you consider precession or absence of it?

There was never any precession to speak of in my test runs, and the hula-hooping I reported earlier disappeared once I closed off the upflow of air around my lens (so that air could only enter my air gap laterally). Hence, hula-hooping and precession played no role in the final ground-effect results I reported in Replies #135 and #141.

« Last Edit: April 11, 2021, 06:44:12 PM by Jeremy McCreary »
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Playing with the physical world through LEGO

Jeremy McCreary

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Re: Flywheels and fairings and spokes, oh my!
« Reply #155 on: April 11, 2021, 06:49:09 PM »

A few quick points while I work to reconcile my AMI for Top D with Iacopo's for Nr. 22... 

I'm not so sure they cannot be both right. Maybe the intuition here is failing because the dependence on the square of the radius.

Beginning to think you may be right.

Jeremy, do you find something wrong in these simple calculations ?  I believe that you messed with something, maybe you used the diameter instead of the radius in your calculations.

It will take me some time to go through your calculations and make my own estimate of Nr. 22's AMI. Meanwhile, no, I didn't use diameters where I should have used radii. Nor could I find any other simple math or unit errors.

These calculations are very familiar territory for me. As I stated before...

So I triple-checked my moment formulas and all measured inputs, and all check out. I'm therefore standing by my estimated moments for Top D: AMI = 8.2e-4 kg m², and TMI at the tip = 5.2e-4 kg m².
« Last Edit: April 11, 2021, 08:21:44 PM by Jeremy McCreary »
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Iacopo

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Re: Flywheels and fairings and spokes, oh my!
« Reply #156 on: April 12, 2021, 03:50:27 AM »

I'm not so sure they cannot be both right. Maybe the intuition here is failing because the dependence on the square of the radius.

Beginning to think you may be right.

The problem is that the radii are similar, (40 mm vs 42 mm), the distributions of weights are similar, then the top which weighs four times than the other has less moment of inertia...  No, this is not possible.

While Jeremy calculates the moment of inertia of my top, I will do the same for his top;

these calculations are not familiar territory for me, but I will be very very simple.

The formula for to calculate the moment of inertia is:

r x r x m = I

r  is the radius of gyration, (m)
m  is the mass, (kg)
I  is the moment of inertia, (kg m2)

The mass of the top of Jeremy is 0.165 kg.
The radius of gyration is unknown but it is certainly less than the geometrical radius, 42 mm.
Since I want to stay very simple, I will use 42 mm as it was the radius of gyration, so I am certainly going to overestimate the moment of inertia.

The calculation is straightforward:

0.042 x 0.042 x 0.165 = 0.00029  kg m2

I can't be simpler than this.

Jeremy, the moment of inertia of your top is surely less than 0.00029 kg m2.
It could be about 0.0002 kg m2, which is 1/4 of your estimate, (0.00082), for this reason I thought that you could have used the diameter instead of the radius in your calculations.
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ortwin

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Re: Flywheels and fairings and spokes, oh my!
« Reply #157 on: April 12, 2021, 04:10:18 AM »

... I thought that you could have used the diameter instead of the radius in your calculations.
Or maybe this tau vs. pi business caused confusion? I was never a fan of that discussion, as I see it mostly potentially causing completely unnecessary confusion without adding anything of relevance. But maybe it was not the fault of poor little tau, just a guess.
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ta0

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Re: Flywheels and fairings and spokes, oh my!
« Reply #158 on: April 12, 2021, 10:36:23 AM »

The problem is that the radii are similar, (40 mm vs 42 mm), the distributions of weights are similar, then the top which weighs four times than the other has less moment of inertia...  No, this is not possible.

Oops! I did enter 84 mm as Jeremy's radius!  :-[

Actually:
1. Flywheel, spoke, stem, and tip assemblies, max radius 84 mm

ortwin is right: it's the tau vs pi curse!

An  interesting fact is, that the CM is exactly at the upper surface of the beer.
I need to think about that.
A more realistic scenario for this problem would be drinking beer while fishing on a boat (slowly) rocked by the waves.
« Last Edit: April 12, 2021, 11:17:29 AM by ta0 »
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Iacopo

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Re: Flywheels and fairings and spokes, oh my!
« Reply #159 on: April 12, 2021, 12:20:44 PM »

Oops! I did enter 84 mm as Jeremy's radius!  :-[

Actually:
1. Flywheel, spoke, stem, and tip assemblies, max radius 84 mm

I don't know why, I thought it was the diameter !   :-[ :-[ :-[ :-[
Probably because I am used to think to the diameter when I consider the dimensions of my tops.
I should be more careful while reading.

I apologize, Jeremy.  Now everything makes sense. 
« Last Edit: April 12, 2021, 12:22:59 PM by Iacopo »
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Jeremy McCreary

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Re: Flywheels and fairings and spokes, oh my!
« Reply #160 on: April 12, 2021, 12:42:29 PM »

I don't know why, I thought it was the diameter !   :-[ :-[ :-[ :-[
Probably because I am used to think to the diameter when I consider the dimensions of my tops.
I should be more careful while reading.
I apologize, Jeremy.  Now everything makes sense.

No worries, my friend. Funny, I caught this misunderstanding earlier this morning and was just writing a message about it.

AMI (I3): 8.2e-4 kg m²
It seems a very high value, my copper top Nr. 22 weighs 656 grams, weight concentrated outwards, diameter 80 mm, and the AMI is 0.00064, less than this your 165 grams/84 mm top.  It doesn't seem possible.

