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[Jeremy McCreary]

A recent discussion over in Spoke wheel performance inspired me to undertake a series of aerodynamic experiments making maximum use of the rapid prototyping possible with a modular top construction system like LEGO.

First question: How will a long-spinning test top made from a spoked flywheel between smooth fairings perform as the fairings are progressively removed?



Spin times with short stem and fast electric starter:
Flywheel, both fairings .......... 269 s
Flywheel, upper fairing only ... 148 s
Flywheel, lower fairing only .... 131 s
Flywheel only ......................... 79 s
Both fairings, no flywheel ........ 75 s

The fairings' net effect on critical speed is unclear. But the 121 s spin-time gap between the fully faired top and its nearest competitor is HUGE. Unavoidable differences in mass properties and release speeds surely contributed to this performance gap. But I'm confident that most of it came from differences in aerodynamic braking after release.

Specs for fully faired test top with short stem and electric starter:
Best release speed = 3,020 RPM
Best spin time = 269 s (4:29)
Mass = 49.8 g
Maximum radius = 43 mm
Axial length of rotor (flywheel + both fairings) = 40 mm
CM height = 24 mm
Tip radius of curvature = 1.6 mm
Tip material = ABS plastic
Supporting surface = polished fine-grained "granite" (best in the house!)

Best spin time by hand with long stem = 182 s (3:02)

Flywheel, lower fairing only combo: This one surprised me in 2 ways...
1. Thought it would outperform the "flywheel, upper fairing only" combo by virtue of its lower CM and smaller TMI/AMI ratio. Its failure to do so must be aerodynamic.
2. It had an unexplained and irreducible low-speed wobble totally absent in all other combos. Swapped out every part to no avail.

[ta0]

That's a nice top configuration to see different effects of air drag.
It's interesting that the "fairings only" and "flywheel only" spin about the same time but together about 3.5 times better!

Flywheel, lower fairing only combo: This one surprised me in 2 ways...
1. Thought it would outperform the "flywheel, upper fairing only" combo by virtue of its lower CM and smaller TMI/AMI ratio. Its failure to do so must be aerodynamic.
2. It had an unexplained and irreducible low-speed wobble totally absent in all other combos. Swapped out every part to no avail.

Perhaps a "ground effect?

Something I'm curious is the difference between a closed hollow top without internal vanes and with internal vanes or compartments. Can your top be assembled with the flywheel and fairings but without the spokes?

[Iacopo]

Flywheel, both fairings .......... 269 s
Flywheel only ......................... 79 s

You made a nice experiment, Jeremy.
I didn't expect so much difference from the flywheel alone and the flywheel with the fairings, but you have so large spokes, and other elements between them too, after all..

Flywheel, lower fairing only combo:  Thought it would outperform the "flywheel, upper fairing only" combo by virtue of its lower CM and smaller TMI/AMI ratio. Its failure to do so must be aerodynamic.

Maybe in the lower part of the top there is less space for the flow of air so the centrifugal pump effect maybe is less effective, (less air drag) ?
A bit like when closing the air outlet of an hairdryer makes its motor to accelerate, because the pump in not working anymore.
If so, the fairing would be useful especially in the upper part of the top.

[ortwin]

Today I managed to make a better cover for the well of the Spartan top. I used some black adhesive foil. It still does not cover the well totally since the upper knurled part of the stem is a bit wider than the lower one. So I inserted a small O-ring just under the cover and another one above the cover.


With the measurements I did so far, I updated that file with the data I attached to my post in the "spokes" thread.The updated file is attached to this post.




I am planning to try that fairing with the tent look again one of these days.

[Jeremy McCreary]

Interesting data. Looks like your latest well covers for the Spartan are counterproductive.

As Iacopo pointed out recently, since the measured speeds are all far above critical, an aerodynamic cause seems most likely.

[Iacopo]

Flywheel, lower fairing only combo:
Thought it would outperform the "flywheel, upper fairing only" combo by virtue of its lower CM and smaller TMI/AMI ratio. Its failure to do so must be aerodynamic.

