iTopSpin
Current Posts => Collecting, Modding, Turning and Spin Science => Topic started by: Jeremy McCreary on February 20, 2021, 03:24:58 AM
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A recent discussion over in Spoke wheel performance (http://www.ta0.com/forum/index.php/topic,6404.0.html) 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?
https://youtu.be/bbDRmGBFv34
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.
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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!
(https://i.ibb.co/s5MTGPm/image.png)
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?
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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.
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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.
(https://i.ibb.co/hsP5t63/Spartan-black-adhesive.jpg) (https://ibb.co/hsP5t63)
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.
(https://i.ibb.co/NCt5h4B/screenshot-of-document.jpg) (https://ibb.co/NCt5h4B)
I am planning to try that fairing with the tent look again one of these days.
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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.
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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.
(https://i.imgur.com/9wmXLcy.jpg)
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%.
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To have a flat surface under the top near the flywheel is an advantage, not a disadvantage !
This was a surprise, indeed! :o 8)
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. 8)
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@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?
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To have a flat surface under the top near the flywheel is an advantage, not a disadvantage !
This was a surprise, indeed! :o 8)
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.
(https://i.imgur.com/xIi7WlX.jpg)
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.
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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.
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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.
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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 !
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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.
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@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.
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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...
(https://i.ibb.co/0yCGdJ1/20210221-162839.jpg) (https://ibb.co/CKbHT04)
(https://i.ibb.co/vwCQ80Z/20210221-163426.jpg) (https://ibb.co/4mwYxhP)
Bases: Small, intermediate, and large convex lenses -- all lubricated with skin oil, with the degree of minification indicating their relative surface curvatures...
(https://i.ibb.co/0qJvfZB/20210221-171031.jpg) (https://ibb.co/ZdT7hKH)
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.
(https://i.ibb.co/5RxjdLc/20210221-162843.jpg) (https://ibb.co/1mJX3T2)
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!
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No enclosure, 322 s (5:22)
Bell enclosure, 350 s (5:50)
Straight enclosure, 362 s (6:02)*
You have a 12 % improvement of the spin time with the straight enclosure, not bad.
Even with all that empty space in the enclosure the advantage is still evident.
Maybe even a tube, open above and below, could work.. ? I will try something.
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In this context of "fairings" I remembered a detail about my Quark Spinning Top that might be of some relevance here.
(https://i.ibb.co/BTcCpyn/completed.jpg) (https://ibb.co/BTcCpyn)
The body has groves or wells. Why it has those and why they are on the lower side of the top I can only guess. Probably related to an effective production process or/and design aspects.
(https://i.ibb.co/F36FRwt/injection-molded-body.jpg) (https://ibb.co/F36FRwt)
As visible in the next picture, the groves are partially covered with a sticker "Quark by Micro Logic".
(https://i.ibb.co/ZS3TzJ8/Quark-balance.jpg) (https://ibb.co/ZS3TzJ8)
Actually what I mean is not visible that clearly in the picture: The inner grove of the body is covered completely by the sticker, alright. The outer grove is covered only partially by the sticker. The grove is about 3 mm wide but the sticker is hanging about 1 mm over the rim.
Could this be just poor design? Or is some aerodynamic reasoning involved ? Could that lip formed by the overhanging sticker yield some advantage? I am reluctant to rip the sticker off just now and do comparative measurements.
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The body has groves or wells. Why it has those and why they are on the lower side of the top I can only guess. Probably related to an effective production process or/and design aspects.
Is the body made of metal ? Maybe the grooves are for making the body lighter. The top spins longer if the body, (the central part of the top), is lighter.
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No, the body is injection molded plastic. If the groves would be from above, the center of mass would be lower at least.
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Some more tests:
I made some cardboard enclosures and tested them with the top Nr. 29.
The best one is the littlest one, there are only 2 mm clearance all around the top. Advantage 17.4 %, (from 1600 to 1500 RPM).
That with 5 mm clearance all around the top was good too. Advantage 14.2 %.
The largest one, with 15 mm clearance above and below, and 5 mm clearance at the sides, was less effective. Advantage 12.6 %
I also tried a simple ring around the flywheel, clearance 5 mm.
This too reduced the air drag, but very little. Advantage 1.7 %.
(https://i.imgur.com/Gz6zssQ.png)
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No, the body is injection molded plastic. If the groves would be from above, the center of mass would be lower at least.
Agree about center of mass, but removing central mass increases AMI per unit mass, which is also good for critical speed in the same way spokes are -- and come to think of it, maybe in a more aerodynamic way.
The exposed grooves could also reduce total drag in other ways, I suppose, but not in a way I'm familar with.
In the end, however, they covered the grooves with a fairing (sticker). So maybe not.
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In this context of "fairings" I remembered a detail about my Quark Spinning Top that might be of some relevance here.
The body has groves or wells. Why it has those and why they are on the lower side of the top I can only guess. Probably related to an effective production process or/and design aspects.
The grooves cannot have any aerodynamic purpose as they are covered by the sticker. In fact, I didn't know that they were there. Perhaps they provide mechanical compliance for press fitting the metal flywheel.
The best one is the littlest one, there are only 2 mm clearance all around the top. Advantage 17.4 %, (from 1600 to 1500 RPM).
That with 5 mm clearance all around the top was good too. Advantage 14.2 %.
The largest one, with 15 mm clearance above and below, and 5 mm clearance at the sides, was less effective. Advantage 12.6 %
Those are some outstanding numbers! :o
I wonder if several circular ridges over the surface of the top would disturb enough the von Karman pumping mechanism to overcome the increased surface area. :-\
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@Iacopo: Impressive results!
My lightweight tops and relatively shallow concave bases would never work with even 5 mm of clearance, as the tops are too easily pulled off-center by aerodynamic forces at their highest speeds.
With a 3,000 RPM vertical launch on a concave base, generally takes the test top here 120-150 s to settle into quiet sleep after covering it with one of the 2 enclosures shown above. In open air, it reaches quiet sleep in 0-30 s, depending on the quality of the launch.
The motion most commonly induced or at least exaggerated by the enclosure isn't a typical precession. Instead, the tip orbits the bottom of the concavity at decreasing radius with the top at near-zero tilt.
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The grooves cannot have any aerodynamic purpose as they are covered by the sticker.
What no visible groves in your Quark? I checked the picture again that I posted earlier. Since I just borrowed it from another
post of yours in another thread I figured this is what you have. And indeed there is no visible groove.
My theorie on all this mess now goes as follows:
- ta0 you have the tungsten quark. That has a smaller diameter I read. I have the brass Quark that is somewhat larger.
- the Quark top was produced with different bodies, depending on the flywheel in use. The picture in my post earlier probably shows bodies for the brass Quark
- only one sticker was designed for the Quark. It fits the tungsten top perfectly, but in my brass top it leaves the outer grove partially uncovered.
(https://i.ibb.co/W5gv3T6/DSC-0003.jpg) (https://ibb.co/W5gv3T6)
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So, no physical finesse here it seems. Just some laziness in designing a second sticker. Like my laziness in taking a photo of my own Quark right at the start.
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I wonder if several circular ridges over the surface of the top would disturb enough the von Karman pumping mechanism to overcome the increased surface area. :-\
We're clearly dealing with some very complicated phenomena here.
Agree, suppression of the energy-consuming pumping action seems like a promising strategy. We need to keep an open mind as to how that's best done. Trying to think of a way to test this interesting suggestion in LEGO.
As I keep telling my fellow LEGO club members, who wonder why I'm still making tops 6 years later...
Tops are way more complicated than they look. And for a topmaker, therein lies the fun.
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The motion most commonly induced or at least exaggerated by the enclosure isn't a typical precession. Instead, the tip orbits the bottom of the concavity at decreasing radius with the top at near-zero tilt.
Yes, I know it, I call it "hula hoop".
This is the reason that I don't use ball tips in my tops with a recessed tip, otherwise they hula hoop.
If you have the possibility to use a tip with a littler radius of curvature, maybe you can avoid this kind of wobble.
But large and light tops like the your are very sensible to the air drag so you can detect air drag differences even with a lower speed, as you did nicely with your latest test.
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I wonder if several circular ridges over the surface of the top would disturb enough the von Karman pumping mechanism to overcome the increased surface area. :-\
I would like to know that there is a surface treatment which could make the surface more slippery for the air.
But I don't know if this is even possible, (I don't know anything about this issue).
Ridges seem to increase the air drag, at least at high speed, in the test I made.
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The motion most commonly induced or at least exaggerated by the enclosure isn't a typical precession. Instead, the tip orbits the bottom of the concavity at decreasing radius with the top at near-zero tilt.
Yes, I know it, I call it "hula hoop".
This is the reason that I don't use ball tips in my tops with a recessed tip, otherwise they hula hoop.
If you have the possibility to use a tip with a littler radius of curvature, maybe you can avoid this kind of wobble.
But large and light tops like the your are very sensible to the air drag so you can detect air drag differences even with a lower speed, as you did nicely with your latest test.
Hula hoop -- perfect term!
Already close to the practical lower limit of tip radius of curvature in LEGO plastic, but will investigate non-LEGO tip options in LEGO tip holders.
You're right about experimenting at lower speeds.
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Yesterday I did some measurements with my brass Quark, and then I ripped that sticker fairing off and did them again.There is no big difference as can be seen in the table below. The difference between sticker and no sticker is not larger as the difference in consecutive runs without the sticker.
(https://i.ibb.co/KGdkPTB/screendhot-of-table.jpg) (https://ibb.co/KGdkPTB)
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Yesterday I did some measurements with my brass Quark, and then I ripped that sticker fairing off and did them again.There is no big difference as can be seen in the table below. The difference between sticker and no sticker is not larger as the difference in consecutive runs without the sticker.
(https://i.ibb.co/KGdkPTB/screendhot-of-table.jpg) (https://ibb.co/KGdkPTB)
I would trust more in the higher RPM lapses, and in the 1400-1000 RPM lapse the top with the sticker seems slightly better.
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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.
(https://i.ibb.co/YdrgTD9/20210224-095202.jpg) (https://ibb.co/hdq01X5)
(https://i.ibb.co/BgqnF9G/20210224-095320.jpg) (https://ibb.co/brzbDkF)(https://i.ibb.co/R76cRQN/20210224-095619.jpg) (https://ibb.co/ZNgxqcS)
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.)
(https://i.ibb.co/QHYPYv5/20210224-100356.jpg) (https://ibb.co/5jsrsh7) (https://i.ibb.co/JBymDL0/20210224-100345.jpg) (https://ibb.co/w0wB5H3)
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 ωC = 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 tC, the time to critical speed, but I'm ignoring the small errors here and equating tC 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 (tC,ωC) via
ω(t) = ω0 exp(-t / T),
where the case "lifetime" T is given by
T = tC / ln(ω0 / ωC) = 0.418 tC
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.
(https://i.ibb.co/CsMJKcg/Screenshot-2021-02-24-223532.png) (https://ibb.co/M5G8kvr)
In a given case, spin time ends when its SDC reaches the dotted horizontal black line at ω = ωC. 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.
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Great work!
If you search for pictures on "von Braun space station" you find more of these beautiful things:
(https://i.ibb.co/S33fJsf/von-Braun-space-station.jpg) (https://ibb.co/S33fJsf)
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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.
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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.
(https://i.imgur.com/BWfXG12.jpg)
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@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.
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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.
(https://i.ibb.co/rt6cXBX/20210225-133529.jpg) (https://ibb.co/yRyYxzx)
Spokes orbiting at maybe 700-900 RPM under illumination pulsing steadily in the 200-300 Hz range...
(https://i.ibb.co/7RFS4NR/20210224-114345.jpg) (https://ibb.co/rcJQsfc)
Spinning under steadier illumination....
(https://i.ibb.co/qJGwzx1/20210224-114414.jpg) (https://ibb.co/PDp8RtC)
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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.
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They should offer you a serious discount on your first trip there Jeremy! And Lego should sell your model as related merchandising product.
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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.
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@ortwin: Kind words! A space station would have been a good place to be starting around February, 2020. Provided no one new came aboard.
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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.
(https://i.ibb.co/wJpFFzw/20210226-125352.jpg) (https://ibb.co/ZHcppMY) (https://i.ibb.co/bbXv8Dv/20210226-125233.jpg) (https://ibb.co/rdHp1Np)
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.
(https://i.ibb.co/SVtnxkT/20210226-122928.jpg) (https://ibb.co/BTyZPhD)
(https://i.ibb.co/br0ydbY/20210226-123103.jpg) (https://ibb.co/p37sXhN)
Top B. Upper fairing only, 42.8 g, ω0 ≤ 3,800 RPM.
(https://i.ibb.co/HY37Ctw/20210226-123348.jpg) (https://ibb.co/P40xMcX)
Top C. Lower fairing only, 42.8 g, ω0 ≤ 3,800 RPM.
