# Packing fractions

#### marmot

Hey. I have a question. What is the packing fraction of a container full of randomly jammed cylinders? Also, does the packing fraction depend on the ratio of the radius to height of the cylinder? There is some contest of finding certain amount of cylindrical objects inside a container (I cant weight it) and I know that for certain shapes, you can use the packing fraction to estimate (Spheres have a random packing of .64). I already planned the way I am doing this (finding volume, size of discs, etc) and this would be perfect with the packing fraction of cylinders. Youll help me loads.

Thanks

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#### CompuChip

Homework Helper
Isn't the packing fraction just the filled volume divided by total volume?
So it would depend on the radius and height of the cylinders, and how many of them there are. If you have N cylinders of radius r and height h in a container of volume V then the packing fraction is
$$\eta = N \pi r^2 h / V.$$

Ah, sloppy reading from my part. I guess your actual question is: if we throw in with randomly oriented cylinders until no more can be fitted in the volume, what is the expectation value of N?[/edit]

#### marmot

Exactly. The random packing fraction of a shape depends greately on its degrees of freedom and "contact point". It is used a lot in thermodynamics but you can use it to find the number of randomly packed things in a container too. It is different from "closest" packing fraction, which would be the most efficient way to pack a certain shape.

Here is a paper on jammed MandMs:

http://www.cims.nyu.edu/~donev/Packing/JammedMM.pdf