Circle challenge

Hi forum,

I have a challenge for you. It’s real world, not a dreamt up case. Rocket Science of sorts…

I need to fit as many 21 mm dia circles within a circle dia 297 mm.

I tried two approaches.

  1. Start with one in center, then a ring of 6 elements 60 deg apart. And so. That turns out to be rows 36.373 mm apart. Neatly aligned. But it gives a lot of holes around the edge.

  2. Then tried starting with 44 elements spaced 8.18182 deg apart on the outer edge. But that becomes a mess, since space gets less and less and you go inward.

This is not to make fun of Shapr3D lack of array copy, but it would be really useful here… Do you guys have a better workaround than just copy/rotating one, then 2 and then 4 etc???

I wanted to upload my two attempts, but apparently “new users” are not allowed to do so…

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The 21 dia circles cannot touch each other? What is the minimum acceptable distance between them?
I got 163 pieces….


Something like this….

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The parts are actually 18 mm, but need 3 mm of space, so I said 21 to make it easier. So yes, they can touch but not overlap.

Cicles outer start.shapr (31.6 KB)
Cicles center start.shapr (30.4 KB)

I have now been upgraded, so here are the files…

edit: wrong outer dia…

I get 132.
(if you move the grid around, you might get a couple more.)
I see the error in my method. I didn’t take into account the hex pattern nesting.

Yep, that’s the design I ended up with too. Except I miss read the spec and used the wrong total dia. Your layout made me realize that :slight_smile: Big Thanks for that.

My current design. Now that I got the outer dia right, there is only 13 up/down and not 15 as I had. But this makes the gaps smaller, so probably as good as i gets…
Cicles center start.shapr (36.1 KB)

Your drawing has several double lines, two circles or more at the same position.
Select one circle and then delete, if you still see a circle, there where 2 or more of them….that make your drawing much slower to load…And might be an issue for cutting…

Yeah. I started out in center and copied radially, but once the pattern became clear, I switched to copying lines/rows instead, so there was some overlap.
This is just POC state, so it all needs to be cleaned up. But thanks for pointing it out.

157 pieces

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As this is a 3D program the question could be: how many spheres of the smaller diameter in a sphere of the larger diameter…all very Platonic…

Thanks. But the first one you made had 163 didn’t it?

I think we can call it done now. :slight_smile:

If anyone is interested in the “product”, this is what it’s for. Just a bigger version. About 20 times more thrust.