(https://i.ibb.co/26H4m9J/20210226-123206.jpg) (https://ibb.co/fSLwBgJ)
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.
(https://i.ibb.co/hLQFKpR/20210226-123321.jpg) (https://ibb.co/9cKHqR9)
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.
(https://i.ibb.co/rkVRBWY/20210215-161107.jpg) (https://ibb.co/K6Jpt1d)
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.
(https://i.ibb.co/6w8MB61/20210226-174320.jpg) (https://ibb.co/54k0Fqn)
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.
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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.
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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.
(https://i.ibb.co/5rh4h3z/no-fairings.jpg) (https://ibb.co/5rh4h3z) (https://i.ibb.co/k8TF9Hb/bottom-covered.jpg) (https://ibb.co/k8TF9Hb) (https://i.ibb.co/TYdt7gG/upper-side-covered1.jpg) (https://ibb.co/TYdt7gG) (https://i.ibb.co/sQ80qTS/both-sides-covered.jpg) (https://ibb.co/sQ80qTS)
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......
(https://i.ibb.co/cC5mpgQ/screenshot-of-diagram.jpg) (https://ibb.co/cC5mpgQ)
(https://i.ibb.co/5c93tNK/screenshot-data.jpg) (https://ibb.co/5c93tNK)
host html file online (https://de.imgbb.com/)
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.
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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?
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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.
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A little test, I spun this top with and without a fairing covering the gap between the flywheel and the stem.
Best timing has been 70.9 seconds, from 1900 to 1600 RPM, for both of them.
Because of tip friction variability, I spun the top 26 times, and avaraged the results.
Average 1900-1600 RPM spin time without fairing: 64.6 seconds.
Average 1900-1600 RPM spin time with fairing: 65.8 seconds.
The difference is very little.
(https://i.imgur.com/7RcmROj.png)
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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.
Yes, or maybe too much lateral viscous coupling to the relatively tight-fitting shroud. Don't forget that tread pattern. Unlike the blue top, these tops never settled into quiet sleep inside their shroud. But they did outside.
I think part of that had to do with the concave lens. On concave surfaces, I find that tops like these having length/radius ratios in the 1-2 range have to be released just so to go right to sleep. Even though they may sleep readily on flat surfaces. Something inside the shroud seemed to exaggerate this tendency on the concave lens. But I needed the concavity to keep the tops from traveling on their fine but non-spike tips.
Tops C and D never scraped the shroud before falling on their own. But I think all that hula-hooping and precession under the shroud diverted a lot of energy from spin.
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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?
Correct, but if I have time, I'll try this one fairing configuration in both directions with the electric starter. This experiment was time-consuming enough in just one direction!
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Case B1. Upper fairing only, ≤ 3,800 RPM, no shroud ..... 64 s
Case B2 = Case C1 under shroud ................................ 122 s
Case C1. Lower fairing only, ≤ 3,800 RPM, no shroud ..... 188 s
Case C2 = Case B1 under shroud ................................. 54 s
You either mixed up the B's and C's, or you are trying to confuse me :P
(https://i.ibb.co/5rh4h3z/no-fairings.jpg)
(https://ibb.co/5rh4h3z)
Your top seems to have three balance screws on the inside but look too small to compensate for the asymmetric arm. Anyway, I have seen similar tops with no screws.
How is it balanced?
- 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......
Good that you took a second measurement.
Because of tip friction variability, I spun the top 26 times, and avaraged the results.
Iacopo is the gold standard in experimental measurements!
Average 1900-1600 RPM spin time without fairing: 64.6 seconds.
Average 1900-1600 RPM spin time with fairing: 65.8 seconds.
The difference is very little.
With the cover the area in contact with the open air decreases while the von Karman pumping probably increases. Perhaps they compensate each other.
I'm printing a 3D top to try something related.
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@ortwin: Interesting experiment. Not sure why the no-fairing case behaved so inconsistently.
But I do see one common finding in all the experiments in this thread: For the spoked flywheels we tested, covering the spokes with lightweight fairings above and below improved spin time.
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@ta0: Nope, those findings for Tops B and C were consistent over at least 5 repetitions each.
This top's trying to confuse us all, and I think it's doing a pretty good job. ???
A lesson in humility, perhaps.
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@Jeremy You call Case B2 = Case C1 under shroud and Case C2 = Case B1 under shroud. ???
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Your top seems to have three balance screws on the inside but look too small to compensate for the asymmetric arm. Anyway, I have seen similar tops with no screws.
How is it balanced?
Yes I slightly modified this one: replaced the steel ball tip for a ceramic ball of the same size from a bearing. I glued three little magnets to the inside so I could change the balance by adding magnetic stuff to those magnets wherever needed. Across from the arm there is a second magnet. The weight is enough since the arm seems to be only plastic.
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@Jeremy You call Case B2 = Case C1 under shroud and Case C2 = Case B1 under shroud. ???
Rats! Double-checked my notes, and the times for Cases B2 and C2 are correct. Only the "= Case X under shroud" parts were wrong.
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
But the time for Case B1 (upper fairing, no shroud) was off as shown above. The shroud still helped Top B -- and Top B alone -- but by a much smaller margin than originally shown. More importantly, the corrected B1 time shows that adding only an upper fairing brings a 9% spin-time gain outside the shroud.
So any fairing helps this spoked flywheel spin longer outside the shroud -- especially both fairings. Ditto for the blue top's spoked flywheel.
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.
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The results of Jeremy are so confusing that I wanted to repeat a similar test, with a very tall flywheel.
I simulated a tall flywheel (44 mm) with a cylinder of paper wrapped around my top Nr. 15.
Top diameter is 52 mm.
Does the tall flywheel air drag increase or decrease under a shroud ?
The shroud is a simple paper cylinder with a hole for the laser tachometer.
Clearance between the sides of the top and the shroud, 10 mm.
(https://i.imgur.com/hcBlBj1.jpg)
Here I have very good quality contact points and with tops not too heavy, like this one, the tip friction variablity is low, so in this case I don't need many measurements:
1400-1200 RPM
- No shroud: 63.3 seconds
- With shroud: 72.5 seconds
- No shroud: 62.4 seconds
- With shroud: 72.8 seconds
The top spins 15% longer with the shroud
So nothing strange is happening here.
Jeremy, I think that it is just all that wobble you have that makes your top to slow down so rapidly under the shroud.
My top does not wobble at all with the shroud, but I have a spiked tip, and a very little base.
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A little test, I spun this top with and without a fairing covering the gap between the flywheel and the stem.... The difference is very little.
I think I now see a trend in our experiments...
Removing central mass generally lowers critical speed by increasing AMI per unit mass. If you like, you can then add the mass removed to the outer part of the rotor -- thus further increasing AMI per unit mass without increasing weight on the tip. If you remove central mass by digging a deep well next to the stem from above with no fenestrations (as in your test top here and in ortwin's Spartan), you also lower the CM with an additional reduction in critical speed -- a double win!
The good news: The aerodynamic penalty for removing central mass this last way now appears to be quite small. But if you remove it with rotor fenestrations (like the holes between spokes) exposed to the air, the aerodynamic penalty is quite high. And that's where low-mass fairings might help -- as you might be able to remove more central mass with fenestrations, or a fenestrated well, than with a well alone.
Again, it all comes down to playing the many trade-offs between your critical speed and air resistance reductions just so. The classic Simonelli design plays them beautifully, though in a somewhat different way.
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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?
Correct, but if I have time, I'll try this one fairing configuration in both directions with the electric starter. This experiment was time-consuming enough in just one direction!
Only the lower fairing, no shroud! That would be enough I think. Quite curious If a directional effect is visible.
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Only the lower fairing, no shroud! That would be enough I think. Quite curious If a directional effect is visible.
No clear difference in this limited test of Top C (lower fairing only), no shroud, spokes blowing...
Upward: 166, 172
Downward: 165, 163
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It's the little things...
Test top: 168 mm, 133-137 g flywheel top with long spokes, a very low critical speed of ~95 s, and a strong predilection for quiet sleep.
Driver and base: Fast electric driver with drop-out chuck, concave lens of mild to moderate curvature
Measurements: Best spin time of 3 runs from the same release speed with 2 different sets of spokes.
(https://i.ibb.co/7NP1fx1/20210301-110123.jpg) (https://ibb.co/0VTG7pG)
Measured spin times ran from release to first scrape. Started the clock in each run at approximately ω0 ~ 94.2 rad/s (900 RPM). Remarkably, once I took steps to keep release speed constant, spin times for each spoke design varied by only 0.6%! Also did 1 run with the thick spokes under the same cylindrical shroud used last time with this test top. As before, this shroud cleared the rotor by 10 mm of laterally and 46 mm above.
Top A. Same spoked flywheel top as last time: Thin splined black spokes 4.8 mm in diameter.
(https://i.ibb.co/YdrgTD9/20210224-095202.jpg) (https://ibb.co/hdq01X5)
(https://i.ibb.co/BgqnF9G/20210224-095320.jpg) (https://ibb.co/brzbDkF)(https://i.ibb.co/R76cRQN/20210224-095619.jpg) (https://ibb.co/ZNgxqcS)
Top B. Thicker yellow spokes 7.2 to 7.5 mm in diameter adding 4.3 gm mass, with a cross-section somewhat similar to that in Case A. No other changes.
(https://i.ibb.co/rt6cXBX/20210225-133529.jpg) (https://ibb.co/yRyYxzx)
How the spoke cross-section changed...
(https://i.ibb.co/M7d93wW/20210224-095508.jpg[/img[/url] [url=https://ibb.co/rcJQsfc][img width=400 height=300]https://i.ibb.co/7RFS4NR/20210224-114345.jpg) (https://ibb.co/89kXSvT)
Varied parameters
1. Total spoke mass (5.9 vs. 10.2 g)
2. Frontal spoke thickness (4.8 vs. 7.5 mm)
Ignoring the 3.8% difference in total spoke mass relative to flywheel mass...
Controlled parameters (reasonably constant from case to case)
1. Spoke length and attachments
2. Flywheel, stem, hub, and tip assemblies
3. CM-contact distance ~ 24 mm
4. Flywheel AMI I3F ~ 6.9e-4 kg m²
5. Release speed ω0 ~ 94.2 rad/s (900 RPM)
6. Critical speed ωC ~ 9.9 rad/s (95 RPM)
7. Tip-related braking torque vs. speed curve (guessing a very gradual decay of some kind)
Best spin times
Top A (thin spokes), no shroud ................ 184 s (3:04)
Top B (thick spokes), no shroud ............... 170 s (2:50)
Top B (thick spokes) under shroud (1 run) ... 314 s (5:14)
Conclusions
When you're looking to maximize spin time, small things clearly count. The 14-second no-shroud spin time difference between Tops A and B was small but consistent. And a lesson for endurance top designers. You know those intricate carvings on many pricey EDC tops claiming record spin times? Well, they're shooting themselves in the foot endurance-wise.
Note that the flywheel's large AMI of 6.9e-4 kg m² failed to protect spin time from the spoke change. This AMI falls roughly halfway between the AMIs Iacopo measured for his Nrs. 23 and 9. As tops go, the latter's AMI is huge. Fancy EDC tops generally have much smaller AMIs.
Shroud: As with the blue test top above, the shroud increased spin time dramatically. Whatever air flows the shroud might have forced here, the spokes were clearly getting push-back, as spin time increased by 75% with the thin spokes and by 85% with the dirtier thick spokes.
Personally, I'm going with the "von Braun space station" look with the thicker yellow spokes. It's gonna cost me 7.6% in spin time, but spin time isn't everything.
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Jeremy, so you say by this I should really go for the 0.04 mm fishing line instead of the 0.3 mm line I am currently using?
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Jeremy, so you say by this I should really go for the 0.04 mm fishing line instead of the 0.3 mm line I am currently using?
Test, test, test!
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Jeremy, so you say by this I should really go for the 0.04 mm fishing line instead of the 0.3 mm line I am currently using?
Test, test, test!
Alright, I am preparing for the test!
Ordered 10 m of this one:
(https://i.ibb.co/Wgwj5Bm/d-nste-angelschnur-bestellt.jpg) (https://ibb.co/Wgwj5Bm)
0.04 mm and 3 kg sounds good. The one I used in the CRTs so far read 0.3 mm an 4 kg.
Actually you could also use thin nylon strings instead of your spokes, right? Or do you have some kind of contract with LEGO that does not allow for this kind of mixing something else into the system?
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Yes, planning to try more "suspension tops" with cables instead of spokes. Some interesting engineering challenges there.
Or do you have some kind of contract with LEGO that does not allow for this kind of mixing something else into the system?
Surprisingly touchy subject. The "purists" among adult fans of LEGO use only official, unadulterated parts. They look down on some of the ways legitimate parts can be joined and might get physically ill if forced to watch me alter one. Some view anyone who doesn't build this way as a heretic. Every hobby has zealots. No contract. They do it to themselves.
