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[nitro2k01]

Greetings from Sweden. Here's my story. I recently bought an Ender-3 3D printer. It's far from my first time using 3D printers as I'm a member of a well equipped local makerspace. But having one at home is a different thing entirely. So much easier to start a print at home, without needing to go somewhere, or wait in line for someone else to finish using the printer. I've been printing a lot of random stuff, and so on a whim I wanted to print a spinning top. I went for this model on Thingiverse in case anyone is interested. And while it was printing I went online to research the physics and design principles of spinning tops and ended up here. Nice to see that there's a community of enthusiasts even for something as niche as spinners.

The print finished and I assembled the spinner. Here's the first question for someone more knowledgeable than me. When spinning it up, it seems to jump at a steady pace on the table until (I assume) its momentum goes below some threshold. Then it starts spinning very beautifully. How would one go about "troubleshooting" the construction of a spinner based on symptoms like that? Is it a balancing problem, lack of weight or maybe just my technique? It's printed with only 10% infill, so it's almost hollow inside, but the upshot is that the model consists of a top and bottom part screwed together, so I could easily print a new bottom half with more infill. (Based on the assumption that bottom heavy is preferable.)

Which leads me to my next question. I would like to try making my own designs. Any tips on resources for learning the design principles for spinners. Obviously, you'd generally want them radially symmetrical, unless perhaps you wanted to introduce a wobble on purpose. But what are the principle on the top/bottom weight distribution? Am I right in thinking that generally you want a spinner to be bottom heavy if you want it to be stable, and the only reasons to move the center of mass up is either because you need ground clearance, to improve aerodynamics, or to add mechanical rigidity up top? But not for the sole purpose of shifting the center of mass up? Ie, the theoretically ideal design would be a stick and a disc in some dense material.

Finally, I'd be interested in learning about screaming spinners. I've already watched Maker's Muse video on the topic, but any more good resources would appreciated. As he points out at the end of the video, any internal geometry is possible to create with a 3D printer, and there should be a lot of fun designs waiting to be discovered.

Over and out for now.

[Jeremy McCreary]

Welcome aboard!

High-speed hopping: Common problem in low-mass tops launched at very high speed. Since your top settles into very smooth spins at lower speeds, probably not a static unbalance issue. And barring internal density variations, the shape largely excludes a significant couple unbalance. (See Wikipedia page on rotating unbalance.)

That leads me to suspect your tip and/or launching technique. Some things to try...

1. Examine the tip under magnification. (a) Make sure that when the top's vertical, the contact patch is perfectly centered on the top's overall symmetry axis. (b) Also make sure that the contact patch is perfectly smooth and symmetrical. Burrs, dents, and other irregularities can promote hopping, wobble, or both.

2. Practice smooth launches, making sure the tip is firmly planted at the moment of release.

Screaming top: Don't have all the answers here, but a single large resonant cavity inside the top seems to do the trick in many commercial versions. A mostly flat cavity floor and ceiling may help. Pitch and timbre depend mostly on the cavity's size and shape. Loudness depends more on the size and number of its air ports.

But large air ports, or too many air ports, will reduce spin time by increasing air resistance, which generally slows a top a lot more than tip resistance at all but the slowest speeds.

I'll post some general finger top engineering rules of thumb shortly. How do you feel about math?

[ta0]

Welcome nitro from Sweden!

I agree with Jeremy and also suspect that the tip might be bad. If the tip is fine and centered, then the top has some imbalance that creates enough centrifugal force at high speed to be comparable to the top weight. That design, if built with uniform density, should not jump at any speed.

Any tips on resources for learning the design principles for spinners. Obviously, you'd generally want them radially symmetrical, unless perhaps you wanted to introduce a wobble on purpose. But what are the principle on the top/bottom weight distribution? Am I right in thinking that generally you want a spinner to be bottom heavy if you want it to be stable, and the only reasons to move the center of mass up is either because you need ground clearance, to improve aerodynamics, or to add mechanical rigidity up top? But not for the sole purpose of shifting the center of mass up? Ie, the theoretically ideal design would be a stick and a disc in some dense material.

The top does not really need to be symmetric. In principle, you can spin any arbitrary solid shape stably around two particular axes that go through the center of mass.
See this thread for this:



Yes, a disk with a light stem is almost the perfect top with respect to weight distribution. Even better, if you replace the disk with a ring (and light spokes). But it actually does not have to be a circle or even have any radial symmetry. Any flat shape will be stable if spun around a perpendicular stem going through its center of mass.  Like these from the Don Olney:

A taller top will need a higher speed to stay up.

