How smaller circles will fit inside one big circle?

My question is realted to construction in the cellular phone tower
industry.  I would like a formula or equation to determine how many 6"
Circles (Conduits) will fit inside one larger 26" circle (Monopole)?
I would like to be able to figure this out in the future with
different dimensions (inches).

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Request for Question Clarification by pafalafa-ga on 26 Nov 2005 06:54 PST

Apparently, there's no straightforward formula for this
tricker-than-you'd-expect math problem.

There are some sites you can visit which provide answers for a range
of diameters, however.

Try this one:


http://www.stetson.edu/~efriedma/cirincir/
Circles in Circles


For the case you mentioned, 6" conduits inside a 26" pipe, the ratio
of the diameters is:

26/6 = 4.333

which should allow you to get 14 conduits in the pipe.


This is because the value shown for 14 circles is r = 4.328 (smaller
than 4.333), while the next value up -- at 4.521 -- is a bit too
large.


I'm assuming, of course, that the 26" is the *inside* dimension of the pipe.


The above link should give you some good rules of thumb for at least
20 conduits in a pipe, with the smaller diameter being about one-fifth
the size of the larger pipe.

Larger ratios than 1:5, however, and you're on your own!


Does that help?


pafalafa-ga

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Request for Question Clarification by pafalafa-ga on 26 Nov 2005 07:54 PST

Here's another table that will cover you up to hundreds of circles-in-a-circle:


http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html


It's intended for mathmeticians and programmers, but the use of the
table is the same as above.  Find your ratio, and then look up the
ratio in the table that's just smaller than the one you're dealing
with.

The number in the N column, on the left hand side, is the number of
circles that will fit... a ratio of 4.333, again, gives an answer of
14 circles.

paf