Personally, I'm a selective impurist, as are many who build working gizmos. Once I have a functional goal, I do my best to get acceptable performance as purely as possible. That's part of the challenge. But if the laws of physics insist, I'm off to the hardware store. Among my many sins...
o Parts of parts, like most of my top tips
o Non-LEGO functional stuff -- springs, elastics, strings, pneumatic tubing, electricals, boat propellers, etc.
o Rarely, metal axles and supports
o And a few times, (gulp) glue -- mainly for centrifugal safety.
There's a bounty on my head.
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.... Some interesting engineering challenges there.
(https://i.ibb.co/9p537Lq/Lego-guitar.jpg) (https://ibb.co/9p537Lq)
If these ones really do what I think they should, I do not see the challenges even if you want to stay a purist. You could do the balancing by ear and you would call it tuning!
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Yes, tuning the centering would be one issue, and there I think I'd want no-stretch cables with secure but adjustable cable mounts (for the same reason you want balancing screws). Your idea of guitar tuning screws might be just the thing for a big non-LEGO version.
Use your audible tuning method to even out the tensions in the return elastics below. Otherwise, you get unbalance wobble from uneven expansion/contraction. Seems like no 2 rubber bands have exactly the same tension vs. stretch curve.
https://youtu.be/jEMUGFQTux0
In flexible tops like these, you can also get nasty wobbles from structural oscillations excited during spin-up. A suspension top would be subject to that. Don't mind short spin times when necessary, but I really don't like wobble. I tolerate it above only for the cool mechanical effect.
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Your idea of guitar tuning screws might be just the thing for a big non-LEGO version.
Non-LEGO version?? The picture in my last post here shows LEGO guitars. They offer a Fender Stratocaster set, I read. Does it not have strings and tuning screws?
https://www.nme.com/en_asia/news/music/lego-to-release-fan-created-fender-stratocaster-brick-set-2781950
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Non-LEGO version?? The picture in my last post here shows LEGO guitars. They offer a Fender Stratocaster set, I read. Does it not have strings and tuning screws?
Yes, but...
1. The tuning screws are too bulky for a LEGO top of reasonable size.
2. Don't even want to think about the aerodynamics.
3. I'm sure the screws have a lot of backlash (as all LEGO gears do), and that could make precise tuning of a top suspension cable quite difficult.
All that said, the guitar and amp are very cool builds. Thanks for sharing!
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All that said, the guitar and amp are very cool builds. Thanks for sharing!
Sharing? Seriously? I would NEVER have thought I could show something that is new to YOU in the LEGO world!
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Ordered 10 m of this one:
0.04 mm and 3 kg sounds good. The one I used in the CRTs so far read 0.3 mm an 4 kg.
That's really thin, specially considering that is braided! :o Each strand must not be more than 10 microns! If black they would be perfect for magic tricks >:D
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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.
- 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.
Just now looking over your nice experiment here. Before the 2nd bare run, my corrected results and yours pointed toward the same conclusions regarding the value of fairings WRT spin time.
Despite the confounding 2nd bare run, I think the value of 2 fairings seems likely to be a reliable finding.
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Despite the confounding 2nd bare run, I think the value of 2 fairings seems likely to be a reliable finding.
Nevertheless I took further steps today towards the building of a more serious top than the Curtain-Ring-Series with thinnnnn spokes. They can be covered later anyways to test the difference.
I contacted my man with the golden hand at the lathe and proposed this little project. He is willing to help so I am very happy about that.About most parts of the spinning top we are going to build I have a clear picture in my head. Once I have put it to some kind of constructive sketch I will show it, so we can discuss it before it is actually being build. I think the contour of the flywheel has the most potential for discussion. Below is a rough picture of the evolutionary stage the flywheel has in my head at the moment.
(https://i.ibb.co/R7T04j9/flywheel-evolution.jpg) (https://ibb.co/R7T04j9)
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Below is a rough picture of the evolutionary stage the flywheel has in my head at the moment.
Ooooh, interesting!
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Below is a rough picture of the evolutionary stage the flywheel has in my head at the moment.
Ooooh, interesting!
Once evolution took a few further steps in the right direction and the flywheel provides good results ( spin times), I might get T-shirt with something corresponding to this one:
(https://i.ibb.co/gWFvyv3/evolution-human-silhouette-vector-260nw-1127956067.webp)
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Osmium is the densest metal. Just sayin'.
PS: But maybe not the best choice for a finger top, as the inevitable oxide coating would be quite poisonous. I'd go with irridium instead.
Osmium a noble metal with beastly properties (https://blogs.unimelb.edu.au/sciencecommunication/2017/08/11/osmium-76os-a-noble-metal-in-character-but-with-beastly-properties-and-a-heart-of-gold/)
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Once evolution took a few further steps in the right direction and the flywheel provides good results ( spin times), I might get T-shirt with something corresponding to this one:
Please order an extra for me!
My wife sometimes thinks I'm an evolutionary throwback. Now that I see that last step in posture, she could be right. Just this once.
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Once evolution took a few further steps in the right direction and the flywheel provides good results ( spin times), I might get T-shirt with something corresponding to this one:
Please order an extra for me!
So what is your guess? What will the last flywheel contour on our T-shirt look like?
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The ideal shape of the flywheel is a very interesting subject.
The ideal moment of inertia is given by the power of the fingers.
Once selected the material, the density is the other design constraint.
I wanted to figure out what would be the toroid with the smallest area if the moment of inertia and density are fixed.
I turns out that the area decreases as the radius is larger (notice that it gets thinner to keep I constant). It is inversely proportional to the square root of the radius.
However, the total air drag torque is the the torque per square cm integrated over the area. This torque is equal to the radius at each point times the drag force per square cm. And we saw that this force increases with speed. If it increases linearly, that's also proportional to the radius at the point.
So, it seems that the gain due to area with larger radius, 1/sqrt(R), is overwhelmed by the increase in torque by unit area, at least proportional to R2.
If this reasoning is correct, a fat small flywheel beats a thin large flywheel, even before considering the drag of the spokes. I was expecting the reverse :o
But air drag is not the only factor. Weight affects tip friction and there is also the effect on critical speed. A very complex optimization problem.
My current guess for the ideal flywheel is a squarish toroid, with bottom and top surfaces slanted outwards (so it's taller on the outside).
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The ideal moment of inertia is given by the power of the fingers.
Is that so? I don't see this directly. Probably has been discussed here many times before. Maybe you could point me to one of those discussions if it can't be made clear in two sentences or so.
Also does that not also depend on the spinning technique? Two fingers of one hand, two fingers of two hands (like you start a stemless one), a Frisbee style throw, a handle like you would spin a curling stone.... They all should give different max possible power/force/strength/speed and also different ratios of those factors that could be relevant here.
Sorry up to this point I am not really making helpful contributions for the theory, only asking questions. ...
Tip friction I would ignore at this stage I think it is of less importance. Maybe only 1/5th or so as important as air drag. Main argument: vacuum experiments of Iacopo and others.
For low critical speed we have to bring the center of mass as far down a possible, right?
In the design I favor at the moment (see below), looks, maybe by chance maybe not, a bit like the Kemner Dynamo top. There are some practical things that influences parts of the contour: I want a few flat millimeters on the upper surface for the "laser balancing method". The outer vertical line should be straight for a good two hand two finger start if stemless. There should be enough material (~8 mm) across so I can put the setscrews in that I want so badly. Same thing in vertical direction for dynamical balancing.
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Yes, it depends on the spinning technique.
There is no gearbox between your fingers and the top, so ideally you would design the top for a moment of inertia at which there is maximum transfer of power. From Iacopo's measurements on the order of 0.0001 kg m2, for a single twirl, but it depends on the person and technique.
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The ideal shape of the flywheel is a ... very complex optimization problem.... My current guess for the ideal flywheel is a squarish toroid, with bottom and top surfaces slanted outwards (so it's taller on the outside).
You could be right!
Battle of the toroids
ta0 got me thinking about "toroidal" finger tops with various toroids for flywheels. So I did a spreadsheet experiment taking advantage of the centroid theorem of Pappus to calculate toroid surface areas and volumes. Assumed that each top would have the same low-mass "core" (combined stem+hub+tip assemblies) but then promptly ignored both the core and how the toroids might attach to it.
Also like ta0, I settled first on a flywheel AMI I3 known to give good release speeds with a single twirl at low vertical ground clearance G without scraping. My choice was Simonelli Nr. 33's AMI of 8.02e-5 kg m². Flywheel mass M then became a derived figure of merit, as smaller M would mean less total weight on the tip contact would mean less tip resistance.
Toroids à la Pappus
To make a toroid, you pick a closed plane figure called a "generator" and an axis in the same plane but outside the generator. Then you put the generator into circular orbit about the axis with its centroid at constant "major radius" R, yielding an orbital circumference of C = 2 π R. The generators I examined were the circle, square, and equilateral triangle.
I scaled each generator's size by the toroid's "minor radius" r -- the circle's radius for the circle, and the inradius (https://en.wikipedia.org/wiki/Inradius) for the polygons. From r, I got the generator's own perimeter p and area a as shown below. And from Pappus, I then got the toroid's total surface area A = C p, volume V = C a, and surface/volume ratio B = A / V = p / a. Moments are a different story, but as long you twist a generator in-plane about its centroid, A, V, and B all stay the same -- even if the generator twists as it orbits! Twisty donuts, anyone?
(https://i.ibb.co/2Kxr8bS/twisted-churro-donut.jpg) (https://imgbb.com/)
Adjustable parameters
This handy way of describing toroids left my 3 toroidal tops with 4 adjustable parameters each: Major radius R, minor radius r, uniform density ρ, and with the toroid mounted on the core, ground clearance G. Could have equalized the toroids' AMIs by varying any combination of these parameters, but this time I varied only minor radius r. Every top then had R = 35 mm, ρ = 8,500 kg/m³ (typical brass), and a challenging G = 4 mm.
Each top's maximum radius X, minimum radius x, central moments I3 and I1, center of mass (CM) to contact distance H, and critical speed ωC followed. The toroidal moments for the circular and square generators came from Wikipedia's list (https://en.wikipedia.org/wiki/List_of_moments_of_inertia). For the triangle, however, I had resort to the convenient but powerful methods of Diaz et al. (2005) (https://ia800901.us.archive.org/34/items/arxiv-physics0507172/physics0507172.pdf).
Generator = circle: Here, r is just the circle's radius. Then X = R + r, x = R - r, p = 2 π r, a = π r², A = 4 π² R r, V = 4 π² R r², and B = 2 / r.
Generator = square: The near and far sides parallel the axis. The inradius r gives the side length s = 2 r. Then X = R + r, x = R - r, p = 4 s = 8 r, a = s² = 4 r², A = 16 π R r, V = 4 π² R r², and again B = 2 / r.
Generator = equilateral triangle: Per ta0's vision, the far side parallels the axis. The inradius r gives the side length s = (6 / √3) r. Then X = R + r, x = R - 2 r, p = 3 s = (18 / √3) r, a = (3 √3) r², A = (36 / √3) R r², V = (6 √3) π R r², and B = 2 / r yet again!
Results
Using rcircle = 3.33 mm, rsquare = 2.95 mm, and rtriangle = 2.59 mm, I dialed in I3 = 8.02e-5 kg m², the AMI of Simonelli Nr. 33.
1. Equalizing the AMIs also equalized the masses and central TMIs. Don't understand the latter, but per Pappus, the former happened because generator areas and toroid volumes all came out the same.
2. All masses M were ~65 g, about 15% under Nr. 33's by virtue of using brass instead of tungsten.
3. All maximum radii X were ~38 mm, also very close to Nr. 33's. The minimum radii x were 32, 32, and 30 mm for the circle, square, and triangle, resp.
4. The triangular and square generators produced 29% and 13% more surface area than the circle due to the same variations in their perimeters.
5. The toroids were 7, 6, and 9 mm tall for the circle, square, and triangle, resp.
6. Top CM-contact distances were 7, 7, and 8 mm for the circle, square, and triangle, resp.
7. Top critical speeds were 422, 410, and 460 RPM for the circle, square, and triangle, resp.
Bottom line
No clear winner here to my eye -- in large part because surface area alone is unlikely to be a good predictor of air resistance. (Wasn't for von Karman's disk, either.) The aerodynamic shear stress on any small part of the flywheel's surface will vary with both surface orientation and distance from the axis. And even if you came up with an expression for that stress, as von Karman did, you'd still have to integrate it over the entire surface of the flywheel. Easy for a thin disk with negligible edge effects, but a daunting task for a toroid.
Surprising findings
Didn't expect that the formula B = 2 / r for surface/volume ratio would be the same for all 3 generators! Also surprised that mass, major max radius, and central TMI varied so little from top to top, even though they were free to do so. As a result, the small differences in critical speed mainly reflected differences in CM-contact distance.
