iTopSpin
Current Posts => Collecting, Modding, Turning and Spin Science => Topic started by: Aerobie on November 18, 2017, 12:49:24 AM
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I've been looking at some math to compare spins of different sizes of tops and differing launch twirl RPM.
First of all, most of my twirler spin durations are proportional to launch twirl RPM^0.63.
Next, I wanted to account for top diameter and weight. This led to the following:
Merit = Seconds / (RPM^0.63 x Diameter^0.5 x Weight)
If diameter is in mm and weight is in Kg, merit for my better tops and twirls is about 20 ish.
My record twirler computed as follows:
Diameter = 57.15mm
Weight = 0.145 Kg
Best ever spin time = 26:05 or 1,565 seconds for a twirl of 860 RM
Merit for this twirl = 1,565 / (860^0.63 x 57.15^0.5 x 0.145) = 20.2
A 1,587 RPM twirl of 16:25 duration with a smaller top (38mm, .082Kg) had a merit of 18.7
This might be used to predict spin seconds ~ 20 x RPM^.63 x Diameter^.5 x Kg
Try this with some of your twirls.
Alan
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Here are some data of my tops. All the following tops have an external, non recessed tip, and they have been spun by a single twirl. They all have a brass flywheel.
Weights in kilograms and diameters in millimeters.
Top Nr. 25, toroidal flywheel, ruby tip, glass spinning surface.
Diameter = 54.9
Weight = 0.187
Best spin time = 23'56", started from 1238 RPM.
Merit = 11.6
Top Nr. 25, toroidal flywheel, carbide spiked tip, carbide spinning surface.
It is the same top as above, but with a carbide tip instead of the ruby tip.
Diameter = 54.9
Weight = 0.187
Best spin time = 24'38", started from 1234 RPM.
Merit = 12.0
Top Nr. 26, squared edge flywheel, carbide spiked tip, carbide spinning surface.
Diameter = 59.9
Weight = 0.107
Best spin time = 26'20", started from 1162 RPM.
Merit = 22.3
Top Nr. 27, squared edge flywheel, carbide spiked tip, carbide spinning surface.
Diameter = 52.0
Weight = 0.156
Best spin time = 25'40", started from 1220 RPM.
Merit = 15.5
Top Nr. 28, squared edge flywheel, carbide spiked tip, carbide spinning surface.
Diameter = 47.0
Weight = 0.216
Best spin time = 20'10, started from 1194 RPM.
Merit = 9.4
Top Nr. 29, toroidal flywheel, carbide spiked tip, carbide spinning surface.
Diameter = 59.0
Weight = 0.119
Best spin time = 29'38", started from 1310 RPM.
Merit = 21.1
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The higher starting speed of the top Nr. 29 is due to the long stem.
The long stem makes the top easier and more stable to spin.
I think your formula is too punishing for the heavier tops;
the tops with the higher merit are the lightest ones, and the worst are the heaviest ones.
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...most of my twirler spin durations are proportional to launch twirl RPM^0.63.
Good to have you back, Alan! That's a remarkable result. How many tops in your sample? What were they like in terms of shape and construction?
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Hello Iacopo,
Considering that launch RPM is part of the formula, I think linear weight is theoretically appropriate. I note that your toroidal wheels have lower merit than your square edged wheels. Of course a square edged wheel has greater rotational inertia than a toroid of equal diameter and weight.
Here are some merits. All are cylindrical, except "toroidal" OD.
Average Best
Diameter Grams Merit Merit
25.4mm 43 18.6 19.2
31.5 58 17.9 19.5
38.1 104 14.6 15.2
50.8 78 18.3 20.2
50.8 105 16.6 18.4
57.1 158 15.7 17.2
57.1 183 10.7 12.8 "toroidal" OD
57.1 114 13.2 15.9
76.2 105 15.4 16.4
One could argue that heavier tops are penalized by the formula.
Sometimes a top spins longer than expected for its launch RPM, yielding a merit closer to 20.
Best,
Alan
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I note that your toroidal wheels have lower merit than your square edged wheels. Of course a square edged wheel has greater rotational inertia than a toroid of equal diameter and weight.
Yes, I thought the same, this is the reason why I specified what shape have the flywheels.
Using the radius of gyration instead of the diameter would be more accurate, but I understand that this last one is easier to measure.
The fact that my toroidal wheels have lower merit than my squared edges (cylindrical) ones is misleading, in fact by the time I collected data that show that toroidal wheels spin a bit longer than cylindrical ones.
For example, my tops Nr. 26 (cylindrical) and Nr. 29 (toroidal) have similar diameter and weight,
and the toroidal one has lower merit in spite of the fact that it spins longer, (29'38" vs. 26'20");
it could be thought that the toroidal one spinned longer just because it was started from a higher speed and no other reasons, but reality is that the toroidal one spins longer even at parity of starting speed, (up to about 28'10" started from 1160 RPM).
Your formula rewards the cylindrical wheel, partly because, as you noted, it overestimates the rotational inertia in toroidal wheels, and partly because this cylindrical wheel is lighter, and your formula rewards lighter tops.
Also I made an experiment which showed that a wheel with rounded edge seems to have lower air drag than a wheel with squared edge, (at the tested speeds):
https://www.youtube.com/watch?v=6bUf2UBVQkk
Considering that launch RPM is part of the formula, I think linear weight is theoretically appropriate.
I think it depends on the exact meaning you give to the term "merit" and what you are looking for.
If you want a light top that spins for long, it could be ok. You are not simply looking for the top that spins longer, rather, with this formula, you are looking for a compromise between the lightest top and the longest spin.
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Still unclear as to what this figure of merit means at a practical level. If the merit of top A is greater than that of top B, what does that tell us?
Clearly if A and B have the same diameter and mass and start at the same launch speed, the merit will be proportional to spin time. But here, we're comparing tops with significant differences in diameter, mass, and launch speed.
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Still unclear as to what this figure of merit means at a practical level. If the merit of top A is greater than that of top B, what does that tell us?
Clearly if A and B have the same diameter and mass and start at the same launch speed, the merit will be proportional to spin time. But here, we're comparing tops with significant differences in diameter, mass, and launch speed.
My intent with this figure of merit is to answer the question, "How long does this top spin, after correcting for its size, weight, and launch RPM?" because when evaluating the merit of design parameters I rarely have two tops of identical size and weight available for comparison. Examples of design parameters are, aspect ratio (diameter / thickness), or perimeter shape (square, rounded, or toroidal).
Note that I've posted merit for tops ranging over a factor of 3 in diameter and a factor of 4 in weight, yet merits are pretty similar.
Alan
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I'm surprised that my 57mm tops spin longest when twirled, because one could argue that larger tops would spend more of their spin time in the lower speed range, where aero drag is lower.
I've been assuming that twirl energy (RPM^2 x inertia) is constant for tops of different diameters. But I've just realized that I've not verified that. Perhaps I can review launch RPM for tests of various diameters and see if this is true. Stay tuned.
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I've been assuming that twirl energy (RPM^2 x inertia) is constant for tops of different diameters. But I've just realized that I've not verified that. Perhaps I can review launch RPM for tests of various diameters and see if this is true. Stay tuned.
This is something I observed in my tops, and I can say that the energy I can put in a top with a single twirl of my fingers is relatively constant, even when the rotational inertias are quite different between them.
Here are some data;
Top Nr. Moment of inertia Energy
kg-m2 joule
3 0.000003 0.09
1 0.000006 0.11
10 0.000064 0.51
8 0.000045 0.52
18 0.000063 0.53
13 0.000068 0.57
12 0.000069 0.59
6 0.000304 0.61
15 0.000076 0.67
20 0.000142 0.70
14 0.000067 0.71
Apart from the first two super light tops, all the others receive, with a single twirl, a quantity of energy which ranges from 0.5 to 0.7 joule.
The giant top Nr. 6 receives 0.6 joule, so it is not substantially different from the others tops.
The lightest tops instead are different. There is no way to put much energy into the lightest tops. The Nr.1 can't receive more than 0.11 joule. The Nr.3 no more than 0.09 joule. So, very light tops cannot spin for long. Since the moment of inertia is low, energy can come only in the form of higher rotational speed, but there is a physiological limit to speed for the fingers. I have never been able to spin a top to more than 2400 RPMs (it is 40 rounds per second !) with just one twirl of the fingers, and at this so high speed the top has still only 0.09 joule, (the top Nr. 3).
There are two reasons for the variability from 0.5 to 0.7 joule, it's not a totally random variability;
The tops which I can spin with more energy have knurled stems, and their stems are long.
The two my absolute best tops as for the quantity of energy I can put in them, (Nr. 14 and Nr. 20), have the two longest stems of all of my tops.
My tops unable to receive more than 0.55 joule have all a smooth stem and/or a short stem.
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Hello Iacopo,
I greatly enjoy our discussions.
So, if twirl energy input is relatively constant (except for very light tops), then do you agree that bigger and heavier tops would launch at lower RPM and spend less time in the RPM range dominated by aero drag? And, if so, why don't tops bigger than 57 or 59mm spin longest?
At high RPM drag, is aero and tip friction.
At low RPM, aero drag tends to vanish, leaving only tip friction.
Best,
Alan
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do you agree that bigger and heavier tops would launch at lower RPM and spend less time in the RPM range dominated by aero drag? And, if so, why don't tops bigger than 57 or 59mm spin longest?
Yes, I agree, in this sense bigger tops have an advantage.
Anyway, bigger tops also have a disadvantage: at parity of toppling down speed, a bigger top has more energy than a littler top, when they topple down. So, the larger the top, the larger the quantity of energy lost when it topples down.
In other terms, it could be said that larger tops are more efficient, (they lose less RPM per minute than littler tops), but, on the other hand, they are launched at lower speed, while the toppling down speed is not necessarily lower, (being unrelated to the size of the top), so there are less RPM useful for a longer spin. For very large tops the difference between starting speed and toppling down speed can be very little.
In your formula you are using Merit as a fixed number for to foresee the spin time of a top, but for my taste there is still a bit too much difference between the merits, (ranging from 12.8 to 20.2 in your tops and from 9.4 to 22.3 in the mine). I believe the reason is because the formula considers that a heavier top always spins longer, but this is true only up to a certain weight, about one hectogram for single twirl tops with non recessed tip. From there, the heavier the top, the less it spins.
I am not very good at mathematics, but I think that if you can find a way to consider this in the formula, the merits of the various tops would be more similar.
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I have made tops, which don't topple when spun on an ordinary concave mirror. They stop, still standing - every time.
I achieve this by a combination of good balance, a very low clearance between the bottom surface of the wheel, and a larger ball tip. (All my tops have a ball tip). But the increased aero shear of the low clearance and the increased friction of the larger ball erases the benefit of no topple. So they are nearly my best, but not quite my best. But perhaps I should apply this to a larger top.
Another interesting parameter is shaft diameter. It like choosing the best gear ratio for a dragster. Currently my best diameter is about 6mm, but larger might be preferred for a larger top.
Considering your impressive spins, I'd love for you to spin some of my tops. I'll bet you're a stronger spinner than I am. Let's get together by messenging and I'll send you a top to spin.
Alan
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The tops which I can spin with more energy have knurled stems, and their stems are long.
This makes sense to me. When we twirl hard there is some unwanted lateral motion. The longer the stem, the smaller the tilt angle imparted by that lateral motion. So long stems are more tolerant of unwanted lateral motion and permit us to twirl harder.
Alan
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The tops which I can spin with more energy have knurled stems, and their stems are long.
This makes sense to me. When we twirl hard there is some unwanted lateral motion. The longer the stem, the smaller the tilt angle imparted by that lateral motion. So long stems are more tolerant of unwanted lateral motion and permit us to twirl harder.
Alan
This is a very good observation that hadn't occurred to me before. Thanks!
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Iacopo,
Have you ever tried aluminum tube for a stem? It's much stiffer for it's weight than solid wood, which is weak in torsion. It's available with thin wall. I might try that for a long stem. If so, I'll insert a temporary plug during knurling.
My present stems are effectively aluminum or brass tube. I knurl solid rod, then drill it leaving a thin wall. When I spin with string, I insert a shaft into the center hole, to support the top while I pull on the string.
Alan
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The tops which I can spin with more energy have knurled stems, and their stems are long.
...When we twirl hard there is some unwanted lateral motion. The longer the stem, the smaller the tilt angle imparted by that lateral motion. So long stems are more tolerant of unwanted lateral motion and permit us to twirl harder.
This is a very good observation that hadn't occurred to me before. Thanks!
These issues also arise with LEGO tops, and similar solutions apply. Longer stems definitely reduce hopping and sliding of the tip while improving control over tilt angle during strenuous twirls.
(http://images.mocpages.com/user_images/99234/1489996100m_SPLASH.jpg)
Tilt control is even better when one hand stabilizes the desired tilt while the other applies the torque -- hence the manual 2-handed detachable "Twirl-o-matic" stem extenders below (details here (http://www.moc-pages.com/moc.php/438999)). Iacopo and Alan might be able to rig up extenders without modifying or marring their beautiful tops...
https://www.youtube.com/watch?v=SL9KBh2z6uQ
A geared-up 2-handed coaxial manual starter (3:03 above) improves both tilt control and launch speed, while a spring-powered or motorized starter (10:23 below) supplies all the torque, leaving the user to concentrate solely on tilt control. Alan's string-launch system uses a similar strategy.
https://www.youtube.com/watch?v=IMYx-DBrHcs
But one can go a step further and eliminate the stem during spin-down. During spin-up, you then transmit torque to the rotor through a dog or centrifugal clutch designed to disengage cleanly at the end (details here (http://www.moc-pages.com/moc.php/425637)). These fully detachable stems work best with a suitable starter but with practice also work by hand...
(http://images.moc-pages.com/user_images/99234/1456207606m_SPLASH.jpg)
(http://images.moc-pages.com/user_images/99234/1456207595m_SPLASH.jpg)
https://www.youtube.com/watch?v=ZoAS2nzLsho
Long stems inevitably increase both CM height and TMI about the tip. The result is a higher critical speed and an increased tendency to precess rather than sleep -- both of which cut into spin time. This may not be a practical problem with the heavy metal rotors Iacopo and Alan use, but it definitely limits stem length in some of my plastic tops. Detachable stems and stem extenders end-run the problem.
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Have you ever tried aluminum tube for a stem? It's much stiffer for it's weight than solid wood, which is weak in torsion.
A few times I used aluminum or ergal for the stems, (not tubes), like this:
(https://i.imgur.com/gM64NtS.jpg)
This stem is made of ergal, it is empty inside, and with a pattern with holes.
It weighs 12.4 grams, (the whole top weighs 187 grams).
But I prefer wood anyway, for my stems:
robustness is absolutely not a problem, at times I use even obeche for making the stem, which is a very light wood, (density 0.38), even for long and narrow stems, even if I spin the top aggressively, and I never had weakness problems. And a long stem made of obeche weighs only 1 gram or little more, so it's very light. Wood is an excellent material for making stems, and some species of wood also are very beautiful.
I have made tops, which don't topple when spun on an ordinary concave mirror. They stop, still standing - every time.
In this case, maybe a bigger top could spin longer, but I am not sure... I have contradictory data.
It would be interesting to know how much tip friction increases at the increasing of weight, at parity of radius of gyration.
Another interesting parameter is shaft diameter. It like choosing the best gear ratio for a dragster. Currently my best diameter is about 6mm, but larger might be preferred for a larger top.
By the time I tried different sizes, and found that, for my fingers, the best diameter is between 3 and 4 mm, (for single twirls and tops weighing up to about 200 grams).
Probably there is a different best diameter for each different hand.
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Another interesting parameter is shaft diameter. It like choosing the best gear ratio for a dragster. Currently my best diameter is about 6mm, but larger might be preferred for a larger top.
By the time I tried different sizes, and found that, for my fingers, the best diameter is between 3 and 4 mm, (for single twirls and tops weighing up to about 200 grams).
Probably there is a different best diameter for each different hand.
I generally get my fastest launch speeds with a 4.8 mm splined stem (black below). But to maximize speed in heavy tops (up to ~180 g in my case), I have to start them at 6.0 mm (brown below) and then shift my fingers upward to the 4.8 mm part for final spin-up. Hence this stepped stem...
(http://images.mocpages.com/user_images/99234/1449791093m_SPLASH.jpg)
Iacopo does the same with his tapered stems.
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I've computed merit for several small tops, 38mm, 45g merit=27 and 51mm, 74g merit=21.
I'm inclined to think that my formula favors light weight. As I gather more data, I may have a stab at adding an exponent for weight. The exponent would be in the ballpark of 0.75. But the approximate merit would no longer be 20 ish.
Happy thanksgiving.
Alan
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A few days ago, I defended taking weight linearly, but I realize now, that's only true during the high speed portion of the spin, when tip friction is small compared to aero drag. During the slow portion of each spin, tip friction dominates and one could argue that weight is completely canceled, which is the equivalent of wt^0. (Any number ^ 0 = 1).
Thus during the high speed portion of the spin, we have wt^1 (linear), and during the slow portion of the spin we have wt^0. I tried various exponents between 0 and 1, and wt^.50 worked well. So here's a revised figure of merit.
Merit = seconds / (launch RPM^.63 x diameter^.5 x kg^.5)
A group of my tops have merit about 5.8-ish +/- 4% (with linear wt, variation was +/- 35%)
Iacopo's tops have merit about 5.9-ish, +/- 22% (with linear wt, variation was +/- 63%)
I expect Iacopo's tops to have a higher figure of merit because most of them spin on a sharp point and all of mine spin on a ball. But 5.8 vs 5.9 is closer than I expected.
This can also give an approximate prediction of spin time.
seconds ~ 5.8 x RPM^.63 x Diameter^.50 x Kg^.50
Best regards,
Alan
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seconds ~ 5.8 x RPM^.63 x Diameter^.50 x Kg^.50
This formula says "the larger/heavier, the better".
Here I try a different approach, that of energy decay.
Since with a single twirl different tops are started with the same amount of energy, the one which consumes energy more slowly, will spin longer.
The graph below is a comparison between energy decay in a big/heavy top and a littler/lighter top;
red line: 656 grams top
blue line: 186 grams top
The two tops are both started with one twirl of the fingers; the initial angular velocity of the heavier one is lower than that of the other one, but the initial amount of energy is the same in the two tops.
The red line is shorter because the heavy top topples down much sooner.
(https://i.imgur.com/DqNzMl2.jpg)
At high speed the heavier top is more efficient, probably because it has less air drag.
At slower speed air drag becomes more and more negligible, so energy consumption becomes more and more driven by tip friction.
At slower speed the heavier top has become less efficient than the other one.
At parity of energy, it seems like heavier/bigger tops tend to have less air drag, but more tip friction than littler tops.
So, even in the case of tops that do not topple down, it is not very clear if a bigger/heavier top can spin longer than a littler/lighter one, with a single twirl, or not. I think there is an ideal weight, a best compromise between the two frictions.
I am making a vacuum chamber, when ready I will use it for to study energy decay of different tops, in air and without air, for a better understanding of how much energy is lost because of air drag and how much because of tip friction. I will post here the results.
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Nice work Iacopo.
I'm very impressed that a single twirl powered a 656g top for 22 minutes.
And I'm even more impressed that you twirled a 186g top to run for 52 minutes!
Tell us more. Diameters, photos, launch RPM, etc.
Calculate merit for each.
Best regards,
Alan
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EDC
Every Day Carry? Do I want to carry a top? No. But it's interesting to explore the limits of spin time for a small top. Most small tops sold by US makers are about 1" diameter and less than 50g. They brag if they spin for 7 minutes.
But I've learned from my merit formula that doubling the diameter and weight offers double the potential spin time. But the merit doesn't tell how fast we can twirl a top. If we double the 1"/50g up to 2"100g, merit suggests it will spin twice as long when twirled just as fast as the 1" top. But we can't twirl it just as fast. Despite that, I have several tops within the 2"/100g limit that exceed 16 minutes.
Perhaps a compromise for a small top would be about 1.5" diameter and 75g. And the top should spin on an almost flat surface. It's amusing to read listings for small concave lenses on amazon. They talk about spinning tops on them. A 2" concave lens is easy to carry.
Does this interest any of you makers? Perhaps we should also rule out tungsten. I love it, but it's difficult to buy and expensive.
