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[Bill Wells]

Completed off-center top.
116mm diameter Jatoba/Pine top.
Stem is 1/4" brass with pointed tip. String pull spin.
 Jatoba is dense, Pine light.
About 3 min spin.
Can't find any correlation to golden ratio.
Calculated centroid was close, but completed top required about 3g of static balancing.

[ortwin]

...
For the general case, it's not true that you get "ak" for the distance between C_T and C_H. It should be "a(k²-1)" (see reply 135).
A little more work to be done . . . 

You are right, I also realized over night that I ran directly into that trap I was trying to avoid. 
But not all is lost I think, I will try again.

...
By the way, the thread is on the 12th page and 167th reply! 
...

Is that good or bad? Something to be proud of? The other thread (curtain ring tops... ) has even more replies (271 today). It is even ranked 3rd if you order the threads in "Collecting, Modding, Turning and Spin Science >" by the number of replies - but of course if you subtract my own posts from that, things would look different I guess.

 

[ortwin]

...
Calculated centroid was close, but completed top required about 3g of static balancing.

Looks great to me!! Hopefully a video is on the way.
How did you apply those 3g for balancing?

[Jeremy McCreary]

Bill: Well done! Elegant design, and plenty of offset to make someone think it shouldn't spin smoothly.

The experimentally verified von Karman model of a thin disk spinning in still air predicts air resitance with a speed exponent of 1.5. Your disk may be thick enough to introduce edge effects von Karman ignored, but it would be interesting to see someday if its speed exponent is close to 1.5.

[ortwin]

Quasi Golden Ratio LEGO top spinning for a minute plus

Very nice! And it did spin for over a minute. But my own tests on a flat surface with a much finer tip (17 vs. 1.5 mm radius of curvature) indicate that a top like this spins down to critical speed in 10-15 s at most.

That is what I found too: if I use those ceramic balls (4mm diameter) as tips, I struggle to get to the 30 seconds. The 17 mm radius of that flat tip is doing a lot good for this top and the fact that it sometimes completely forgets to fall gave me another idea (not related to offset tops):

Is there a reversing top that regularly forgets to fall over when it is slowing down? Would be cool in a way.
And another thing: in German "Das Ei des Kolumbus" is a proverbial phrase.
I do not know how well it is known in other parts of the world:It refers to the story that the famous Columbus was given the task to sit an egg on its tip. Everybody thought it would be impossible but he just smashed the egg with its tip a bit onto the table. The tip broke a bit, but it sat on its tip now.
Now, if we spin a hard boiled egg it will rise and continue spinning on its tip. So in principle if someone is extremely lucky, the egg could also forget to fall as it spins down, we would have another "Ei des Kolumbus".

[Jeremy McCreary]

ortwin: You could improve your odds by genetically modifying chickens to lay flat-tipped eggs. But I think that would qualify as cruelty to animals.

[ortwin]

next attempt:

As ta0 reminded us: "For the general case, it's not true that you get "ak" for the distance between C_T and C_H."
Therefore it is now "ax" as in ta0s reply #136
With that in mind I get   x = (1 - 1/k) / (2/k - 1) if I divide (1) by (2) in my reply #161  
From ta0 in  reply #136 we have  x = k² - 1
 We arrived at those two formulas for x in different ways from different sides. If I put them together and rearrange a bit I get this cubic formula for k:
k³ - 2k² + 1 = 0
This is the same formula as in reply #81 which will lead again to k being the Golden Ratio. 
Edit: no, it is not the formula from reply #81 ! ta0 caught my mistake, see (the now modified  ) reply #174. Luckily and surprisingly the two formulas give similar results, so it is still correct that the formula here is leading to the Golden Ratio, while the one in reply #81 lead to its inverse (which I didn't even realize at the time)  End Edit

Less false this time?

[ta0]

Completed off-center top.
116mm diameter Jatoba/Pine top.
Stem is 1/4" brass with pointed tip. String pull spin.
 Jatoba is dense, Pine light.
About 3 min spin.
Can't find any correlation to golden ratio.
Calculated centroid was close, but completed top required about 3g of static balancing.

It looks nice! And 3 minutes is a good spin!

[ta0]

next attempt:

As ta0 reminded us: "For the general case, it's not true that you get "ak" for the distance between C_T and C_H."
Therefore it is now "ax" as in ta0s reply #136
With that in mind I get   x = (1 - 1/k) / (2/k - 1) if I divide (1) by (2) in my reply #161 From ta0 in  reply #136 we have  x = k² - 1
 We arrived at those two formulas for x in different ways from different sides. If I put them together and rearrange a bit I get this cubic formula for k:
k³ - 2k² + 1 = 0
This is the same formula as in reply #81 which will lead again to k being the Golden Ratio.

Less false this time?

Yes, I did it from scratch and I also got the cubic k³ - 2k² + 1 = 0. But note that this is different than the one on reply #81: x³ - 2x + 1 = 0
This one has the solutions 1, φ and -1/φ while the other has the solution 1, -φ and 1/φ. Anyway, it's now proven by assuming the symmetry of the diameter and not the golden ratio. 

[ortwin]

... I need to check if the centroid falls close to the center of the horizontal line.

...

If it does not, then just go for a line where it does, there is at least one. That could also look cool if the hole is still completely included in the outer shape .

[Jeremy McCreary]

Maybe we could work our offset magic on this baby:



More adults -- or should I say, more men -- would take up this hobby if they understood that building any kind of craft -- for air, space, or even sea -- gives you complete license to swoosh it around the house whenever you like.

My wife finally understands this, but she's not giving me a pass on the bath towel cape.

[Bill Wells]

How did you apply those 3g for balancing?

Ortwin, on my wooden tops, I drill 1/8" hole into edge of disc then insert piece of 1/8" solder. 1" of solder is about 1g. After I am happy with balance, I glue the weights in place.
OK on the video. Will be forthcoming.

[ortwin]

How did you apply those 3g for balancing?

Ortwin, on my wooden tops, I drill 1/8" hole into edge of disc then insert piece of 1/8" solder. 1" of solder is about 1g. After I am happy with balance, I glue the weights in place.
OK on the video. Will be forthcoming.

For balancing I prefer grub screws in the edge. I have three or four threads placed symmetrically around the flywheel. With wood you might need additional measures if a thread directly in the wood is too fragile.
The big advantage I think is, that you can fine tune the balance with the position of the grub screws a lot easier and make changes fast without the need of many tools. And I found good balancing to be of an importance that can't over exaggerated. Good balancing can easily boost spin time by a factor of two in comparison to mediocre balancing.

[Bill Wells]

Is there a reversing top that regularly forgets to fall over when it is slowing down?

A tippe top will continue to spin vertically until something causes it to tilt. So if the top is too perfect and spun vertically on a smooth surface it will forget to fall over.

[Jeremy McCreary]

Is there a reversing top that regularly forgets to fall over when it is slowing down?

A tippe top will continue to spin vertically until something causes it to tilt. So if the top is too perfect and spun vertically on a smooth surface it will forget to fall over.

When not inverted, right? (Resting vertically on the body, not the stem.)

When inverted, the end of the stem would need a central flat for that to happen with any frequency.