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Didn't expect that the formula B = 2 / r for surface/volume ratio would be the same for all 3 generators! Also surprised that mass, major radius, and central TMI varied so little from top to top, even though they were free to do so. As a result, the small differences in critical speed mainly reflected differences in CM-contact distance.
The same ratio B for the three shapes looked too much of a coincidence. So I thought about it, and found this is a general property for any regular polygon. If you divide an n-polygon into n triangles, each one with base the polygon side (L) and height the inner circle radius (r) the perimeter is n L and the area is n 1/2 L r => B = 2/r.
That the circular and square toroids have similar weight for the same AMI is not too surprising. I'm more surprised about the triangular toroid. Maybe there is a simple reason, if the centroid is at the same distance to the axis. I need to think about it.
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The same ratio B for the three shapes looked too much of a coincidence. So I thought about it, and found this is a general property for any regular polygon. If you divide an n-polygon into n triangles, each one with base the polygon side (L) and height the inner circle radius (r) the perimeter is n L and the area is n 1/2 L r => B = 2/r.
That the circular and square toroids have similar weight for the same AMI is not too surprising. I'm more surprised about the triangular toroid. Maybe there is a simple reason, if the centroid is at the same distance to the axis. I need to think about it.
Nice explanation of the surface/volume ratio formula!
If you or anyone else comes up with other toroid generators of interest with fairly simple mathematical descriptions, happy to add a column to my spreadsheet.
Unfortunately, that criterion pretty much excludes ortwin's planned flywheel and most of Iacopo's as well.
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If you or anyone else comes up with other toroid generators of interest with fairly simple mathematical descriptions, happy to add a column to my spreadsheet.
Unfortunately, that criterion pretty much excludes ortwin's planned flywheel and most of Iacopo's as well.
Since it will be very late in to the year when I finally will have digested all the calculations you present, I might must as well propose the generator shape of interest to me right now. In my evolutionary diagramm it would be just the one before the last one. The right angle triangle. The center os mass should be lower for this one.
There is a link missing in my evolutionary diagram: the additive combination of the tall and narrow rectangle with the flat and wide rectangle. Maybe this shape could also be of interest and not too complicated for describingit mathematically.
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@ortwin: The surface area and volume of a toroid with a right triangle generator will be easy. The moments of inertia will be the hard part.
Assuming you want the hypotenuse sloping upward and outward. Will need a specific slope (e.g., rise over run) to put numbers to it.
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@ortwin: The surface area and volume of a toroid with a right triangle generator will be easy. The moments of inertia will be the hard part.
Assuming you want the hypotenuse sloping upward and outward. Will need a specific slope (e.g., rise over run) to put numbers to it.
Isoscelic, is that the word? 45 degrees.
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...
My current guess for the ideal flywheel is a squarish toroid, with bottom and top surfaces slanted outwards (so it's taller on the outside).
Not sure I understand exactly what you mean by this. Something like the flywheel contour on the left side of the stem in the sketch below?
(https://i.ibb.co/jZqFmQV/flywheel-contour-ta0.jpg)
:-\ Not directly visible before you click the pic. >:( I have to read up one of these days how to properly post the pictures here.
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Will need a specific slope (e.g., rise over run) to put numbers to it.
Can't you just have the results presented as formula where that slope is still a parameter? I guess that is not easily possible, otherwise we could easily differentiate by that parameter and optimize the slope.
Probably same story with rectangles where you leave the height to width ratio open or with an ellipse where you do not specify height to with.
Could you show me the formula for the critical speed? If I am not too scared by the first look of it, I just might try to understand some of it and draw conclusions.
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My current guess for the ideal flywheel is a squarish toroid, with bottom and top surfaces slanted outwards (so it's taller on the outside).
Not sure I understand exactly what you mean by this. Something like the flywheel contour on the left side of the stem in the sketch below?
:-\ Not directly visible before you click the pic. >:( I have to read up one of these days how to properly post the pictures here.
Close, but the bottom surface slanted the other way. My idea was to restrict a bit the Von Karman pumping on the top and bottom.
But my thinking is evolving . . .
To post the whole image, just replace the thumbnail with a direct link to the complete image. But you don't want to link to a very large image. When you upload it, there is a pencil icon that you can click to edit the size.
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Close, but the bottom surface slanted the other way. My idea was to restrict a bit the Von Karman pumping on the top and bottom.
But my thinking is evolving . . .
My reasoning for slanting it like this, is to bring the CM further down compared to the contour on the right side while keeping the scraping angle and AMI the same.
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Can't you just have the results presented as formula where that slope is still a parameter?
Sure. Is your triangle slanted out (taller on the outside) or slanted in (taller close to the axis)?
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Can't you just have the results presented as formula where that slope is still a parameter?
Sure. Is your triangle slanted out (taller on the outside) or slanted in (taller close to the axis)?
Taller outside.
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Taller outside.
By integration I get that the moment of inertia increases linearly with the height of the triangle, if you you keep the the other side and the distance to the axis constant.
The equation is:
I = ρ 2 π h/L [(R+L)4 (L/5-R/20) + R5/20]
where ρ is the density, R the inner radius, L the base of the triangle and h the height.
Edit: Changed the last - to +. Thanks Jeremy for pointing out the error.
I also realized that it could be calculated without any integration. Just add the moment of inertia of a cylinder and a small cone and subtract a large cone.
In general the moment of inertia of any toroid with triangular cross section can be calculated by the sum and subtraction of the moments of inertia of cones and perhaps a cylinder.
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The equation is:
I = ρ 2 π h/L [(R+L)4 (L/5-R/20) - R5/20]
where ρ is the density, R the inner radius, L the base of the triangle and h the height.
Thank you very much, but how to compare this now to the results Jeremy presented? For example to the triangle with three 60 degree angels that you suggested?
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The equation is:
I = ρ 2 π h/L [(R+L)4 (L/5-R/20) - R5/20]
where ρ is the density, R the inner radius, L the base of the triangle and h the height.
Thank you very much, but how to compare this now to the results Jeremy presented? For example to the triangle with three 60 degree angels that you suggested?
To bring a new generator into my Pappus- and Diaz-based framework, I need to parameterize its orientation, size, and exact shape (mass distribution), including the coordinates of its centroid.
Specifying "equilateral triangle" or "isoceles right triangle" (as ortwin did earlier) allows all that in a way that "generic right triangle" does not.
I can move ahead with the isocelese case with one side facing outward. And I'll see how much I can generalize. But in the end, I'll need a specific right triangle in a specific orientation to compare the resulting toroid to the ones already evaluated.
Remember, we want to end up with toroid mass, critical speed, and total surface area at constant AMI. And for the critical speed, we need TMI as well.
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Once evolution took a few further steps in the right direction and the flywheel provides good results ( spin times), I might get T-shirt with something corresponding to this one:
Please order an extra for me!
My wife sometimes thinks I'm an evolutionary throwback. Now that I see that last step in posture, she could be right. Just this once.
So I take it you and your wife are already wearing these? :
(https://i.ibb.co/M1xtFBx/Screenshot-20210307-212333-Chrome.jpg) (https://ibb.co/M1xtFBx)
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@otrwin: Great T-shirt, but I don't think she views my continuing de-evolution as an improvement.
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Will need a specific slope (e.g., rise over run) to put numbers to it.
Can't you just have the results presented as formula where that slope is still a parameter?
Figured out a way to parameterize a right triangle generator with one leg (non-hypotenuse) facing outward in terms of its inradius and the angle pointing inward. Will explore 2 toroids with angles of 30° and 60° and go from there.
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Examined 3 more toroids using right triangle generators with one leg parallel to the plane of the toroid and inner angles of 30°, 45°, and 60°. Computing the moments of inertia was no fun.
Highlights...
1. The square's toroid still had the lowest critical speed at 410 RPM, but the 30° right triangle's was a close 2nd at 416 RPM. The 60° right triangle had the highest at 495 RPM -- mainly due to having the largest central TMI and CM-contact distance.
2. The square's toroid had 13% more surface area than the circle's, while the 30° and 60° right triangles' had ~43% more. All other toroids were in between.
3. All toroids had maximum radii of 38±1 mm.
4. As before, the circle's toroid had largest central opening. The 30° right triangle came in with the smallest.
5. As before, the square's toroid had the shortest axial length. And as you might guess, the 60° right triangle came in with the tallest.
6. Toroid masses varied by <1%. Hence, when mounted on the same core, the resulting tops would have about the same tip resistance.
Actual relative air resistances remain unknown.
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Examined 3 more toroids using right triangle generators with one leg parallel to the plane of the toroid and inner angles of 30°, 45°, and 60°. Computing the moments of inertia was no fun.
No fun is not good! Thanks for doing it anyway! What I take home from your highlights is, that the right angle triangle that I proposed is probably not an evolutionary step forward from the square. But I am quite sure slanting it like on the left side of the stem would provide a little improvement.
(https://i.ibb.co/jZqFmQV/flywheel-contour-ta0.jpg)
That is by reasoning:
My reasoning for slanting it like this, is to bring the CM further down compared to the contour on the right side while keeping the scraping angle and AMI the same.
The surface area is a bit larger, but my feeling is that the lower CM is more important.
This optimization step in construction should work for most generators:
- imagine your flywheel is cut from a roll of aluminum sheet rolled around the stem
- draw your scraping line
- let all your thin aluminum tubes gravitate towards that scraping line.
-> CM came down, AMI stayed constant, surface increased a bit
Ah, and Jeremy, you probably missed my request below:
Could you show me the formula for the critical speed? If I am not too scared by the first look of it, I just might try to understand some of it and draw conclusions.
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Could you show me the formula for the critical speed? If I am not too scared by the first look of it, I just might try to understand some of it and draw conclusions.
Not missed, just deferred, as the formula deserves some explanation.
For a top in steady precession (no wobble) at tilt angle θ, the formula you usually see is for the square of the critical angular speed ωC in rad/s:
ωC² = 4 M g H I1tip cos(θ) / I3²
where M is the mass in kg, g = 9.81 m/s² is the acceleration of gravity, H is the CM-contact distance in m, I1tip is the transverse moment of inertia (TMI) about the tip (contact point) in kg m², and I3 is the axial moment of inertia (AMI) in kg m². When you have a sleeper with θ = 0, the cos(θ) factor goes away.
Technically, ωC includes both the pure spin rate and a component of the precession rate. But for design purposes, you can interpret ωC as the critical spin rate to a good approximation, as the precession rate involved is usually much smaller.
Making that which is hidden seen
The problem with using I1tip is that it buries a hugely important dependency on H. To get the latter out in the open where it belongs, I prefer the "central TMI" I1cm -- i.e., the TMI about the CM. An added advantage is that I1cm is the TMI you see in tables of formulas like the one on Wikipedia (https://en.wikipedia.org/wiki/List_of_moments_of_inertia). The parallel axis theorem shows how the two TMIs are related:
I1tip = I1cm + M H²
With H exposed in all its glory, the critical speed is then
ωC² = 4 M g H (I1cm + M H²) cos(θ) / I3²
So your plan to minimize H and maximize I3 for a given scrape angle is well founded, as H is the most influential parameter here, with I3 not far behind. You can also see why we sometimes talk about the TMI/AMI ratio.
Forget the mass
But the mass M turns out to be just confusing clutter, as both moments are also proportional to M. To give M the boot it deserves, I prefer to use the "specific moments" Ji (aka moments per unit mass), like so...
J3 = I3 / M and J1 = I1 / M
For example, in the formula I3 = 1/2 M R² for the AMI of a thin disk of radius R , the specific AMI is just the 1/2 R² part.
The critical spin rate then reduces to
ωC² = 4 g H (J1cm + H²) cos(θ) / J3²
In words, critical speed has nothing to do with mass. To minimize it, you need to focus on maximizing J3 and minimizing both J1cm and H. As an added bonus, you can then get all the AMI you need with the least weight on the tip.
Practical applications
Unlike the regular moments, the specific moments are purely geometric in nature. For example, the specific AMI J3 measures the efficiency of a top's mass distribution about the spin axis without regard to how much mass there actually is.
Suppose you have two lumps of clay, A and B, of the same mass M. You mold A into a solid disk and B into a hollow toroid of the same maximum radius R. Since B will get more AMI out of the same mass, it will have the greater specific AMI.
I find it useful to think in terms of specific moments when I'm optimizing top designs -- especially J3. But you also have to play a delicate trade-off with the absolute AMI I3, as AMI is the inertia that opposes any change in spin rate -- during both spin-up and spin-down. Too much AMI, and you'll limit the release speed your fingers can attain in the brief time available during a single twirl. Too little, and air and tip resistances will chew up your hard-won release speed that much faster. Test, test test!
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You explained that formula very nicely Jeremy! I just need to find an explanation of how this formula comes about. It seems only then I am fully prepared to believe I can too draw conclusions from it. Don't worry, if you don't have an explanation ready, I try to find something in the books. "Critical angular speed" is the term I should start looking for?
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Hope it helps your design process. Look for Jerry Ginsberg's excellent textbook Advanced Engineering Dynamics, free online.