Alan
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Attempting to rationalize the math.
Iacopo finds that twirl energy is constant.
That means that RPM^2 x diameter^2 x mass is constant for different tops.
Suppose we take a top of diameter and mass = 1 and RPM=1
Now double the diameter and mass so RPM^2 x 2^2 x 2 = 1, thus RPM=.353 because
.353^2 x 2^2 x 2 = 1
I have experimental evidence that spin time ~ 6 x RPM^.63 x dia^.5 x mass^.5
For the top of diameter and mass = 1 we have spin time ~ 6 x 1^.63 x 1^.5 x 1^.5 = 6
For the top of twice the diameter and twice the mass, RPM=.353 for the same twirl energy and
6 x .353^.63 x 2^.5 x 2^.5 = 6.23, which is only about 1.04x longer.
But my 2", 100g tops generally spin about 1.5x longer than my 1", 50g tops.
Update: I went back and calculated twirl energy for many twirls of different tops. I see a trend of increasing twirl energy with larger tops. That means that my strength is more consistent than my speed. The trend shows my twirl energy for 2" dia tops is about double the energy for 1" dia tops. This explains why my 2" tops run about 1.5 times longer than my 1" tops, not 1.04x longer as expected for constant twirl energy. "Your results may vary".
Alan
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I'm having trouble rationalizing the math.... Jeremy - Help.
I have some suggestions, but I'm not confident that they'll get you to your goal -- namely, reliable spin time prediction from a presumed universal constant (your figure of merit), launch speed, and just 2 top parameters. I think you'll need a lot more parameters and some hard-core dimensional or multivariate statistical analysis to succeed. Moreover, some of the parameters you're likely to need (e.g., the coefficient of sliding friction at the tip) are hard to come by.
Units: Mass, length, and time units have to match on both sides of any valid equation, and that may not be the case with your formulas.
Top classes: I think you'll need to divide your tops into 2 classes -- those that fall, and those that come to rest upright -- with separate merits and spin time formulas for each. For tops that fall, you probably need to add tip-CM distance H as a parameter, as H affects critical speed wC more than any other factor, and small differences in critical speed can lead to large differences in spin time in tops that spend a lot of time at low speed.
In addition, wC is just the highest speed at which the top can fall. When it actually falls once below wC depends on environmental factors partly beyond your control. The resulting spin time variance could be a significant source of error in your falling tops.
Iacopo finds that twirl energy is constant.
Launch energy: Launch energy seems to be roughly constant for Iacopo's tops in Iacopo's hands, but that may not be true of your tops in your hands. Better confirm that before building it into your spin time predictions.
That means that RPM^2 x diameter^2 x mass is constant for different tops.
Not exactly. Since most of your tops have heavy cylindrical rotors with relatively light stems and tips, I'll assume that geometry and ignore all stem and tip mass properties from here on out. To simplify the math, I'll also work in MKS units, in outer cylinder radius R rather than diameter D, and in angular speed w in rad/s rather than in RPM. Of course, R = ½ D, and w = pi RPM / 30, so what's qualitatively true of diameter and RPM is also true of radius and angular speed.
True, initial kinetic energy (KE) is given by
T0 = ½ I3 w02,
where I3 is the AMI (axial moment of inertia) in kg m2, and w0 is the launch angular speed in rad/s. But you're assuming that the AMI depends only on mass and radius, and there are 2 potential sources of error here:
1. Mass and radius are coupled through density, rotor shape, and volume, and hence through top proportions -- at the very least, through the aspect ratio
A = L / R,
where L is the cylinder's axial length.
2. Many of your tops have heavy metal rims with lower-density plastic cores, and for these, the AMI also depends strongly on the rotor densities involved and on the radius ratio
X = RC / R,
where RC is the core radius. If you want better than 50% accuracy in your spin time predictions, these complications may be important.
In addition, the top, if launched vertically, also has an intial gravitational potential energy (GPE) given by
V0 = M g H,
where M is the total mass in kg, and g is the acceleration of gravity in m s-2. GPE can feed precession at the end of the spin -- another way for H to affect spin time in your falling tops.
I have experimental evidence that spin time ~ 6 x RPM^.63 x dia^.5 x mass^.5
Honestly, this seems unphysical to me. How big are your samples, and how good are your correlations? Does the underlying data include tops with the all diameters and masses you hope to cover? If not, you may be on thin ice with some tops.
Suppose we take a top of diameter and mass = 1 and RPM=1
Now double the diameter and mass so RPM^2 x 2^2 x 2 = 1, thus RPM=.353 because
.353^2 x 2^2 x 2 = 1
For the top of diameter and mass = 1 we have spin time ~ 6 x 1^.63 x 1^.5 x 1^.5 = 6
For the top of twice the diameter and twice the mass, RPM=.353 for the same twirl energy and
6 x .353^.63 x 2^.5 x 2^.5 = 6.23, which is about 3.8% greater.
But my 2", 100g tops generally spin about 1.5x as long as my 1", 50g tops.
But doubling the diameter quadruples the mass at constant uniform density. Ignoring that throws off underlying assumptions about AMI.
An alternative: If you want to compare your tops using a single number, I recommend the method ta0 introduced in this 2009 post (http://www.ta0.com/forum/index.php/topic,153.msg875.html#msg875). I expanded on the theory and application here (http://www.ta0.com/forum/index.php/topic,5047.msg53269.html#msg53269). This method fits an exponential decay to the actual decay curve and delivers a hypothetical decay time constant useful in performance comparisons, but it doesn't allow spin time predictions. The data collection is more onerous than taking a few quick top measurements, and the data processing involves more than plugging into a simple formula. But it's easy to fit an exponential trend line in Excel, and the time constant is just the reciprocal of the decay constant reported in the trend line label.
Sorry this got so long. Hope it helps.
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The graph below is a comparison between energy decay in a big/heavy top and a littler/lighter top....
Interesting data! What kind of graph is that? The horizontal axis is clearly linear. The vertical axis looked logarithmic at first, but the distances between powers of ten as marked aren't uniform.
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Hello Jeremy,
Thank you for your post. Here are a couple of comments.
I used about a dozen of my tops to develop the approximate duration prediction. They ranged from 1" to 3" diameter and 43 grams to 158 grams. Proportions are not constant. When I increase diameter I decrease thickness because these are all twirlers and I want to keep inertia from getting too great. I also used about ten twirls of each top.
All of the tops have brass or bronze perimeters and lightweight hubs. So the relationship of inertia/(mass x dia^2) is approximately constant. I've graphed my test results vs diameter and vs mass and the formula doesn't appear to have a size bias.
Yes, my twirling ability appears to differ from Iacopo's. As I wrote, "Your results may vary". I sent Iacopo a top recently and am looking forward to learning how fast he can twirl it.
It's interesting that duration for the same top and the same twirl speed can vary. Most likely the variation is related to lube of the mirror. I always lube the mirror with my skin oil, applied with a few wipes of my thumb.
I find the merit formula useful to compare some design variations. For example some of my lightweight hubs consist a very thin sheet of the perimeter material. In this case, I can put the sheet at the bottom, which reduces Cg and topple speed, or at the top, which reduces aero shear, but slightly elevates Cg. There's no obvious advantage to either choice.
Best,
Alan
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The graph below is a comparison between energy decay in a big/heavy top and a littler/lighter top....
The vertical axis looked logarithmic at first, but the distances between powers of ten as marked aren't uniform.
In fact it is not exactly logarithmic. I made the graph starting inserting the minutes, then I drew the straight blue line indicating energy decay of the littler top, then I inserted the relative values of energy at the left.
So uniformity is in the shape of the blue line, (straight), instead of in the distances between the horizontal lines.
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Update: I went back and calculated twirl energy for many twirls of different tops. I see a trend of increasing twirl energy with larger tops. That means that my strength is more consistent than my speed. The trend shows my twirl energy for 2" dia tops is about double the energy for 1" dia tops. This explains why my 2" tops run about 1.5 times longer than my 1" tops, not 1.04x longer as expected for constant twirl energy. "Your results may vary".
1" diameter tops are still far too little.
Tops between approximately 1" and 2" are still in the range where, increasing their size/weight, increases the energy that can be transferred from the hand to the top.
We both experienced the same.
But over approximately 2", and over 100-200 grams, you can see that it becomes more and more difficult to increase the energy you can put into the top, at the increasing of its size, (and this makes sense, because the power of the hand doesn't increase, so there is a limit).
Also I believe that, at some point, (some kilograms ?), there is a reversal;
the bigger the top, the less the energy transferred from the hand to it with a single twirl, (simply it becomes too difficult to even move it).
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Iacopo,
All of your post above is in agreement with my observations. My twirl energy rises between 1" and 2", then tends to level above 2".
But although 1" is small, as I mentioned in my EDC post, a lot of 1" tops are sold and carried in a pocket.
I've often said that while we strive for long spin time, it can be boring. Would we play with a top that spun for 24 hours? So, although I'm as susceptible as anyone to the siren song of long spin time, I try to remember that there are other factors of interest.
Best regards,
Alan
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I've often said that while we strive for long spin time, it can be boring. Would we play with a top that spun for 24 hours? So, although I'm as susceptible as anyone to the siren song of long spin time, I try to remember that there are other factors of interest.
Couldn't agree more. I worked hard to get my best spin time by hand (~5 minutes), but I spend most of my time designing for play value, appearance at rest, visual effects at speed, and the smoothest possible spins. Some of my favorite tops stay up for less than 20 sec...
(http://images.mocpages.com/user_images/99234/1499802025m_SPLASH.jpg)
(http://images.mocpages.com/user_images/99234/1500673689m_SPLASH.jpg)
(http://images.mocpages.com/user_images/99234/1447273455m_SPLASH.jpg)
(http://images.mocpages.com/user_images/99234/1448557628m_SPLASH.jpg)
https://www.youtube.com/watch?v=91UHZzEZPyo
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Iacopo,
All of your post above is in agreement with my observations. My twirl energy rises between 1" and 2", then tends to level above 2".
But although 1" is small, as I mentioned in my EDC post, a lot of 1" tops are sold and carried in a pocket.
I've often said that while we strive for long spin time, it can be boring. Would we play with a top that spun for 24 hours? So, although I'm as susceptible as anyone to the siren song of long spin time, I try to remember that there are other factors of interest.
Best regards,
Alan
Personally I would find a top able to spin for 24 hours a very interesting object.
That said, each one of us is free to choose the aims he prefers, of course.
Portability is an added value, but even a 2" top can still stay in a large pocket..
The few times I had to carry my tops, I never found them difficult to carry.
The real reason why, (in my humble opinion), many metal finger tops sold in the market are little, about 1" diameter, is not because of portability. Even it is not because a larger top would spin for too long. I believe the real reason is that that is the size more suitable for making money. Something related to costs of production, number of sales, earnings,...
There are makers that made much money selling tops of that size.
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Now that's cool. It looks FANTASTIC with the sharks. Now use little ablone to balance it. Maybe more spin time.
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Also I believe that, at some point, (some kilograms ?), there is a reversal;
the bigger the top, the less the energy transferred from the hand to it with a single twirl, (simply it becomes too difficult to even move it).
In electronics we call it impedance matching. In mechanics gearboxes are used to match the input power with the output load. The stem with tapered diameter works like a gearbox of sorts. What makes me wonder if it wouldn't be possible to drive a very heavy finger top using an actual gearbox in line with the stem :-\
Now that's cool. It looks FANTASTIC with the sharks. Now use little ablone to balance it. Maybe more spin time.
The Titanic top is hilarious!
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Now that's cool. It looks FANTASTIC with the sharks. Now use little ablone to balance it. Maybe more spin time.
Thanks, Cecil! Not to hijack Alan's thread, but the top is very close to perfect balance just by virtue of the high precision of LEGO parts. I can fine-tune the balance as needed by sliding the sharks along their rails and adjusting the postures of the life raft occupants.
But there is a tie to the discussion of AMI and twirlability. The intermittent wobble is due to flexure of the rotor -- which I could only make so rigid given the design, the size, the plastic material, and my determination to keep the top twirlable by hand.
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The Titanic top is hilarious!
Thanks! This is the part of the Titanic story they didn't want you to know. Personally, I feel sorry for the sharks, who swim round and round but never get a bite to eat. Sharks have to make a living too, you know.
In electronics we call it impedance matching. In mechanics gearboxes are used to match the input power with the output load. The stem with tapered diameter works like a gearbox of sorts. What makes me wonder if it wouldn't be possible to drive a very heavy finger top using an actual gearbox in line with the stem :-\
Intriguing idea! At 0:57 in the Titantic top video, I use a bulky inline planetary gearbox (single-stage, 1:4 overdrive) as a detaching starter. Unfortunately, that's as compact as a symmetrical inline gearbox can get in LEGO for want of a suitable ring gear, but it would certainly be possible to fabricate a planetary gearbox light enough and small enough and balanced enough to build into a top -- say, at the base of the stem.
Hmmm, come to think of it, pump tops already have internal inline gearboxes. And they require only one hand to operate.
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More about optimum stem diameter
My stems have a central hole. I use that to stabilize the top if I spin it with a string. I also sometimes push a rod through the hole to eject a damaged tip ball.
Many of my smaller tops have approx 6mm knurled stem, but I've made larger tops with larger stems.
I tried inserting a 6.4mm knurled stem-extension into a couple of tops to see if this smaller and longer stem facilitated faster twirls. It extended the stem by about 20mm but it didn't help. Here are two I tried.
38mm 92g top with 9.3mm dia stem.
The above extension reduced average twirl speed by 11%
I also tried a 100mm wood extension with rubber tape at the top for grip. It resulted in equal average spin speed to no extension, but the weight of the extension caused much earlier topple.
44mm 99g top with 8.4mm dia stem.
The extension reduced average twirl speed by 9%,
Best,
Alan
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extended the stem by about 20mm but it didn't help.
Not sure about the reason, but I can suppose the following:
The clearance between the bottom of your tested tops and the spinning surface is large enough, so that you can spin hard your tops with a short stem without having the problem of the sides of the bottom of the flywheel touching too easily/often the spinning surface during the spinning action.
You should reduce that clearance, (recessing the tip a bit more), because you need less of it, thanks to the longer stem.
So you could see the advantage, because the overall center of mass would be slightly lower, in spite of the longer stem, (if it is built very light).
If the clearance is little, you can see a difference in starting speed, using a short stem instead of a long stem, because it is difficult to spin hard a top with little clearance and a short stem.
You simply added a stem extension to your existing tops, which you made with a clearance optimized for their short stems; that is a larger clearance, which already allows for hard spins with no problems, even if the stem is short.
So adding to them a stem extension doesn't increase their starting speed.
___________________________________________________________
I add as a side note that, in my case, when I use the pedestal as spinning surface, the problem is different;
I have plenty of free space below the top, and the top could be tilted a lot during the spinning action, with no problems.
The problem here is not tilting, but the resistance to tilting which develops when the top grows in rotational speed during the spinning action.
Because of this resistance, the unwanted lateral motions of the hand are transmitted to the top only partially in the form of tilting of the top, then also they are trasmitted to the top as lateral movements of the top itself.
This is a problem for me, because the spinning surface of the pedestal is very little.
The top tends to exit from the base.
The longer stem decreases the change of angle of tilting of the top during the spinning action, and the force that pushes the top out of the base.
For this reason I can spin harder my tops with longer stems, on the pedestal.
All this is true also for tops with recessed tips.
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Hello Iacopo,
This brings up an interesting design parameter. What is your maximum angle of lean before scraping the flywheel? Currently I aim for about 8 degrees.
Best regards,
Alan
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What is your maximum angle of lean before scraping the flywheel? Currently I aim for about 8 degrees.
It is about 4 degrees in my latest tops, and I have no problems spinning them hard on a flat surface, with stems about 70 mm long.
If you use a concave mirror, you need more degrees, probably about 5, but this depends on how much concave it is.
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Optimal knurl diameter
This is my top Nr. 22.
It weighs 656 grams, diameter 80 mm.
(https://i.imgur.com/bccTV88.jpg)
The knurl is tapered.
The upper side is too small for an efficient single twirl, but the lowest side is too large.
I can transfer the highest energy to this top with a single twirl when I spin it with my fingers at the height where the knurl has 5 mm diameter.
So, the optimal "gear ratio" for my fingers is a 5 mm stem for to move a kg-m2 0.000636 rotor.
Accordingly, rotors with less moment of inertia will require smaller knurls, to maintain this optimal "gear ratio".
So, a more normal top, like my Nr. 29, whose moment of inertia is one tenth of that of the Nr. 22, will require an ideal diameter of the knurl which is:
mm 5 : square root of 10 =
5 : 3.16 = mm 1.6
But 1.6 mm is too small. Not for the "gear ratio" issue but for another reason;
A so thin knurl would offer too little surface in contact with the skin of the fingers, the grip would be too poor, and the fingers would slip on its surface trying in vain to spin it hard.
Also, if the knurl is too thin, the two fingers would be in contact each other, and part of the energy would be lost for the friction between the two fingers themselves.
This is the real reason why the majority of my tops has knurls with diameter between 3 and 4 mm.
It is the thinnest diameter that my fingers can still grasp well.
This means that all my tops up to 300 grams have a too large knurl, in the sense that they have not an optimal "gear ratio".
The red line in the graph below, (which I already showed you), is that of the top Nr. 22
(https://i.imgur.com/DqNzMl2.jpg)
But the red line was cut, and I started it at 0.6 joule, the same as the blue line, for an easier comparison.
Reality is that that spin of the Nr. 22 started about 6 minutes earlier, and its initial energy was 1.03 joule.
This is much more initial energy than that of my other tops, at first I was unsure what to think about this, and I avoided to mention this fact.
But there are not errors in the calculations, this is real.
So, here it is:
the top Nr. 22 is my real best top as for the energy it can receive by a single twirl.
The reason is that it is my only top with a best "gear ratio" and a knurled stem.
The other my three giant tops have smooth stems, or a knurl with a wrong size for a single twirl.
All my other tops have a less or more unfavourable "gear ratio", because I can't make knurls smaller than 3-4 mm.
_____________________________________________________________
Conclusions:
When designing the knurl of a spinning top, the challenge is not to realize what diameter give to it, for to have the best "gear ratio", because we already know that whatever diameter we choose, is too large, (for a normal size top).
The challenge is to design a knurl with the littlest diameter but with enough surface area for the fingers.
A way to obtain this is to make the knurl long. Long and narrow.
As an artisan, my fingertips are a bit callous, and, maybe, this helps me spinning small knurls.
But also I believe that one reason why I can do so is exactly because my knurls are long. The precious surface area lost in width because of a more narrow knurl, is gained again, in length.
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Optimal knurl diameter
The knurl is tapered.... The upper side is too small for an efficient single twirl, but the lowest side is too large.
I'd put tapered stems on all my "heavy" tops if LEGO parts allowed, but steps are the best I can do. The starting step here is 6.0 mm in diameter, and the finishing step is 4.8 mm.
(http://images.mocpages.com/user_images/99234/1449791093m_SPLASH.jpg)
A tapered stem is to a continuously variable transmission as a stepped stem is to a gearbox with a few fixed drive ratios. If LEGO made the parts, I'd try an 8-2 mm taper for my own use. Who knows, maybe I'd expand my twirling skills and top designs.
That said, most of my tops perform best with just the 4.8 mm stem -- thanks in no small part to its 4 deep splines and the grip they provide.
(http://images.mocpages.com/user_images/99234/1447534055m_SPLASH.jpg)
I only go thinner (here to 3.0 mm) in very small, very "light" tops. But other users -- especially very young kids -- might find more use for 3.0 mm or even smaller stems.
(http://images.mocpages.com/user_images/99234/1447463085m_SPLASH.jpg)
We all know what "heavy" and "light" feel like in this context, but as you point out, we're feeling AMI here, not mass per se. Mass reliably tracks AMI only when specific AMI (AMI per unit mass) is more or less constant. My rotor geometries vary a lot more than yours and Alan's do, and their specific AMIs are all over the map. Mass is vastly easier to measure than AMI, but alas, tracking AMI with mass just does't work for me.
So, the optimal "gear ratio" for my fingers is a 5 mm stem for to move a kg-m2 0.000636 rotor.... Accordingly, rotors with less moment of inertia will require smaller knurls, to maintain this optimal "gear ratio".
