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[Iacopo]

What exactly is hoola hooping?

I don't know if there is another name to call it, it is how I call the wobble that a top with a ball tip makes while spinning on a concave base at high speed.  The larger the ball tip, the littler the radius of curvature of the base, the higher the speed, and more probably the top will hula hoop.

If you spin my top with the ball tip on the pedestal, it should hula hoop.


 

[Iacopo]

I think I remember seeing  some calculations done by Jeremy that suggested big size tops would not spin as long

As a matter of fact, the spin decay of larger tops is slower, they lose less RPM per minute than littler tops. The larger, the better.
At parity of starting RPM speed, they generally spin longer.

But when the limit of energy transmitted to the top is considered, things change;
at parity of kinetic energy at the start, the bigger top spins more slowly, and if the starting speed is too slow, it will not spin for long, so there is a compromise between size and kinetic energy at the start.  With more energy, the optimal size, (for longest spin), is larger.
 

[ortwin]

What exactly is hoola hooping?

I don't know if there is another name to call it, it is how I call the wobble that a top with a ball tip makes while spinning on a concave base at high speed.  The larger the ball tip, the littler the radius of curvature of the base, the higher the speed, and more probably the top will hula hoop.

If you spin my top with the ball tip on the pedestal, it should hula hoop.

Now I have never seen such a clean hoola hooping before! I also would never have thought a  fine spinning top of yours would make such insinuating moves. Mistress von Karman comes to mind.

I think I remember seeing  some calculations done by Jeremy that suggested big size tops would not spin as long

... With more energy, the optimal size, (for longest spin), is larger.
 

That means  if we want o follow this path at all we need to check how much spin energy we can put into a bicycle wheel or a  larger steel disk by a handle like a curling stone has? If we have that energy we can estimate if we can expect substantial longer spin times after some optimization?

[Jeremy McCreary]

I discussed the many complicated trade-offs surrounding absolute size as scaled by maximum radius here...

http://www.ta0.com/forum/index.php/topic,6392.msg69157.html#msg69157

I don't think we have the data needed to calculate in advance the optimal absolute size or spin time for any top -- not even a simple thin disk with von Karman swirling flow.

[ta0]

Thanks Iacopo for the explanation of what you call Hoola Hopping. I think the name is perfect!
Jeremy's gyrocyclotron = hoola hoop regeneration.

Your top can stay surprisingly vertical while doing hoola hoops. I guess it's because the low center of mass.
I'm gong to put the ball tip on my and try it.

[Iacopo]

I also would never have thought a  fine spinning top of yours would make such insinuating moves. Mistress von Karman comes to mind.

For this reason I don't use anymore ball tips for tops with a recessed tip, for a long time.
 

That means  if we want o follow this path at all we need to check how much spin energy we can put into a bicycle wheel or a  larger steel disk by a handle like a curling stone has? If we have that energy we can estimate if we can expect substantial longer spin times after some optimization?

If you already have decided what kind of top to use, for example, a bycicle wheel, and you want the longest possible spin with it, you simply start it at the highest possible RPM.  Until you don't have structural resistance problems, or balance problems, or what else, the more energy you put in it, the longer it should spin.

But if you start your project deciding first how much energy you may have for your top, and you want the longest spin, the problem is reversed;  for example, if you want to make a finger top to be spun with one single twirl of the fingers, you will have to find what is the optimal size/weight for that amount of energy.  I can put about 0.5 - 0.7 joule of kinetic energy in a top, with a single twirl.  It doesn't matter if the top is large or little, the little top will spin very rapidly, and the large one slowly, with a single twirl, but the amount of energy transferred is about the same.  I am not able to calculate theoretically what is the optimal size/weight for a given amount of energy, but I have some experience with finger tops, and I know empirically what is approximately a best size/weight for a finger top.
I show you some data; they are the longest spins of three different tops, by a single twirl, and by multiple twirls:

TOP   WEIGHT   DIAMETER     AMI          LONGEST SPIN     LONGEST SPIN
Nr.      grams         mm         kg-m²          single twirl          multiple twirls

14        165            52         0.000067           39:52                  46:15
23        298            60         0.000146           28:00                  58:19
9          847           101        0.001560             3:34                  41:25

The Nr. 14 has an optimal size/weight for single twirl spins, and it spins longer than the other two ones with a single twirl;
by multiple twirls it doesn't spin much longer because the top is little/light and it already has high RPM after a single twirl, it is difficult to accelerate it much more with additional twirls.
The Nr. 23 is a bigger/heavier top, optimized for multiple twirl spins.
The Nr. 9 is simply too big/heavy for to be spun with fingers; with a single twirl it spins very slowly and it topples down soon after;
by multiple twirls I can start it at a decent speed but the top is still over sized even for multiple twirls.
Anyway, using a motor to start the three tops with sufficient speed and energy, I am sure that the Nr. 9 would become the best of these three.

The optimal size/weight of a finger top changes a bit depending on some other parameters, like the density of the flywheel, the kind of the contact points, the design of the top, the position of the tip, (recessed or external)...  I think it would be extremely complicated to calculate it theoretically.  And, in any case, there is lacking of accurate data, as Jeremy says, about both the tip friction and the air drag.