His formulas differ a bit in that he gives the critcal spin rate (not the total angular speed) directly -- but with the complication of a non-physical result in the unlikely event that TMI about the tip is less than the AMI. I like his derivation and stability analysis, though. See chapter 10.
The excellent article by Provatidis, "The spinning top revisited" gives the formula I used explicitly. It's also less intimidating but is no longer free online.
Another good online freebie is Chloe Elliot's "The spinning top" -- maybe part of a thesis. Nice explanations of many things, but she takes a lot longer to get around to critical speed.
The above are all for "symmetric tops" with only 2 distinct principal moments of inertia. Most real tops are of that kind but need not be.
For a fascinating engineering approach to asymmetric tops, see the superb free online article "Spin-it: optimizing moment of inertia for spinnable objects" by Bacher et al. of Disney Research. They give a critical speed formula unique to such tops but don't derive it. I found the nomenclature in their source for it utterly impenetrable.
(https://i.ibb.co/PWgMstM/20191217-145903.jpg)
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@ortwin: Since we both seem to like space stations and tops, one of my favorite tops...
(https://i.ibb.co/mFGswFQ/20210308-162956.jpg)
(https://i.ibb.co/kgQ4YMw/20210308-163130.jpg)
An older version below. Of course, no need to worry about air or tip resistance in space.
https://youtu.be/h0MtHhijJAk
One of the best musical themes in all of TV if you ask me.
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That wormhole sink makes me laugh quite hard! ;D
The excellent article by Provatidis, "The spinning top revisited" gives the formula I used explicitly. It's also less intimidating but is no longer free online.
I could still download it for free and I'm attaching it to the post just in case it's unavailable in the future. I don't think I would call it less intimidating ::) Also, I didn't see the equation for the critical spin when I browsed it.
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It's kinda scary having a wormhole in your sink.
You know how they say never to put your hand down a Dispose-All? Well, that goes about a thousand times for a wormhole when the rest of you won't fit.
And you wouldn't believe the things that come out of it! My kitchen's that Star Wars bar scene in miniature every day!
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https://videoportal.uni-freiburg.de/video/Supraleiter-auf-Moebiusband/f489e06ec021b42a23780fe7fbf861d2
cooool video of super conductor on moebius strip.
That is nothing new of course and not really directly related to the topic of this thread. But have a look at those strings where the möbius strip hangs from: If we tension them, we have our minimalistic spokes and a moebius flywheel. Jeremy please do a quick calculation of the generator for that and put it into you spreadsheet! Is it better or worse then the square?
No, not serious. Regardless if it is better or worse for spin time, it would be cool to have a moebius flywheel top. Any 3-D printing specialist around?
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Jeremy please do a quick calculation of the generator for that and put it into you spreadsheet! Is it better or worse then the square?
No, not serious. Regardless if it is better or worse for spin time, it would be cool to have a moebius flywheel top. Any 3-D printing specialist around?
Piece of cake! And yes, we have some very adept 3D-printers.
That hanging Mobius goes way beyond cooool, my friend. It's gorgeous, too! Elegant kinetic sculpture, fascinating geometic model, and spectacular science demo all in one. Hats off to the artist.
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Now I want a flywheel like one of these:
(https://i.ibb.co/cYQdVW7/Mobius.jpg) (https://ibb.co/cYQdVW7) (https://i.ibb.co/74HmtL8/mobius2.jpg) (https://ibb.co/74HmtL8) (https://i.ibb.co/Zzwz2GH/Mobius3.jpg) (https://ibb.co/Zzwz2GH)
I can't even really tell if you have to go around two times or four times here to get back to the start. Both variations are a possibility.
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Twisting toroids, Batman! These would look great. And if anybody could make a suspension top out of them, it'd be you.
In fact, these look like great testbeds for evaluating suspension system designs.
Welcome to aerodynamic hell.
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I hadn't seen the superconductor running on a Mobius band before. It's super cool! 8)
I'm guessing the moment of inertia is intermediate to that of a vertical track and a horizontal track (corrected for the added mass given by the longer path), which for a thin track would not be very different to the mass times the radius (at the center) squared. The complicated part is the air drag . . .
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I'm guessing the moment of inertia is intermediate to that of a vertical track and a horizontal track ....
Probably a very good guess. Those two are also on my sketch for the evolutionary T-shirt. But Jeremy has not presented any results on these. So they might be quite mediocre?
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I hadn't seen the superconductor running on a Mobius band before. It's super cool! 8)
https://youtu.be/8tFsrGRwOOM (https://youtu.be/8tFsrGRwOOM)
So this one is not as cool, since it does not need any cooling, but it is running as long the sun is shining.
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Now I want a flywheel like one of these:
(https://i.ibb.co/cYQdVW7/Mobius.jpg) (https://ibb.co/cYQdVW7)
I can't even really tell if you have to go around two times or four times here to get back to the start.
Made some twisted toroids using flexible LEGO axles and mounted them on appropriate cores with rigid spokes...
(https://i.ibb.co/5nsTYxB/20210311-110046.jpg)
Below is the smaller one on the right at speed...
(https://i.ibb.co/8DHcFNf/20210311-110332.jpg)
The twisted toroid on this one turns out to be a trefoil knot.
(https://i.ibb.co/7QQfksf/Tricoloring.png)
(Public domain image from Wikipedia's trefoil knot page.)
If the white axles were the edges of a continuous ribbon, the ribbon would form a 3-pi Mobius strip.
The other one turned out to be too hard to balance, so I scrapped it for this soft suspension top...
(https://i.ibb.co/P6kpSmG/20210312-162913.jpg)
This one and the trefoil top only stay up 10-15 s, but I like them anyway.
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Made some twisted toroids using flexible LEGO axles ......
LEGO, really? You? Looks like licorice candy sticks to me. Although I did not know they come in white also.
No, really cool stuff. The last one looks as if you were trying to simulate a Curtain-Ring-Top. ;)
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Made some twisted toroids using flexible LEGO axles ......
The last one looks as if you were trying to simulate a Curtain-Ring-Top. ;)
I was!
Working now on a video exploring some of the engineering challenges involved in suspending a toroid from an inherently unstable core using only chains, cables, strings, etc. Interesting stuff.
Sent you a PM about it.
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Sent you a PM about it.
Something must have gone wrong there. My post box is still empty.
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Sent you a PM about it.
Something must have gone wrong there. My post box is still empty.
Interesting. I'll try again.
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Experiment: "von Braun space station" top with and without fairings*
(https://i.ibb.co/WyrM3XC/20210401-112320.jpg)
Test top: High-AMI, low-CM spoked flywheel top with 2 easily removed rigid (HDPE?) disk fairings of negligible thickness
Base: Concave lens, modest curvature, lubed with skin oil. Taken at the horizontal flywheel's lower outer edge, the top has 22 mm of ground clearance on the lens and 12 mm on a flat surface.
(https://i.ibb.co/FY17WN9/20210331-200708.jpg)
Measurements: Best spin time of 3+ runs from 1,010±10 RPM and 0° tilt to first audible scrape.
Top A. Bare top, short test stem, no fairings
(https://i.ibb.co/vsB3Jz2/20210331-213456.jpg)
Top B. Top A + single 17.2 g fairing below flywheel (bore sealed from below)
(https://i.ibb.co/VwNxBHY/20210331-213044.jpg)
Top C. Top A + single 11.6 g fairing above spokes (bore not entirely sealed from above)
(https://i.ibb.co/CwYq6Ps/20210331-213344.jpg)
Top D. Top A + both of the fairings above
(https://i.ibb.co/J7Sm8xz/20210401-213720.jpg)
Variables
1. Total mass (M): 137 - 165 g
2. CM-contact distance (H): 24 - 26 mm
3. Total AMI (I3): 7.1e-4 - 8.2e-4 kg m²
4. Total TMI at tip (I1t): 4.5e-4 - 5.2e-4 kg m²
5. Critical speed (ωC): 10.8 - 11.4 rad/s (103-109 RPM)
6. Scrape angle (θmax): 15° on lens, 8° on flat surface
Controlled parameters (reasonably constant from top to top)
1. Flywheel, spoke, and core assemblies, max radius 84 mm
2. Release speed (ω0): 106 rad/s (1,010±10 RPM)
Best spin times
Top A (no fairings, on lens) .................. 185 s
Top B (lower fairing only, on lens) ......... 188 s
Top C (upper fairing only, on lens) ......... 203 s
Top D (both fairings, on lens) ................ 333 s
Top D (both fairings, off lens) ................ 290 s
Can lightweight fairings improve a spoked flywheel top's spin time? You bet! Fair the flywheel and spokes both above and below, and you get a whopping 64% gain in spin time over the better 1-fairing case (Top C) and an 80% gain over the 0-fairing case (Top A).
With just the lower fairing, Top B stayed up only 2% longer than Top A. But with just the upper, Top C consistently stayed up 10% longer than Top A — and that with an 8 mm air gap still present between the upper fairing and flywheel.
Fairings vs. mass properties: The simple shapes and the few internal air voids involved allowed me to calculate mass properties with decent accuracy. Turns out, the fairings had little impact on CM height: In mm, Top A = Top D = 25, Top B = 24, and Top C = 26.
The moments felt the fairings more. When both were present (Top D), they accounted for ~17% of the top's total mass, ~12% of its total AMI, and ~13% of its total TMI about the tip. However, all 4 tops ended up with nearly identical TMI/AMI ratios at the tip (where it counts).
Fairings vs. critical speed: Estimated critical speed combines all of a top's key mass properties into a single figure of merit with a big impact on spin time. In RPM, Top A = 104, Top B = 103, Top C = 109, and Top D = 107.
So for all the differences in mass properties, little change in critical speed. No good explanation for Top D's dramatic success there, so it must have been aerodynamic.
Ground effect? Most of the 43 s lost when Top D came off the lens must have been lost to air resistance. Why? Well, Tops A-D were already in their death spirals at the 8° scrape angle available off the lens. Takes at most another 5 s to reach the 15° scrape angle available on the lens. The rest of that 43 s had to be aerodynamic, cuz nothing else changed.
With Top D off the lens, there was still a 12 mm air gap beneath the lower fairing. Would a narrower gap have reversed the trend? Hard to say, but it would definitely have made the top harder to twirl on a flat surface.
Suppressing a top's centrifugal pumping action may still be a good thing to try, but top aerodynamics are clearly way more complicated than that.
Play value: I really enjoy this space station top. Plan to hang on to the fairings, but prefer the top without them. It's big and bold, loves to sleep, and stays up 130 s with a single twirl without fairings. When I want more spin time, I'd rather go to a fun starter instead.
(https://i.ibb.co/kcvxDzZ/20210401-214013.jpg)
* Acknowledgments: Thanks to Iacopo for pushing me to do this experiment. Sorry it took so long. Also thanks to ortwin for pointing out that von Braun beat me to this top's basic design 70 years ago (https://en.wikipedia.org/wiki/Rotating_wheel_space_station). (And some Russians long before him.) Not sayin' Werner had it easy, but no gravity or air resistance to contend with in orbit.
https://youtu.be/5JJL8CUfF-o
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https://www.google.com/amp/s/www.space.com/amp/gateway-foundation-von-braun-space-station.html
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https://www.google.com/amp/s/www.space.com/amp/gateway-foundation-von-braun-space-station.html
Very cool! I'd go for a week with a suitcase full of tops to test in the various (fake) gravity environments available.
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Best spin times
Top A (no fairings, on lens) .................. 185 s
Top B (lower fairing only, on lens) ......... 188 s
Top C (upper fairing only, on lens) ......... 203 s
Top D (both fairings, on lens) ................ 333 s
Top D (both fairings, off lens) ................ 290 s
As I expected, the top without fairings has the worst time.
But there are also results which I didn't expect in this experiment.
One fairing should be sufficient to cut the Von Karman flow and improve the spin time significantly, but in this your experiment both the fairings were necessary. Why ?
I suspect that the reason is the large spokes. These spokes work like a fan and they probably have a large air drag relatively to the flywheel.
The fairing attached below the top, (top B), seales the bore, reducing the Von Karman flow under the top, (how much is the clearance between the flywheel and the table when the top spins on the lens ? With too much clearance the ground effect is little.)
But the spokes are still exposed to the air.
The fairing above the top, (top C), isolates the spokes from the air above, still this could be not sufficient to interrupt the pump mechanism, because the air can enter below the top, then it can rise passing through the bore of the top, until finding the spokes, and at this point the air is ejected sideways by the spokes working like a fan. The fairing in fact is not in contact with the flywheel, there are openings between them, and the air can be ejected through these openings.
Maybe for these reasons both the fairings are necessary for to reduce efficiently the pump effect;
with both the fairings, the spokes are more efficiently isolated from the outside, and, as for air drag, they become like non existent.