An excellent and very practical way to think about this critical design issue. Play value in my tops hinges on getting the stem geometry right -- especially for the low-skill audiences I usually get at LEGO shows. Every hand seems to have its own optimal stem diameters for a given set of tops. The available diameters that work with my hands are 3.0, 4.8, and 6.0 mm.
A so thin knurl would offer too little surface in contact with the skin of the fingers, the grip would be too poor, and the fingers would slip on its surface trying in vain to spin it hard.... Also, if the knurl is too thin, the two fingers would be in contact each other, and part of the energy would be lost for the friction between the two fingers themselves.
Exactly my experience. Control also gets dicey below 3.0 mm in my hands. I never need to start at more than 6.0 mm at LEGO densities, but the average LEGO show visitor would probably have an easier time if my highest-AMI tops had larger starting steps.
So, here it is: the top Nr. 22 is my real best top as for the energy it can receive by a single twirl.... The reason is that it is my only top with a best "gear ratio" and a knurled stem.
Exactly the way it works with my tops. Problem is, finding the best diameter(s) for a given top can be a chore even if you're just assembling ready-made parts like me.
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I'm thinking about energy imparted to a top when twirled:
1. At the initial instant a torque is applied to the stem and it has not yet rotated.
2. An instant later, the stem rotates away from the applied torque, reducing the applied torque. The lighter the top, the greater the reduction.
So the greatest energy transfer would be to a very heavy top. To the degree that the top rotates, there is a reduction in energy transfer.
Alan
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I'm thinking about energy imparted to a top when twirled...
I think it's fair to say that available finger torque generally goes down as stem speed increases. But the rate of energy transfer is the mechanical power given by the product of torque and angular speed (in rad/s). Hence, the energy transfer rate must be minimal at the start of the twirl and at the end and must peak somewhere in between.
Look up brushed permanent magnet DC motors to see a reasonable analogy. The applied torque is maximum when the motor's stalled and vanishes as the motor approaches its no-load shaft speed. The torque-speed curve is a straight line between these 2 points. Maximum mechanical power output occurs, not at stall, but at 50% of no-load speed.
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So the greatest energy transfer would be to a very heavy top.
So it seems.
For my fingers, it seems to be maybe a 500-700 grams top.
But the rate of energy transfer is the mechanical power given by the product of torque and angular speed (in rad/s). Hence, the energy transfer rate must be minimal at the start of the twirl and at the end and must peak somewhere in between.
This is something interesting I never thought before.
So, the highest angular acceleration is not at the start of the twirl, right ?
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The orange line in this graph represents the maximum energy (joule) I could put in a perfect finger top by a single twirl of the fingers, depending on the moment of inertia of the top.
The red dots are the real, tested spinning tops.
I indicated the weight (grams) of the tops, near the red dots, which is a more intuitive measure than the moment of inertia.
The distance between the dots and the orange line represents the efficiency of the top twirling system;
(https://i.imgur.com/xkeSsqD.jpg)
For example, the top that weighs 329 grams is far from the orange line; it is very inefficient.
Its stem is smooth and relatively slippery. The shape of the stem also is not very good, it is cylindrical, and too large.
So I can spin it only up to little more than 0.6 joule, instead of almost 1 joule, as its size should allow.
The top weighing 165 grams instead is on the orange line, it is very efficient;
it has a tapered stem, it is knurled, there is good grip for the fingers, good diameter, and the stem is very long.
It gets 0.7 joule, which is excellent for a top of this size.
Based on my actual data, I would say:
tops up to 200-300 grams are in the range where, at the increasing of their size, they can receive a higher amount of energy with a single twirl.
500-600 grams tops instead are in the range where the perfect gear ratio is already reached, so it is not possible anymore to further increase the amount of energy given to them simply increasing their size.
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So, the highest angular acceleration is not at the start of the twirl, right?
Yes, but the power (energy transfer rate) at a given moment depends as much on the current speed as it does on the angular acceleration at the time. That means: (i) Of course, no torque, no power. (i) But also, no speed, no power. (iii) High speed can outweigh applied torque in the power game.
My hunch is that power will peak once the top gets up some speed. But angular acceleration is just the applied torque divided by a constant AMI, so what we're really after here is a representative applied torque-speed curve (ATSC).
This hunch comes in part from a mental image of a twirling ATSC that decreases steadily during spin-up. That's how spin-ups feel to me, but I may also be biased by a lot of work with DC electric motors (whose ATSCs decline linearly toward zero at no-load speed). Now, I doubt that twirling ATSCs are linear, but if they do decline roughly with speed, then peak energy transfer will come after start-up.
So, how could we get hold of a representative ATSC? What will it look like? How will it change from top to top and user to user? So many questions. Some "spin-up curves" (speed-time curves during spin-up) would be a good start.
It would be useful to pool the forum's observations on questions like these.
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The orange line in this graph represents the maximum energy (joule) I could put in a perfect finger top by a single twirl of the fingers, depending on the moment of inertia of the top.
A very interesting window onto the mechanics of twirling, Iacopo! I'm still giving the graph the careful study it deserves.
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Yes, but the power (energy transfer rate) at a given moment depends as much on the current speed as it does on the angular acceleration at the time. That means: (i) Of course, no torque, no power. (i) But also, no speed, no power.
Ok. Now I understand better.
We could say that energy and speed do not grow with the same rate, because energy is proportional to speed squared. Energy grows relatively little, at slow speed, at parity of angular acceleration.
So the maximum energy transfer can't be at the start of the twirl, even if the torque is stronger. I see this clearly now.
I suppose acceleration is different.
Without frictions, a constant torque should produce a constant acceleration;
so, if torque is strongest at the start of the twirl, which seems probable, acceleration too should be strongest at the start.
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So the maximum energy transfer can't be at the start of the twirl, even if the torque is stronger. I see this clearly now.
To see how all this plays out in a somewhat analogous case, I highly recommend this well-explained treatment (http://homepages.which.net/~paul.hills/Spinningdisks/DisksBody.html) of a disk spun up by a typical brushed permanent magnet DC electric motor. (The author happens to be writing for fellow battlebot builders.) The disk's AMI is the only load on the motor, as drag and friction are ignored. The graph below nicely summarizes the most pertinent results:
(http://homepages.which.net/~paul.hills/Spinningdisks/Image4.gif)
The torque output of such a motor declines steadily (and linearly) with speed. My guess is that finger torque also declines steadily as a top stem picks up angular speed -- though probably nonlinearly. Nonetheless, it's instructive to see how a declining torque-speed curve impacts a related spin-up process with a simple mathematical description.
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This brings up an interesting design parameter. What is your maximum angle of lean before scraping the flywheel? Currently I aim for about 8 degrees.
Totally agree, Alan: Scrape angle, AMI, twirling skill, play value, and spin time are all coupled, and that can make for some tricky audience-dependent design trade-offs. In my experience, the higher the AMI, or the shorter the stem, the larger the scrape angle must be to get a reasonable shot at a clean twirl -- especially in unpracticed hands.
It is about 4 degrees in my latest tops, and I have no problems spinning them hard on a flat surface, with stems about 70 mm long.
Wow, if that 70 mm goes all the way to the tip, you have at most 5 mm of lateral wiggle room at the stem! That's pretty tight at high torque. The high-AMI, high-drag top on the goniometer below has a scrape angle of ~7.5°. LEGO show visitors never get clean twirls out of it, and even I scrape now and then when I really crank it.
(http://images.mocpages.com/user_images/99234/1512259057m_SPLASH.jpg)
There are several ways to play these trade-offs, each with its pro and cons. Usually, a combination works best for me.- Reducing rotor radius to a comfortable scrape angle at constant ground clearance reduces AMI and CM height -- possibly with an increase in TMI/AMI ratio. If you're after a long-spinning sleeper, only the CM change is good.
- Jacking up the rotor to a comfortable scrape angle at constant rotor radius increases CM height and TMI with (i) a potentially strong adverse effect on spin time, and (ii) some loss of willingness to sleep.
- Elongating the stem with no other change significantly improves tilt control during spin-up at little cost in CM height and TMI. The shorter stem in the foreground works for me, but unpracticed hands would need the longer one.
- Or you could just forget about twirling the top directly and go to a detachable starter. The 2 examples below don't add much launch speed, but they greatly improve tilt control throughout spin-up.
(http://images.mocpages.com/user_images/99234/1512259053m_SPLASH.jpg)
One final point: If I limited myself to tops easily twirled by hand, I'd miss out on a lot of fun designs. Take my "planet tops" Revlon VI and Zargon IV. They're very popular at LEGO shows, but no visitor has ever gotten one to stay up by hand. Heck, I couldn't do it at first, either. Scrape angle isn't the problem, and neither is excessive AMI or drag. Instead, these tops suffer from critical speeds (due to unfavorable TMI/AMI ratios) that most users just can't reach by hand.
(http://images.mocpages.com/user_images/99234/1447739437m_SPLASH.jpg)
With the right starter, however, they're lots of fun. The best part: Since they're my planets, I get to be in charge of everything! >:D
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My longest twirl was achieved with a 2.25" (57.15mm) diameter, 145g spinning on a .5" (12.7mm) ball. An 860 RPM twirl ran for 26:05. But the lube may have been "just right" because a 923 RPM twirl ran 24:27 and a 909 RPM twirl ran 25:28. With balls one can have too much lube. As I've mentioned before, I lube with forehead skin oil, wiped hard on the mirror with my thumb. This top falls at about 133 RPM.
I think 145g may be optimum for a 2.25" top and my personal twirl ability. I haven't measured the rotational inertia of my tops, but they are all fairly similar geometry with brass or bronze rims and lightweight hubs.
For a long time I thought the tip drag of big balls was not a worry. I even went larger to achieve no topple. But lately, I'm seeing longer twirls with smaller balls (.25" and .312"). Iacopo's tips are so sharp that his tip drag must be very low. What's their topple RPM?
As I've mentioned before, the no-topple tops don't spin quite as long because of their big balls.
Today I've been looking at RPM decay rate. Surprisingly, it's a fairly constant 8% to 10% per minute over the entire twirl period for my better 2" and 2.25" tops. I expected a more rapid decay at high speed due to aero drag. But it appears that my twirl ability doesn't get me into the speed range of substantial aero drag.
Alan
PS A comment on the electric motor curve. I would presume that the torque is not affected by RPM, but twirl torque greatly affected by RPM.
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Today I've been looking at RPM decay rate. Surprisingly, it's a fairly constant 8% to 10% per minute over the entire twirl period for my better 2" and 2.25" tops. I expected a more rapid decay at high speed due to aero drag. But it appears that my twirl ability doesn't get me into the speed range of substantial aero drag.
You're describing a classic exponential decay. (See Wikipedia page.) By all accounts, tip friction is independent of speed and hence couldn't possibly cause such a decay. So if aerodynamic drag isn't responsible, what is?
...but twirl torque greatly affected by RPM
Totally agree and said so several times.
PS A comment on the electric motor curve. I would presume that the torque is not affected by RPM.
It's well-known that the torque of a brushed permanent magnet DC motor (the most common kind) decreases linearly with speed, and not just in theory. (See Wikipedia page.) Said that several times, too, and in fact, that's exactly why I suggested this kind of motor as a rough analog offering some potentially valuable insights. Not an exact model of twirling, just a well-understood system with some interesting parallels.
The curves I posted earlier are against time, not speed, but the decline in motor torque with speed still shines through.
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Wow, if that 70 mm goes all the way to the tip, you have at most 5 mm of lateral wiggle room at the stem! That's pretty tight at high torque.
Approximately 70 mm is the stem alone, for my latest tops.
All the way to the tip is about 80 mm.
4 degrees for 80 mm should be the same as 8 degrees for 40 mm, as for lateral wiggle room at the stem.
Sometimes I scrape, spinning hard, but not so often.
Thanks for posting the motor spin-up curves, they were interesting to think about.
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Iacopo's tips are so sharp that his tip drag must be very low. What's their topple RPM?
It is 165-175 RPM in my latest tops, when they are perfectly balanced.
In my experience spiked tips generally have less friction than ball tips, but then also it depends very much on the materials both of the tip and the base. If you still have the tungsten you bought, if you polish it, I think it could be an interesting spinning surface. Glass for spinning surfaces is good but not excellent.
As I've mentioned before, the no-topple tops don't spin quite as long because of their big balls.
Apart from higher friction, there is another reason why very large balls make for shorter spins;
they worsen the distribution of weight of the top, adding weight to the top, (which increases tip friction), without substantially increasing the rotational inertia of the top. This worsens spin decay. For longer spins the countrary is needed, less weight with more rotational inertia, which is obtained concentrating the largest possible part of the weight to the farest outside of the top.
Today I've been looking at RPM decay rate. Surprisingly, it's a fairly constant 8% to 10% per minute over the entire twirl period for my better 2" and 2.25" tops. I expected a more rapid decay at high speed due to aero drag. But it appears that my twirl ability doesn't get me into the speed range of substantial aero drag.
Maybe percentages calculated in this way could be misleading. If you simply look at RPM lost per minute, you see that they are much higher at high speed than at slow speed.
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I have made a slow motion video while spinning this top, and made the following graph from it:
(https://i.imgur.com/D8QKOqn.jpg) (https://i.imgur.com/1v97IDl.jpg)
I expected something different but the strongest acceleration happens in the second half of the curve, and not at the beginning. Maybe it's because the fingers are not in optimal position at the beginning of the twirl, so the torque is weaker at the beginning.
The graph then gives the sensation that the limit is not simply in the power of the hand by itself, but very much in the short duration of the spinning action, which ends after only half a second, when the top is still in full acceleration.
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Nice work (as usual) Iacopo.
I concur with your comment on finger position. I just tried very slowly twirling some tops and noting my finger position. I start with thumb tip and finger tip on the stem, then as I twirl, my thumb and finger roll on stem bringing the stem closer to the root (and the muscle) of my thumb and finger and thus to a location of greater strength.
I also tried reversing the process above. But the RPM is lower. Perhaps with practice??
Best regards,
Alan
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I have made a slow motion video while spinning this top, and made the following graph from it:
Our first finger-powered spin-up curve (SUC)! Our premiere experimentalist strikes again!
My twirls of the high-AMI, high-drag lime and black top I showed earlier also last ~0.5 sec.
I expected something different but the strongest acceleration happens in the second half of the curve, and not at the beginning. Maybe it's because the fingers are not in optimal position at the beginning of the twirl, so the torque is weaker at the beginning. The graph then gives the sensation that the limit is not simply in the power of the hand by itself, but very much in the short duration of the spinning action, which ends after only half a second, when the top is still in full acceleration.
Aside from the downward concavity during mid-late twirl, this SUC does bear some resemblance to the SUC of a high-torque DC motor loaded only by AMI. But if the concavity is real and not just an artifact of finger position, your finger torque-speed curve must be nonlinear with the steepest slope when finger-stem contact was lost.
I like your idea that the short duration of finger-stem contact may have something to do with this SUC shape. Off to twirl some tops with some new things to look for...
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I also tried reversing the process above. But the RPM is lower. Perhaps with practice??
I spin with my right hand and I find very natural to spin clockwise.
I suppose that spinning clockwise (with the right hand) makes for a stronger twirl than spinning counterclockwise, because, while spinning clockwise, the index finger flexes, in the other way instead it would have to extend, so different muscles are involved. Flexor muscles are generally more robust than extensor ones.
if the concavity is real and not just an artifact of finger position,
I observed my hand while spinning. In the beginning the thumb seems moved by the extensor muscles, (which are weaker), then, it becomes moved by the flexors, (which are stronger). Maybe this too explains the concave curve.
When, at the beginning of the twirl, the thumb is behind the index finger, I feel I have not much power in that position. When the thumb goes at the side of the index finger, at that point I feel it becomes more powerful.
Also I agree with Alan when he says:
I start with thumb tip and finger tip on the stem, then as I twirl, my thumb and finger roll on stem bringing the stem closer to the root (and the muscle) of my thumb and finger and thus to a location of greater strength.
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Following Iacopo's lead, I took some slow-motion video of my hand twirling a low-drag LEGO top of (by Iacopo's standards) small to moderate AMI. Twirls appear to start with just the thumb and forefinger, but the wrist soon starts to roll and bend so as to increase relative thumb-finger velocity. These slight wrist motions stop when the fingers stop, right after launch.
Is this wrist involvement consistent with Iacopo's empirical SUC? I think so. Since SUC slope steepens progressively and then levels out quickly just prior to launch, the net torque-speed curve (TSC) torque-time curve (TTC) must do the same at constant AMI. As the wrist enters the twirl, it adds powerful new muscle groups to those already at work. And as Iacopo suggested, the driving finger muscles may get stronger, too. The net torque at the stem would then increase with time due to applied muscle power alone, and the slope of the SUC would follow suit.
But muscle power is surely only part of the story, because the lever arms through which the various muscles act also change as thumb and finger positions and configurations evolve over the course of the twirl. Alan suggested that these lever arms generally become more favorable with time, and like Iacopo, I'm inclined to agree. Hence, net torque at the stem -- and therefore the SUC slope -- would have not just one but two independent reasons to grow through most of the twirl.
What about the very end of the twirl? When SUC slope and net torque finally tail off just prior to launch, perhaps the hand is in part preparing for a release favoring fine tilt control over net torque.
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but the wrist soon starts to roll and bend so as to increase relative thumb-finger velocity.
This is very true. In my hardest twirls I even tend to exaggerate a bit the movement of the wrist and I think it helps.
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A few weeks ago, I tried to stir up some maker interest in EDC tops. I've been pursuing this and today I made a 1.5", 51 gram, top which I twirled for 20:30. I'll bet Iacopo can twirl it longer. Are any of you top makers motivated to beat that? Let's call it the 50 gram division.
Alan
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51 gram, top which I twirled for 20:30. Are any of you top makers motivated to beat that? Let's call it the 50 gram division.
I think I could try, when I will have some more free time.
Now I am taking measurements of tip friction and air drag of different tops of various sizes, the collected data could be useful for improving the design. But it is taking much time. I will post all these data.
Look at this top, it weighs 51 grams, like the your, but it is made of tungsten, (the spindle is made of aluminum and the tip is a ceramic ball); it has been twirled for 49:27. Really impressive. I suspect that the use of denser materials for the flywheel is especially advantageous for littler tops. The top ends spinning in upright position, if it toppled down it would have spun for less time. Even so, this is a really long spin time.
https://www.youtube.com/watch?v=rwk9QKSOPxk
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Wow!!!! You've won the contest already! What is the diameter of the wheel and the ball?
Alan
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Wow!!!! You've won the contest already! What is the diameter of the wheel and the ball?
Oh, it's not me !
George Sherwood, the owner of the top, in the comments below that video in YouTube, says it has been made by Dave Kemner. Dave Kemner has a website where he sells his tops.
https://www.kemnerdesign.com/collections
But I have not seen this tungsten top in his website. You could try to write him, or George, to ask for more info about this top, if you want.
George says it weighs 51.2 grams. So I think the diameter should be about 30-35 mm.
I don't know the diameter of the ball tip, but if you look at the behaviour of the top when it is spun, it doesn't seem a large ball. I would say maybe a 5 mm ball, or something so.
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A few weeks ago, I tried to stir up some maker interest in EDC tops. I've been pursuing this and today I made a 1.5", 51 gram, top which I twirled for 20:30. I'll bet Iacopo can twirl it longer. Are any of you top makers motivated to beat that? Let's call it the 50 gram division.
That 20:30 is a good spin time by any standard. What does the top look like?
The challenge is a 50-gram EDC-style top with an even longer spin time?
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I checked the Kemner site. They don't currently have any tungsten nor any with lightweight (relieved) center hub. All their wheels are currently solid cylinders.
Incidentally, my 20:30 top has a 5mm white ceramic ball. I usually go for steel or tungsten carbide, but grabbed ceramic for this one.
I think that it would be impossible to reach the time in that video. To run that long, the energy input would be about 6 times the input of my 20:30 run. I doubt anyone can twirl that hard. My longest string twirl of a 400g top falls far short of that video.
Alan
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I checked the Kemner site.
