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[Iacopo]

This top was conceived to spin for the longest time, with the constraints of an external not recessed tip, single twirl spins, and a brass flywheel.
I run a test, included in the video, for to find a better shape of the flywheel.
The test was useful.  The best spin of this new top is 29'38", which is very good.



This is a 28 minutes spin of the new top:

[ta0]

It's great information what you found about the compromise between designing for low air drag and for low center of mass and how the latest wins the duration contest.

I admire how you combine meticulous experimentation with artistic flair and love your results.
You are a master!

PS: On the second video I could follow you on the reflection on the rim, picking up the tachometer before a measurement and then writing the results further away. 

[Iacopo]

On the second video I could follow you on the reflection on the rim, picking up the tachometer before a measurement and then writing the results further away. 

Thank you, Ta0.  Yes, this is exactly what I was doing.  Then I was comparing the results with the data of other tops.  So I knew since from the first minutes that the top was going quite well.

[Iacopo]

The tip of this top is a fixed spiked carbide one, not replaceable.
There are not balancing screws in this top: balance is obtained by centering the tip, filing one side of it, as I described in my video "How to fix unbalance in spinning tops".  I have made a honing guide for to ease a bit the operation:

Detecting the heavy side of the top is made with the brush technique, and, thanks to the long stem, it is very accurate and it allows to achieve a perfect balance.
The top weighs 119 grams.  The brass flywheel alone weighs 115 grams, and the stem, the core and the tip all together weigh only 4 grams.  This was obtained by the use of a very light wood, ayous.  So, more than 96 % of the total weight is concentrated in the more external part of the top, the flywheel.  This helps for longer spins because the weight of the central parts of the top contribute to increase the tip friction, without contributing, or contributing very little, to the kinetic energy of the top. For comparison, top Nr. 25 has 87 % of its weight concentrated in the flywheel.
But top Nr. 25 was conceived to be a good spinner, and, above all, to be beautiful and comfortable to set up, thanks to the replaceable tips and the balancing screws, (it is easier to balance a top by the balancing screws than by filing the tip).  Top Nr. 29 instead is conceived above all to be an excellent spinner, (with the choosen constraints that the tip is external, the top is spun by a single twirl, and the flywheel is made of brass).

[Aerobie]

Hello Iacopo,

As usual, beautiful.   My experience with twirlers has been that 2.25" (57mm) diameter twirls longest. 
But that may be dependent of my twirling ability.

What is the diameter of this top?
What is your best diameter for a single twirl (rather than additive twirls like you do), non-recessed tip?

Best regards,

Alan

[Iacopo]

Hello Iacopo,

As usual, beautiful.   My experience with twirlers has been that 2.25" (57mm) diameter twirls longest. 
But that may be dependent of my twirling ability.

What is the diameter of this top?
What is your best diameter for a single twirl (rather than additive twirls like you do), non-recessed tip?

Best regards,

Alan

Hi, Alan,

it's nice to hear from you again. 

At present, my best (able to spin for the longest time) brass single-twirl top, with a non recessed tip, is this one, the Nr. 29;
its diameter is mm 59, so not very different from your mm 57.
Its weight is 119  grams, its moment of inertia kg-m² 0.000063.
Best spin 29'38", with a single twirl of the fingers.

I have made another top, very similar to the Nr. 29, but with tungsten alloy instead of brass.
The best single twirl spin of this tungsten top is 36'11".
So the tungsten top spins longer than the brass one, by 6 or 7 minutes, with a single twirl.
It is my absolute best top with non recessed tip, for single twirl spins.
Its diameter is mm 57.5, weight 119 grams.

[Jeremy McCreary]

Nr.29 is gorgeous, as usual, Iacopo! (Meant to say so at the time, but I was traveling and then forgot.)

Measuring spin decay curves (SDCs) at fixed AMI and launch speed was a truly brilliant experimental move. As a result, the 4 SDCs at 2:34 (1st video) convey much more information than usual.

