**Optimal knurl diameter**This is my top Nr. 22.

It weighs 656 grams, diameter 80 mm.

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-m

^{2} 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

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.

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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.