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[johnm]

Seems like the long stem top might function as Philippe's ball and stem "flip-over" top.  Perhaps I'm a little disappointed that Tim doesn't follow the forum and may not be aware of Philippe's clever design.

[the Earl of Whirl]

A flip over top on a mirror?  That looks like a great idea!!!

[ta0]

The Mount Fuji top is now available from the Grand Illusions shop.

[Jack]

The Mount Fuji top is now available from the Grand Illusions shop.

those are pretty neat, but im a little surprised by th price eh  only 9 of those things would be the equivalent of a giulia 

[Iacopo]

This is a video about spinning tubes, by Tadashi.
I find interesting the way these tubes spin.
The tube acts like a flywheel in a spinning top and precession keeps one side of the tube lifted from the ground.
The precession is super fast !  So the object spins about its center of mass. 
The ratio between the spinning speed and the precession speed is the same as the ratio between the diameter and the length of the tube. Ratios that work better seem to be from 3:1 to 4:1, or even 5:1.
I suspect that one reason is that a more narrow tube would slow down precession and the tube would topple down very soon.
A larger and shorter tube would accelerate precession so the tube would raise up.
The video explains other interesting facts.

The tube is very easy to build.  Today I made one and showed it to some friends of mine, they were astonished.    

[ta0]

Thanks for posting this, Iacopo, I had not seen it. Any video of Numberphile that also features Dr. Tadashi on it can only be good.
I moved it here because it is the same toy as the biconic top (and also their "equidots" top).



I have the smaller version of that top from Grand Illusions and Tadashi's video motivated me to measure it. The distance between the two ridges (where the cusps of the hearts are) is 25.18 mm and their diameter is 23.5 mm or a ratio of about 1:1. So you would expect to see each color once per rotation. In fact, when spinning approximately horizontal, you see very clearly 4 static (or slowly rotating) hearts, one of each color. Nice!   

Interestingly, the stem does not affect the optical illusion. The stem would move the barycenter away from the neck in the direction opposite to the lower ridge which is the one rolling on the floor. I think the effect would be to increase the effective radius of the rolling circle. Mm, I would have expected the ratio to compensate for this to be slightly smaller not larger than 1:1. 

[ryan paul]

      question

   answer

[Iacopo]

Interestingly, the stem does not affect the optical illusion. The stem would move the barycenter away from the neck in the direction opposite to the lower ridge which is the one rolling on the floor. I think the effect would be to increase the effective radius of the rolling circle. Mm, I would have expected the ratio to compensate for this to be slightly smaller not larger than 1:1. 

I agree with your observation.  You could try to lean that top horizontally on the blade of a knife or something so, to check if the center of mass is really shifted towards the stem, or not. Maybe something inside the top compensates for the added mass of the stem.
 
The lower ratio 1:1 (relatively to the ratios of spinning tubes) I think is due to the fact that the biconical top concentrates its mass near the axis of rotation, where the gyroscopic effect works less efficiently.  The mass near the axis of rotation is like a dead weight and for balancing it precession has to be faster than in spinning tubes.

The diameter being a little less than the distance between the two ridges, maybe could be explained by the fact that this toy doesn't spin in horizontal position but in a tilted position, and this makes the circle described on the ground by the lower ridge to be a bit littler, and a bit larger distance between the ridges would compensate for this, so to have the hearts appearing always in about the same position.
 

[ta0]

I hung the top from a thread and the center of mass is indeed shifted towards the stem.

The diameter being a little less than the distance between the two ridges, maybe could be explained by the fact that this toy doesn't spin in horizontal position but in a tilted position, and this makes the circle described on the ground by the lower ridge to be a bit littler, and a bit larger distance between the ridges would compensate for this, so to have the hearts appearing always in about the same position.

That is a good observation and could explain that the ratio of the diameter to the length (between ridges) is slightly smaller than one. But it is surprising that the extra length given by the stem doesn't dominate the effect.

If there is a correction in the dimensions to compensate for the stem, you would expect the illusion not to work that well when rolling on the ridge closer to the stem. In fact, when I tried spinning it upside-down, you can still see the hearts but not static but rotating counter-clockwise (like the top). But in this case, the top has lost more spin when it starts to spin horizontally on the ridge, so this is not conclusive. 

