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Some of you might remember the remarkable…
Packing fraction of M&Ms: 66.5% -- "Improving the Density of Jammed Disordered Packings Using Ellipsoids" Aleksandar Donev, Ibrahim Cisse, David Sachs, Evan A. Variano, Frank H. Stillinger, Robert Connelly, Salvatore Torquato, and P. M. Chaikin, Science 303, 990-993 (2004) (69.5% for minis)
Volume of M&M : 0.715ml
Volume of that Jar 1150ml
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This is really cool. The only thing I don't understand is how you integrate the 66.5% packing fraction into the problem to get the exact number. I'd love it if you could either explain it on here, or shoot me an e-mail.
Andrew K, the packing fraction is the ratio of the actual volume of packed M&Ms to the total volume of the container. 66.5% of the space in the jar is actually occupied by M&Ms, while the rest is filled with air. The jar is 1150 mL, of which 66.5% is M&Ms:1150 * 66.5% =~ 765 mL of raw M&Ms.Each M&M has a volume of 0.715 mL:765 / 0.715 =~ 1070 M&Ms
Yuffles is right. I did mine in this order:
1150 / 0.715 =~ 1608
1608 * 66.5% or 0.665 =~ 1069
I'll definitely take notes.
@Andrew K
it's basic math, but you won't get the exact number, just a really good approximation.
You can combine steps and multiply the volume of the container by .93
Presumably this formulation only works for containers that have no part of their volume smaller than the larger diameter of the object being packed. (For example, a piece of aerogel might have a large total empty volume, but you can't jam an M&M into it.)
That's all v interesting but can someone explain
- how elipsoids like m+m's actually pack - ie what is their optimum close configuration (eg one atop another like and side by side like in an abacus);
- if m+m;s just drop into a jar how will they approximate to the optimum configuration; and
- will shaking the jar approach the optimum configuration or is their a more "scientific" way?!
That 66.5% packing fraction is suspiciously close to 2/3. Coincidence?
@Rob Lewis: it has to be. If it was 3/3, then it would be a 3M chemical and not candy.
Do you measure the radii of the M&Ms in millimeters?