For kicks, I added a few reasonable assumptions to your experimental setup and started doing the math. Pretty soon, useful design predictions were pouring in. Plan to share what I learned shortly, but first, I'd like more data on all 4 tops (26-29) -- including their axial rotor lengths, inner metal ring diameters, tip-CM distances, and any measured AMIs you might have.

I assume that your SDCs were measured with the tops spinning on pedestals. If not, I'd also like the rotor ground clearances when the stems are vertical. The brass and wood densities would be nice, too.

Thanks!

[Iacopo]

Here I had to interpret the results of my test in an intuitive way, my math knowledge is a bit poor..
But the idea of improving the design through mathematical predictions is attractive.
The data you asked:

Spinning top Nr.                            26                   27                  28                  29

Weight, grams                             107                 156                 216                119
Metal ring diameter, mm              59.9                52.0                47.0               59.0
Inner metal ring diameter, mm     43.5                29.0                15.6               38.5
Thickness metal ring, mm              8.6                12.1                16.3               10.1
Height center of mass, mm         6.8-7.6            8.5-9.3          10.6-11.4         7.1-7.5
Radius of gyration, mm                25.0                20.4                17.0               23.1
Axial moment of inertia, kg-m² 0.0000667       0.0000648       0.0000625       0.0000635
Longest spin                               26'20"             25'40"             20'10"             29'38"
Started from, RPM                       1250               1250               1250               1310
Toppled down at, RPM                   178                227                 340                 165
Density of my brass:  8.5
Density of wood, iroko, tops 26-27-28:   0.66
Density of wood, obeche, top 29:   0.38
Weight of the central ergal part of the first three tops:  about 3 grams.
All these tops were spun on the pedestal.
They have approximately the same moment of inertia, which was enough for the experiment.
The lowest toppling down speed of top 29 is partly due to a better balance.

[the Earl of Whirl]

Your tops are absolutely fabulous, Iacopo.  I have enjoyed seeing your amazing progress with your spin times on recordsetter.com

[Iacopo]

Your tops are absolutely fabulous, Iacopo.  I have enjoyed seeing your amazing progress with your spin times on recordsetter.com

Thank you, Earl of Whirl, you are always kind.
I did even better, my actual absolute best spin is 58'19", with my top Nr.23.
Even if I am proud of them, honestly, I have to say that all these very long spins are obtained also thanks to recessed tips and/or twirling the top many times for a higher starting speed, so they shouldn't be compared to the spin times of tops which have not these advantages.

[Jeremy McCreary]

The data you asked...

Thanks for the opportunity to analyze your hard-won data, Iacopo. Here, I'd like to share some initial qualitative findings applicable to all 4 tops unless otherwise noted.

• Your AMIs are effectively identical, and so are your launch speeds, as stated. Variations around the respective means are <3.6%.
• In every case, the brass rim controls the top's spin-down behavior pretty much all by itself. It largely sets CM height and contributes most of the aerodynamic braking torque (ABT) and essentially all of the AMI and TMI. And by dominating top mass and therefore weight, it indirectly causes most of the frictional braking torque (FBT). For example, Top 26's rim accounts for 91% of its mass and ~100% of its AMI.
• The largest specific AMI (AMI per unit mass) is 2.15 times the smallest. In decreasing order: Top 26, 29, 27, and 28.
• Reported topple speeds for Tops 26-28 are remarkably close to the critical spin rates I calculated under the assumption that spin rates were still much greater than precession rates when the tops fell. (The errors were under 17% of reported for Top 26 and under 4% for Tops 27 and 28!) I can't yet calculate a critical speed for Top 29's non-cylindrical rotor.
• ABT and AMI both grow with outer rotor radius, but not in the same way. Since AMI measures the top's ability to resist deceleration by the total braking torque (TBT), and since ABT dominates TBT during most of spin-down, an optimum radius probably exists. Finding it, however, may not be easy.
• When you say that Top A is "more efficient" than Top B over a certain speed range or time interval, I think you're saying that Top A has the slower spin decay rate (shallower slope) in that part of its spin decay curve. If so, identical AMIs make it safe to say that Top A is seeing lower TBTs throughout that range.
• All of your spin decay curves are consistent with drag-dominated TBTs at first, but Top 29 may be the only one to stay up long enough to show a purely frictional linear tail. (Pretty sure my tops never see their own frictional tails.)

