Given a cylinder of radius $R$ and length $L$, I need to find the number of spheres which is possible to pack into the cylinder as a function of the radius $\rho$ of the spheres. I found something about the problem of packing into cubes or other solids, but nothing in a cylinder. Does someone know the solution? Thanks.
Problem of packing spheres of radius $\rho$ into a cylinder
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geometry
packing-problem
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1As long as $\rho \geq 2R/(2+\sqrt{3})$, all optimal packings follow the same strategy: you can view it as the 2-dimensional problem of packing circles into a tall rectangular strip, with the circles touching the left and right walls alternately. In this case, you can get a formula. For smaller $\rho$, the problem will be very complicated, like most packing problems, and is certainly unsolved in general; the best you could hope for are upper and lower bounds. A simple upper bound is given by the result that spheres can fill no more than $74.048\ldots$ percent of space under any packing. – 2012-03-20
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This is what you need. It includes numerical results up to $\rho$/R of about 2.9.
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0the above mentioned paper is not accessible. Is it possible to get a free version of the material – 2014-08-15