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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. 

Buena historia y siempre Gus si fiel estilo ,y salvador sin duda lo que hace en el metro es de mucho respeto, imagino no que día pasaste con estos dos tipos mexicanos girando ...

@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.

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.. ?
 

@Joah: The paintbrush method works fine at 0° phase angle, as your tuning results prove. When you're balancing by removing mass, it only determines where to do it relative to the paint marks.

In a top with a 180° phase angle, you'd have to file or otherwise remove mass opposite the marks to improve balance.

For the simplest explanations of phase angle I know of in the context of static unbalance, see the free online PDF references linked in this post:

http://www.ta0.com/forum/index.php/topic,4941.msg51834.html#msg51834

Start with the first 2 pages of "Balance this".

Rats, most of those links are broken now. Will see if I can find something for you.

Really, all you need to know is in some tops, the marks end up on the light side, not the heavy side.

Joah: Very thoughtful and methodical tuning process -- and tons of work!

You may be aware of this little gotcha in the otherwise reliable paintbrush method: In your case, the phase angle between the heavy side and the paint marks happened to be 0°. And this could well be the case for most if not all beigoma of similar size and mass.

But in some tops, the phase angle is 180°.

We've discussed this well-documented phenomenon many times with no consensus regarding either its cause or a reliable way to predict which top will have which phase angle.

My own opinion is that we're dealing here with a classic case of whirl (in the engineering sense) due mostly to static (as opposed to couple) unbalance. The phase angle then depends on which side of the unbalance's unknown first damped natural frequency the top happens to operate.

Thanks Jeremy! I'm going to have to do some homework, haven't touched physics since high school, which was about a decade ago... The way I figured the whole weight distribution was based on my experience with Beyblade, which is the same shape as a beigoma when all its armor is taken away. Beyblade has interchangeable weight disks, some are made to be heavier on one side to purposely cause the top to spin unbalanced. They did this so tops with crescent-shaped blades would strike up at 45ish degree angle causing opposing tops to be knocked into the air.  I've experimented a lot with changing the weight distribution with Beyblade tops and watching how their movement pattern changes. I applied this to carving the beigoma... Do you have any links to articles or papers I could read on phase angle? Also, because the beigoma is at 0° does this make the paintbrush technique ineffective?

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.

Those are from 2016 but I hadn't seen the last one until now.

This reminds me when I took a city bus with Gus and Salvador in Mexico City. We sat on a 3-person seat with the back towards the window. It then got pretty full and kid about twelve years old got in the bus. I believe he was selling candy but I'm not sure if I recall that part correctly. From his stare you could tell that he noticed the tops we were carrying. Gus took a top and showed it to him. Then he snap started it and did a little routine while he remained seated, ending with a spin on his fingernail. You should have seen the astonished face of the kid! Then Gus gave him the top.

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.

Bastante bueno