Next up is a description of your key experimental givens and assumptions in mathematical terms.

[Iacopo]

When you say that Top A is "more efficient" than Top B over a certain speed range or time interval, I think you're saying that Top A has the slower spin decay rate (shallower slope) in that part of its spin decay curve. If so, identical AMIs make it safe to say that Top A is seeing lower TBTs throughout that range.

You thought absolutely right.
In the next weeks I will have better and new interesting data;  I want to shave some brass from these cylindrical tops so to have a more similar moment of inertia between them.  I will use these and other tops in the vacuum chamber.  I am waiting for a new vacuum pump I ordered, because with the old one I couldn't have less than about 30 millibar as ultimate pressure.  The new one is advertised to reach 0.001 millibar as ultimate pressure.  If this is true, (I will test it), there should be no more measurable air drag for a top spinning in my new vacuum chamber.  For each top it will be possible to study spin decay due to tip friction alone. Knowing tip friction and spin decay in air, it will be possible to study spin decay due to air drag alone.
As you suggested long time ago, I think I will measure the decays differently, not at fixed intervals of time, but at fixed intervals of lost RPM, for easier calculations.
 

[Jeremy McCreary]

In the next weeks I will have better and new interesting data

Exciting news! Can't wait to see the results.

As you suggested long time ago, I think I will measure the decays differently, not at fixed intervals of time, but at fixed intervals of lost RPM, for easier calculations.

Did I really say that? Sorry. Fact is, you don't need regular intervals in time or speed to make useful spin-decay curves (SDCs). You just need reasonably short intervals to capture the actual SDCs as faithfully as possible.

Once your have your SDCs, one valuable way to compare them, as mentioned previously, would be to fit a purely exponential decay to each SDC and then compare the fitted decay time constants. (The more data points per curve, the better, but regular spacing isn't necessary.) In your terminology, a longer decay time constant would mean a more "efficient" top overall. This is easily done in Excel, and I'd be happy to do it for you.

[Iacopo]

Did I really say that? Sorry. Fact is, you don't need regular intervals in time or speed to make useful spin-decay curves (SDCs).

Sorry Jeremy, I was wrong, you never said something so.  My memory isn't always so good..

I understand I don't need regular intervals in time or speed to draw the spin decay curves, but I was thinking something else:

it would be easier to compare the two curves of spin decay of the same top, in air, and without air, if these curves have the same lenghth.
If I measure at RPM intervals, and the top is started both times with the same speed, the two curves would have the same number of points and the same lenghth.
There would be corresponding intervals in the two curves and so it would be easy to calculate from these data the third curve, that of air drag alone.
If I measure at time intervals instead, since the top will spin longer in the vacuum, the two curves would have different lenghths and a different number of points, and it would be more difficult, (at least for me), to calculate from them the curve of air drag.
 

[Jeremy McCreary]

Sorry Jeremy, I was wrong, you never said something so.  My memory isn't always so good..

No worries. Mine isn't always so good, either.

If I measure at RPM intervals, and the top is started both times with the same speed, the two curves would have the same number of points and the same length...

Sounds like a workable approach to the data processing and curve comparisons, but there are other ways to go about it, and they'd probably save you time and effort in the long run. They'd also give you a lot more flexibility WRT how you graph and analyze your data.

Do you have a spreadsheet program like Excel? If so, the first step would be to enter the raw time-speed data for each SDC -- say, elapsed times since launch in one column and the speeds at those times in the next column. From there, it would be an easy step to plot your SDCs on the same graph or on separate graphs as you choose. If that's unfamiliar territory, maybe I could help you get started via Skype.

[Iacopo]

If that's unfamiliar territory, maybe I could help you get started via Skype.

Thank you, Jeremy, you are kind and helpful.
I don't use Skype, and I know nothing about Excel. I could try to learn it but I have little free time and I don't know how much time it would take.