At the bottom of this page I have found a picture of this tungsten top where you can see its ball tip:
https://www.kemnerdesign.com/blogs/news?page=1
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The Kemner tungsten top is approximately like my most successful design. My design is basically a cylinder with a groove on either the upper or lower surface to eliminate weight in the center. The "hub" thickness at the bottom of the groove is about 1 mm.
I began top-making with Delrin hubs, but a single material and 1 mm bottom thickness is about the same weight. Although the same weight, the grooved design has more "wetted" surface. But the performance is similar, so I think the air in the groove rotates with the top.
I've not explored rounding as much as Iacopo has. Most of my tops are square edged.
Lately I prefer the groove on top, so I can machine the groove, center hole (for the ball) and stem with the same setup. This achieves very good concentricity and balance. Then I part it from the bar stock and turn the top around. I can face the bottom so it's parallel to the top of the rim within .00001" (100 millionths).
This photo shows 1.75" OD and 1.5" OD tops. Both wheels are about 0.25" thick.
Alan
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This photo shows 1.75" OD and 1.5" OD tops. Both wheels are about 0.25" thick.
Very cool tops, Alan. The base is pretty cool, too. Did you make it?
Lately I prefer the groove on top, so I can machine the groove, center hole (for the ball) and stem with the same setup. This achieves very good concentricity and balance. Then I part it from the bar stock and turn the top around. I can face the bottom so it's parallel to the top of the rim within .00001" (100 millionths).
This suggests a spin-time experiment with something useful to say about the air flows around more or less cylindrical top rotors -- including rotors like yours and Iacopo's. One of you may have tried it already.
Experimental setup: Reasonably realistic, I think...
o Sleeping top on perfectly smooth, flat, horizontal "ground": Constant or slowly decaying spin rate about a vertical stem (no precession or wobble of any kind).
o Still ambient air: No air currents other than those stirred by the top itself.
o Dominant rotor: The rotor controls AMI, TMI, CM height, and all aerodynamic effects with no significant tip or stem contributions.
o Top "U": Hub is flush with the upper face of the outer metal "ring" and recessed below.
o Top "L": Hub is flush with ring's lower face and recessed above.
o Equal CM heights and TMIs: The hub is so much lighter than the ring that Top U and Top L are effectively equal here.
o Otherwise identical: Tops U and L are the same in all other respects -- including mass, rotor length, AMI, surface roughness, and rotor rounding.
Experimental question:
o Which has the longer spin time, Top U or Top L?
o Does spinning them on the same tall, narrow pedestal change anything?
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Jeremy,
Thank you, but I need translation of your abbreviations. In general, I'm unsure of your intent in this and several earlier posts.
I've mentioned in a prior post that the performance of the groove on top vs groove on bottom is about the same. At one time I expected lower aero shear drag for groove on bottom. But if it's lower, it's damn close. I think the air in the groove rotates with the top, so the bottom surface still "looks" about flat.
Alan
PS That's a standard mirror with my added thumb screws. I use the screws to either level it, or tilt it slightly every few minutes during a spin - to move the top to some fresh lube. These mirrors are 2X magnification, which is hard to find, but gives longer spin time than higher magnification surfaces, which grip the ball at a wider radius. They are about $12 on amazon.
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Which has the longer spin time, Top U or Top L?
o Does spinning them on the same tall, narrow pedestal change anything?
In my experience, the spinning of a top with its bottom very near to the spinning surface, does not decrease significantly the spin time. On the other side, lowering the center of mass even by just one millimeter, increases the spin time by 2-4 minutes, in tops like the mine.
So the top "L" would win.
Spinning them on a tall and narrow pedestal wouldn't change anything.
The advantage of the pedestal is not about aerodynamics; the advantages are that it allows to spin tops with lower center of mass, then tungsten carbide spinning surfaces, which I use in my pedestals, are better than common glass ones, they are more slippery and more wear/scratch resistant.
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That's a standard mirror with my added thumb screws. I use the screws to either level it, or tilt it slightly every few minutes during a spin - to move the top to some fresh lube. These mirrors are 2X magnification, which is hard to find, but gives longer spin time than higher magnification surfaces, which grip the ball at a wider radius. They are about $12 on amazon.
Leveling screws -- what a great idea! Agree, lesser mirror curvature (magnification) improves spin time -- not only by reducing tip friction, but also by making it easier to twirl a sleeper from the very start. Greater curvature is better only when you're mainly after precession or strong tip containment.
Thank you, but I need translation of your abbreviations.
Sorry, AMI = axial moment of inertia, TMI = transverse moment of inertia about the tip, CM = center of mass. These acronyns have become fairly common on this forum. I'd normally define any others on 1st use in each post, but maybe I missed some.
In general, I'm unsure of your intent in this and several earlier posts.
I've mentioned in a prior post that the performance of the groove on top vs groove on bottom is about the same. At one time I expected lower aero shear drag for groove on bottom. But if it's lower, it's damn close. I think the air in the groove rotates with the top, so the bottom surface still "looks" about flat.
Sorry, didn't recall that prior post of yours. The only intent in the last post of mine was to suggest an experiment much like the one you've already performed. Just wanted to be clear as to exactly what I was proposing. Unfortunately, it's not an experiment I can do properly with LEGO.
The experimental questions I posed were only partly about what goes on beneath the rotor. The 3D flow patterns above and below a cylindrical rotor are probably quite different -- in part, due to (i) blockage of inflow by the ground, and (ii) potential viscous coupling between rotor and ground (your aero shear drag). Each of these flows might interact differently with a rotor grooved above than with one grooved below.
Not sure I'm prepared to say what the flows in deep, steep-walled grooves like yours might look like, but it may not matter, and that may explain your null result (no clear difference in Top U and Top L spin times).
If the minimum air gap below the rotor is taller than a few mm, the viscous coupling may be negligible regardless of groove location, as the boundary layer along the bottom of the rotor may not reach the ground at the topple speeds we tend to get. (This boundary layer will tend to get even thinner at higher speeds.) For similar reasons, high-speed industrial rotors can have tightly fitting shrouds with tiny air gaps on either side and still lose very little power to viscous coupling.
In my experience, the spinning of a top with its bottom very near to the spinning surface, does not decrease significantly the spin time. On the other side, lowering the center of mass even by just one millimeter, increases the spin time by 2-4 minutes, in tops like the mine.... The advantage of the pedestal is not about aerodynamics....
These observations lend some credence to the boundary layer view. Many of my tops make it easy to change CM height without changing anything else. I also observe that even tiny changes in this all-important parameter can have big effects on spin time, presumably via critical speed.
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Many of my tops make it easy to change CM height without changing anything else. I also observe that even tiny changes in this all-important parameter can have big effects on spin time, presumably via critical speed.
Recently I shortened the tip of one of my tops, reducing the height of center of mass from 7.2 mm to 5.5 mm.
This improved its best spin, from 26'20" to 30'25".
The spin decay curve is practically the same, but the toppling down speed has changed, from 178 to 128 RPM;
it takes about four minutes to go from 178 RPM to 128, so the reduced toppling down speed is the only reason of the longer spin.
Some time ago I tried to take some comparative measuraments of air drag in different flywheels, using a little electric engine. One thing I tried was to observe if there was difference of air drag between the flywheel spinning far from whatever surface, and spinning very close to it, at about 1 mm of distance.
I didn't see any difference.
Maybe the viscous coupling substitutes for the viscous pump effect, so that the air drag doesn't change significantly.
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In addition to height of Cg, the ball diameter affects topple speed. I'm in constant trade-off between lower friction (smaller ball) and lower topple speed (larger ball).
Alan
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Hi Alan,
today I received the package with your top and your AeroPress coffee maker.
It was a nice present, thank you !
This is the spinning top:
(https://i.imgur.com/pNziMvf.jpg)
I had to paint the upper side black and white, otherwise my tachometer couldn't read the RPM reliably.
I tried about 30 hard spins with this top; the highest initial speed I reached by a single twirl was 1132 RPM.
If I insist I think I can make better than this, but not much better.
The weight of the top is 86.1 grams.
I measured/calculated its moment of inertia, which is kg-m2 0.0000901.
So the energy it has at 1132 RPM is 0.63 joule.
0.63 joule is the maximum energy I could put in this top with a single twirl.
This is a comparison with my tops, (the red dots).
This graph is about the maximum energy I can put in each top with a single twirl of the fingers.
The curved line passes through the best tested tops, (the ones able to receive more energy with a single twirl).
The green dot is your top.
The numbers near the dots are the weight (grams) of the tops.
(https://i.imgur.com/M7f2vgU.jpg)
I found the twirling system of this top quite good;
The knurl is very large, compared to that of my tops, and the grip is excellent.
The fingers can grasp it securely and I found to spin this top easy and comfortable.
So the top has a nice playability. Also I like the way the top precesses, making large circles on the spinning surface, thanks to the large ball tip.
Anyway spinning hard this top was a bit difficult; often the flywheel touched the mirror surface, in spite of the large clearance between the flywheel and the mirror.
But this isn't only because of a short stem.
I find the large ball tip quite slippery on the glass mirror, it reminds me my teflon tips.
This is a bit different from spiked tips, which tend to stay in place without slipping around.
This effect, added to the unwanted lateral motions of the hand, and the short stem, make more difficult to control the verticality of the top axis during a hard spinning action.
I suspect that the large knurl could contribute to this difficulty, but I am not sure:
the large knurl makes for a shorter and a more abrupt acceleration.
A more narrow knurl makes for a more gradual acceleration, spread on a longer spinning time action, and, maybe, this could help to control the verticality of the top.
I timed a spin of this top on my concave glass mirror;
I started the top at 1187 RPM by multiple twirls. At high speed the top slowed down rapidly and I thought it couldn't spin for long, but then at low speed was more efficient, also it toppled down at very low speed.
The spin time was 19:02.
RPM measured minute after minute:
1187 - 995 - 849 - 735 - 641 - 564 - 500 - 445 - 399 - 358 - 322 - 291 - 263 - 237 - 215 - 194 - 175 - 158 - 143 - 129.
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As I've written several times, I expected Iacopo's twirling power to exceed mine.
My best twirl with this top is rather poor at only 690 RPM. But I've only recorded three twirls with this top.
With a 105g version of this top I recorded more twirls and my best twirl with that is 77% of Iacopo's energy.
As I've posted earlier, my longest spins are with 2.25" (57mm) tops, so I haven't pursued this larger 3" size.
I attach a top view of an earlier iteration of this same top so you can see the wood center and bronze rim. This iteration had a stem with knurled flutes. I subsequently changed to a plain knurled stem of slightly smaller diameter. That's the version which Iacopo tested.
Regards,
Alan
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The weight of the top is 86.1 grams.
I measured/calculated its moment of inertia, which is kg-m2 0.0000901.
So the energy it has at 1132 RPM is 0.63 joule.
0.63 joule is the maximum energy I could put in this top with a single twirl....
I timed a spin of this top on my concave glass mirror; I started the top at 1187 RPM by multiple twirls. At high speed the top slowed down rapidly and I thought it couldn't spin for long, but then at low speed was more efficient, also it toppled down at very low speed.... The spin time was 19:02.
RPM measured minute after minute:
1187 - 995 - 849 - 735 - 641 - 564 - 500 - 445 - 399 - 358 - 322 - 291 - 263 - 237 - 215 - 194 - 175 - 158 - 143 - 129.
This data describes a spin decay curve (SDC) with an excellent exponential fit (R2 = 0.9942):
N(t) = N0 exp(-t / T),
where N is the speed in RPM, t is the time after launch in sec, N0 = 1,037 RPM is the fitted launch speed, and T = 533 sec is the characteristic decay time. The last means that for each and every 533 sec interval during the exponential decay described by this equation, the ending speed will be 36.8% of the starting speed.
Prior to 300 sec or so, the actual SDC lies slightly above and is somewhat steeper than the fitted exponential decay curve. After ~550 sec, however, the fit is almost perfect, with no sign of a purely frictional linear tail.
Hence, the total braking torque acting on this top still had a significant speed-dependent component down to the lowest recorded speed (129 RPM at 1,140 sec). If you used no lubricant, that component was most likely aerodynamic.
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Nice observation Jeremy.
I mentioned recently that many of my tops decay about 10-12% of their RPM per minute and that I was surprised how constant it is over the entire spin history.
Alan
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As I've written several times, I expected Iacopo's twirling power to exceed mine.
I am an artisan, a manual worker, and also for this reason I have robust hands..
But I am not extraordinary. A person who has one of my tops can spin it a bit stronger than me.
the total braking torque acting on this top still had a significant speed-dependent component down to the lowest recorded speed (129 RPM at 1,140 sec). If you used no lubricant, that component was most likely aerodynamic.
I used a very thin layer of oil. I believe that in this top air drag is quite more important that tip friction.
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the total braking torque acting on this top still had a significant speed-dependent component down to the lowest recorded speed (129 RPM at 1,140 sec). If you used no lubricant, that component was most likely aerodynamic.
I used a very thin layer of oil. I believe that in this top air drag is quite more important that tip friction.
By all accounts, dry tip friction doesn't depend on speed. If that were the only braking torque acting on the top at the end of the spin, the SDC would have a straight line for a tail. But this top's tail is curved with an ever-decreasing slope. So the braking torque must still be decreasing as the speed continues to decay. We know that aerodynamic drag behaves this way. So can lubricated friction. I'm guessing that the aerodynamic torque would outweigh the other lubricated frictional torque with just a thin film of oil, but I don't know that for a fact.
Repeating the experiment with no oil might shed some light.
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Jeremy,
You should join us lathe turners. Turning parts on a lathe is one of the most enjoyable pursuits around. You can buy a small lathe for surprisingly little cost. I'll bet that if you take the plunge, you'll thank me for this nudge.
Alan
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By all accounts, dry tip friction doesn't depend on speed. If that were the only braking torque acting on the top at the end of the spin, the SDC would have a straight line for a tail. But this top's tail is curved with an ever-decreasing slope. So the braking torque must still be decreasing as the speed continues to decay. We know that aerodynamic drag behaves this way. So can lubricated friction. I'm guessing that the aerodynamic torque would outweigh the other with just a thin film of oil, but I don't know that for a fact.
Interesting observation. My preliminary tests in the vacuum chamber seem to confirm what you say.
I haven't tried without oil, but even with the oil the tip friction doesn't change a lot during the spin.
Air drag instead changes radically during the spin, it is very high at the start, and decreases more rapidly at the beginning of the spin. I confirm that in the whole air drag is quite greater than tip friction.
When ready I will post all the measurements of air drag and tip friction in various tops in a new thread.
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You should join us lathe turners. Turning parts on a lathe is one of the most enjoyable pursuits around. You can buy a small lathe for surprisingly little cost. I'll bet that if you take the plunge, you'll thank me for this nudge.
Thanks for the invitation, Alan! LEGO tops and turned tops are in many ways complementary. I'd love to work on your side of the design space, too, but my wife would have to park her car on the street to make room for a lathe at home.
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Interesting observation. My preliminary tests in the vacuum chamber seem to confirm what you say.
I haven't tried without oil, but even with the oil the tip friction doesn't change a lot during the spin.
Air drag instead changes radically during the spin, it is very high at the start, and decreases more rapidly at the beginning of the spin. I confirm that in the whole air drag is quite greater than tip friction.
When ready I will post all the measurements of air drag and tip friction in various tops in a new thread.
Really looking forward to seeing your data, Iacopo! I think we'll learn a lot from it.
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...my tops decay about 10-12% of their RPM per minute... I was surprised how constant it is over the entire spin history.
You can use this observation to estimate the characteristic decay time T as defined a few posts ago, under the reasonable assumption of a near-exponential decay...
T = (t2 - t1) / ln(N1 / N2),
where t is the time in sec after launch, ln() is the natural log function, N is the speed in RPM, and the subscript "1" points to the earlier time-speed measurement. In your case, t2 - t1 = 60 sec, and N1 / N2 ~ 1 / (1 - 0.11) = 1.12, where I took the middle value of 10-12%. The estimated decay time is then
T = 60 sec / ln(1.12) = 515 sec,
which isn't far from the value of 533 sec obtained by fitting an exponential curve to Iacopo's spin-down data on the top you sent him.
Decay times like this make it easy to compare tops with near-exponential spin decay curves, as many of our finger and throwing tops seem to have. To my knowledge, ta0 was the first to propose this. The beauty of the method is that you can use any 2 time-speed points from the exponential-looking part of the curve and get similar results.
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T = 60 sec / ln(1.12) = 515 sec
How can I calculate the natural log function ln() ?
A special calculator is needed ?
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How can I calculate the natural log function ln() ? A special calculator is needed ?
It's on many calculators, including the one that comes with Windows and most of the calculator apps available for Android phones. Same is probably true for Macs and iPads and iPhones, and it's defnitely on all handheld scientific calculators -- even the cheap ones for school kids.
The ln() function is also available in Google Sheets, the free online Google Docs spreadsheet app -- which you might want to check out for your data processing anyway. It's a powerful, well-documented Excel knock-off, but getting started is easy.
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Really looking forward to seeing your data, Iacopo! I think we'll learn a lot from it.
These are the first coming data. The top is my Nr. 26b, which is similar to that sent me from Alan, but a bit smaller and more thick, and with a carbide spiked tip, spinning on a carbide base, with a thin film of oil. Weight 103.8 grams.
Spin time from 1250 to 150 RPM, 28'07" with air and 116'49" in the vacuum.
(https://i.imgur.com/DGm7bGN.jpg)
Everything is new, the pump, and the chamber. The ultimate pressure indicated in the plate of the pump is 0.3 Pascal, (0.003 millibar). It would be excellent but I don't know if this is true.
The vacuometers I have are far too rough, I can have 20 millibar of error with them.
So I am thinking if there is a way for knowing the real ultimate pressure, without spending a lot of money for an accurate vacuum gauge.
I tried making an absolute pressure gauge with a transparent tube closed at one hand, filled of water, with the same layout of the Torricelli barometer; 10 mm of difference in height of the levels of water is about 1 millibar of absolute pressure. But water boils in the vacuum so it doesn't work. I tried motor oil instead of water but motor oil boils too. Then I found ethilene glycol doesn't boil so I tried it and it works much better in fact.
It seems that the ultimate pressure is really low, a fraction of millibar.
But I am not totally sure, because at times there is some bubbles formation even in the ethilene glycol; the bubbles form always in the same spots of the plastic surface in contact with the liquid, so it is not the ethilene glycol by itself, but some interation of the liquid with the plastic surface in these spots; maybe there is some pollution there, maybe a fingerprint, I don't know. I tried to clean but it is difficult to eliminate completely these bubbles formations.
Someone has ideas ?
It is not important to know if there is a tiny difference like 0.005 millibar instead of 0.003, but it would be good to know for sure at least that there aren't a lot of millibars in the ultimate pressure, (10, 20 or more), because this would make inaccurate the measurements.
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Almost two hours spin in vacuum with a 100 gr finger top? Wow! :o
Great data you collected! Congratulations!
I don't have time now to totally absorb it, but it will be very useful in the future.
I'm guessing you calculated the torque at each rotational speed by calculating the deceleration at that interval, times the moment of inertia that you experimentally measured for the top.
If the vacuum is not perfect, that only means that the real difference between air drag and tip friction would be even greater. There is no doubt that only at very low spinning rates close to topple spin would the tip friction matter.
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Iacopo and ta0: This is an exciting day! I think an experimental tour de force like this deserves its own topic -- especially given its importance. If both of you are agreeable, maybe ta0 can make that happen.
These are the first coming data. The top is my Nr. 26b, which is similar to that sent me from Alan, but a bit smaller and more thick, and with a carbide spiked tip, spinning on a carbide base, with a thin film of oil. Weight 103.8 grams.
Spin time from 1250 to 150 RPM, 28'07" with air and 116'49" in the vacuum.
Wow, you nearly quadrupled spin time with the vacuum! Sounds like topple speed was the same at both pressures, as expected.
How does Nr. 26b differ from Nr. 26? Do the specs and atmospheric pressure spin-down data you recently gave for Nr. 26 still hold?
If the rotor is still cylindrical rather than toroidal, the rotor's size and shape allow theoretical calculation of the aerodynamic braking torque (ABT) coming from the rotor faces using the highly accurate von Karman swirling flow model (https://en.wikipedia.org/wiki/Von_K%C3%A1rm%C3%A1n_swirling_flow). The ABT coming from the rotor edge is harder to predict but is likely to be a small fraction of the facial ABT given the rotor's small aspect (length/radius) ratio.
