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Author Topic: Efficiency of Spinning top Nr.17 (95%!)  (Read 330 times)

James

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Efficiency of Spinning top Nr.17 (95%!)
« on: October 15, 2019, 08:46:38 AM »

Hey!

I recently conducted an efficiency test on my best and newest spinning top - Nr.17. It spun for 42 minutes precisely. It started at 2180 RPM and fell at about 160 RPM. Here is the raw data:

Min   RPM   Efficiency   RPM drop
0   2180   94.08   129
1   2051   94.10   121
2   1930   94.15   113
3   1817   94.33   103
4   1714   94.40   96
5   1618   94.50   89
6   1529   94.51   84
7   1445   94.60   78
8   1367   94.59   74
9   1293   94.74   68
10   1225   94.69   65
11   1160   94.74   61
12   1099   94.81   57
13   1042   94.72   55
14   987   94.63   53
15   934   94.65   50
16   884   94.80   46
17   838   94.99   42
18   796   94.85   41
19   755   94.70   40
20   715   94.83   37
21   678   94.84   35
22   643   94.71   34
23   609   94.58   33
24   576   94.62   31
25   545   94.68   29
26   516   94.38   29
27   487   94.25   28
28   459   94.12   27
29   432   94.21   25
30   407   93.86   25
31   382   93.72   24
32   358   93.85   22
33   336   93.45   22
34   314   93.31   21
35   293   92.83   21
36   272   92.65   20
37   252   92.06   20
38   232   91.81   19
39   213   92.02   17
40   196   91.33   17
41   179   89.39   19
42   160   0.00   160

From this I made two graphs.





Above is an image of the 'efficiency against time' graph. You can see that the efficiency rises from 94%, peaking at 95% 17 minutes in (about 850 RPM). Then the efficiency degrades at increasing rate until, in the last minutes, the efficiency drops to almost 89%. This is a similar result to the efficiency tests of Nr.15. This top experienced almost no wobble or flutter until the last few minutes.





Above is an image of the 'RPM against time' graph. This shows how RPM is lost progressively slower. The line of best fit from a polynomial of order 5 is very close to the data points.

I am not sure why the efficiency degrades at the halfway mark. Do you have any ideas? Or any questions? Thanks for reading.
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Jeremy McCreary

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Re: Efficiency of Spinning top Nr.17 (95%!)
« Reply #1 on: October 15, 2019, 01:45:12 PM »

Many thanks for sharing your raw spin decay data and spin decay curve (SDC). Of course, no good deed goes unpunished...

Q1: What was the best-fit polynomial's correlation coefficient or R2 value?

Q2: Same question for an exponential SDC fit?

Iacopo's supplied most of the raw SDC data I've had a chance to analyze to date. In all cases, the SDCs gradually transitioned from a nearly exponential decay to a nearly linear decay as the SDC tail approached the horizontal.

One reasonable way to model the speed dependence of the total braking torque Q responsible for spin decay is with a power law in angular speed w...

Q = A wn,

where A is a constant, and n is the power law exponent.

In the early exponential decay phase, n ~ 1, meaning that Q was approximately proportional to speed during that phase. In the late linear phase, n ~ 0, implying a very weak speed dependence, as you'd get with a simple tip friction model depending only on top weight.

« Last Edit: October 15, 2019, 01:59:10 PM by Jeremy McCreary »
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James

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Re: Efficiency of Spinning top Nr.17 (95%!)
« Reply #2 on: October 15, 2019, 08:14:46 PM »

Hi, Thanks for the reply.

The is the equation excel gave as the best fit curve for efficiency against time: y = -8E-06x4 + 0.0005x3 - 0.0141x2 + 0.1878x + 93.782
R² = 0.9678


This is the equation excel gave as the best fit curve for SD: y = 4E-07x6 - 7E-05x5 + 0.0046x4 - 0.193x3 + 5.892x2 - 146.34x + 2320.7
R² = 1
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Iacopo

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Re: Efficiency of Spinning top Nr.17 (95%!)
« Reply #3 on: October 16, 2019, 03:47:47 AM »

That's a really very good efficiency !
You matched the same efficiency of my best tops, (with a similar weight and diameter).
In fact these my tops too spin for about 42 minutes in the same lapse of RPM, (2180-160).
This tells that you did everything very well, the aerodynamics and the contact points are top notch !

At this point, if you want longer spins, the easiest way is to recess the tip a bit more; you can get up to about additional 10 minutes spinning in this way. 
Also, you could try to start the top at higher RPM, if possible. A longer stem would make a bit easier to spin the top at very high speed.
Starting the top at 2510 RPM would add about two minutes of spin time. 
If you make the stem narrower, you decrease a tiny bit the air drag, which would help too.

