Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[Jeremy McCreary]

Test top: 168 mm, 137 g flywheel top with long, thin spokes, a very low critical speed of ~95 s, and a strong predilection for quiet sleep.

Measurements: Best spin time of several tries in 3 different aerodynamic cases, with the same electric starter on the same lubricated concave lens each time...

Case A. No shroud -- just spinning in the open air on the lens shown.




Case B. Under a cylindrical shroud closed all around (not shown). Shroud clearances = 26 mm laterally, 34 mm above flywheel.

Case C. Same shroud, but open upward.  Shroud clearances = 26 mm laterally, unlimited above. (NB: The shroud ridges shown are all external.)


Important constants from case to case
1. Top dimensions, shape, and mass properties (including CM-contact distance)
2. Release speed ω₀ = 108.9 rad/s (1,040 RPM)
3. Critical speed ω_C = 9.9 rad/s (95 RPM)
4. Tip-related braking torque vs. speed curve (guessing a very gradual decay of some kind)

Measured spin times ran from release to first scrape. These generally overestimate t_C, the time to critical speed, but I'm ignoring the small errors here and equating t_C with measured spin time. Also ignoring some small variations in ω₀, as they had little effect on spin time.

Best spin times
Case B. Full shroud ........................... 346 s
Case C. Lateral shroud (open above) ... 212 s
Case A. No shroud ............................ 199 s

The verdict is clear: The full shroud greatly reduced this top's air resistance.

Synthetic spin-decay curves for Cases A and B

To get a feel for the relative braking torques involved in Cases A and B, I'll approximate their unmeasured spin-decay curves (SDCs) with "synthetic" exponential decays calculated from their measured SDC endpoints (0,ω₀) and (t_C,ω_C) via

ω(t) = ω₀ exp(-t / T),

where the case "lifetime" T is given by

T =  t_C / ln(ω₀ / ω_C) = 0.418 t_C

The lifetimes in Cases A and B are then 83.2 and 144.6 s, resp. The solid lines below are the synthetic SDCs, with Cases A's in red. Since many real SDCs turn out to be nearly exponential, these plots should be good enough for our purposes.



In a given case, spin time ends when its SDC reaches the dotted horizontal black line at ω = ω_C. And its first lifetime ends when the SDC reaches the dashed horizontal black line at ω = 0.368 ω₀. You can play with this plot at https://www.desmos.com/calculator/jwzclfiwu1.

To read total braking torque Q off any SDC, look at its slope dω/dt = Q / I₃, where I₃ is the top's axial moment of inertia. Since I₃ is the same in all cases here, Case A's steeper slope at all times can only mean a larger Q at all times. And since the tip-related component of Q is the same in all cases, that can only mean a greater aerodynamic component in Case A at all times.

These synthetic SDCs are probably reasonable approximations. If so, I can go one step further: Since the differences in slope extend far beyond the spin times involved, air resistance likely dominated Q the entire time the top was standing, regardless of shroud status.

Conclusions
The shroud clearly reshaped the air flow around the top in significant ways -- and with it, the air resistance acting on the top as a whole. The full shroud of Case B reduced this resistance dramatically. Suppression of the axial inflows and lateral outflows set up by any centrifugal pumping action may well have contributed. But the air flows bathing the spokes and inner flywheel teeth might have been favorably altered as well.

[ortwin]

Great work!
If you search for pictures on "von Braun space station" you find more of these beautiful things:

[Jeremy McCreary]

Great work!
If you search for pictures on "von Braun space station" you find more of these beautiful things:

Amazing match! Will definitely look that up.

[Iacopo]

Case B. Full shroud ........................... 346 s
Case C. Lateral shroud (open above) ... 212 s
Case A. No shroud ............................ 199 s

The verdict is clear: The full shroud greatly reduced this top's air resistance.

Excellent test, Jeremy !
 
Certainly tops with poor aerodynamics benefit more from an air drag reduction, but I suspect that in your case there is something else happening;

I believe that your top, spinning without shroud in free air, does not benefit from the ground stopping the air which feeds the Von Karman flow under the top, because that air can come directly from above, through the big hole in the flywheel, (first sketch). 

Maybe for this reason you may have this huge difference with and without the full shroud.
Without the shroud you have a full and efficient Von Karman flow both above and below the flywheel, with great air drag.

Simply closing that hole in your top should disable the Von Karman flow under the top, (second sketch in the photo), and make the top spin longer.

If all of this is true, it may be better to have a full core in the center of the top, and not a hole, as for longer spin times.
Even if space station style tops are cool for aesthetics.

[Jeremy McCreary]

@Iacopo: Thanks! I think the flows shown in your drawings are on the right track -- including the implications for the flows around spokes.