Was the cake good, at least ? :)
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Was the cake good, at least ? :)
Chantilly cake -- yum! (In a PM to Iacopo about this experiment, I mentioned that the fairings were cut from supermarket cake and pie containers.)
But there are also results which I didn't expect in this experiment.
That makes 2 of us, though perhaps for different reasons.
These spokes work like a fan and they probably have a large air drag relatively to the flywheel.
Absolutely! We already have strong experimental evidence that the fully exposed spokes in Tops A and B were major sources of air resistance. Also agree that hiding them even partially from the surrounding air under an upper fairing had much to do with the significantly longer spin times turned in by Tops C and D.
One fairing should be sufficient to cut the Von Karman flow and improve the spin time significantly, but in this your experiment both the fairings were necessary. Why ? ... how much is the clearance between the flywheel and the table when the top spins on the lens ? With too much clearance the ground effect is little.
Potential roles of von Karman-like flows: I try keep this diagram of a pure von Karman swirling flow in mind when imagining the flow around disk-like tops. Remember, this flow pattern's generated by a solid disk spinning in otherwise still air.
(https://i.ibb.co/fXVc0Zm/Screenshot-2021-02-18-111916.png) (https://ibb.co/Cwpr04x)
But the flywheel here wasn't even close to a solid disk, as its inner/outer radius ratio was 85%. Guessing therefore that the flow around the flywheel in Top A was mostly not von Karman-like. Perhaps not in Top B, either.
Was there still some centrifugal pumping action with no fairings? Surely, but likely with a very different geometry — perhaps a cross between your 2 recent diagrams below...
(https://i.imgur.com/BWfXG12.jpg)
Hence, covering one flywheel face with a flat fairing made the flow over that face much more von Karman-like, not less. Moreover, when such a flow was present, there was nothing on that side of the flywheel to disrupt it. Also, unlike the von Karman case, edge-effects were likely important given the flywheel's (axial length)/(outer radius) ratio of 29%.
Potential ground effect: First, please remind me of the experimental evidence we have for a pure ground effect -- i.e., a clear-cut aerodynamic benefit obtained solely with a small ground clearance (no upper or lateral shrouds or fairings involved). Link to the post?
At release and critical speeds of ~1,000 and ~100 RPM, respectively, all of my test tops had Reynolds numbers of 5.0e4 and 5.3e3, resp. Hence, all operated largely in the laminar regime (save for any turbulence generated by the spokes and inner gear teeth). Fair to say, then, that the exposed side of each fairing had (laminar) boundary layer thicknesses of 2.0 or 6.3 mm, resp.
But when sleeping on a flat surface, Top D's lower fairing had a uniform ground clearance of 12 mm -- at least twice its underside boundary layer thickness at any speed. Aerodynamically speaking, then, Top D would not even have felt the table's presence in my experiment.
In the engineering of disk-like rotors inside tightly fitting shrouds, all it takes to keep the shroud from slowing down the disk is an air gap thicker than the disk's boundary layer at operating speed. Not sure what opportunity this leaves for a beneficial ground effect under a top in the laminar regime.
That said, will try to test a Top D variant on a flat surface with a ground clearance under 6 mm.
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please remind me of the experimental evidence we have for a pure ground effect
Look at replies #5 and #8 in this thread.
I had the best ground effect with clearances from 1 to 5 mm. Your top is larger and moves more air so in your case the optimal clearance could be larger, but I am not sure.
I believe that the ground effect works because, for the air to be ejected outside from the bottom of the spinning flywheel, first the air has to reach the bottom of the top, but the only possible entrance for the air is the clearance between the flywheel and the ground, so in the same clearance there are two flows of air in opposite directions, which obviously disturb each other, especially with a narrow clearance, this is what weakens the Von Karman flow and reduces the air drag.
In the engineering of disk-like rotors inside tightly fitting shrouds, all it takes to keep the shroud from slowing down the disk is an air gap thicker than the disk's boundary layer at operating speed. Not sure what opportunity this leaves for a beneficial ground effect under a top in the laminar regime.
A shroud surrounding the whole top is another way to take care of the Von Karman flows, which is more effective probably because it works with the flows both above and below the top.
We already have strong experimental evidence that the fully exposed spokes in Tops A and B were major sources of air resistance.
covering one flywheel face with a flat fairing made the flow over that face much more von Karman-like, not less[/i].
I agree that your space station top is something more complicated.
I would say that the pump effect and the associated air drag come from
- The Von Karman flow around the flywheel, and/or the fairings.
- And, above all, the spokes, which work like a fan.
Even if the fairings increase the Von Karman flows, on the other hand they isolate the spokes, and in the overall costs/benefits balance
there is obviously advantage because your top spins much longer in this way.
This is how the air could move in you top C, (one fairing above the top).
The spokes eject the air outside and they can do so because there is an inlet for this air, the clearance under the flywheel and the bore in the top; this air is sucked from the spokes/fan and ejected sideways.
So one fairing on the top is not sufficient to break the pump effect of the spokes, and top C isn't much better than top A, (no fairings).
(https://i.imgur.com/F7m2FbZ.jpg)
But when the second fairing is applied, (top D), the bore in the top is sealed from below, and there are no more air inlets for the spokes, which can't work anymore. The big pump effect of the spokes is killed. The Von Karman flows instead are increased because of the fairings but in the whole the pump effect and the air drag are much lower and the spin time quite longer.
At this point, finding the optimal clearance between the flywheel and the ground could weaken the Von Karman flow under the top, with further reduction of the air drag.
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Once my "Easy Listening" (http://www.ta0.com/forum/index.php/topic,6419.msg70037.html#msg70037) suspension top is running stable, with reproducible results, balanced and with reliable RPM readings available, I hope to make some measurements with/without fairings that contribute towards the questions that come up with the topic here. I think it is suited well for this task.
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I hope to make some measurements with/without fairings that contribute towards the questions that come up with the topic here. I think it is suited well for this task.
I am sure it will be interesting.
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@Iacopo: Thanks for pointing me to your ground effect experiments. You clearly demonstrated a benefit for the 2 tops tested, especially with a 3 mm air gap beneath their rotors.
Q1: Which top did you test in Reply #5 and what's its diameter and metal?
Meanwhile, from your Reply #5...
(https://i.imgur.com/9wmXLcy.jpg)
OMG, look at that Simonelli top collection in the background!
Q2: Would you be willing to give us a video tour when you have the time? Pretty please?
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Q1: Which top did you test in Reply #5 and what's its diameter and metal?
Q2: Would you be willing to give us a video tour when you have the time? Pretty please?
It is the Nr. 15, lead, 52 mm.
I made a little stand for my tops, I keep them on the table in my bedroom.
I am drawing my new top in this moment. I had practically so little free time during the last three months, but now I will have the next one or two months free for my tops, a breath of fresh air !
(https://i.imgur.com/Z4sxy3K.jpg)
Each one of these tops can be seen in my YouTube channel, so a photo should be enough here;
from left to right, and from below to above, they are the Nr. 6, 9, 18 in the white egg, (first row), 8, 10, 12, 13, 14, 15,(second row), 20, 38, 29, 30, (third row). All the other metal tops have been sold. The eggs and the spheres are materials I could use for new tops, there are two nice malachite eggs which I will certainly use, sooner or later.
(https://i.imgur.com/DwzMPDR.jpg)
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It is the Nr. 15, lead, 52 mm.
I am drawing my new top in this moment. I had practically so little free time during the last three months, but now I will have the next one or two months free for my tops, a breath of fresh air !
Thanks! A very happy turn of events -- and one that can only work to our benefit. Excuse me while I drool over the photo some more...
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The website on your screen looks familiar . . . ;D ;D ;D
Yeah, nice collection of tops! 8)
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... will try to test a Top D variant on a flat surface with a ground clearance under 6 mm.
Looks like that's gonna take a while. For now, a much easier follow-up on my last experiment (Reply #117)...
Top E: Top A (no fairings) with hub shortened to reduce flywheel ground clearance.
All changes, Top A to Top E
1. Flywheel ground clearance (G): 22 to 13 mm on lens, 12 to 3 mm off
2. Scrape angle (θmax): 15° to 9° on lens, 8° to 2° off
3. CM-contact distance (H): 25 to 16 mm
4. Total mass (M): 137 to 134 g
5. TMI at tip (I1t): 4.5e-4 to 4.0e-4 kg m²
6. Measured critical speed (ωC): 95 to 62 RPM
Unchanged
1. Flywheel, spoke, stem, and tip assemblies, max radius 84 mm
2. No fairings
3. Release speed (ω0): 1,010±10 RPM
4. AMI (I3): 7.1e-4 kg m²
Best times on lens, from 1,010±10 RPM to first audible scrape
Top A, H = 25 mm, G = 22 mm .................. 185 s
Top E, H = 16 mm, G = 13 mm .................. 254 s*
* Time for Top E includes a 1 s credit to compensate for its much smaller scrape angle.
Top E's impressive 37% spin-time gain here has little to do with aerodynamics. In this comparo, CM height H went from Top A = 25 mm in to Top E = 16 mm. Measured critical speed changed accordingly, from ~95 RPM to ~62 RPM, resp. And it takes Top E a full 60 s to cover this 33 s critical speed gap. So on the lens, aerodynamic effects could have contributed no more than 9 s of Top E's 69 s of added spin time.
Now for a purely aerodynamic difference: Top E on and off the lens, always stopping the clock at 100 RPM to eliminate the scrape-angle difference...
Best Top E times from 1,010±10 RPM to 100 RPM
Top E, G = 13 mm .................. 185 s
Top E, G = 3 mm .................. 183 s
Since there were no offsetting factors to explain this null result, it's fair to say that reducing G from 13 to 3 mm in Top E had no beneficial aerodynamic effect.
Ground effects: In airplanes, a beneficial aerodynamic "ground effect" reduces airspeed and thrust requirements at altitudes under 1 wingspan or so. Helicopters enjoy a beneficial ground effect all their own, and race cars use theirs to improve cornering by adding an aerodynamic downforce on their tires.
The underlying mechanisms in these 3 cases are completely different, and none apply to spinning tops. But in Replies #5 and #8 of this thread, Iacopo clearly demonstrated yet another beneficial ground effect: In 2 different classic Simonelli tops, reducing G with no other change prolonged the time needed to spin down from 1,600 to 1,500 RPM by up to 7%, with the greatest benefit at G = 3 mm.
Question is, why did Iacopo see a small but significant ground effect at G = 3 mm when I found none? Two reasons, I think:
1. My rotor had a big hole in the center for air to flow through, and his had none.
2. His tops were completely streamlined in all directions and operated entirely in the laminar regime. Mine, on the other hand, had spokes, gear teeth, and sharp edges capable of generating vortices, turbulent wakes, and other flow complications.
Take-home lesson: Arguably, the 2 most counterintuitive areas in all of classical mechanics are rigid body and fluid dynamics, and here we're trying to tackle both at once! Imagining the air flows our tops stir is tricky business. Imagining how those flows affect the air resistances our tops encounter is even trickier.
Note on play value: The more muscle needed to start a top by hand, the more wiggle room needed to avoid scraping during the twirl. With its 2° scrape angle on a flat surface, Top E had this problem in spades. Though Top E had decent play value on the lens, I view Top A as the keeper here for its superior ease of use.
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Best Top E times from 1,010±10 RPM to 100 RPM
Top E, G = 13 mm .................. 185 s
Top E, G = 3 mm .................. 183 s
This is what I meant when I suggested that tops with a bore do not benefit from the ground effect.
Your experiment confirms it.
But if you can use your top with the fairings, I am sure you will see the difference, even more than me, because your top is large and light and very sensible to aerodynamics.
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More ground effect tests
Sheesh, now I understand why von Braun decided to spin his space stations in a vacuum! Back now to fully faired space station Top D — this time with the width G of the uniform "air gap" beneath the lower fairing ranging from 2 to 20 mm at constant CM height.
Top D: Spoked flywheel top, max flywheel radius R = 84 mm, flat fairings above spokes and below flywheel. When vertical on a flat surface, G = 12 mm.
(https://i.ibb.co/GtQp5q0/20210406-115249.jpg)
Base: Small, deeply concave lens on right below, lubed with skin oil.
(https://i.ibb.co/hFxYShp/20210406-105917.jpg)
Bottom shroud: Clear round disk mounted around lens as shown. Flat part of shroud has max radius R + 6 mm.
(https://i.ibb.co/6vpNP5w/20210406-105714.jpg)(https://i.ibb.co/qNV1FJc/20210406-105820.jpg)
Variables
1. Air gap thickness beneath bottom fairing (G): 2 - 20 mm
Constant across all time measurements
1. Release speed (ω0): 1,010±10 RPM
2. Final speed (ωF): 120±1 RPM
3. CM-contact distance (H): 25 mm
4. Total mass (M): 169 g
5. AMI (I3): 8.2e-4 kg m²
6. TMI at tip (I1t): 5.2e-4 kg m²
7. Measured critical speed (ωC): ~110 RPM
Best Top D times from 1,010±10 to 120±1 RPM, on lens over shroud unless otherwise noted
G = 2.0 mm .............................. 303 s
G = 5.2 mm .............................. 310 s*
G = 8.4 mm .............................. 310 s*
G = 11.6 mm ............................. 319 s*
G = 20 mm, on lens sitting on table ..... 317 s*
Ground effect? Still no evidence for a beneficial aerodynamic ground effect in this top. In fact, just the opposite, as times only grew as G increased from 2 to 20 mm. Must be aerodynamic, as nothing else changed.