Making sounding tops is an art. Humming tops work as resonant cavities while on whistling tops the aperture is more important. Some whistling top have actual whistles in the air path, and some have vibrating reeds.

[Jeremy McCreary]

ta0 made some excellent points regarding top design. Definitely read the paper he recommended: Bächer et al., 2014, Spin-It: Optimizing Moment of Inertia for Spinnable Objects. (Free PDF here.) Many important practical concepts for the top designer, including "spinnability" -- a big part of play value.

Since everything affects everything else in a top, design comes down to playing the many trade-offs just so. I usually start by setting some performance and esthetic goals to guide my choices. These common goals often conflict:
o Play value (almost always my primary goal)
o No wobble or hop (usually 2nd priority)
o Easy launches by hand without scraping, or high-speed launches with a dedicated starter
o Some cool visual effect at speed
o A particular spin-down behavior -- e.g., sleep, steady precession, self-righting, or fast travel
o A particular look at rest
o Performance in battle
o Longest possible spin time given higher priorities

You'll have to experiment to get a feel for the trade-offs involved. Many common goals carry a spin-time penalty.

Yes, a disk with a light stem is almost the perfect top with respect to weight distribution. Even better, if you replace the disk with a ring (and light spokes).

"Perfect" and "better" for spin time, but not necessarily for other goals. Below are 3 LEGO finger tops with peripheral mass concentrations and the same small ball tip.



Left: Mass = 48.6 g, max radius = 34 mm, CM height = 25 mm, sleeping spin time by hand = 152 s. Since the black rubber tire is a good bit denser than the ABS plastic, most of the top's mass resides near max radius. And the center of mass (CM) is quite low. Combine this very favorable "down-and-out" mass distribution with good aerodynamics, and you get over 2.5 minutes of spin time.

Middle: Mass = 40.5 g, max radius = 34 mm, CM height = 33 mm, sleeping spin time by hand = 68 s. Max radius same as above, and the aerodynamics are comparable. But the mass is 17% smaller, and the mass distribution isn't as down-and-out. Result: 55% shorter spin time, but I really like the way this one looks -- both at rest and at speed.

Right: Mass = 54.8 g, max radius = 64 mm, CM height = 30 mm, sleeping spin time by hand = 14 s. The mass distribution has 6-fold rather than circular rotational symmetry, but it's still fairly peripheral. Yet spin time totally tanked -- mainly due to the very dirty aerodynamics.

As you can see, spin time correlates rather poorly with total mass, max radius, and CM height. Instead, it's mostly about radial mass distribution and aerodynamics.

But spin time isn't everything. The top on the left may spin a long, long time for a LEGO top, but it's kinda boring to watch. The top on the right, on the other hand, spins only 9% as long, but the lime and orange of the spokes mix to match the gold of the the central ornament at speed. I really like color-mixing effects.

But it actually does not have to be a circle or even have any radial symmetry. Any flat shape will be stable if spun around a perpendicular stem going through its center of mass.

That's true only to a point. Below are 3 perfectly balanced simple LEGO test tops differing only in max radius, rotor aspect ratio, or both. Those at far left and far right have 1:1 aspect ratios. And both are quite stable at finger speeds despite the four-fold difference in max radius. But it takes a very lucky twirl to get the one in the center (2:1 aspect ratio) to stay up at all. Yet any aspect ratio between 1:1 and 2:1 spins quite nicely.



Except for color, the 2 assembled tops below use the same parts (here laid out between them) and therefore have the same mass. But the one on the left (1:1 aspect ratio) stays up easily, while the one on the right (4:1 aspect ratio) crashes to the ground right away every time.

[Iacopo]

Is it a balancing problem, lack of weight or maybe just my technique?

Welcome to the Forum, Nitro2k01.

It is a balancing problem.  There is a problem of lack of accurate simmetry, somewhere, maybe in the tip, which could be dented or slightly bended.
Or maybe the density of the material is not homogeneous where needed.
Recently I made a little wooden top. The shape is symmetrical, but the wood is not homogeneous, the top was very unbalanced, so I had to add a brass piece in the flywheel to make it balanced. Only after having added the brass piece the top spins well.





Certainly in your case it is not lack of weight, nor the spinning technique.

[Jeremy McCreary]

Found the supplemental video for the Spin-It article by Bacher et al. (2014). Amazing feats of top balancing by moving and re-orienting principal axes of inertia and lowering center of mass with a 3D printer...

[Jeremy McCreary]

For anyone still interested in the origins of high-speed hop, I just posted some new experimental results here.