This observation inspired me to make the following experiment.

At first I didn't feel like to try this.  Long time ago I tried to spin a top inside a glass and it didn't spin for a longer time, so I didn't expect very much to find something different now, anyway I tried.

With a cardboard disk fixed to the base, at 3 mm from the bottom of the top, the top spins longer by about 5%, (from 1600 to 1500 RPM).  I suppose that the disk cuts the flow of air coming from below so that the viscous pump dynamics of the spinning flywheel becomes less effective, so the air drag decreases.

This is an important discovery for making tops which have to spin for longest times.
To have a flat surface under the top near the flywheel is an advantage, not a disadvantage !
Something I will consider in the design of my future tops.     



I also tried to make a full cover for the flywheel.
The idea is that the air, trapped inside the cover, spins together with the flywheel;
like in a vacuum cleaner, or an hair dryer, if you close the air inlet/outlet, the fan starts spinning more rapidly, which means that it has less air drag, because the air trapped inside the fan chamber is spinning together with the fan, and the fan doesn't have to accelerate continuously new air coming in.

The full cover gives further advantage.  Tip friction variability has to be considered so I alternated timings with and without the cover.
(65"4, 59"4, 66"2, 60"4). Advantage is almost 10%.

[ta0]

To have a flat surface under the top near the flywheel is an advantage, not a disadvantage !

This was a surprise, indeed! 

The idea is that the air, trapped inside the cover, spins together with the flywheel;
like in a vacuum cleaner, or an hair dryer, if you close the air inlet/outlet, the fan starts spinning more rapidly, which means that it has less air drag, because the air trapped inside the fan chamber is spinning together with the fan, and the fan doesn't have to accelerate continuously new air coming in.
. . . Advantage is almost 10%.

This is something I wondered about. Nice to see it finally experimentally tested. 

[Jeremy McCreary]

@Iacopo: Fascinating results! Gotta love aerodynamics -- always full of surprises.

In my crystal ball, I see a beautiful Simonelli top sleeping serenely inside an elegant Bell jar resting on a disk of gorgeously finished exotic wood slipped over the pedestal -- just as you did here in cardboard. Before the sleeping princess awakes and falls, the topmaker will have a new world record in spin time.

Of course, I have questions...

Q1: How much clearance between your top and its cardboard shroud?

Q2: What does the bottom of this top look like?

[Iacopo]

To have a flat surface under the top near the flywheel is an advantage, not a disadvantage !

This was a surprise, indeed! 

I too was surprised, so much that I wanted to repeat the test with another top, (the Nr. 29).

I spun this top with and without a compact disc below it.
The compact disc is leaned on the base, it does not spin.
The position of the CD can be adjusted so that I could test different distances between it and the bottom of the top.
All the timings are for the top spinning from 1600 RPM to 1500 RPM.
I alternated timings with and without the disk, to minimize the error due to tip friction variability.



The indicated distance, (mm), is that of the clearance between the CD and the bottom of the top.
If the distance is not indicated, the top was spun without the CD.

 - 1 mm  41"3
 -    -      39"0
 - 1 mm  41"8
 -    -      39"2

 - 3 mm  40"6
 -    -      37"7
 - 3 mm  40"4
 -    -      37"8

 - 5 mm  41"1
 -    -      38"6
 - 5 mm  40"4
 -    -      39"1

 - 9 mm  39"8
 -    -      39"1
 - 9 mm  40"6
 -    -      39"6

I can confirm that there is less air drag with a flat surface near the bottom of the top.
The average advantage is 6.3 % with 1 mm clearance, 7.3 % with 3 mm clearance, 6.1 % with 5 mm clearance, and 2 % with 9 mm clearance.  The bottom of this top is flat and the diameter of the top is 60 mm. 

[ta0]

Fascinating!

If the reason is that the plate stops the von Karman flow, a thin circular wall under the top might do the same. Perhaps it could be just slightly larger than the top, so the top can lean during start up and at the end of the spin.