So why did Simonelli Nr. 29 below see a clear and beneficial ground effect? Starting to think that flywheel profile matters.
(https://i.imgur.com/xIi7WlX.jpg)
Was the shroud's radius large enough? Probably, but planning one more test with a much larger shroud radius at the same G values. Just waiting on the material.
Hula-hooping instability: Top D was happy to sleep quietly from release to fall at G > 5.2 mm. But at smaller air gaps, it insisted on hula-hooping with decreasing amplitude from release to ~300 RPM. Why? Guessing some kind of periodic instability in the restricted air flow beneath the top. The larger, shallower lens used in all previous tests (above, left) couldn't contain the hula-hooping reliably — hence the lens change.
Will this study ever end? Every time I think it's done, it just keeps going. Which reminds me of a song...
https://youtu.be/xz6OGVCdov8
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G = 2.0 mm .............................. 303 s
G = 5.2 mm .............................. 310 s*
G = 8.4 mm .............................. 310 s*
G = 11.6 mm ............................. 319 s*
G = 20 mm, on lens sitting on table ..... 317 s*
You made a large hole in the bottom shroud, so the air fueling the Von Karman flow under the top can come directly from there, if the bottom shroud stays higher than the lens. Maybe when the bottom shroud is in a lower position, (gap 20 mm), its hole is sealed by the lens, and you have a bit of ground effect, but when you rise the bottom shroud for to reduce the gap, a gap forms between the lens and the bottom shroud, so you lose the ground effect.
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Once my "Easy Listening" (http://www.ta0.com/forum/index.php/topic,6419.msg70037.html#msg70037) suspension top is running stable, with reproducible results, balanced and with reliable RPM readings available, I hope to make some measurements with/without fairings....
Just a quick result from "Easy Listening" on concave mirror: no fairing 8:45Directly after this run I applied a foil to the upper side: upper fairing 8:50
So really about the same. Actually I am surprised that the time did not become smaller.Maybe I am with my top geometry accidentally in the cross over region where benefits and costs of a fairing cancel themself out more or less?Methodically it would be better not to compare the full spinning times, but the times of the spin down from 500 RPM to 450 RPM for example
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So really about the same. Actually I am surprised that the time did not become smaller.Maybe I am with my top geometry accidentally in the cross over region where benefits and costs of a fairing cancel themself out more or less?Methodically it would be better not to compare the full spinning times, but the times of the spin down from 500 RPM to 450 RPM for example
It is 1% difference, very little. I agree with your observations; with the fairing, you probably have the advantage of the ground effect and at the same time the disadvantage of more surface for the Von Karman flows. If you can test at higher speed the difference should become more evident, even 500-450 RPM should be better than full spinning times, if you can be accurate enough as for the timings.
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Final ground effect tests
You made a large hole in the bottom shroud, so the air fueling the Von Karman flow under the top can come directly from there, if the bottom shroud stays higher than the lens. Maybe when the bottom shroud is in a lower position, (gap 20 mm), its hole is sealed by the lens, and you have a bit of ground effect, but when you rise the bottom shroud for to reduce the gap, a gap forms between the lens and the bottom shroud, so you lose the ground effect.
No beneficial ground effect detected: In the latest tests reported below, I blocked the flow of air around the lens and into the uniform "air gap" beneath the lower fairing when the top's vertical
Quite sure now that my fully faired spoked flywheel top "Top D" sees no beneficial ground effect at G = 3.0, 6.2, 9.4, 12.6, or 20 mm, where G is the height of this air gap. Also confident that if there were such a ground effect in Top D, this range of air gaps would have captured it.
Yet, Iacopo found a clear beneficial ground effect in 2 of his classic tops at G <= 9 mm. (See Replies #5 and #8, this thread.) I can only conclude that some tops generate beneficial ground effects, and some don't. Doubt any of us knows why at this point.
Measurements: Best of 3+ decay times from 1,010±10 to 500±2 RPM at each air gap. New lens/shroud mount (below), but Top D, lens, and bottom shroud same as last time (Reply #131).
(https://i.ibb.co/cFW7mdX/20210408-100247.jpg)(https://i.ibb.co/JRq1rTZ/20210408-100236.jpg)
Variables
1. Air gap thickness beneath bottom fairing (G): 3 - 20 mm
Constant across all time measurements
1. Release speed (ω0): 1,010±10 RPM
2. Final speed (ωF): 500±2 RPM
3. Critical speed and all mass properties same as last time.
Best Top D decay times from 1,010±10 to 500±2 RPM, on lens over shroud unless otherwise noted
G = 3.0 mm .............................. 65 s
G = 6.2 mm .............................. 66 s
G = 9.4 mm .............................. 66 s
G = 12.6 mm ............................. 65 s
G = 20.0 mm ............................. 65 s*
G = 12.0 mm ............................ 65 s**
* Tip on lens on flat counter, which took the place of the shroud. Lens/shroud mount taken away.
** Tip directly on counter. Lens and lens/shroud mount taken away.
Adverse ground effect found last time: In my last test series (Reply #131), I see now that Top D encountered an adverse ground effect giving rise to a hula-hooping instability at G <= 5.2 mm and speeds above 300 RPM...
Hula-hooping instability: Top D was happy to sleep quietly from release to fall at G > 5.2 mm. But at smaller air gaps, it insisted on hula-hooping with decreasing amplitude from release to ~300 RPM. Why? Guessing some kind of periodic instability in the restricted air flow beneath the top.
No matter what other aerodynamic effects might have been present, I believe that the hula-hooping increased dynamic tip resistance whenever present, thus shortening decay time.
Was the shroud's radius large enough? Probably, but no plans to prove it.
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Yet, Iacopo found a clear beneficial ground effect in 2 of his classic tops at G <= 9 mm. (See Replies #5 and #8, this thread.) I can only conclude that some tops generate beneficial ground effects, and some don't. Doubt any of us knows why at this point.
At this point I have no more ideas why we have different results.
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At this point I have no more ideas why we have different results.
I'm puzzled as well. The 3 obvious differences in our experiments were top size and shape and test speeds -- the latter 1600-1500 RPM in your case and 1000-500 RPM in my last experiment.
Though speed may have contributed to our disparate results, size and shape are my prime suspects.
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I'm puzzled as well. The 3 obvious differences in our experiments were top size and shape and test speeds -- the latter 1600-1500 RPM in your case and 1000-500 RPM in my last experiment.
Though speed may have contributed to our disparate results, size and shape are my prime suspects.
Maybe 20 mm is still a too narrow clearance in your top, for to have a free Von Karman flow under it... ? ???
If you put your lens on a pedestal not larger than the lens and at least three or four inches tall, and spin your top D on it, there would be a lot of free space under the top for the air to move as it wants. Maybe this could make a difference.. ?
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@Iacopo: Maybe I'll come back to that test. But for now, I'm declaring this experiment that never ends officially ended!
However, really think I would have detected a beneficial ground effect with the air gaps in my last experiment. Your were seeing one with gap/radius ratios of 3-20% or so. My ratios were 4-24%. Proportions are important in aerodynamics. At times, small differences in shape can also be important.
Besides, not sure that von Karman-like flows are the dominant players here. Until we image the flows involved, hard to say what's really going on under our tops.
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However, really think I would have detected a beneficial ground effect with the air gaps in my last experiment.
In fact I find this quite strange. If I find a bit of time I will try again with a 84 mm top with flat bottom like the your, to see what it happens.
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.
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However, really think I would have detected a beneficial ground effect with the air gaps in my last experiment.
In fact I find this quite strange. If I find a bit of time I will try again with a 84 mm top with flat bottom like the your, to see what it happens.
OK, one last ground-effect test: But only because I found this reasonably secure pasta sauce pedestal in the pantry. Tip resistance is the same as in the last 2 tests (Replies #131 and #135), as the recessed lid happens to hold the same lens in place quite nicely.
(https://i.ibb.co/jh0gbZ8/20210410-110647.jpg)(https://i.ibb.co/zX4jBs4/20210410-105833.jpg)
Adding the data from this pedestal (in bold) to that in Reply #135, we still have a null result...
Best Top D decay times from 1,010±10 to 500±2 RPM, on lens over shroud unless otherwise noted
G = 3.0 mm .............................. 65 s
G = 6.2 mm .............................. 66 s
G = 9.4 mm .............................. 66 s
G = 12.6 mm ............................. 65 s
G = 20.0 mm ............................. 65 s*
G = 194.0 mm .......................... 65 s**
G = 12.0 mm ............................ 65 s***
* Tip on lens on flat counter, which took the place of the shroud. Lens/shroud mount taken away.
** Tip on lens on pasta sauce pedestal, with counter serving as bottom shroud.
*** Tip directly on counter. No lens or pedestal of any kind.
Time to face the music: No ground effect in Top D — at least not at 1,010±10 to 500±2 RPM.
Unfortunately, intuition doesn't get you very far in fluid dynamics. Lacking a way to visualize the flows around our respective tops, I believe we're in no position to understand why a classic Simonelli top produces a measurable ground effect and my Top D doesn't.
Might Top D see a beneficial ground effect at higher speeds? Conceivably. But I have no plans to pursue that possibility for at least 2 reasons:
1. It's not really practical to test Top D at 1,600 to 1,500 RPM.
2. The space station top in its normal configuration below seldom spins faster than 1,000 RPM in play.
(https://i.ibb.co/gWhvV86/20210410-111330.jpg)
Iacopo: Could you instead repeat your tests in Replies #5 and #8 at 1,000 to 500 RPM?
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Not directly to the subject, but those pictures strongly reminds me of something I did myself a few days ago:
(https://i.ibb.co/QbVFc7B/Barilla.gif) (https://ibb.co/QbVFc7B)Click to see the animation.
Base made in Italy! Seems to be fashionable these days. Must all be Iacopo's influence.
I tried a few different lid sizes, also did some more experiments on the variable base. We started to discuss that with Jeremy in a different thread. After all I think I should start a "Base-ic" topic to concentrate some recent thoughts about bases there.
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@ortwin: Hard to beat Italian food! Many of the things not improved by adding chocolate can be improved by adding a nice Italian sauce instead.
The metal lid on my unopened pasta sauce pedestal has a shallow central depression to contain travel, so the lens was necessary only for consistency with earlier experiments. The metal caps on some unopened glass bottles also work well...
https://youtu.be/u7_azTiWxyw
(See description for explanation, as YouTube removed the captions.)
Problem is, once you open these containers, they become useless as top pedestals, as the central depressions pop out to become domes instead.
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I like the set up and the video. Thanks for the inspiration!
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CORRECTION: Apparent discrepancy resolved here (http://www.ta0.com/forum/index.php/topic,6408.msg70162.html#msg70162).
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. 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.
My confidence here stems in part from the fact that Top D can be broken into components (flywheel, spokes, core, fairings) with (1) simple shapes and reasonably uniform densities, (2) easily measured masses and key dimensions, and (3) easily calculated AMIs and TMIs using standard formulas like those in Wikipedia's list of moments of inertia (https://en.wikipedia.org/wiki/List_of_moments_of_inertia). Ditto for the other space station top moments I've posted.
Further corroboration comes from the fact that my estimated critical speeds for these tops are based on my AMI and TMI estimates. If the latter estimates were too large by, say, a factor of 10, my estimated critical speeds would be too large by a factor of sqrt(10) = 3.16. Instead, they're only ~10% above measured values.
Your way of measuring moments could also be at fault.
https://youtu.be/ONMoFBENOUE
After reading this video's description and your first lengthy comment carefully, I have 2 main concerns:
1. Your trifilar pendulum strings aren't vertical, as they are in every article I've seen on the trifilar pendulum method.
2. Can't quite figure out what formulas you're using to turn measured pendulum periods into moments of inertia.
From du Bois et al., 2009, Error analysis in Trifilar Inertia Measurements, PDF here (https://people.bath.ac.uk/jldb20/pubs/duBois.etal2008ErrorAnalysisin.pdf), the correct formula is
Itop + Iplate = P² (Mtop + Mplate) g R² / (4 π² L),
where Itop is the top's central moment about the vertical in kg m², Iplate is the central moment of the pendulum's lower plate about the vertical in kg m², P is the pendulum period in s, Mtop and Mplate are the top and lower plate masses in kg, g is the local acceleration of gravity in m/s², R is the distance from the center of the lower plate to each of its string attachments in m, and L is the string length in m.