Congratulations for the goal achieved !
 
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James

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Re: Efficiency of Spinning top Nr.17 (95%!)
« Reply #4 on: October 16, 2019, 08:02:08 PM »

Thank you for the advice!
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Jeremy McCreary

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Re: Efficiency of Spinning top Nr.17 (95%!)
« Reply #5 on: October 16, 2019, 08:30:16 PM »

At this point, if you want longer spins, the easiest way is to recess the tip a bit more; you can get up to about additional 10 minutes spinning in this way. 
Also, you could try to start the top at higher RPM, if possible. A longer stem would make a bit easier to spin the top at very high speed.
Starting the top at 2510 RPM would add about two minutes of spin time. 
If you make the stem narrower, you decrease a tiny bit the air drag, which would help too.

It's worth emphasizing that if you're recessing the tip just to reduce CM-tip distance, the same measures improve spin time in just about any top. CM-tip distance really impacts my LEGO spin times.
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Iacopo

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Re: Efficiency of Spinning top Nr.17 (95%!)
« Reply #6 on: October 20, 2019, 01:27:23 PM »

I am not sure why the efficiency degrades at the halfway mark. Do you have any ideas?

Be aware that this is a particular way to measure the efficiency, it's a relative and not an absolute efficiency.
In absolute terms, there is the best efficiency when the top spins at the lowest speed, and you can see this looking at the RPM drop, for example. You had the best efficiency, 94.99%, at minute 17; but in that minute the top lost 42 RPM, while at the end of the spin the top lost less than 20 RPM per minute, so, in absolute terms, the top is more efficient at the end of the spin.
Even considering the energy consumption, the lowest consumption is at the end of the spin.
This is normal, because both the air drag and the tip friction increase with speed, so tops become less and less efficient at the increasing of speed.

So, this is a relative efficiency, which does not tell the "real" efficiency of the top.
It is not very meaningful to compare differences of this "relative efficiency" along the same curve.

Anyway this relative efficiency data can be useful for comparing different tops;
one way is to plot in a graph, relative efficiency vs. RPM, (to compare differences of efficiency at parity of RPM).
To compare differences of this "relative efficiency" in different tops, makes sense, because a top which loses speed more rapidly than another one, at parity of RPM, is certainly less efficient in real terms. 
The graph makes available various informations at a glance, which may be interesting.
For example:



This is about the "efficiency" of my tops Nr. 20, 23 and 33.

The starts and the ends of the curves tell the starting speed and toppling down speed;
The Nr. 20 can be started at the highest speed thanks to a quite long stem, while the Nr. 33 has a short stem and it is difficult to spin it hard.  Nr. 20 and 23 topple down at very low speed because of their deeply recessed tips.

The efficiency at high speed, is especially related to air drag, (because air drag is generally very high at high speed), and moment of inertia. The best efficiency at high speed is obtained with the most compact, littlest shapes, having the highest moment of inertia.
Little shapes with high moment of inertia means to use dense materials, like metals. 
So, the parts of the curves at the left, tell above all the ratio between the moment of inertia and the aerodynamic efficiency.
Nr. 20 and 23 have flywheels with same shape and dimensions, but the Nr. 23 has three holes for the balancing screws in the flywheel, and for this reason its aerodynamics is not so good like that of the Nr. 20, which has not these holes; the curve of the Nr. 23 starts lower in the graph than that of the Nr. 20.
The Nr. 33 is a light top with large diameter, so it has poor aerodynamic efficiency, and poor moment of inertia, and in fact the curve of this top at the left is very low in the graph.

At very low speed, air drag nearly disappears. So, the efficiency at very low speed is especially related to the tip friction, and to the moment of inertia.
Tip friction is related to the shape and quality of the materials of both the contact points, the lubricant, and the balance of the top.
Best efficiency here is obtained with the largest radius of gyration, so to have the highest moment of inertia with the littlest weight.
At parity of the other factors, light tops are more efficient, because tip friction is not proportional to weight, but increases a bit more rapidly than weight.
The parts of the curves at the far right tell above all the ratio between the moment of inertia and the tip friction. 
The Nr. 23 has a slightly better tip friction than the Nr. 20, because of the better quality of the tip material, (carbide for the Nr. 23, HSS for the Nr. 20).
The Nr. 33 has very good efficiency at very low speed, because it is light, and it has a large radius of gyration.
« Last Edit: October 20, 2019, 01:53:14 PM by Iacopo »
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James

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Re: Efficiency of Spinning top Nr.17 (95%!)
« Reply #7 on: October 20, 2019, 08:53:03 PM »

Thank you very much for the great reply! Lots of useful information there for us.
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