[Iacopo]

I hung the top from a thread and the center of mass is indeed shifted towards the stem.

In this case it seems like the biconic top doesn't precess about its center of gravity.
I don't know the reason, but maybe I have an idea;

maybe the top is driven by the precession speed more than the center of mass wanting to stay in the center of revolution.

If so, I would expect a slower precession speed (and a larger circle described on the ground), when the top rolls on the ridge closer to the stem;  this is because in this case the weight of the stem is in the sense of slowing down precession.

When the top rolls on the lower ridge instead, the weight of the stem should accelerate precession.

With an accelerated precession, the circle described on the ground would be littler, and the center of mass would become shifted towards the stem.

Different sizes of the circle described on the ground would then affect if and in what direction the hearts appear to move.

But it's just an idea, I am not sure ...

-----------------------------------------------------

Today I have tried using a full rod instead of a tube, and a tube less or more partially filled with clay at one extremity.
These objects seem always to precess consistently about the center of mass.
The kind of surface (glass, smooth stone, wood not varnished) seem not to influence the behaviour.
So, I would think that my explanation above is uncorrect.

[Iacopo]

I have made a quick copy of the biconic top;
the center of mass, (the blue line), is not exactly in the neck but a bit shifted towards the stem.
It can be seen in the pictures that the top rolls about its center of mass.
I added a red line, to see how it appears from above while spinning;
the point where it appears more crisply is at the level of the ridge lifted from the ground, (the side where there is the stem).

[ta0]

Very good, Iacopo!

Yours seems to have the center of mass much closer to the neck than mine.
I guess the ratio between the distance of the ridge to the neck and the radius at the ridge is very close to 1:1.

The photos are quite informative. They clearly show the blue to be the center of rotation and the ridge to be frozen at its highest point.
The "bow" made by the red line is interesting. I think it is produced because the ratio varies from 1:1 as you move along the slope.
When you get closer to the neck, the ratio is lower than 1. At the highest point the forward revolution around the center of mass will be slower than the backwards rotation due to the spin. But a little before and a little later the apparent backwards rotation will be smaller, so you get frozen spots to each side.
I believe that if the neck is very narrow you should get a crisp line without the bow effect as the slope will be 45 degrees. In this way, the biconic top is superior to the "cylinder top".

The bottom of the top cannot give a frozen pattern as the movement due to the top revolution around the vertical axis and the spin rotation are in the same direction. But I am a little surprised that you can see the arms extend on the other side of the ridge, away from the neck. I will have to think about that.

I need to record this in slow motion, but I won't have time this week.

[Iacopo]

I believe that if the neck is very narrow you should get a crisp line without the bow effect as the slope will be 45 degrees. In this way, the biconic top is superior to the "cylinder top".

You make me think that the straight line between the crisp point on the upper ridge, and the center of mass, defines the optimal cone for the crispest images.
It could be nice to make a biconic top in that way...

The slow motion is a good idea !

[ta0]

Tim made a new video showing the biconic/cylinder tops.

[Jeremy McCreary]

If you skip to 8:02 below, you'll see a LEGO top producing the same illusion (at least in person) as Tim's spinning tubes...



You always see the orange and lime colors, but the color farther from the ball tip is always much more pronounced. Swapping the colors reverses the effect. A blacklight version (not shown) with contrasting fluorescent color markers makes the illusion even stronger.

Another effect Tim demonstrated: As my top spins down with rapid precession, the ball between the color-bearing black rotors appears to descend vertically. Otherwise, it looks motionless. That illusion requires the ball to be centered precisely on the top's CM. Since that takes some fiddling, I reverse the color illusion by swapping the orange and lime parts rather than by moving the ball tip to the other end of the axle.

Prior to 8:02, you'll see other behaviors from Tim's video. I call these small, high-CM, high-speed finger tops "gyrophonic sidewinders": "Sidewinders" for their ability to rotate rapidly on their sides just before coming to rest, and "gyrophonic" for the distinctive sounds their ball tips make on a suitable soundboard. Sidewinders show many unexpected spin-down behaviors.

See the video description for details.