If you'd be willing to supply your hard-won raw time-speed data points (either here or by PM), I'd be happy to post a thorough spreadsheet analysis with appropriate curve-fittings and graphs.
Then I found ethilene glycol doesn't boil so I tried it and it works much better in fact.... But ... at times there is some bubbles formation even in the ethilene glycol; the bubbles form always in the same spots of the plastic surface in contact with the liquid, so it is not the ethilene glycol by itself, but some interation of the liquid with the plastic surface in these spots; maybe there is some pollution there, maybe a fingerprint, I don't know. I tried to clean but it is difficult to eliminate completely these bubbles formations.
Guessing that you're getting close to ethylene glycol's boiling point at your lowest pressures. Any small irregularity in the plastic surface could then trigger premature cavitation (vapor bubble formation) -- which would look just as you described. (For similar reasons, ship propeller blades are finished to a high polish to delay suction-induced cavitation as long as possible.) Can you borrow/rent a more accurate vacuum gauge just for the calibration?
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Magnificent! A beautiful experiment. We spinning top aficionados are fortunate to have Iacopo!
Congratulations.
Alan
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Then I found ethilene glycol doesn't boil so I tried it and it works much better in fact.... But ... at times there is some bubbles formation even in the ethilene glycol; the bubbles form always in the same spots of the plastic surface in contact with the liquid, so it is not the ethilene glycol by itself, but some interation of the liquid with the plastic surface in these spots; maybe there is some pollution there, maybe a fingerprint, I don't know. I tried to clean but it is difficult to eliminate completely these bubbles formations.
Wait, we might be able to get a ballpark calibration with a little thermodynamics...
Q1: When the bubbles start to form, what's the ethylene glycol's concentration and temperature?
Q2: If not 100% ethylene glycol, is water the solvent?
Q3: When the bubbles start to form, what's your pressure reading?
Q4: Can you see any surface defects where the bubbles tend to show up first?
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I'm guessing you calculated the torque at each rotational speed by calculating the deceleration at that interval, times the moment of inertia that you experimentally measured for the top.
Yes, this is exactly how I did.
Now I want to know better what is the real ultimate pressure, then I will collect all the data, and start a new thread where I give them, raw data included, graphs, calculations... for various tops.
It will take some weeks, (I am very busy), but I will do it, a step at a time.
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Wait, we might be able to get a ballpark calibration with a little thermodynamics...
Q1: When the bubbles start to form, what's the ethylene glycol's concentration and temperature?
Q2: If not 100% ethylene glycol, is water the solvent?
Q3: When the bubbles start to form, what's your pressure reading?
Q4: Can you see any surface defects where the bubbles tend to show up first?
I have to check it, but it should be pure, no water in it, no solvents. I will let you know tomorrow.
Temperature 18 °C.
Pressure reading... as said, the gauges are rough, (they are cheap), the full scale is 1065 millibar, they are not reliable for a 10 millibar reading. I can check it better, but it seems like the needle doesn't move anymore when bubbles start to form.
Also I will try to look for a more accurate gauge.
I don't see defects on the plastic surface where bubbles form. But if I put the ethylene glycol in a glass, I see it doesn't form bubbles. Maybe if I can find a U glass tube, it could solve the problem.
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If you'd be willing to supply your hard-won raw time-speed data points (either here or by PM), I'd be happy to post a thorough spreadsheet analysis with appropriate curve-fittings and graphs.
First I would want to know better the ultimate pressure, then I will give all the data, the raw time-speed ones, and the data of each tested top.
Can you borrow/rent a more accurate vacuum gauge just for the calibration?
I have ordered this one, I should receive it in the first days of January;
the full scale is 20 mm hg, about 27 millibar. Much better than my actual vacuum gauges.
https://www.ebay.it/itm/132427555661
With my actual gauges the problem is not calibration, but the fact that their needles nearly don't move with 1, or even 5 millibars differences of pressure; it's a bit like trying to weigh a feather with a big scale.
Data of the ethylene glycol:
http://www.ebay.it/itm/262314816445
Also I will try again with the ethylene glycol, using glass containers, in some way. I have an idea how to do it, even without a U glass pipe.
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The vapor pressure of Ethylen Glycol at 20 degrees C is 0.05 mm Hg. If it doesn't boil that tells you that the pressure should be higher. This is 20 times the pressure nominally achievable with your pump (0.0022 mm Hg).
A gauge with a 20 mm Hg full scale should have an absolute error of not more than 0.2 to 0.5 mm Hg.
It seems you should be able to pin your pressure pretty accurately.
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The vapor pressure of Ethylen Glycol at 20 degrees C is 0.05 mm Hg. If it doesn't boil that tells you that the pressure should be higher. This is 20 times the pressure nominally achievable with your pump (0.0022 mm Hg).
A gauge with a 20 mm Hg full scale should have an absolute error of not more than 0.2 to 0.5 mm Hg.
It seems you should be able to pin your pressure pretty accurately.
This is another useful piece of information, thank you.
Since a glass of ethylene glycol doesn't boil at all, then the pressure should be higher than 0.05 mm Hg.
But maybe it is not far from it, since there is bubble formation in this liquid when it is contained in the transparent plastic tube, maybe a premature cavitation triggered by small irregularities in the plastic surface, as Jeremy noted.
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The vapor pressure of Ethylen Glycol at 20 degrees C is 0.05 mm Hg. If it doesn't boil that tells you that the pressure should be higher. This is 20 times the pressure nominally achievable with your pump (0.0022 mm Hg).
That's where I was headed, too, but you found a vapor pressure first. I just found 2 sources quoting 0.06 mm Hg at 20°C, but let's go with yours. Adjusting it to Iacopo's 18°C (291 K) with the Clausius-Clapeyron equation reduces it by ~17%, from 6.7 to 5.5 Pa. The latter is still some 18 times the claimed ultimate pressure of 0.3 Pa.
That said, a very thorough MEGlobal Product Guide for pure ethylene glycol gives a 6-parameter Antoine equation for the vapor pressure valid for 260-720 K. This equation gives 1.8 Pa at 18°C, which is only 6 times the claimed ultimate pressure.
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Inspired by Iacopo, I've been experimenting with longer stems. This photo shows a 2" long thin-wall aluminum tube on a 1.75" 52g top. The tube weighs 1 gram. I enjoy twirling it with the extension, and my percent of twirl-crashes is greatly diminished.
The extension is delicate, and it has bent a few times. I true it by setting the wheel in my lathe and bending the stem with gentle pushes of my fingers until it indicates true to about .001".
Being delicate, and rather long, it eliminates this top as a contender for EDC (every day carry).
Working with this stem got me thinking about a question for Iacopo that I may have posed a year ago.
How do you know that your stem is true with your flywheel when you use it (with paintbrush) for balancing?
Best regards,
Alan
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How do you know that your stem is true with your flywheel when you use it (with paintbrush) for balancing?
I always turn the flywheel and the stem together, on the lathe, so I know that they are precisely concentric and aligned. I don't have problems of this kind. I use only stable and well seasoned wood for my tops, and I varnish it with epoxy resin, which is an excellent barrier against humidity, to assure dimensional stability. Also, it never happend to me that one of my stems becomes distorted or broken because of a too hard spin, (and I can spin quite hard), even when the stem is long, narrow and made of a very light wood like obeche.
In brief, I don't have this problem.
Some times I still check it anyway;
first I balance the top as usual, using the paintbrush on the upper part of the stem;
the result is that the balanced top will spin with the stem perfectly steady, no wobbling at all in the stem, at least at the height where the stem receives the marks of the brush.
At this point I observe the outline of the flywheel of the top while it is spinning, with a 20x lens;
the littlest wobbling of the flywheel will be easily noticed.
If the flywheel spins smoothly without any wobbling, as the stem does, it is ok.
If there is some wobbling of the flywheel, in vertical direction, it means that the stem is distorted.
If there is some wobbling of the flywheel, in horizontal direction, it means that the tip is off centered.
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Inspired by Iacopo, I've been experimenting with longer stems. This photo shows a 2" long thin-wall aluminum tube on a 1.75" 52g top. The tube weighs 1 gram. I enjoy twirling it with the extension, and my percent of twirl-crashes is greatly diminished. The extension is delicate, and it has bent a few times.
What about a solid, tapered, knurled extension of something even less dense than aluminum -- say, Delrin or ABS or titanium alloy or even wood? Guessing that this top has a high-enough axial moment of inertia to benefit from a stem taper with a starting diameter of ~8 mm below and a final diameter of 3-4 mm above. In my experience, such a taper should cover an axial length of ~32 mm for best results in single-twirl play.
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At this point I observe the outline of the flywheel of the top while it is spinning, with a 20x lens; the littlest wobbling of the flywheel will be easily noticed.
If the flywheel spins smoothly without any wobbling, as the stem does, it is ok. If there is some wobbling of the flywheel, in vertical direction, it means that the stem is distorted. If there is some wobbling of the flywheel, in horizontal direction, it means that the tip is off centered.
Brilliant! Never thought to examine my wobbles under magnification.
Most of my LEGO tops are built around through-going central plastic axles 4.8 mm in outside diameter and 16-96 mm in length.
(http://images.mocpages.com/user_images/99234/1447463033m_SPLASH.jpg)
(http://images.mocpages.com/user_images/99234/1447539743m_SPLASH.jpg)
The good news: LEGO remains a world leader in precision plastic molding with dimensional tolerances on the order of 1 part in 10,000, and the dimensional stability of their proprietary ABS plastic is phenomenal. Hence, any axially symmetric arrangement of fully seated parts is guaranteed at least static balance. The bad news: Not sure why, but well over 50% of the axles I use most (64 and 80 mm lengths) are out of true fresh out of the box, and used axles are even worse.
Despite my best screening and engineering efforts, undetected axle bends and inadequate structural rigidity of the top as a whole are my main sources of wobble by far. Maximizing rigidity within LEGO constraints is a challenge I enjoy, but a new approach to bent axles is clearly in order. In the photo below, I'm looking for wiggle at the free end while I turn a 64 mm axle manually at various speeds...
(http://images.mocpages.com/user_images/99234/1481086150m_SPLASH.jpg)
Anyone: So, looking for suggestions on (i) axle screening and (ii) straightening splined plastic axles with bends I can't see. NB: All axles have 4 deep full-length splines as at upper left and hence are not free to roll under gravity alone. An axle can be bent anywhere along its length.
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Long Stems:
I forgot to mention that I'm experimenting with lift-off stem extensions. My first try only works occasionally, but I hope to improve that.
Jeremy. One way to check for straightness of a shaft it to chuck it in an electric drill or Dremel and run it. You'll see bend - especially with magnification.
One thing to keep in mind with plastic pieces is that all thermoplastics have huge coefficients of thermal expansion.
Regards,
Alan
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What about a solid, tapered, knurled extension of something even less dense than aluminum -- say, Delrin or ABS or titanium alloy or even wood? Guessing that this top has a high-enough axial moment of inertia to benefit from a stem taper with a starting diameter of ~8 mm below and a final diameter of 3-4 mm above. In my experience, such a taper should cover an axial length of ~32 mm for best results in single-twirl play.
Thin wall aluminum is lighter than the materials above, which must be solid, except for titanium, which is about 50% denser than aluminum. My present aluminum tubes are pretty soft. I've ordered some hardened aluminum tubing. And some titanium tubing, carbon fiber, and even ceramic (alumina). That should keep me busy for a while.
And I'm also experimenting with lift-off stems. Or, if not lift-off, still detachable for pocket carry.
Best,
Alan
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One thing to keep in mind with plastic pieces is that all thermoplastics have huge coefficients of thermal expansion.
Thanks, Alan! Didn't know that, but it could have something to do with why so many axles come bent. Axles presumably come out the mold warm to hot and then drop onto a rather disordered pile of axles in a bin below. Lots of opportunities for sagging and uneven cooling there.
Hmmm, wonder if the high thermal expansivity could be used in straightening somehow?
One way to check for straightness of a shaft it to chuck it in an electric drill or Dremel and run it. You'll see bend - especially with magnification.
Yes, I was doing the manual eye-ball version of that in the photo, but adding magnification could help a lot. Low finger speeds generally work best for me, but different bends seem to become apparent at different speeds. Hence, I have to sweep the speed up and down in both directions with fine control with each and every axle.
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Everything is new, the pump, and the chamber. The ultimate pressure indicated in the plate of the pump is 0.3 Pascal, (0.003 millibar). It would be excellent but I don't know if this is true.
Learned something interesting today. For a top the size of your Nr.26 at 18°C, 0.3 Pa happens to mark the (rather fuzzy) upper pressure limit of a "molecular free flow" (MFF) regime in which viscosity has no meaning. Scary, I know, but there's a silver lining.
The good news: We've never had a reliable way to calculate aerodynamic braking torque (ABT) in tops at room pressure, where air molecules exchange momentum with each other vastly more often than they do with any solid surfaces involved. (That's fundamentally why air can normally be treated as a viscous fluid.) But we do have a simple and reliable way to calculate ABT in the MFF regime, where air molecules effectively exchange momentum only with the top.
In fact, the MFF ABT calculation is predictive enough to underpin one of the mainstays of modern high-vacuum technology -- the spinning rotor manometer. In this regime, ABT is strictly proportional to the current angular speed, and the proportionality constant is easily calculated from widely available data. If ABT were the only braking torque, MFF spin decay curves would then be exactly and reliably exponential.
This fact might open up some valuable experimental opportunities for you -- provided your apparatus can reach MFF pressures.
The bad news: Below ~23 Pa, a top like Nr.26 enters a "transitional" flow regime where neither MFF nor viscous treatments like the von Karman swirling flow model (https://en.wikipedia.org/wiki/Von_K%C3%A1rm%C3%A1n_swirling_flow) apply.
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0.3 Pa happens to mark the (rather fuzzy) upper pressure limit of a "molecular free flow" (MFF) regime in which viscosity has no meaning.
Below ~23 Pa, a top like Nr.26 enters a "transitional" flow regime...
I will not be able to measure fractions of Pa. Even with the new gauge I should receive in January, there could be measurement errors of maybe 25 Pa, maybe more.
Do you think this could be a problem ? Isn't air drag torque practically irrelevant, compared to tip friction torque, both at 0.3 Pa, and, let's say, 30 Pa, whatever the flow regime ?
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Balancing again.
I think Iacopo posted something along these lines about a year ago.
I have a 31mm, 41g top, spinning on a 6mm ceramic ball. A small fraction of my tops go through a speed of large wobble, then smooth somewhat. This top does that, with max wobble at about 550 RPM and topple just under 330 RPM. (Most of my tops just gradually wobble prior to topple, without this intermediate peak wobble).
I observed the reflected laser beam in the manner taught by Quark. The laser test is supposed to indicate the angle on the wheel which needs more weight. This angle suddenly shifts 90 degrees clockwise as the declining speed passes through the speed of peak wobble.
Help. Iacopo.
Best regards,
Alan
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Isn't air drag torque practically irrelevant, compared to tip friction torque, both at 0.3 Pa, and, let's say, 30 Pa, whatever the flow regime ?
I'd be happy to go along with that if the red curve labeled "Tip friction" in your last graph were perfectly flat. But it clearly slopes down to the right, and we need to know why.
If I understand this red curve correctly, it really plots total braking torque (TBT) vs. speed at your actual ultimate pressure PU, whatever that may be. If so, the TBT at PU still includes a contribution varying directly with speed. Could be nothing more than "wet" (lubricated) friction, but we're not yet in a position to rule out aerodynamic drag.
I recommend repeating the experiment "dry" -- i.e., without lubrication of any kind. If the dry red curve comes out flat, you'll have your answer: Any aerodynamic braking torque (ABT) remaining at PU must be very small compared to the observed TBT. But if the dry red curve still slopes down to the right, the remaining ABT can't be ignored. The outcome could vary from top to top.
This strategy rests on 3 very reasonable assumptions with lots of experimental support in related settings:
1. Aerodynamic drag varies directly with speed, regardless of flow regime.
2. Wet friction can also vary directly with speed.
3. Dry friction does not vary with speed.
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I recommend repeating the experiment "dry"
Thank you, Jeremy. I will do this, and see what it happens.
You understood the red curve correctly, it is about the TBT at the ultimate pressure.
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A small fraction of my tops go through a speed of large wobble, then smooth somewhat. This top does that, with max wobble at about 550 RPM and topple just under 330 RPM. ...intermediate peak wobble.
An intermediate peak wobble, based on my experience, is not due to unbalance, but to weared contact points.
With a new ball tip, the defect should disappear.
This angle suddenly shifts 90 degrees clockwise as the declining speed passes through the speed of peak wobble.
This is something interesting, I have an idea..
If possible, could you post a picture of this top, (a side view) ?
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They are 1.24" diameter bronze, about 40-50g, with top groove or not and flat bottom or shallow cone. I have three like this. The flat bottom one looks like the recent pic I posted of 1.5" and 1.75" tops together on a mirror with greenish frame. This is also the one I did the described laser work with. But the other two also have intermediate wobble and may do the same thing.
All three 1.24" tops are machined from an ugly old rod of bronze. I'm suspicious that this piece has non-uniform density. I may try the same design with a rod of brass.
One bit of clarification is that the shift occurs over a range of about 20 RPM. It's pretty quick, but not bistable. Mid point on the shift is probably the RPM of maximum wobble.
12/23 Update: I just discovered that the ball tip is .0035" off center. It's pocket is at the end of a 0.94" drilling which began at the top of the stem. I had presumed that the drill remained centered, guided by it's own body like rifle bores. But it wandered .0035" off center, which results in .007" peak-to-peak eccentricity!! Yoiks! I'll fix that today.
Centered ball within about .0001 to .0002" and intermediate wobble is gone.
But on a slightly larger (1.5" diameter, also 50g) top I tried a 2.6" long carbon fiber stem. Despite truing the stem, this top has a huge intermediate wobble around 420 RPM. Shortening the stem to 1.5" totally eliminated the intermediate wobble.
Alan
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I'm suspicious that this piece has non-uniform density.
One bit of clarification is that the shift occurs over a range of about 20 RPM. It's pretty quick, but not bistable. Mid point on the shift is probably the RPM of maximum wobble.
But it wandered .0035" off center,
Centered ball within about .0001 to .0002" and intermediate wobble is gone.
long carbon fiber stem. Despite truing the stem, this top has a huge intermediate wobble around 420 RPM. Shortening the stem to 1.5" totally eliminated the intermediate wobble.
I thought for some time to all these your observations, but I am confused.
Normally, wobbling due to unbalance becomes more and more intense while the top slows down, and it reaches the peak of intensity when the top topples down.
This is the common situation, with my tops.
It doesn't matter the cause of the unbalance, whether the tip is off centered, or whether the distribution of weight is asymmetric.
There is not an intermediate peak wobble.
I didn't observe differences in this behaviour related to the lenght of the stem.
If something different happens, it is because there is a superposition of another movement, nutation or maybe precession, that makes things more complicated.
A few times I observed in my tops an intermediate peak wobble:
this peak wobbling was not due to unbalance, but to the top starting to nutate (nutation) spontaneously at a certain speed. The nutation, mixed with the unbalance, caused the temporary increase of intensity of the wobbling.
Later during the spin, nutation disappeared, as spontaneously as it started.
This spontaneous nutation is triggered by a large contact point, (it can be a weared spiked tip, or maybe a very large ball tip, or a ball tip with even minimal wear, because the contact point in ball tips enlarges very rapidly with wear).
Lack of lubricant makes the nutation to happen with stronger intensity and for a longer time.
I am not sure, but still I think that the intermediate peak wobble you see could be due to nutation:
it is difficult to say from a distance, but you can recognize nutation because it has a different speed from spin speed.
An easy way to check this, is with the tachometer. Measure spin speed as you do usually.
Then direct the tachometer at the upper part of the stem. Hold a piece of white paper behind the stem. The stem wobbling will intercept the light reflected from the white paper at intervals, and will let you know the speed of the wobbling.
If spin speed and wobbling speed are the same, this wobbling is due to unbalance.