As this formula shows, better to work directly in moments, as the calculations get a lot messier when trying to work in radii of gyration — especially when Mtop and Mplate are of comparable size.
As another check, happy to estimate Nr. 22's moments by breaking it down into manageable components like I did with Top D. I'd need at least the following:
1. Top, side, and bottom views
2. The copper flywheel's inside and outside diameters and maximum axial length
3. Total axial length of wooden core + tip assembly
4. Metal flywheel and wooden core masses — or at least their approximate densities
5. The top's overall CM-contact distance.
If you have one of your beautiful engineering drawings for Nr. 22 to share, so much the better!
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....
Problem is, once you open these containers, they become useless as top pedestals, as the central depressions pop out to become domes instead.
That is not a problem , it is a possibility for the variable base you asked for. If you can draw vacuum from the inside you can switch between states.
If you don't have that possibility, you can fill your bottle/jar with hot water (but not completely, leave some air inside) , put the lid back on and wait until it cools down, the dimple will pop back inwards.
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Problem is, once you open these containers, they become useless as top pedestals, as the central depressions pop out to become domes instead.
That is not a problem , it is a possibility for the variable base you asked for. If you can draw vacuum from the inside you can switch between states.
If you don't have that possibility, you can fill your bottle/jar with hot water (but not completely, leave some air inside) , put the lid back on and wait until it cools down, the dimple will pop back inwards.
Cool! I mean hot, then cool!
Hmmm, refilling the jar with sand would make the pedestal even more stable. Hope my wife doesn't catch me heating up sand in the oven!
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1. Your trifilar pendulum strings aren't vertical, as they are in every article I've seen on the trifilar pendulum method.
I did in this way because the pendulum oscillates more slowly in this way and timings are more accurate. It was calibrated with various cylinders of known weight and radius of gyration. The pendulum works well, this is not the cause of the large difference we are facing.
better to work directly in moments, as the calculations get a lot messier when trying to work in radii of gyration — especially when Mtop and Mplate are of comparable size.
The oscillation of the trifilar pendulum is proportional to the radius of gyration, so if you use a trifilar pendulum the radius of gyration can't be ignored, because it stays necessarily at the core of the calculations. The explanation you read is a bit lenghty because I tried to explain the logicality of the calculations step by step.
Anyway, I am far from to be perfect, and it could be that somewhere I made an error, so I want to estimate the moment of inertia of my top Nr. 22 with a different, simpler approach, for to see if there is really a large error in my previous calculations.
This is the design of the top:
(https://i.imgur.com/rdN6CHn.jpg)
The central parts of the top are light parts with very little influence on the total moment of inertia of the top, so I ignore them, (it is not the case to observe the single leaves when we don't see the forest).
Nearly all the moment of inertia is in the flywheel. So I consider just it and nothing else.
For to make the calculations easier, instead of the torus I consider an approximately equivalent holed cylinder, having the same inner and outer diameters, (43 and 80 mm), and the same weight, (600 grams).
The height of such a holed cylinder is 19 mm, (the flywheel is made of copper, density 8.96).
The orange rectangle is the section of this holed cylinder. It is superposed to the section of the flywheel. It has its same diameters, the height is a bit littler, but some parts are larger, (the corners), so the area is similar, and certainly the moment of inertia of this holed cylinder will be not very different from that of the top, but much easier to calculate.
First I calculate the data of the WHOLE CYLINDER without the hole:
VOLUME: 0.04 x 0.04 x 3.14 x 0.019 = 0.0000955 m3
WEIGHT: 0.0000955 x 8.96 = 0.000855 ton = 0.855 kg
RADIUS OF GYRATION: 0.04 x 0.707 =0.02828 m
MOMENT OF INERTIA: 0.02828 x 0.02828 x 0.855 = 0.000684 kg m2
Then I calculate the data of the inner cylinder ,(THE HOLE),to be subtracted from the data above:
VOLUME: 0.0215 x 0.0215 x 3.14 x 0.019 = 0.0000276 m3
WEIGHT: 0.0000276 x 8.96 = 0.000247 ton = 0.247 kg
RADIUS OF GYRATION : 0.0215 x 0.707 = 0.0152 m
MOMENT OF INERTIA : 0.0152 x 0.0152 x 0.247 = 0.000057 kg m2
Then I calculate the MOMENT OF INERTIA OF THE HOLED CYLINDER:
0.000684 - 0.000057 = 0.000627 kg m2
This is not far from the data I obtained with the trifilar pendulum, (0.000636).
Considering that this is an approximative estimate, and that the little moment of inertia of the core of the top has to be added, the matching is good.
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.
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The geometric and density values for a holed cylinder that Iacopo used lead to the AMI he is giving.
At least I get the same result when I enter those values in an online calculator. It is a German version, but I think you can guess most of the words.
(https://i.ibb.co/1ZG31cC/AMI-Nr22.jpg) (https://ibb.co/1ZG31cC)
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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.
(https://i.imgur.com/zjxVbdj.jpg)
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.
(https://i.imgur.com/8NEHlXF.jpg)
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).
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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?
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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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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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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.
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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.
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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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... 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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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.
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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.
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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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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.
(https://i.ibb.co/gWhvV86/20210410-111330.jpg)
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 > K3 ≥ r
Another handy fact: These formulas also apply to a solid cylinder. Just set r = 0 or q = 0 as needed.
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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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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.
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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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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.
Yes, 10° is quite comfortable -- though it may take some practice with single twirls of high-AMI tops.
Eager to see this new top! If I were that close to the 1 hour wall, I'd do whatever it took, play value be damned! (Not that I'll ever be in that enviable position.)
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...Coins are problematic in an international forum, though. A universally recognizable marker like the first 50 mm of a ruler would be best. ...
Here you contradict yourself quite severely in a single line! Quarter + Euro less universal recognizable then mm? Ha! I don't think so. Take US Americans:
Wasn't the wrongly done conversion from inch to mm the cause for a lost satellite some years ago?
As far as I know the British love their strange units also a lot. Oh, and the finger: Did you ever compare the average Uruguayan finger length to a German one? On the net I find that there is a difference of 6 cm (Well that is for the complete height of men) !
No, ta0 should supply copies of figaro to us for these pictures.
If I were that close to the 1 hour wall, I'd do whatever it took, ....
Jeremy, please don't push Iacopo into the black market for osmium, at least not not in the open like this so everybody can read it!
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Oh, and the finger: Did you ever compare the average Uruguayan finger length to a German one? On the net I find that there is a difference of 6 cm (Well that is for the complete height of men) !
What finger are we talking about? >:D
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This is the drawing of the new top.
There is a plexiglass shroud around the flywheel; the shroud can be removed partially, (with only the lower part there shoud be a bit of ground effect but the longest spins will be with the shroud), or completely, for to see a precession or a nutation with a larger angle of tilting.
I will make also another top slightly different from this one, and I will show them together, in May, when they will be ready.
(https://i.imgur.com/fUHNs8x.jpg)
Jeremy, please don't push Iacopo into the black market for osmium, at least not not in the open like this so everybody can read it!
Too easy to spin one hour with heavy metals. I have at least 1 kg tungsten and I am not using it. Let's figure out more esoteric metals, I am not interested. I use plain brass for these tops, it is possible to spin for long even with the humble brass.
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What finger are we talking about? >:D
I know only about five different fingers plus mirror symmetry. Just chose one, I give you a thumbs up for whichever one you take.
....and now I just learned: "ladyfingers"; In Uruguay and Venezuela: plantillas... which again insinuates something small.
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What finger are we talking about? >:D
I know only about five different fingers plus mirror symmetry. Just chose one, I give you a thumbs up for whichever one you take.
....and now I just learned: "ladyfingers"; In Uruguay and Venezuela: plantillas... which again insinuates something small.
It's true that the Frau I once dated looked me straight in the eyes (she was clearly above the average German women height), but she never complained about any of my fingers. ;)
PS: I wonder how I will title this thread if I have to split it and move it to the NSTR section :P
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Oh, and the finger: Did you ever compare the average Uruguayan finger length to a German one? On the net I find that there is a difference of 6 cm (Well that is for the complete height of men) !
What finger are we talking about? >:D
Thumb would be my 2nd choice. >:D
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...Coins are problematic in an international forum, though. A universally recognizable marker like the first 50 mm of a ruler would be best. ...
Here you contradict yourself quite severely in a single line! Quarter + Euro less universal recognizable then mm? Ha! I don't think so. Take US Americans:
Wasn't the wrongly done conversion from inch to mm the cause for a lost satellite some years ago?
Not just a satellite — a billion $125M-dollar Mars Climate Orbiter! Don't get me started about Imperial Units. >:( >:(
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Those tops are going to be superb, Iacopo. I hope you can break the 1 hour barrier using them. The brass 1 hour barrier!
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This is the drawing of the new top.
There is a plexiglass shroud around the flywheel; the shroud can be removed partially, (with only the lower part there shoud be a bit of ground effect but the longest spins will be with the shroud), or completely, for to see a precession or a nutation with a larger angle of tilting.
Gorgeous! Love the shroud design. Can't wait to see it in action!
We burned up a lot of brain cells and testing time on shrouds in this thread. But it clearly wasn't in vain. Your new design is the payoff! Your competitors and mimickers won't know what hit them.
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I hope you can break the 1 hour barrier using them. The brass 1 hour barrier!
Fingers crossed !
We burned up a lot of brain cells and testing time on shrouds in this thread. But it clearly wasn't in vain. Your new design is the payoff!
Jeremy, you are a father of this top.
I wouldn't have discovered these new things if you didn't start this thread.
Your knowledge, tests and observations, have been an important stimulus for the mine.
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Fingers crossed !
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I am also wishing you good luck with this beauty, but at the same time I fear you might get bored by spinning tops and turn to another hobby, once you crossed the one hour barrier. I would not want that to happen.
And while you are going for the one hour barrier, I will try to convince Brass Band to cross the half hour line (in recessed mode).
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I am also wishing you good luck with this beauty, but at the same time I fear you might get bored by spinning tops and turn to another hobby, once you crossed the one hour barrier. I would not want that to happen.
Thank you, Ortwin. My will at present is to continue making tops for a long time. I like to make them. Now, also, I have an economic incentive which I didn't have in the first years, because I have many requests, and prices are not low. I like that I can make each top a bit different from the others, I can always experiment new details of the design, new materials, then the physics of the spinning top by itself, I find it interesting, so in the whole it is difficult that I become bored, at the countrary, I feel lucky that I can do something I like and that I can even gain some money for it.
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Jeremy, you are a father of this top.
I wouldn't have discovered these new things if you didn't start this thread.
Your knowledge, tests and observations, have been an important stimulus for the mine.
That goes both ways, my friend!
One of the best things about this forum is that it provides a productive place to discuss top engineering and share our R&D efforts to the benefit of all the topmakers here, regardless of medium and genre.
And where else do you get to wallow in the unexpected complexities of these "simple" little toys?
ta0 deserves a lot of credit here -- not only for his own valuable contributions along these lines, but also for fostering such things in general.
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ta0 deserves a lot of credit here -- not only for his own valuable contributions along these lines, but also for fostering such things in general.
If it wasn't because of the people that post on a regular basis we wouldn't have a forum. So, thank you guys!
I believe that the advantage we have with respect to social media is that we can discuss topics in depth and that top information is documented for the future.
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ta0 deserves a lot of credit here -- not only for his own valuable contributions along these lines, but also for fostering such things in general.
If it wasn't because of the people that post on a regular basis we wouldn't have a forum. So, thank you guys!
I believe that the advantage we have with respect to social media is that we can discuss topics in depth and that top information is documented for the future.
Well said!
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Spokes
Just found that Billetspin has/had a 3-spoked top.
Jester 3
(https://i.ibb.co/2ycR7TK/billetspin-Jester-3.jpg) (https://ibb.co/2ycR7TK)
From youtube videos it seems to be able to run for about 15 minutes.
Did you know about that line, or are are we just choosing to ignore EDC tops?
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Yes, we know about EDC tops and BILLETSPIN.
I like that Jester 3, but most BILLETSPIN and EDC top designs leave me cold -- mainly because they're too ornate for my taste. Not to mention aerodynamically whacko for tops heavily marketed on spin time. And typical EDC marketing hype and engineered scarcity are big turn-offs for me. (Went through that with the kids and Beanie Babies.)
That said, this Jester's spoke-and-flange core is like the lowest-drag car wheel we discussed here (http://www.ta0.com/forum/index.php/topic,6404.msg69208.html#msg69208).
PS: Just saw that BILLETSPIN now distinguishes between "performance" and "art" tops in their store. Good distinction to make about tops in general.
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Rich Stadler, the owner of Billetspin, is a member of this forum (Rich S). You can check his posts. But he stopped posting after he realized there were not many EDC collectors around here. At the time there was a limited interest in finger tops in general, but Jeremy and Iacopo have greatly increased the number of posts on those tops. ;)