I am trying to calculate the packing density of cylindrical bottles in a box, assuming that the bottles are randomly dumped in the box.


I have read on the packing density of spheres here <https://en.wikipedia.org/wiki/Random_close_pack>
but have found nothing on cylinders.


For example, if I randomly dump bottles with a diameter of 75 mm and a height of 145 mm in a volume of 0.6 cubic meters, what would be the packing density (the end goal is to calculate how many bottles could approximately fit in such a space).



Random packing density of cylinders in a volume
An overview of results for the random packing densities of basic 3D objects, including cylinders, is given in [this article](http://link.springer.com/article/10.1007/s11434-009-0650-0) (2010). Here is the plot for cylinders as a function of aspect ratio (height over diameter):


![](https://ilorentz.org/beenakker/MO/cylinders.png)


The peak value of 0.72 is reached for an aspect ratio of 0.9. These are numerical results. The maximum (rather than random) packing density of cylinders is the densest ordered packing of circles in 2D, which is $(\pi/6)\sqrt 3=0.9069$.