Plan to test this top with some lightweight fairings soon.

Going back to the study of the aerodynamic braking torque on car wheel designs spinning in place without translation, the wheel with a full cover came in 2nd or 3rd as I recall, the one with fan spokes pumping outward 3rd or 2nd, and the one half-covered with short spokes centrally did best.

Of course, a low-slung unshrouded top operates in a very different setting -- floor not far below, no treadmill belt to one side, no wheel well serving as a partial shroud.

But in ortwin's spirit of broad thinking, I still want to give a top based on the best wheel design a try. And I think I can do it with this test top.

Pretty sure now that variants of von Karman's pump will turn out to be major players in the spin-down of many if not most tops
-- even peg tops! But as the wheel results suggest, it may not be the only flow we need to design against.

Then there are the trade-offs between aerodynamic considerations and critical speed.

[Jeremy McCreary]

Great work!
If you search for pictures on "von Braun space station" you find more of these beautiful things:

Look, Papa's got brand new spokes! (Air resistance test coming soon to this thread.)

Funny, I use my spoked flywheel to thumb my nose at gravity, and Werner uses his to make a gravity substitute.

I like the look with these thicker yellow spokes. No other change from above.


Spokes orbiting at maybe 700-900 RPM under illumination pulsing steadily in the 200-300 Hz range...


Spinning under steadier illumination....

[Jeremy McCreary]

Holy moly, this just showed up in my news feed!

https://www.space.com/orbital-assembly-voyager-space-station-artificial-gravity-2025

These guys got nuthin' on me.

[ortwin]

They should offer you a serious discount on your first trip there Jeremy! And Lego should sell your model as related merchandising product.

[ortwin]

Funny, I use my spoked flywheel to thumb my nose at gravity, and Werner uses his to make a gravity substitute.

Quite  ironic! Love it that you picked this one up and brought it to our attention.

[Jeremy McCreary]

@ortwin: Kind words! A space station would have been a good place to be starting around February, 2020. Provided no one new came aboard.

[Jeremy McCreary]

Here's a puzzle for you guys...

Test top: 68 mm, 38-48 g spoked flywheel top based on a rare large Znap wheel with fan-like spokes.

Starter and base: Very fast unidirectional (CCW) wind-up starter, concave lens of mild-moderate curvature.

Shroud: Straight cylinder, 88 and 92 mm in inside diameter and height, resp. Clearance: 10 mm laterally, 46 mm above.


Measurements: Best spin time of at least 5 tries in 4 different top configurations with and without shroud -- always with the spokes blowing upward. Measured spin times ran from release to first scrape.

Top A. No fairings, 37.6 g, ω₀ ≤ 4,100 RPM. Starter and lens on right.




Top B. Upper fairing only, 42.8 g, ω₀ ≤ 3,800 RPM.


Top C. Lower fairing only, 42.8 g, ω₀ ≤ 3,800 RPM.


Top D. Both fairings, 47.8 g, ω₀ ≤ 3,600 RPM. Seam between wheel halves stands ~32 mm above the contact with the lower fairing in place and 30 mm without.


Key parameters
Mass properties necessarily varied with fairing configuration. Importantly, axial moment of inertia (AMI) was greatest for Top D and least for Top A, but it was the other way around for AMI per unit mass. CM height was greatest for Top B and least for Top A but varied only a few millimeters. Guessing critical speed i]ω[/i]_C was lowest for Top A and highest for Top D.

Release speeds ω₀ fell in the 377-429 rad/s range (3,600-4,100 RPM), varying inversely with AMI but with no clear trend WRT likely air resistance. Top D put 27% more weight on its tip than Top A, but how much tip resistance varied as a result is unclear. Minimum ground clearances ranged from 7 mm in Tops C and D to 12 mm in Tops A and B.

Best spin times (case numbers follow top names above)
Case A1. No fairings, ≤ 4,100 RPM, no shroud ..............  95 s
Case A2 = Case A1 under shroud .................................  *
Case B1. Upper fairing only, ≤ 3,800 RPM, no shroud .....  64 104 s
Case B2 = Case C1 B1 under shroud ................................ 122 s
Case C1. Lower fairing only, ≤ 3,800 RPM, no shroud ..... 188 s
Case C2 = Case B1 C1 under shroud .................................  54 s
Case D1. Both fairings, ≤ 3,600 RPM, no shroud ............ 206 s
Case D2 = Case D1 under shroud .................................  82 s

* Top immediately drawn into collision with inner shroud wall.