[Jeremy McCreary]

The optimal size of a finger top changes a bit depending on some other parameters, like the density of the flywheel, the kind of the contact points, the design of the top, the position of the tip, (recessed or external)...  I think it would be extremely complicated to calculate it theoretically.  And, in any case, there is lacking of accurate data, as Jeremy says, about both the tip friction and the air drag.

Agree with everything Iacopo said in that post -- especially the part where he agreed with me!

Some additional points regarding tops in quiet sleep...

AMI: The mass, size, and shape of a top affect air and tip resistances in very complicated ways that we usually know little about. They also come together in much more predictable ways in 2 absolutely fundamental measures of mass distribution -- axial moment of inertia (AMI) and transverse moment of inertia (TMI) about the center of mass (CM).

TMI affects spin time only via critical speed. Ditto for CM-contact distance. And simple mass or weight enters spin time only via its effect on tip resistance, with no effect on critical speed or precession rate.

One way or another, all other practical design parameters affecting spin time come back to either AMI or AMI per unit mass.

To begin with, the effect of AMI per unit mass on critical speed is second only to that of CM-contact distance. And in efficient, high-performance tops, spin time is very sensitive to critical speed.

AMI limits the release speed you can reach by hand and determines the optimal stem diameter or taper in finger tops. Ditto for any other starting method (e.g., a wind-up or ribbon-pull) with only a limited time to charge the top with angular momentum. In geared starters with a limited time to act, AMI determines the optimal gearing for max release speed.

During spin-down, the larger the AMI, the shallower the slope of the spin-decay curve for a given total braking torque. And the shallower the slope, the longer it will take to spin down to critical speed and fall.

Stem design: Iacopo didn't mention it explicitly, but you can't ignore stem design in finger tops, as we've discussed elsewhere. Ergonomics matter, and the AMI to be overcome is key.

Bottom line: Air and tip resistances aside, the physical processes affecting spin time pay no attention to simple weight and size. But they pay very close attention to AMI. Problem is, tops of the same size or mass can have vastly different AMIs and vice versa.

To learn top engineering, learn to think in terms of AMI instead.

Avoid descriptors like big, small, heavy, and light, as they only confuse things. A good start is to learn to spot which of 2 tops is likely to have the greater AMI. Wikipedia is there to help.

[Iacopo]

Jeremy, ok, I corrected a bit my post to make it less confusing and added the AMI data.

Problem is, tops of the same size or mass can have vastly different AMIs and vice versa.

In any case, if the basic design of the tested tops is always approximately the same, the weight and the diameter are sufficient to give a good, (and more intuitive), idea of the relative proportions of their AMI. 

Bottom line: Air and tip resistances aside, the physical processes affecting spin time pay no attention to simple weight and size. But they pay very close attention to AMI.

AMI by itself is not so significative.  Tops with the same AMI can have very different diameters, weights, and spin decays.  A large paper origami top can have the same AMI of a little metal top but it will slow down much more rapidly because of the air drag.     

[Jeremy McCreary]

Jeremy, ok, I corrected a bit my post to make it less confusing and added the AMI data...

In any case, if the basic design of the tested tops is always approximately the same, the weight and the diameter are sufficient to give a good, (and more intuitive), idea of the relative proportions of their AMI. 

Thanks! Not being able able to see the tops or give them a twirl myself, I found the differences in AMI very helpful -- in fact, all I really needed to know about them to get your point without ambiguity.

And even your tops vary enough that it's much more useful to know AMI in addition to the more easily grasped size and weight.

AMI by itself is not so significative.  Tops with the same AMI can have very different diameters, weights, and spin decays.  A large paper origami top can have the same AMI of a little metal top but it will slow down much more rapidly because of the air drag.   

Totally agree that size and shape (including any streamlining or lack there of) have a huge impact on spin time via air resistance.

After all, I deal with many unconventional shapes and surface textures, and I think I struggle with air resistance more than most topmakers.

But you still need a good feel for a top's AMI to understand its response to the total resistance it encounters.

So it's not that AMI is more or less important than resistance. It's that they're inextricably linked when it comes to spin time. And you have to pay close attention to both at once.

[ortwin]

Thank you Jeremy and Iacopo for all your tips! I will try to keep as many of them in mind when I play around and build spinning tops.
I find it inspiring that spinning tops of so different sizes and concepts (stemmed, stemless, handle) seem to have the possibility to play in the same league when the goal is spin time. Even with the same set of rules: hand start, single twirl, no recessed tip....

Thanks Iacopo for the explanation of what you call Hoola Hopping. I think the name is perfect!
Jeremy's gyrocyclotron = hoola hoop regeneration.

That reminds me of how I understand the "Levitron Perpetuator". I also use the term "hoola hoop" for that. Although, since there the precession and the precession frequency  play a vital role over there, a further twist is added to the equation.
That regeneration also reminds me of the Swiss tradition of "Talerschwingen" (spinning a coin).