I need to read more carefully, too. When I first saw your comment above, I mistook Nr. 22's diameter of 80 mm for its radius, because I usually think in radius rather than diameter. Hence we both ended up thinking that these tops have similar outer radii, though of very different sizes!

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Jeremy McCreary

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Re: Flywheels and fairings and spokes, oh my!
« Reply #161 on: April 12, 2021, 01:10:31 PM »

Well, now that we've cleared up The Great AMI Misunderstanding of 2021 (for which I'm as guilty as anyone), I'd like to share the formulas I use to estimate the AMI, "specific AMI" (AMI per unit mass), and axial radius of gyration of a flywheel approximating a hollow cylinder. These are handy formulas for any topmaker, as many tops can be usefully decomposed into a series of coaxial cylinders for AMI estimation purposes. The simple rule: AMIs about the same axis add, while specific AMIs and radii of gyration do not.

I'll use my von Braun space station top's big yellow flywheel as an example. Here's the flywheel in the "Top A" variant with no fairings.



This hollow cylinder has outer radius R = 84 mm, inner radius r = 71 mm, and inner/outer "radius ratio" q = r / R = 85%. Its mass M = 114 g accounts for 83% of Top A's total mass and 69% of fully faired Top D's.

AMI: Since the flywheel's density is fairly uniform, and the inner gear teeth are negligible, its AMI I3 is easily and reliably estimated using the formulas

I3 = ½ M (R² + r²) = ½ M R² (1 + q²) = ½ π ρ L R4 (1 - q4),

where ρ is mass density in kg/m³, and L is the cylinder's axial length in m. I prefer the versions with radius ratio q, as they highlight the roles of max radius and relative wall thickness. (Turns out, it's often useful to scale top dimensions by max radius. Then you're left with a bunch of proportions and one very conspicuous measure of absolute size.)

After converting millimeters to meters and grams to kilograms, this gives a flywheel AMI of

I3 = 6.9e-4 kg m²

This figure represents a whopping 96% of Top A's estimated total AMI and 84% of fully faired Top D's.

Specific AMI: The flywheel's specific AMI J3 is just

J3 = I3 / M  = ½ R² (1 + q²) = 6.1e-3 m²

Adding spokes and a core to make Top A bumps AMI from 6.9e-4 to 7.1e-4 kg m² but reduces specific AMI to 5.2e-3 m². And adding 2 disk fairings to turn Top A into Top D further reduces it to 5.0e-3 m². With each step, the structure as a whole becomes less mass-efficent.

Axial radius of gyration: The flywheel's axial radius of gyration K3 is just

K3 = sqrt(J3) = R sqrt[(1 + q²) / 2] = 93% R = 0.078 m

Specific AMI and axial radius of gyration are strictly geometric measures of mass distribution. In its own way, each gauges how much AMI a top gets out of the mass it has. The larger they are, the lower the critical speed. The axial radius of gyration is also useful in AMI measurement with a trifilar pendulum.

Not only that. The relative axial radius of gyration K3 / R = sqrt[(1 + q²) / 2] is something you can learn to eyeball in a top. For example...

Handy fact: The axial radius of gyration of a hollow cylinder always lies within its wall. This example is no exception. In flywheels with large radius ratios, this fact gives you a way to eyeball K3. Mathematically,

R > K3r

Another handy fact: These formulas also apply to a solid cylinder. Just set r = 0 or q = 0 as needed.
« Last Edit: April 12, 2021, 07:20:28 PM by Jeremy McCreary »
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ortwin

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Re: Flywheels and fairings and spokes, oh my!
« Reply #162 on: April 12, 2021, 02:09:26 PM »

Tt does not help at all in understanding ground effect /no ground effect , but I am happy that things cleared up on the AMI.  Maybe we should all put more often something for size comparison into the pictures of our tops. The coins (quarter and Euro) I used a few times were fine with the size of the curtain ring tops. They would be quite small next to Iacopo's tops or the von Braun space station. A regular 5.7 cm Rubik's cube would often work fine, what do you think?
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Jeremy McCreary

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Re: Flywheels and fairings and spokes, oh my!
« Reply #163 on: April 12, 2021, 02:18:03 PM »

Tt does not help at all in understanding ground effect /no ground effect , but I am happy that things cleared up on the AMI.  Maybe we should all put more often something for size comparison into the pictures of our tops. The coins (quarter and Euro) I used a few times were fine with the size of the curtain ring tops. They would be quite small next to Iacopo's tops or the von Braun space station. A regular 5.7 cm Rubik's cube would often work fine, what do you think?

You're absolutely right about including a size marker in photos where size matters. First thing you learn in field geology. Coins are problematic in an international forum, though. A universally recognizable marker like the first 50 mm of a ruler would be best. A finger would also work well.

As for ground effects, I'm perfectly happy to leave it at this: Some tops have them, some don't. In my book, ruining play value by reducing ground clearance to the point of a 2° scrape angle or less just to get a 6% ground effect in spin time is a bad deal.
« Last Edit: April 12, 2021, 02:52:31 PM by Jeremy McCreary »
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Iacopo

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Re: Flywheels and fairings and spokes, oh my!
« Reply #164 on: April 12, 2021, 02:51:12 PM »

In my book, ruining play value by reducing ground clearance to the point of a 2° scrape angle or less just to get a 6% ground effect in spin time is a bad deal.

In the top I am making the scrape angle is about 10°, which is comfortable to spin.
The spin time gain will be not a lot but consider that at present my longest spin is 58 minutes, and if I can improve just a bit, I can break the one hour wall for a finger top, which in my case is a value.
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