[Jeremy McCreary]

Fascinating!

If the reason is that the plate stops the von Karman flow, a thin circular wall under the top might do the same. Perhaps it could be just slightly larger than the top, so the top can lean during start up and at the end of the spin.

Can't wait to try out these new top shroud ideas! But we need to talk clearance.

My reading about the aerodynamics of spinning things at one point led to the engineering of a common industrial occurrence -- a high-speed rotor inside a tight-fitting shroud.

I was surprised by 2 things:
1. The shroud-rotor clearances typically in use seemed way too small.
2. For disk-like rotors, von Karman's model was often used to estimate rotor drag and set the minium clearance -- despite the obvious disruption of the far-field flow.

The key lesson: Keep the shroud outside the disk's von Karman boundary layer, and the disk will hardly know it's there!

The outer limit of any boundary layer is set at the point where the portion of the flow still partially adhering to the solid surface has come up to 99% of the speed of the free (non-adhering) flow beyond.

In a von Karman swirling flow, the thickness of the boundary layer over a disk face is

d = 5.4 sqrt( k /  w),

where  w is the angular speed in rad/s, and  k = 1.5e-5 m²/s is the kinematic viscosity of air at room temperature. For a disk top spinning at 100 rad/s, d = 0.4 2.1 mm. At 25 rad/s, d is double that but still under 1 5 mm!

Bottom line: A top shroud shouldn't get too close, but the optimal clearance might be smaller than you think. Critical speed might set the lower limit.

CORRECTION: Sorry, forgot the 5.4 in the equation. Bounday layer thickness estimates revised accordingly.

[Iacopo]

If the reason is that the plate stops the von Karman flow, a thin circular wall under the top might do the same. Perhaps it could be just slightly larger than the top, so the top can lean during start up and at the end of the spin.

Good ideas, I believe that they will work, I am thinking to the design more in detail now.  Thanks !

[Iacopo]

Bottom line: A top shroud shouldn't get too close, but the optimal clearance might be smaller than you think!

Thank you, Jeremy, for this info.
In fact I see that even with 1 mm clearance the air drag is still low.
I could use little clearance at the sides of the flywheel and more clearance below, for allowing for some tilting of the top, as Ta0 says.
And maybe a plexiglas removable cover.  Your crystal ball works well.

[Jeremy McCreary]

@Iacopo: See my correction above.

Should have clarified that the boundary layer calculation above is only for disk faces. Von Karman ignored edge effects. And to a very good approximation, they are negligible for thin disks up to a thickness/radius ratio of ~10%.

However, I recall seeing industrial shrouds with very tight edge clearances as well.

Still searching for a practical treatment of the flow at a thick disk's edge.

[Jeremy McCreary]

Some very preliminary results regarding enclosed tops...

Test top: The fully faired 50 g, 86 mm top introduced at the start of this thread.

Enclosures: "Straight" with 120 mm ID, and taller "bell" with 104 mm opening and 130 mm ID at rotor level...





Bases: Small, intermediate, and large convex lenses -- all lubricated with skin oil, with the degree of minification indicating their relative surface curvatures...



Observations: The enclosures consistently drew the top toward their walls at the highest speeds (up to 3,000 RPM) -- especially the bell. (Coanda effect?) The smallest, deepest lens was most effective at keeping the top off the wall, and the largest and shallowest lens, not at all.



Since the sometimes effective intermediate lens consistently turned in the longest spin times with and without enclosure, here are its results in full:

No enclosure, 322 s (5:22)
Bell enclosure, 350 s (5:50)
Straight enclosure, 362 s (6:02)*

Same trend with the small lens, which also had its best spin time of 338 s (5:38) in the straight enclosure.

Because release speeds varied slightly with the electric starter, I'm planning to Iacopo's more reliable method, which compares speed lost over the same high-speed interval.

Will try to find clear enclosures with much less clearance above the top. Doubt that a lateral clearance smaller than that of the straight enclosure (~17 mm) will be feasible.

* First time I've ever passed 6 minutes with a LEGO top!