If spin speed is different from wobbling speed, this wobbling is due to nutation.
If wobbling speed is twice the spin speed, and you pointed the tachometer at the center of the movements of the stem, this wobbling is unbalance, and the wobbling speed is twice because the tachometer reads two light interceptions for one round of the stem, one time when the stem goes to the right and another time when it comes back to the left. I point the tachometer a bit sideways, so I have one light interception for each round of the stem.
Precession is slow so it is easily recognizable. But at the very end of the spin, precession, if present, becomes fast, and could contribute to confuse ideas.
All the times I had an intermediate peak wobbling, this was due to nutation.
I never had an intermediate peak wobbling due to unbalance alone
If you are seeing something different, it is something I still don't understand.
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Thank you Iacopo. I hadn't thought of aiming the tach at the top of the stem. I like that idea. I'll have to restore some long stems to do it.
I've seen confluence of nutation and vibration. One behavior is a periodic "twitch" when they momentarily sync.
I've tried to use your paintbrush on light (50g) tops with problems. The lightest contact causes the stem to "grab" the wet brush and tilt towards it. Have you successfully used that method with such a light top?
One thing of interest is that the intermediate wobble speed is repeatable, which tends to rule out nutation.
Happy Christmas
Alan
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But on a slightly larger (1.5" diameter, also 50g) top I tried a 2.6" long carbon fiber stem. Despite truing the stem, this top has a huge intermediate wobble around 420 RPM. Shortening the stem to 1.5" totally eliminated the intermediate wobble.
Sounds like some sort of "resonance". The top is probably too rigid for this to be due to some elastic deformation of the top. But perhaps there is coupling between spin and wobble (nutation? as Iacopo suggests) due to an imbalance and the coupling depends on frequency. It would be interesting to change the stem length in little steps and see if the spin rate of maximum wobble changes accordingly.
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For years, I've found a spreadsheet convenient for recording spins. It's easy to add a column which instantly provides useful info. Below, I'll list some of my columns:
Twirl energy: Iacopo does this correctly by measuring the inertia of each top, but I haven't measured the rotational inertia as he does, so my lazy formula for "relative" twirl energy is:
E=KiloRPM^2 x kilograms x Diameter^2 Diameter is inches.
He measured the inertia of the 3" top I sent him, which provided an opportunity for comparison.
My lazy E came out to be 1.57 x his measured joules.
Merit: This evolved from the start of this thread and settled at:
Merit = Seconds / (RPM^0.63 x Diameter^.5 x kilograms^.5) diameter is millimeters
My best twirlers have merit in the range of 6 to 8
I use merit to answer the question,
"How does this top compare to my others, allowing for twirl speed and top dimensions?"
Average decay per minute = (twirl RPM / topple RPM)^(1/duration in minutes)
Example 1.085 is my best 2.25", 143 gram twirler
1.125 is typical of small 50 gram twirlers
As Jermemy posted, this can predict duration of spin.
Duration (minutes) = Ln(twirl RPM / topple RPM) / Ln(Average decay per minute)
You can use this to predict minutes remaining by using present RPM instead of twirl RPM
Happy Christmas
Alan
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As Jermemy posted, this can predict duration of spin.
Duration (minutes) = Ln(twirl RPM / topple RPM) / Ln(Average decay per minute)
You can use this to predict minutes remaining by using present RPM instead of twirl RPM
I think you're referring to my post at http://www.ta0.com/forum/index.php/topic,5161.msg55049.html#msg55049. How are you calculating "average decay per minute"?
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I've tried to use your paintbrush on light (50g) tops with problems. The lightest contact causes the stem to "grab" the wet brush and tilt towards it. Have you successfully used that method with such a light top?
I've had good luck with a slack chalk line -- even with LEGO tops much lighter than that.
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Sandpaper Glued to Stem Handle
I glued a strip of 320 grit sandpaper to the carbon fiber stem on this 1.5" diameter, 50 gram top.
This is the nicest grip I've ever tried. Better than knurls.
Alan
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perhaps there is coupling between spin and wobble (nutation? as Iacopo suggests)
I am not sure about Alan's tops, but what I see in my tops I believe it is indeed nutation;
the following method is a more refined version I used for to recognize nutation from other kinds of wobbling:
some time ago Russpin gave an interesting formula for to know nutation speed;
for very little angles of tilting, the proportion between spin speed and nutation speed is equal to the proportion between transverse moment of inertia and axial moment of inertia.
A practical sample with numbers:
This is my top Nr. 15:
Axial moment of inertia: kg-m2 0.0000765
Transverse moment of inertia: kg-m2 0.0000429
Ratio between the two moments of inertia: 0.0000765 : 0.0000429 = 1.78
The transverse moment of inertia has to be measured at the tip. The trifilar pendulum measures it at the center of mass, not at the tip, anyway in this top the tip is really very close to the center of mass, so I didn't apply the parallel axis theorem.
(https://i.imgur.com/KfryxAB.jpg)
I used the tachometer to know spin speed and nutation speed:
Spin speed: 247 RPM
Nutation speed: 415 RPM
Spin speed, second check: 229 RPM
Average between 247 and 229 is 238;
in the instant when nutation speed was at 415 RPM, spin speed was at about 238 RPM.
Ratio between the two speeds:
415 : 238 = 1.74
which is very near to the ratio between the two moments of inertia we have seen before, 1.78.
So we can see there is a correspondence.
This helps to make clear what is the kind of wobbling we can see in a top.
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I have nutation in my tops in three different situations:
- When the top is spun, usually there is at least a bit of nutation.
- When I kick the stem of the top with a finger while it is spinning. In these first two situations, nutation becomes weaker and weaker by the time, until disappearing completely; it takes some seconds up to some minutes for this to happen, depending on the kind of the top and the initial intensity of the nutation.
- When the contact point is large enough, (this happens when the tip is weared, after many hours of spinning, especially with ball tips), and especially if there is no lubricant. In this case the top starts nutating spontaneously at a certain speed, then it stops nutating spontaneously, a few minutes later, while the top continues spinning.
Some sort of "resonance effect" seems to trigger this effect, when the spin speed is favourable.
When the contact point is still larger, (tip badly weared), the top nutates for the whole duration of the spin.
Nutation is the only one reason I know for an intermediate peak wobbling.
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I've tried to use your paintbrush on light (50g) tops with problems.
I past and copy here one of my comments to Bob Gunther:
"This is because your tops are light. It may help using a brush with a little diameter, (1 mm or so), with long and soft bristles. I would use the tip of the brush (for a softer touch) and not the sides of the bristles as in the video, (the top in the video is relatively heavy so it's a different situation). A correct amount of color in the bristles and a correct dilution of the color also may help; to me it works better when there is a tiny drop of color on the tip of the bristles, so the lightest touch leaves a clear mark. Another trick could be not to hold the brush by hand, but to use a support for it, (I use a glass), placed on the table, so it is easier to control the tiny movements of the brush.
You can try not to touch directly the stem with the brush, go with the brush very very close to it, (I use magnifier glasses here), then wait for the top to barely touch the brush. As soon as you see the first mark, suddenly remove the brush, to avoid the top to receive other marks in different positions, in case the first touch of the brush was hard enough to make the top to move in a disorderly way."
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I glued a strip of 320 grit sandpaper to the carbon fiber stem
This is the nicest grip I've ever tried.
I believe you. 8) 8) 8)
Original, and ingenious !
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(https://i.imgur.com/DGm7bGN.jpg)
I'd be happy to go along with that if the red curve labeled "Tip friction" in your last graph were perfectly flat.
But it clearly slopes down to the right, and we need to know why.
If I understand this red curve correctly, it really plots total braking torque (TBT) vs. speed
at your actual ultimate pressure PU, whatever that may be.
If so, the TBT at PU still includes a contribution varying directly with speed.
Could be nothing more than "wet" (lubricated) friction,
but we're not yet in a position to rule out aerodynamic drag.
I recommend repeating the experiment "dry"
Here it is:
I spun the same top, on the same spinning surface, with and without oil.
I tested with air, not in the vacuum.
The top was started at 1250 RPM and toppled down at 195 RPM, in both tests.
RPM minute after minute, with oil:
1250 - 1163 - 1084 - 1014 - 950 - 890 - 836 - 786 - ? - 697 - 656 - 620 - 584 - 552 - 520 - 491 - 463 - 436 - 412 - 388 - 365 - 343 - 323 - 303 - 285 - 267 - 250 - 235 - 219 - 206.
Spinning time: 29'25"
RPM minute after minute, without oil:
1250 - 1154 - 1070 - 992 - 922 - 856 - 795 - 738 - 684 - 634 - 588 - 544 - 503 - ? - ? - 392 - 358 - 327 - ? - 266 - 237 - 211.
Spinning time: 21'30"
This is an efficiency graph, calculated as percentage of retained speed after one minute spinning:
For example, the first minute without oil is:
1154 : 1250 = 0.923 = 92.3 %
(https://i.imgur.com/89paoFI.jpg)
The graph makes evident that the top is more efficient with the oil, (obviously), but also it makes evident that the advantage is stronger at low speed.
Spin time Spin time
with oil without oil
From 1250 to 730 RPM 8'15" 7'10"
From 730 to 416 RPM 9'35" 7'10"
From 416 to 195 RPM 11'35" 7'10"
This seems to demonstrate that there is viscous friction in play with the oil, which becomes stronger at higher speed.
So, Jeremy, it seems that you are correct suggesting that the slope at the right in the first graph could be due to "wet" friction.
I can't calculate the torque from these data so I can't be totally sure that there isn't any residual air drag in action,
(in the red line of the first graph), we will see this better in the next weeks.
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some time ago Russpin gave an interesting formula for to know nutation speed; for very little angles of tilting, the proportion between spin speed and nutation speed is equal to the proportion between transverse moment of inertia and axial moment of inertia. ... This helps to make clear what is the kind of wobbling we can see in a top.
You've turned Russpin's formula into an excellent diagnostic test for gyroscopic nutation, Iacopo! A word of caution about its use at low speeds, though: The derivation assumes a so-called "fast top", which by definition has much less gravitational potential energy than it has kinetic energy about the spin axis. In practice, this limits the formula to speeds far above the "critical speed" for stable steady precession or sleep.
Edit: Ratios below were accidentally inverted first time around. Fixed now. Conclusions remain valid.
Importantly, the formula clearly shows that the kind of wobble underlying the paintbrush method can't be gyroscopic nutation in the general case. When the paintbrush method is applied to a fast top spinning much faster than it precesses, the nutation formula reduces to
s / w = I1 / I3,
where s is the pure spin rate, w is the wobble rate, I3 is the AMI, and I1 is the TMI about the tip. Now, for the paint to end up on the same side of the stem every time, s / w must be a whole number (1 or greater) to a high degree of precision -- regardless of the wobble's cause. But for nutation to work, the same must be true of I1 / I3 as well.
Now think of all the tops to which the paintbrush method has been successfully applied. What are the odds that I1 / I3 just happened to be a whole number in each and every case? Zero. Hence, the success of the paintbrush method must rest on a kind of wobble other than gyroscopic nutation -- one that guarantees a whole-number s / w -- regardless of I1 / I3. I know of only one kind of wobble capable of that -- the fundamentally non-gyroscopic wobble engineers call "whirl".
Whirl can result from either unbalance or misalignment, and sharp resonances in whirl amplitude with speed are the rule. Moreover, whirl predicts that as a top spins down through each resonance, the phase angle (in our case, between the heavy spot and the paint mark) will change in just the ways we observe. Whirl can also excite superimposed nutation under the right circumstances.
I have nutation in my tops in three different situations:
- When the top is spun, usually there is at least a bit of nutation.
- When I kick the stem of the top with a finger while it is spinning. In these first two situations, nutation becomes weaker and weaker by the time, until disappearing completely; it takes some seconds up to some minutes for this to happen, depending on the kind of the top and the initial intensity of the nutation.
Agree that the wobble in these cases is likely to be mostly nutation -- especially if the tops were already balanced and aligned. Far above critical speed, small forced nutations can die out from gyroscopic damping alone.
- When the contact point is large enough, (this happens when the tip is weared, after many hours of spinning, especially with ball tips), and especially if there is no lubricant. In this case the top starts nutating spontaneously at a certain speed, then it stops nutating spontaneously, a few minutes later, while the top continues spinning.
Not convinced that the wobble in this case is purely nutation. This would be a good one to test with your nutation diagnostic.
Some sort of "resonance effect" seems to trigger this effect, when the spin speed is favourable.
When the contact point is still larger, (tip badly weared), the top nutates for the whole duration of the spin.
I also find that tips with large radii of curvature tend to promote wobble of some kind. Still not sure why.
Nutation is the only one reason I know for an intermediate peak wobbling.
Here we disagree. IMO, a wobble that behaves like this is much more likely to be whirl than nutation. Below are some free online PDFs with good introductions to whirl...
Swanson, E., et al., 2005, A Practical Review of Rotating Machinery Critical Speeds and Modes (http://sandv.com/downloads/0505swan.pdf)
Nelson, F., 2007, Rotor Dynamics without equations (http://www.ewp.rpi.edu/hartford/~ernesto/F2013/SRDD/Readings/Nelson2007-RDwithoutEqns.pdf)
Freese, T.D., and Grazier, P.E., 2004, Balance this! (http://www.engdyn.com/images/uploads/93-balance_this!_-_peg&tdf.pdf)
If you read only one, make it Swanson. For something more mathematical, and with discussions of rotating machines closer to spinning tops, try
Nelson, H.D., and Talbert, P.B., 2003, Rotordynamic considerations (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.456.1145&rep=rep1&type=pdf) (chapter 10 of unknown book)
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You guys are amazing. And you did all that on Christmas Day?
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You guys are amazing. And you did all that on Christmas Day?
Well, the writing, maybe, but we've been working up to this stuff for a long time. Kinda like that day you juggled bowling balls on a unicycle. Now, that was amazing!
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You've turned Russpin's formula into an excellent diagnostic test for gyroscopic nutation, Iacopo! A word of caution about its use at low speeds, though: The derivation assumes a so-called "fast top", which by definition has much less gravitational potential energy than it has kinetic energy about the spin axis. In practice, this limits the formula to speeds far above the "critical speed" for stable steady precession or sleep.
I think your reasoning is valid for tops with the tip at some distance from the center of mass;
in the case of the top I tested, (Nr. 15), the tip, recessed, is so near to the center of mass that the top is free to nutate without any significant influence from gravity.
As a matter of fact, in the test, the ratio between the two moments of inertia and the ratio between the two speeds were very similar, so Russpin's formula seems essentially still valid here.
Importantly, the formula clearly shows that the kind of wobble underlying the paintbrush method can't be gyroscopic nutation in the general case.
..for the paint to end up on the same side of the stem every time, s / w must be a whole number (1 or greater) to a high degree of precision -- regardless of the wobble's cause.
I know of only one kind of wobble capable of that -- the fundamentally non-gyroscopic wobble engineers call "whirl".
Obviously nutation is not related to what I call "unbalance wobbling", they are two totally different and independent kinds of wobbling.
For detecting unbalance, the paint brush method has to be used with "unbalance wobbling", not with nutation.
It doesn't make sense to check for unbalance marking a stem which is undergoing nutation; in this case the marks would appear randomly distributed around the stem, (which is another simple way for distinguishing nutation from "unbalance wobbling").
I think we agree, until here.
We have different ideas about the nature of this "unbalance wobbling", you see it as "whirl", but I don't think so;
tops have only one pivot, the tip, there is freedom of tilting, then generally tops are rigid; I can't imagine whirl to happen here.
My explanation is that, in tops like the ones I and Alan make, unbalance shows as the top spinning with the heavier side of its flywheel at a lower height, because of gravity. The lighter side stays at an higher height. A bit like the arms of a scale, where the one with more weight sinks down. So the stem of the top stays always leaned towards the heavy side of the top. At whatever speed, the top stays always leaned exactly towards its heavy side, and this makes the paint brush technique reliable, the marks on the stem are always in the direction of the heavy side of the top.
If something different happens, it is because there are other movements superposed to "unbalance wobbling".
Or maybe even it is not "unbalance wobbling" but another movement, nutation or precession.
Far above critical speed, small forced nutations can die out from gyroscopic damping alone.
This also depends very much on the distance between the tip and the center of mass.
When the tip is at the center of mass, nutation can last for minutes, but when the tip is far from it, nutation disappears rapidly.
- When the contact point is large enough, (this happens when the tip is weared, after many hours of spinning, especially with ball tips), and especially if there is no lubricant. In this case the top starts nutating spontaneously at a certain speed, then it stops nutating spontaneously, a few minutes later, while the top continues spinning.
Not convinced that the wobble in this case is purely nutation. This would be a good one to test with your nutation diagnostic.
I haven't tested it with the "nutation diagnostic", (I will try), but it seems very much nutation to me.
Anyway I still don't understand the mechanism that triggers it, I only see that it is related to a large contact point/lack of lubrication.
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As a matter of fact, in the test, the ratio between the two moments of inertia and the ratio between the two speeds were very similar, so Russpin's formula seems essentially still valid here.
It's very clever of you Iacopo to apply the free precession formula to your top. As you point out the key assumptions for the formula are:
1) No external torques are applied to the system.
2) A small angle between the angular velocity vector and the symmetry axis.
Given these two conditions the formula is valid for any spin rate.
Great work on the vacuum spin down measurements. I think you are breaking new ground here!
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Obviously nutation is not related to what I call "unbalance wobbling", they are two totally different and independent kinds of wobbling. For detecting unbalance, the paint brush method has to be used with "unbalance wobbling", not with nutation. It doesn't make sense to check for unbalance marking a stem which is undergoing nutation; in this case the marks would appear randomly distributed around the stem, (which is another simple way for distinguishing nutation from "unbalance wobbling").
I think we agree, until here.
Completely.
We have different ideas about the nature of this "unbalance wobbling", you see it as "whirl", but I don't think so;
tops have only one pivot, the tip, there is freedom of tilting, then generally tops are rigid; I can't imagine whirl to happen here.
Some of the reasons I like whirl as at least a qualitative analogy for your "unbalance wobbling"...
1. We know a lot about whirl from an engineering standpoint.
2. Unbalance is the simplest cause of whirl and generates all of its essential behaviors.
3. Whirl's lowest-speed "rigid body modes" involve no bending whatsoever. They require only "soft bearings" with some slop. These are the modes I see as applicable to tops.
4. Rigid-body whirl from unbalance captures all the behaviors we see in unbalance wobbling.
5. The stem of a spinning top isn't completely free to tilt. It's constrained by gyroscopic torques acting mainly on the rotor. These torques are to some extent analogous to soft bearing forces acting on the stem.
6. Rigid-body whirl also occurs in overhung rotors with one free end.
7. Whirl is an inertial phenomenon seen with both horizontal and vertical spin axes. It may be modified by gravity somewhat, but its essential behaviors don't depend on gravity.
My explanation is that, in tops like the ones I and Alan make, unbalance shows as the top spinning with the heavier side of its flywheel at a lower height, because of gravity. The lighter side stays at an higher height. A bit like the arms of a scale, where the one with more weight sinks down. So the stem of the top stays always leaned towards the heavy side of the top. At whatever speed, the top stays always leaned exactly towards its heavy side, and this makes the paint brush technique reliable, the marks on the stem are always in the direction of the heavy side of the top.
If something different happens, it is because there are other movements superposed to "unbalance wobbling".
Or maybe even it is not "unbalance wobbling" but another movement, nutation or precession.
When paint marks fall consistently on the heavy side of the rotor, let's call that a "phase angle" of 0°. You've reported tops with phase angles of 180°, and I've seen that in some of my tops as well. You suggested that CM height might control phase angle, and I think you're onto something there. Russpin even replicated that behavior in his computer simulations.
We've also seen reports of 90° phase angles, perhaps most recently from Alan. In its totality, this odd phase angle behavior can't be explained solely with gravity or even with gyroscopic effects. But it's a well-documented and well-understood part of whirl.
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I glued a strip of 320 grit sandpaper to the carbon fiber stem on this 1.5" diameter, 50 gram top.
This is the nicest grip I've ever tried. Better than knurls.
Great idea, Alan! LEGO purists will disapprove, but I'll definitely give it a try in one of my highest-AMI tops.
Q: What's the final stem diameter with the sandpaper?
