Print

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

[Jeremy McCreary]

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).



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 (ω_F): 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.

[Iacopo]

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.

[Jeremy McCreary]

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.

[Iacopo]

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.. ?
 

[Jeremy McCreary]

@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.

[Iacopo]

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. 

[Jeremy McCreary]

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.



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.



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

[ortwin]

Not directly to the subject, but those pictures strongly reminds me of something I did myself a few days ago:

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.

[Jeremy McCreary]

@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...



(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.

[the Earl of Whirl]

I like the set up and the video.  Thanks for the inspiration!

[Jeremy McCreary]

CORRECTION: Apparent discrepancy resolved here.

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. 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.



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, the correct formula is

I_top + I_plate = P² (M_top + M_plate) g R² / (4 π² L),

where I_top is the top's central moment about the vertical in kg m², I_plate is the central moment of the pendulum's lower plate about the vertical in kg m², P is the pendulum period in s, M_top and M_plate 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 M_top and M_plate 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!

[ortwin]

....
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.

[Jeremy McCreary]

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!

[Iacopo]

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 M_top and M_plate 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:


 
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.

[ortwin]

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.