# how to determine how many wires through given diamter

Hello, I have a bunch of set diameter tubes which need to fit inside another tube tightly. The numbers needed prevent getting them together and
measuring the diameter so how could i find out what the inner diameter of the outer pipe should be with x number of inner pipes with diameter of D? Hope thats clear, Thanks in advance
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izzi4 wrote:

try here:
http://www.stetson.edu/~efriedma/packing.html
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Steve Walker
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"izzi4" wrote: (clip) how could i find out what the inner diameter of the outer pipe should be with x number of inner pipes with diameter of D? (clip) ^^^^^^^^^^^^^^ Hexagons pack tightly to form a honeycomb pattern. Each hexagon can have an inscribed circle, which will be tangent to all the inscribed circles around it, so the circles pack with the same density as the hexagons. So, I would lay out a honeycomb pattern with the correct number of circles/hexagons. Then find the smallest circle which can fit over the cluster of inscribed circles. This could be done graphically, or it could be calculated.
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7 is the smallest number of largest diameters that can fit inside a given circle. 3 times the small circle diameter equals the outer circle's diameter. I s'pose you could do something recursive on this (-: or follow the hexagon layout suggestion given earlier, 7 / 3 is just a special case of that.
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Back when I was a cable design engineer, at the age of 19, we derived this information graphically. We drew the theoretical sizes in a 5:1 scale and then scaled the result. We were right nearly as often was we were wrong so the company always ordered the jackets after the cable had been laid up. With cables the tigher the lay pattern the biger the jacket had to be. I don't know about your situation. Leigh at MarMachine
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Once you do that, figure out how many items of *different* diameters can fit inside a given circle.
Then do it in three dimensions!
Jim
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Your problem is a generalization of the Soddy Circle problem. For more information on Soddy Circles and related problems, see:
http://mathworld.wolfram.com/SoddyCircles.html
Regards, Marv
Home Shop Freeware - Tools for People Who Build Things http://www.geocities.com/mklotz.geo
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