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The stem of a spinning top isn't completely free to tilt. It's constrained by gyroscopic torques acting mainly on the rotor. These torques are to some extent analogous to soft bearing forces acting on the stem.
This analogy sounds a little forced to me...
When paint marks fall consistently on the heavy side of the rotor, let's call that a "phase angle" of 0°. You've reported tops with phase angles of 180°, and I've seen that in some of my tops as well. You suggested that CM height might control phase angle, and I think you're onto something there.
I tried to keep things simple to avoid a longer explanation, so I said "in tops like the ones I and Alan make", which are generally large and low.
I have made 31 tops, at present.
29 tops, out of them, stay always leaned towards their heavy side, when they are unbalanced;
speed has no effect on their direction of leaning, they stay always leaned towards their heavy side, at whatever speed.
Then I have one top, (Nr. 8 ), which behaves differently, because it leans towards its light side, when it is unbalanced: the first time I tried to balance this top I was very confused, because I didn't expect this behaviour, and, at that time, I had no explanation for it.
Some months later I suspected that that behaviour depends on the height of the center of mass, or more precisely on the ratio between AMI and TMI at the tip, because the Nr. 8 was the most tall and narrow top I had made.
So I made a new top, (Nr. 17), with a movable axis, allowing large changes of the height of the center of mass, for to see how the top behaves changing this parameter.
The result was that, with low center of mass, the top, unbalanced, stays always leaned towards its heavy side, at whatever speed.
With high center of mass, the top, unbalanced, stays always leaned towards its light side, at whatever speed.
Then there is an intermediate set up, by which the top, unbalanced, stays leaned not towards the heavy side nor towards the light side, but somewhere in between.
This is the only set up where the direction of leaning of the top depends also on speed.
But, generally, tops rarely behave in this way, because having a tip longer/shorter by just about two millimeters is sufficient to exit from this intermediate set up.
So the great majority of the existing tops, when unbalanced, stay always leaned towards the same side, (the heavy or the light one), without any influence by speed.
I have an explanation for these behaviours, it would take a long post to explain them barely decently, with my poor language.
It isn't about gravity alone, but its interaction with centrifugal force and inertia.
Gyroscopic torques are not involved here, they are less or more present but they are related to precession and not to "unbalance wobbling".
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More on sandpaper stem grip:
I've been using this stem and absolutely love it.
It's a bit tricky to neatly glue a wrap of sandpaper. So I just ordered some sandpaper sleeves with 1/4" and 3/8" OD and 1/2" and 3/4" length. They are cheap and available in many grits.
Iacopo will have to lay-out arc-shaped pieces to fit his tapered stems.
Alan
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Variation in tip drag with speed:
First of all, I haven't carefully read this discussion, nor Jeremy's links. But I'll throw this into the discussion anyway.
Friction creates heat, and the energy which produces the heat reflects back to the top as a torque load. This process isn't necessarily linear. For example radiative heat transfer = t^4, where t is absolute scale.
If there is lubricant present, centrifugal force will "hurl" the lube radially outward by the spinning tip. So there would be less lube at high speed. That process, and the viscose drag of the lube are also not linear.
I find Iacopo's data quite adequate and am not motivated to fine-tune the details of the vacuum curve.
Alan
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free precession formula ... key assumptions for the formula are:
1) No external torques are applied to the system.
2) A small angle between the angular velocity vector and the symmetry axis.
Given these two conditions the formula is valid for any spin rate.
Thank you for the clarification/confirmation, Russpin !
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Iacopo will have to lay-out arc-shaped pieces to fit his tapered stems.
Also it could be possible to glue a layer of sand in the upper part of the stem, for to have the same effect of the sandpaper, with the freedom of shaping the stem as wanted.
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Iacopo will have to lay-out arc-shaped pieces to fit his tapered stems.
Also it could be possible to glue a layer of sand in the upper part of the stem, for to have the same effect of the sandpaper, with the freedom of shaping the stem as wanted.
Yes. I've used the same carborundum grit to grind telescope mirrors.
Alan
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Testing Effect of HCG:
I made a simple 1.74" OD wheel with no groove and adjustable height. Wt =90g, .188 ball
Scrape angle 5 deg: HCG~.20" minimum RPM~220, Decay for a minute following 600 RPM = 13%
Scrape angle 7.5 deg: HCG~.233 min RPM~224, Decay for same interval = 11.3%
Scrape angle 10 deg: HCG~.277 min RPM~255, Decay for same interval = 10.3%
My minimum RPM is the lowest reading possible before wobble disables my tach.
I was surprised by the tiny increase in minimum RPM between 5 deg and 7.5 deg scrape angle.
The lower decay rate of the higher CG is attributable to reduced aero shear between the bottom of the wheel and the surface. Higher CG also reduces failed twirls due to scrapes.
I've decided to concentrate on 7.5 degree scrape angle for a while. That's similar to many of my prior twirlers.
Best regards,
Alan
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The lower decay rate of the higher CG is attributable to reduced aero shear between the bottom of the wheel and the surface.
A difference from 10.3 % to 13 % is high.
Since I usually use pedestals with my tops, I have not much experience with this reduced aero shear drag, but I made some tests in the past, and I never noticed a worsening of the decay rate because of a reduced space between the bottom of the top and the spinning surface.
Maybe you are having something else in play.
If you add a piece of paper below the flywheel, very near to it, while the top is spinning, I think you shouldn't notice any worsening of the decay rate. The piece of paper would allow you to make the comparison with the same top, without changing the height, which could be more reliable.
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Interesting results, Alan. The
inverse direct relationship between HCG and minimum speed is at least qualitatively in line with basic top theory.
How are you calculating the decay figures you gave?
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I repeated the test, to show you the results:
I made my top Nr. 15 spin with and without a cardboard near to its bottom, to see if the cardboard worsens the aerodynamics of the top.
The cardboard is placed very near to the bottom, (less than 1 mm), at one side of the top, as you see in the picture.
(https://i.imgur.com/3VArSHv.jpg)
I timed a few one minute lapses, as follows:
From RPM to RPM Efficiency
1150 1087 no cardboard 94.5
944 894 with cardboard 94.7
870 826 no cardboard 94.9
763 724 with cardboard 94.9
705 670 no cardboard 95.0
635 604 with cardboard 95.1
Efficiency here is calculated as percentage of speed retained after one minute spinning;
1087 : 1150 = 0.945 = 94.5 %,
894 : 944 = 0.947 = 94.7 %,
and so on.
It can be seen that efficiency is lower at higher speeds, which is usual and normal.
Above all, it can be seen that the presence of the cardboard does not have any significative consequence on the efficiency of the top.
The spinning time, with or without the cardboard, would be very similar.
The experiment is very simple, you can repeat it, and you should have the same result.
The lower decay rate of the higher CG is attributable to reduced aero shear between the bottom of the wheel and the surface.
I don't think this is possible, for what I showed above. There must be another reason for the lower decay, but I am not sure what it could be.
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Thank you Iacopo and Jeremy.
My decay is essentially 100-Iacopo's efficiency. It's RPM/(RPM a minute later)-1
Example 600/540-1=.111=11.1% decay.
After experimenting with scrape angle, I analyzed some existing stem heights. As Iacopo said, longer stems are easier to twirl and I've stated that they have less lateral shift for a given tilt angle. So I looked at max lateral shift of stem top, which is tan(scrape angle) x (total height tip to tip).
I have tops where max lateral shift is 0.25", which I find ok to twirl. But reducing this only slightly to 0.16" results in a top which scrapes a lot when I attempt hard twirls.
Although Iacopo favors long stems, I've tried to keep recent small tops pocketable. I've also posted that long stems on these small, 50g tops often increases wobble, because the small, light wheel is easily disturbed by small errors in stem alignment.
Incidentally, I've used 0.25" ID sanding drums for the grip on two recent tops. Here's a photo.
The top on right is the simple wheel with adjustable height.
Best,
Alan
(http://image.ibb.co/ctz1gb/Tops_with_sanding_drum_stems.jpg)
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Hi Iacopo,
You suggested that I try your cardboard test. I will, with a sheet of rubber to conform to the mirror concavity. But I can't see the difference. I lowered the wheel by raising the spindle. You raised half of the surface.
I think the reason you didn't see this effect is that your wheels are much heavier.
Best,
Alan
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I think the reason you didn't see this effect is that your wheels are much heavier.
My top weighs 186 grams, the your 90 grams.
Still this doesn't seem to me enough to explain a so drastic difference in what we observed:
you had a difference in the spin decay by 2.7 % while I instead had a difference by 0.0 %.
Also, in my case, the cardboard was placed really very near to the bottom of the top, which should help to detect the difference, but, in spite of this fact, I detected no worsening at all in the spin decay.
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I expected a drag increase near the surface. It's been studied in computer hard drives. I believe Jeremy or I posted some references about a year ago.
Another difference between our tops is that mine has a perfectly flat bottom, so all of its bottom area is in aero shear.
Alan
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Thinking more about our differing observations of aero shear, I note that the outermost region, where shear has the greatest leverage, departs from the surface with your rounded tops. I tried a rounded top and didn't observe benefits from the rounding. But you have. Perhaps there was some defect in that top.
Also, my longest-spin-ever top has a large chamfer on the lower corner. I added that to remove a dent after it crashed. Of course, it too departs from the surface where shear has the greatest leverage. Perhaps there is something to learn here. Maybe the bottom corner is the place where rounding helps, despite its raising the CG.
Best regards,
Alan
Upate: I chamfered the bottom of a 1.75", 90g top. Reducing its weight to 85g.
Average decay over the entire 15 minute spin increased to 13.1% (from a prior 12.2%). This is despite having reduced the stem height, which should have also reduced decay slightly. So for this experiment, I can't endorse the bottom chamfer. But spins do not necessarily repeat exactly due to variations in lube. However I'll continue with no bottom chamfer for now.
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Another difference between our tops is that mine has a perfectly flat bottom, so all of its bottom area is in aero shear.
This makes sense, I didn't think to it.
I repeated the experiment with my top Nr. 27b, which has a squared edges flywheel and a flat bottom.
(diameter mm 52, weight 155 grams).
The cardboard was placed at 1 mm from the bottom of the top, and it covered a bit less than half the surface of the bottom, like in the first test with top Nr. 15.
One minute lapses: Efficiency, Efficiency,
From RPM to RPM with cardboard without cardboard
954 892 93.5
834 783 93.9
734 688 93.7
666 626 94.0
586 551 94.0
518 486 93.8
442 414 93.7
Now I too see a difference.
Average efficiency with the cardboard is 93.7 and without cardboard 93.9
The difference between them is 0.2.
If the cardboard covered all the bottom of the top, instead of about 2/5 of it, the difference of efficiency would rise, to maybe 0.5.
This value is still far from the 2.7 you had with your top, in spite of a larger clearance in your top, (with a 1.74" OD wheel and a scrape angle 5 deg, you should have about 2 mm clearance), so the mistery remains.
At higher speed the difference of efficiency in this my top seems a bit stronger, as could be expected.
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Tilting Mirror to Move Top to New Lube
I often tilt my mirror slightly during a run. Just enough to move the top a millimeter to pick up some fresh lube (forehead oil). My favorite mirror is supported on three thumscrews, which makes this easy. I've been rather casual about this, tilting when it comes to mind, which averages about every two or three minutes. But I just tried two runs, the first tilted casually, the second not tilted. The tilted run had merit 35% higher, which means that for the same launch speed, it would run 35% longer.
I had no idea that tilt was so important. It casts doubt on some of my decay readings because some intervals had fresh lubes and some did not. I may repeat some experiments with more rigorous tilting, such as once per minute.
Incidentally, I also see (and expect) greater decay at high speed due to aero drag. But then near the end of a run, many tops begin to wobble slightly and that pushes the decay rate up.
Regards,
Alan
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I had no idea that tilt was so important.
Me too. Interesting.
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Hello Iacopo,
Let's talk about balancing.
I'm beginning to think that my machining method, which places the ball within about .0002" of center may not justify further balancing. With your lighter tops, how close to perfect centering must you get before further improvements are of limited value?
For example if my minimum RPM is 200, and perfect balance would reduce that to 195, that would only extend spin time by about 15 seconds or 1.3% of total. Perhaps that's not enough to justify dynamic balancing and movable weights, etc.
Also, there are alternative ways to reduce, minimum RPM, such as lowering the CG.
Best regards,
Alan
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Also, there are alternative ways to reduce, minimum RPM, such as lowering the CG.
Or increasing specific AMI, decreasing specific TMI about the CG, or reducing the acceleration of gravity -- as we would have seen if the Apollo astronauts had had the good sense to take tops to the moon instead of golf clubs. (Here, "specific" means "per unit mass".)
Of these, lowering the CG and increasing the specific AMI would have the greatest effect.
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AMI?
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my machining method, which places the ball within about .0002" of center may not justify further balancing.
Not sure but I think all the big makers do not balance their tops but they use accurate machining methods, as you do, so that their tops come out from the lathe already balanced.
I prefer a more accurate balance for my tops so I always fine tune it. I do so mainly because I don't like the wobbling due to unbalance which comes out at slow speed.
I check for static balance, wich is more than sufficient, and only rarely dynamic balance;
because of the way I make my tops, I can have the tip slightly off centered, which causes static unbalance, but not couple unbalance, so practically I only need to correct the static one.
I use the balancing grub screws only in tops with replaceable tips; each time a tip is replaced, the top needs to be balanced again, and the screws are very practical for this aim.
With a fixed tip instead, if needed, I prefer to correct the position of the tip and/or add a permanent weight in the top.
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AMI?
AMI is axial moment of inertia, TMI transverse moment of inertia.
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Thank you Iacopo. Do you have a guess at the increase (if any) of minimum RPM which would result from moving the tip from perfectly centered to .0002" off center?
Best,
Alan
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Do you have a guess at the increase (if any) of minimum RPM which would result from moving the tip from perfectly centered to .0002" off center?
This is half a hundredth of millimeter.. not a lot..
Maybe, it would cause a 1 - 3 % reduction in minimum RPM ?
I never observed carefully this aspect.
I think there is always at least a bit of loss in the spin time, anyway, also because, apart from probable reduced minimum RPM, there should be more friction in the tip especially at high speed, when the tip is not well centered.
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Thank you Iacopo.
I asked that question because I have recently noticed that extra efforts to precisely center the tip have not yielded significant reductions in minimum RPM. So I'm thinking the tip should be well centered, but perhaps it's not worth the effort to get it better than about .0002". I'll continue to monitor this and refine my data. Perhaps you will too.
Also, the above number relates to small tops. Your larger tops may tolerate greater eccentricity.
Best regards,
Alan
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My tops with long stems have strong intermediate wobble a few hundred RPM above the minimum RPM. Shortening the stem usually greatly reduces this, but doesn't eliminate it. The decay rate is higher during wobble. Wobble is also more likely as height of CG increases.
But even my tops with short stems have slight intermediate wobble, perhaps at an RPM much closer to the minimum RPM.
Today, I made my most precise 1.5" top ever. It weighs 62 grams and looks like recent photos that I've posted of grooved brass tops. Stem is only 0.7" long. But even this top has slight intermediate wobble. I've twirled it for 20:52 resulting in a record merit = 7.6. To achieve this time, I tilted the mirror (to move the top to fresh lube) continuously. Right after that, a run with no tilt has 19% shorter duration. So lube is very important.
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a run with no tilt has 19% shorter duration. So lube is very important.
I agree, I too see quite shorter durations, without lube.
As for the intermediate wobble, I still can't understand what it could be; based on my experience, it should be nutation triggered by large contact points, otherwise it is something I don't know.
If it is nutation, a good lubrication, (which you achieve also tilting often the mirror), should reduce it.
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For a long time, I was using 3/8" and 1/2" balls. Lately, I'm using mostly 3/16" balls and have started to notice the intermediate wobble. I define this as a wobble which peaks (well above minimum RPM), then smooths.
I watch my tachometer, which declines in one RPM steps. Then, near the end, the top wobbles and when the wobble is severe the tach can't read properly and declines in a larger step. I'm defining minimum RPM as the last reading before the larger step. Normally the top falls within a second or two of this last reading.
Alan
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I think Alan's intermediate wobble is unlikely to be pure gyroscopic nutation. Perhaps he could use Iacopo's nutation diagnostic to test that hypothesis.
Iacopo's original description of the nutation test (http://www.ta0.com/forum/index.php/topic,5161.msg55244.html#msg55244)
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Alan, could you try to mark the stem of your top during that intermediate wobbling ?
If yes, the marks appear all on the same side of the stem, or they are randomly distributed around it ?
I know it is a bit difficult to do this with light tops; for having more marks, it could help to spin the top more than one time.
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Alan, could you try to mark the stem of your top during that intermediate wobbling ?
If yes, the marks appear all on the same side of the stem, or they are randomly distributed around it ?
I know it is a bit difficult to do this with light tops; for having more marks, it could help to spin the top more than one time.
Ah yes, a much simpler test if feasible. I've had good luck marking light tops with a slack chalk line. To use the rate-comparison test I was thinking of, you'd need to know the top's AMI to at least 2 significant digits.
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I can do this with my strobe light, and with slow-motion video. I'll post some stuff in several days.
Alan
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I can do this with my strobe light, and with slow-motion video. I'll post some stuff in several days.
Alan
A slow-motion video would be fantastic. It would be important to have a mark at one side of the top, so it would be possible to evaluate spin speed in the video, together with the wobbling.
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More on "no-fall" tops.
The simplest approach is a top with a thin "platter" flywheel which has a Cg lower than the center of the (large) ball tip. I've made many of these. I even have a spreadshseet which calculates the height of the Cg. Example, a top with 0.5" diameter ball and Cg lower than 0.25".
In addition to this, I've found that a very well balanced top won't fall if the Cg is only slightly above the center of the ball.
Finally, getting the Cg low, even if not low enough to prevent fall, might provide extended spin time because of low topple speed. I made a 1.75" diameter, 54g top tonight which topples at 85 RPM, less than half the topple RPM of most of my small tops.
But there is "no free lunch". These tops have larger balls and lower scrape angles. The greater decay rate of the larger ball consumes the benefit of the lower topple speed. And, do we enjoy 25 minutes spins if the top scrapes half the time we twirl due to the low scrape angle?
Developments full of trade-offs like this consume a lot of time. I'm constantly trading parameters in pursuit of best compromises. And best for me, won't necessarily be best for other twirlers.
Alan
PS I haven't forgotten the original topic of this thread "A Figure of Merit for Twirler Spin Time". I compute merit on every top I make and twirl. I find it helpful when comparing tops of different size and weight. A high figure of merit on a 50 gram top says, "This is a good performer, considering it's 50 gram weight". Conversely a low figure of merit tells me, "This design needs improving", or "This design is inferior to that (other) design". etc
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And, do we enjoy 25 minutes spins if the top scrapes half the time we twirl due to the low scrape angle?
I would say not, unless this is a top for trying to make a record spin.
With my tops I generally scrape once every maybe ten spins.
I tend to make low scrape angles in my tops but the long stems and the narrow knurls make them easy to spin without scraping.
If this didn't work, I would be making larger scrape angles in them.
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But there is "no free lunch". These tops have larger balls and lower scrape angles. The greater decay rate of the larger ball consumes the benefit of the lower topple speed. And, do we enjoy 25 minutes spins if the top scrapes half the time we twirl due to the low scrape angle?
Depends on the audience. When I let visitors at LEGO shows spin my tops, they quickly get frustrated with the chronic scrapers and move on to tops they can twirl with reasonable success. As you'd expect, these more forgiving tops have smaller AMIs, larger scrape angles, or both.
These relatively unskilled show visitors consistently value ease of use over long spin times. Having had a lot more practice, I still find great play value in the tops they abandon. But some tops frustrate even me. In my design priorities, play value, including ease of use, is up there with visual effects at speed, interesting behavior during spin-down, resting appearance, and spin time.
Developments full of trade-offs like this consume a lot of time. I'm constantly trading parameters in pursuit of best compromises. And best for me, won't necessarily be best for other twirlers.
Amen to that! The parameter space is just too vast to explore fully -- even with a modular construction system like LEGO.