Analysis
Struggling to make sense of this spin-time data. For one thing, too many key parameters had to change from case to case. Also the unshrouded spin-time trends generally ignore the trends in release speed, AMI, CM height, and critical speed. Go figure.

Case D1 (both fairings, no shroud) spun the longest, with Case C1 (lower fairing, no shroud) a close 2nd. AMI and ground clearance variation might have contributed, but these tops also had relatively low release speeds and high to midling critical speeds. The shroud proved a major liability with both tops (Cases C2 and D2).

The blue spoked flywheel top tested above also performed best fully faired as seen here. But unlike Top D, it benefitted substantially from its shroud. Top B (upper fairing) was the only one in this series to spin longer under the shroud than out in the open, and by a good margin but only by a small margin.



The fairly tight-fitting shroud induced more hula-hooping and precession in these tops than the blue top saw in its own shroud. Indeed, all settled into quiet sleep out in the open, but Tops C and D never slept under the shroud. In Top A, these induced motions were so extreme that it crashed into the wall the moment the shroud was placed.

Conclusions
This rare LEGO wheel makes for an elegantly shaped finger top with wobble-free spins. On a flat surface, it lasts up to 80 s by hand, generally in quiet sleep. Nothing I saw here would make me want to mess it up with fairings or spin it under a shround.



One thing's for sure: I have no good feel for the flows around these tops -- even for fully faired Top D. Empirically, von Karman's swirling flow solution starts to break down when the disk's thickness/radius ratio exceeds about 10%, as edge effects then become increasingly important. This ratio was ~50% in the blue top above and ≥ 94% for Tops A-D here. The fan-like spokes and lateral tread pattern can't help.

I don't think we're in Kansas anymore, Toto!

CORRECTION
In light of the corrected time for Case B1, I can now say this...

Any fairing helped this spoked flywheel spin longer outside the shroud -- especially both fairings. Ditto for the blue top's spoked flywheel.

New conclusion: Spoked flywheels are great for critical speed, but not for air resistance. Best of both worlds? Shrouds aside, probably a thinly spoked flywheel with very low-mass fairings above and below.

[Iacopo]

Case C1. Lower fairing only, ≤ 3,800 RPM, no shroud ..... 188 s
Case C2 = Case B1 under shroud .................................  54 s
Case D1. Both fairings, ≤ 3,600 RPM, no shroud ............ 206 s
Case D2 = Case D1 under shroud .................................  82 s

So much less spin time under the shroud .. !?

Did the top under the shroud topple down anticipately, because of instability induced by the shroud ?
Or the top under the shroud really slowed down more rapidly ?

Maybe there is a Venturi effect between the side of the shroud and the top coming closer to it, making it less stable.
I too will try a test like this.

[ortwin]

Before I get to your puzzle Jeremy, I need to get presenting my data out of the way:
Since I have this little cheap stemless top with one spoke that can spin up to 13 minutes, I thought I can use it to make some measurements that can help answer some questions posed in this thread.




My procedure was to start the top to spin with more than 1000 RPM. When speed was down to 1000 RPM I started the stop watch and took notes of the time at certain speed values. 

-I did this for the bare top. 
-Then I covered the bottom side and performed the measurement in a similar way on the same base again
-I moved the cover to the upper side, did my "run down curve" again-I made a second cover, applied it to the bottom side, performed the measurements again (both sides covered )

Up to this point all results made some kind of sense at first glance: bottom covered better than bare top, upper side covered a bit worse than with a covered bottom but better than the bare top, both sides covered gave the best results.
Just to quickly check the reproducibility,

- I ripped both covers off and did another measurement on the bare top
This curve ended up somewhere between the others! Which means the whole measurement as I performed it so far can not tell us much.There must be some different effects involved here so that we can not see the aerodynamic effect by the fairings clearly.Might be some imbalance introduced by the fairing or maybe balance by chance. Through that different wobbling that results in different tip related spin decrease......






host html file online

I think I leave this fairing business for a while and go back to make another one or two new Curtain-Ring-Top designs I have in mind.

[ortwin]

Starter and base: Very fast unidirectional (CCW) wind-up starter,

That means you can't do a measurement with  only the lower fairing and opposite spin?

[Iacopo]

There must be some different effects involved here so that we can not see the aerodynamic effect by the fairings clearly.Might be some imbalance introduced by the fairing or maybe balance by chance.

I believe it is the tip friction, that changes continuously, from spin to spin.
You can see this even better comparing different spin times of the same top in vacuum conditions, (5 millibar residual pressure is very little and essentially you can observe the slowing down due to the tip friction alone).
Large and light tops are better for to measure the air drag, because in them the tip friction is little compared to the air drag, and this reduces the inaccuracy of the measurements.