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Lube Tests
I had settled on skin oil as being about as good as any lube when developing Euler discs. I discovered it accidentally when encountering 2x variability in run time which turned out to be due to clean mirrors vs those with some skin oil. Here's my record 5:54 run.
https://www.youtube.com/watch?v=N_bMbuEQ6wM
Tops are different, so I tested decay rates at about 500 RPM with different lubes. Once again, skin (forehead) oil proved about as good as any. I had learned with the Euler discs that an extremely thin layer works best. I touch my forehead and then touch the mirror, leaving a thumb-print. Then I spread it, wiping hard with the side of my thumb or finger. I hard repeat wipes, each time at right angles about 5 times.
I noticed that very thin slippery lubes had much greater decay, even when I tilted the mirror often to move to fresh lube. I was using a top with .375" diam ball and it skated freely with thin lubes, giving me the impression that drag would be very low - but it wasn't. Conversely, I tried some thick grease which damped motion and eliminated skating. With forehead oil, there's moderate skating which settles down as the top self "erects" in one or two minutes.
One other good lube is thin, "Dow Corning 33 Silicone Lubricant". It's much thinner than the silicone grease that I use to improve seals. It's even a bit better lube than forehead oil.
Regards,
Alan
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I had settled on skin oil as being about as good as any lube.... One other good lube is thin, "Dow Corning 33 Silicone Lubricant".... It's even a bit better lube than forehead oil.
Of all the tricks I've learned on this forum, your skin oil and tilting mirror tricks are on my short list of favorites. Skin oil is the best tip lube for LEGO tops yet when both performance and convenience are factored in, and I'm currently working on a 3-point tilting LEGO mirror frame. I find good skin oil on the forehead and temples, behind the ear lobes, and around the base of the nose.
For example, I used skin oil lubrication and the weighted burger top (http://www.moc-pages.com/moc.php/438204) below to get my longest spin times to date -- 3:32 by hand and 4:32 with a 1:16 manual starter. (Record runs not shown.) Not coincidentally, this is about as aerodynamic as a LEGO top can get with currently available parts.
https://www.youtube.com/watch?v=52Sw7xaJqQA
I don't use silicone lube on tips because it's almost impossible to remove from fingers, but it's great in less mess-prone settings -- like the rotor bearings in the 2-DOF LEGO gyro (http://www.moc-pages.com/moc.php/407973) below...
https://www.youtube.com/watch?v=l1_ZmYTRmHU
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Hi Jeremy,
Here are two other tricks you might use.
When the top is spinning slowly and you want to move it a millimeter to fresh lube, you have to be very gentle to avoid inducing wobble and fall. My thumbscrews allow that, but there's another way. I set the mirror on something that has a bit of give -- a cloth placemat. Then, when I want to tilt the mirror very gently, I press down slightly on the edge of the mirror - sinking it slightly into the cloth placemat. When you release pressure, it may return to the prior location, but it has picked up a bit of lube.
The other trick is to blow gently on the perimeter of the top. I like to do that with a straw. When I do, the top is attracted to the straw! That's Bernoulli effect.
Alan
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When the top is spinning slowly and you want to move it a millimeter to fresh lube, you have to be very gentle to avoid inducing wobble and fall. My thumbscrews allow that, but there's another way. I set the mirror on something that has a bit of give -- a cloth placemat. Then, when I want to tilt the mirror very gently, I press down slightly on the edge of the mirror - sinking it slightly into the cloth placemat. When you release pressure, it may return to the prior location, but it has picked up a bit of lube.
The other trick is to blow gently on the perimeter of the top. I like to do that with a straw. When I do, the top is attracted to the straw! That's Bernoulli effect.
I'll try both of these, Alan! The soft placemat is a simple and elegant solution easily carried to LEGO shows. Beside, I have other uses for the valuable parts a tilting frame would tie up.
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Watching the top move towards you when you blow on the perimeter with a straw is quite unexpected. Try it.
Alan
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Watching the top move towards you when you blow on the perimeter with a straw is quite unexpected. Try it.
Alan
I tried it and.... it works !
I blowed without straw, the top goes towards me, or towards the right side if I blow at the right side of the top, or towards the left side if I blow at its left side.
Something interesting to think about.
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Watching the top move towards you when you blow on the perimeter with a straw is quite unexpected. Try it.
Alan
I tried it and.... it works !
I blowed without straw, the top goes towards me, or towards the right side if I blow at the right side of the top, or towards the left side if I blow at its left side.
Something interesting to think about.
Bernoulli has always been a mystery for me ::) But here I would expect a complicated effect. Remember that when you tilt the surface where the top spins, it travels at 90 degrees to the slope (if the tilt is not large enough to create slipping). Would the walking of the tip plus precession be part of what you are seeing?
As Iacopo said, something to think (and experiment) about. Perhaps a whole new thread . . .
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..when you tilt the surface where the top spins, it travels at 90 degrees to the slope (if the tilt is not large enough to create slipping). Would the walking of the tip plus precession be part of what you are seeing?
It seems to work especially with large and low tops with a ball tip.
Blowing on part of the flywheel pushes that part down. But, because of the gyroscopic effect, the sinking movement happens 90 degrees later, in the direction of spinning. So, if I blow at the front of the top, the top tilts sideways. At that point the top walks on the ball tip because of the tilted position, and it walks towards me, which is logical, after some thinking. When I stop blowing, the top starts precessing, because now it is in tilted position.
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Bernoulli effect is that pressure in a free stream is inverse of velocity. That's why a cambered airfoil generates lift at zero angle of attack.
Alan
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..when you tilt the surface where the top spins, it travels at 90 degrees to the slope (if the tilt is not large enough to create slipping). Would the walking of the tip plus precession be part of what you are seeing?
It seems to work especially with large and low tops with a ball tip.
Blowing on part of the flywheel pushes that part down. But, because of the gyroscopic effect, the sinking movement happens 90 degrees later, in the direction of spinning. So, if I blow at the front of the top, the top tilts sideways. At that point the top walks on the ball tip because of the tilted position, and it walks towards me, which is logical, after some thinking. When I stop blowing, the top starts precessing, because now it is in tilted position.
I haven't had much luck reproducing this effect, but I don't have many large flat tops with ball tips.
Your theory, Iacopo, sounds plausible. If true, the direction of travel should reverse if you blow from the bottom.
I should have mentioned that not only I found the Bernoulli effect counterintuitive, but also the gyrosocopic effect :-[ :P :P :P
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I've thought of the top walking laterally as due to the portion of the ball which is in contact as being off center. Think of the off-center portion of the ball pushing the top like an oar.
Precession isn't applicable here - it causes the axis of rotation to tilt at right angles to applied tilting torque.
Alan
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I have tried blowing with a straw.
If I blow under the flywheel, and the top is spinning on a concave mirror, the side of the top where I blow is sucked down, like if the air passing below it causes a local depression.
I agree with Alan who suggests this is Bernoulli effect.
The side of the flywheel that sinks down is 90 degrees later, because of gyroscopic effect, then the top walks moved by the rolling ball tip.
The effect is evident when the top spins in a concave mirror, but it doesn't work (to me at least), if the top spins on a flat surface.
I suspect that, since the bottom of the top is flat, and the mirror is concave, the air should be constrained to expand, when it is blown under the top, channeled between the two divergent surfaces, which is what causes the depression. When the air reaches the center of the mirror, the surfaces become parallel, and then convergents, so probably the air depression is lost at that point.
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Iacopo's description sounds like air flowing under the toroidal wheel creating Bernoulli suction pulling the wheel down towards the mirror. Then the mirror actually tilting 90 degrees of rotation later, due to rules of gyroscopic precession.
Alan
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Iacopo's description sounds like air flowing under the toroidal wheel creating Bernoulli suction pulling the wheel down towards the mirror. Then the mirror actually tilting 90 degrees of rotation later, due to rules of gyroscopic precession.
Alan
I used the top you sent me, which has flat bottom. It worked anyway.
Yes, the flywheel goes down, not where there is the Bernoulli suction, but 90 degrees later in the direction of spinning.
(But only if the top spins on a concave surface. If the top spins on a flat surface instead, it seems like there is no Bernoulli suction).
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In a free stream, a curved surface is needed to develop suction at zero angle of attack. But when a flat surface is near another surface, the air velocity increases as the air flows through the narrowed space between the two surfaces. It's this velocity which is in the Bernoulli equation, not the shape of the surfaces. So suction does occur between flat surfaces.
Alan
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In a free stream, a curved surface is needed to develop suction at zero angle of attack. But when a flat surface is near another surface, the air velocity increases as the air flows through the narrowed space between the two surfaces. It's this velocity which is in the Bernoulli equation, not the shape of the surfaces. So suction does occur between flat surfaces.
Alan
I looked at the Bernoulli equation, but it is too complicated for me. Even intuitively I admit that I can't understand how it works exactly.
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All you need to know is that pressure decreases with velocity. Many of us view this as counter-intuitive.
Alan
PS This is the pressure which is measured with a sensing aperture at right angle to the flow. When the sensing aperture "looks" into the flow, the pressure increases with velocity. This is "dynamic pressure" and is used to measure airspeed as with a Pitot tube.
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All you need to know is that pressure decreases with velocity. Many of us view this as counter-intuitive.
Alan
PS This is the pressure which is measured with a sensing aperture at right angle to the flow. When the sensing aperture "looks" into the flow, the pressure increases with velocity. This is "dynamic pressure" and is used to measure airspeed as with a Pitot tube.
I have found some videos about the Venturi tube, and an explanation I could grasp a bit, even if the effect isn't very intuitive. I understand that the the "dynamic pressure" is something different.
I tried blowing with a straw under the flywheel of my tungsten top spinning on the table. This top has low scrape angle and there are only about 2 mm between the flywheel and the table. With this top the effect is strong; as soon as I blow, the top tilts rapidly. The suction seems stronger.
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Balancing:
Lately I'm working with tops which have very low topple speed. I watch them at low speed leaning towards the heavy spot without any aids (such as video). Then they come to rest with the same heavy spot touching the mirror. If I hold the top vertical (not spinning) and release it, it falls to the same heavy spot.
This is surprisingly easy.
Incidentally, my tachometer only works down to 60 RPM, but I find it easy to clock a single revolution below 60 RPM with a stopwatch. RPM = 60 / seconds for one rev.
Alan
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I have some copper foil tape. I weighed a large piece and determined that it weighs 0.136 grams per square inch. Then putting little bits of it on the high side of a top I was able to calculate that a 0.125" hole, 0.015" deep (on the low side) would balance a top. It worked.
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they come to rest with the same heavy spot touching the mirror. If I hold the top vertical (not spinning) and release it, it falls to the same heavy spot.
This is surprisingly easy.
When I start balancing a top, first I simply put it on a horizontal flat surface, without spinning it;
the top will stay in contact with the surface by the tip and by a side of its flywheel.
I roll the top a bit, a few times, and every time the top ends with the same side of the flywheel down, in contact with the horizontal surface; this is the heavy side.
This is very easy too, but for fine tuning I then always use brush and paint, which is more accurate.
When I want very accurate balance, in the end, I use the brush with the top spinning slowly.
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Is your top lying on its side? If so, this would find the heavy side of the circle defined by the perimeter, but would not be influenced by the eccentricity of the tip.
alan
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Is your top lying on its side?
No, it is lying on the tip and on the side.
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So the tip and the side are touching the surface and the axis departs from vertical by the scrape angle.
Any special efforts to level the surface? Putting a ball bearing on it would be a sensitive test of level.
Alan
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I never made special efforts to level the surface. I simply use the surface of the table, which is smooth enough and decently level.
But using a good surface like a glass pane, perfectly level, would help; I don't know how much accuracy could be reached in this way, but it is interesting to try.
To use a bearing ball as a level is a very good idea !
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I leveled the flat side of a mirror that I'd installed thumbscrews on. A ball helped as a level. Even more sensitive is a spinning top. In fact it's too sensitive. Iacopo's method of setting the top on its tip and edge is a great start to find the heavy point. As he said, eventually you want more sensitivity. So I twirl and wait for fall.
I've made several "no-fall" small tops lately and have to balance them to achieve "no fall". As I mentioned in a prior post, I stick on bits of copper tape to balance. Then I calculate how much weight I've added to reach balance and bore a little hole on the opposite side. All of this is based on calculations because my scale can't resolve the tiny weights I'm working with.
Incidentally, despite machining to a precision of one or two ten thousandths of an inch, these 50g tops have wobbled slightly below 200 RPM. The wobble disappears nicely when I balance them.
Alan
Update 1/30/18 I just ordered a micro scale that measures to .001 gram for only $20 from amazon. I should have done that years ago.
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I leveled the flat side of a mirror that I'd installed thumbscrews on. A ball helped as a level. Even more sensitive is a spinning top.
I too tried this, yesterday. I used sheets of paper to level my flat mirror, (but your thumbscrews are certainly more practical).
I had the same result, the top seems too sensitive, even with a horizontal mirror the method seems good for starting balancing a top but not for for fine tuning the balance.
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Why Can't I Scale Up Stability?
The top on the left was made a few years ago. 1" diameter, 48 grams, 3/8" ball. I noticed recently that it's more stable than any top I've ever twirled. Knock it while spinning and it rights in a few seconds.
So I thought it would be nice to scale it up. I made one 50% larger with the same proportions. But it doesn't even begin to show stability. Knock it and it remains tilted and orbiting.
Why?
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Have you scaled up the dimensions of the ball tip too ?
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Yes. Correct scale up is 9/16" ball. I tried that and 1/2" too. Strangely, the 9/16" (larger) ball has lower decay rates (~10%), while the smaller ball decay is about 11% to 12%. Both balls are brand new. Perhaps the larger ball has better finish.
But decay is a diversion in this case. I was aiming for stability. The original 1" top is impressive in how rapidly it rights when disturbed.
This has led me to also want to experiment with Cg height and stability. At this time, it appears that higher Cg rights quicker when disturbed, while lower Cg tends to remain tilted and orbit longer.
Alan
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As for what I know, a top should raise faster when Cg is lower, and when the ball tip is larger.
Maybe without lubricant it raises faster.
I noticed that the material of the contact points has an influence; my top Nr. 25 uses replaceable tips; with the ruby tip, the top raises in vertical position in 5 - 10 minutes. But if I use the teflon ball instead of the ruby, (same diameter), the top raises much faster, one minute or less. I don't know why.
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The physics of rising are described in a book I've owned for many decades, Classical Mechanics: A Modern Perspective, by Barger and Olsson. Here is their diagram.
The diagram shows friction, offset from the axis of rotation, being converted to rising torque by gyroscopic precession. Big balls rub the mirror farther from the axis of rotation for a given tilt angle.
In your case, I expect your teflon ball is flattened where it touches the mirror because it is soft. Although it's a low friction material, it's only moderately lower than your ruby (sapphire) which is hard and not flattened. So the flattened teflon rubs the mirror farther from the axis of rotation.
I'm sure that you've noticed that a point has no righting effect.
However, to the degree that a tilted top orbits, friction is reduced. Friction requires slip.
Best,
Alan
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This is something I have to think about.
I can confirm that pointed tips have little righting effect, compared to ball tips. Still there is some righting effect in them because even when they are sharp, their contact points are never exactly an infinitesimal point but they are always at least a bit rounded, so they behave like tiny balls.
When the Cg is very low, as in my tops with a recessed tip, the top rises relatively fast, (a few minutes), even if the tip is spiked.
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"When the Cg is very low, as in my tops with a recessed tip, the top rises relatively fast, (a few minutes), even if the tip is spiked." In this case, is the Cg above or below the tip?
Regards,
Alan
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I made a 1.75" diameter wheel with setscrews to move it up and down a shaft. With very high Cg, it recovers from a deliberate disturbance to vertical, stable spinning more quickly.
The high Cg makes it harder to twirl and shortens the duration due to increased minimum RPM. But it does recover more quickly.
Alan
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"When the Cg is very low, as in my tops with a recessed tip, the top rises relatively fast, (a few minutes), even if the tip is spiked." In this case, it the Cg above or below the tip?
The Cg is above the tip, by maybe 1 mm.
I also tried with the Cg slightly below the tip: at high speed the precession behaviour is similar, but precession happens in the opposite direction of that of a top with Cg above the tip. In both cases the top rises generally in a few minutes.
At very slow speed, with Cg below the tip, the top tends to rise spontaneously.
Your observation of tops with higher Cg that rise faster is interesting. I still have much to learn.
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Regarding a higher Cg. I do not like the resulting increase in minimum RPM. So I strive for low Cg. But the shortened rise time of higher Cg is interesting. The effect is not great, but enough to see. You should try it too.
I've also sometimes gone too low in Cg, resulting in too many scrapes during launch.
Your long stems are great. They permit lower scrape angles. But they too have issues. The stems on my small 50 gram tops aren't any lighter than your wood stems. But they have a greater Cg effect on my small, light wheels -- when compared to your larger and heavier wheels. Also they complicate pocketability, which I often desire. I'm experimenting with removable stems and with twirl, then lift-off stems, leaving the stem-less wheel to spin.
Alan
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I found this video with a very high Cg top, it rises quickly, in a few swconds.
The top was started at very high speed.
https://youtu.be/5TqxF3jGKlQ?t=15
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Fun video. That is quite an assortment of high Cg tops. Some of the comments are hilarious like "is this some sort of fettish or something" and "those should be enemies in dark souls."
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That guy is spinning his high Cg tops at 12k RPM. I'll experiment with some string launches too. But expect more like 4k to 5k RPM.
Alan
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I realized today that my very stable 1" diameter top will orbit for a long time if disturbed at high RPM (1,000 to 2,000).
It is most stable between 700 and 800 RPM. When disturbed while in this range, it orbits for only a few seconds.
Alan
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I realized today that my very stable 1" diameter top will orbit for a long time if disturbed at high RPM (1,000 to 2,000).
It is most stable between 700 and 800 RPM. When disturbed while in this range, it orbits for only a few seconds.
Alan
Perhaps at the lower speeds the tip doesn't slip and just rolls, what makes it more effective at speeding up the precession and thus standing up the top.
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I realized today that my very stable 1" diameter top will orbit for a long time if disturbed at high RPM (1,000 to 2,000).
It is most stable between 700 and 800 RPM. When disturbed while in this range, it orbits for only a few seconds.
I have no ideas about it. I know better spiked tips, I used ball tips only a few times.
But I am making some experiments with ball tips, for my thread about torques measurements.
I noticed that, (with ball tips), there is less tip friction, and the top spins longer, when it orbits, (precession), than when it spins in sleeping position, (at parity of speed).
I tried a few times with two different tops, and this behaviour always happened.
I suppose the cause is that, during precession, the tip rolls, and rolling friction is lower than sliding friction, (which happens when the top spins in vertical, steady, sleeping position).
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I "stumbled across" a video by Billetspin (Rick Stadler) of a top with a high Cg. The Cg is about twice as high as the diameter. He knocks it around while it's spinning.
https://www.youtube.com/watch?v=eGj8ybjzS7Y
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I "stumbled across" a video by Billetspin (Rick Stadler) of a top with a high Cg. The Cg is about twice as high as the diameter. He knocks it around while it's spinning.
This is the same idea as the Japanese Taorenado we discussed before (http://www.ta0.com/forum/index.php/topic,5087.msg53730.html#msg53730). I'm sure Rick is familiar with the koma taisen battles.
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Where can I buy a Taorenado? ebay and amazon came up zero.
Alan
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Some fun little high-CM LEGO tops with all the same behaviors as the BILLETSPIN offering but a whole lot cheaper...
https://www.youtube.com/watch?v=D_btrG34M0Q
You can adjust the behaviors -- and the sounds they make -- in several ways...
1. By adding or removing rotor disks.
2. By adding tires to the wheel-like rotor disks.
3. By moving the rotor up and down along the central axle as a unit.
4. By separating the rotor disks and spacing them out along the axle.
5. By changing the tip's radius of curvature.
Overall, the ball tips shown (5 mm radius) generate the most interesting behaviors.
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Where can I buy a Taorenado? ebay and amazon came up zero.
You can get it from Taka's SpinGear shop:
http://spingear.jp/index.php?dispatch=products.view&product_id=2549
You can select English at the upper right.
This is the thread where we discussed it: Japanese finger tops (http://www.ta0.com/forum/index.php/topic,5087.msg53686.html#msg53686).