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Posted: 7/16/2013 7:16:33 AM EST
.45ACP Calculate how many circles of diameter .480" can fit into a 48" x 30" rectangle.
9mm
Calculate how many circles of diameter .392" can fit into a 48" x 30" rectangle. The math is way beyond me.
I'm a .45 fan, but was thinking a smaller round like 9mm would give me more detail on the design.
Going to be making a glass covered coffee table, with a sort of mural design done with spent casings under the glass.



Classic 'packing problem'.
You should be able to find the solution online for circles in a rectangle. They can be a real PITA to solve from scratch. 


Thanks for the post!



Originally Posted By Dascarecrow72:
Thanks for the post! View Quote It depend on the length to width ratio of the rectangle. www.math.ucsd.edu/~ronspubs/03_01_circles_in_rectangles.pdf It is far from a simple problem. 


.45 ACP close to 6200
9mm close to 9300 


Thanks guys.



Originally Posted By rcb1586:
That is correct if you place them in a simple square pattern like they come in factory boxes. It gets more complicated if you stack them in a hexagonal pattern such as this. I came up with a over 7000 for 45. I didn't do the calculations for 9mm. http://upload.wikimedia.org/wikipedia/commons/6/69/Circle_packing_%28hexagonal%29.svg View Quote View All Quotes View All Quotes Originally Posted By rcb1586:
Originally Posted By InfiniteGrim:
.45 ACP close to 6200 9mm close to 9300 That is correct if you place them in a simple square pattern like they come in factory boxes. It gets more complicated if you stack them in a hexagonal pattern such as this. I came up with a over 7000 for 45. I didn't do the calculations for 9mm. http://upload.wikimedia.org/wikipedia/commons/6/69/Circle_packing_%28hexagonal%29.svg Depends on the length to width ratio of the rectangle. If it does not match the hexagon dimensions you run into problems. The best method is probably to arrange the cases and THEN decide on the table dimensions, not the other way around. 


Originally Posted By brickeyee: Depends on the length to width ratio of the rectangle. If it does not match the hexagon dimensions you run into problems. The best method is probably to arrange the cases and THEN decide on the table dimensions, not the other way around. View Quote View All Quotes View All Quotes Originally Posted By brickeyee: Originally Posted By rcb1586: Originally Posted By InfiniteGrim: .45 ACP close to 6200 9mm close to 9300 That is correct if you place them in a simple square pattern like they come in factory boxes. It gets more complicated if you stack them in a hexagonal pattern such as this. I came up with a over 7000 for 45. I didn't do the calculations for 9mm. http://upload.wikimedia.org/wikipedia/commons/6/69/Circle_packing_%28hexagonal%29.svg Depends on the length to width ratio of the rectangle. If it does not match the hexagon dimensions you run into problems. The best method is probably to arrange the cases and THEN decide on the table dimensions, not the other way around. Need to sketch it out to see what my design will work with I guess.
Thanks again, maybe i'll see if i can round up a couple thousand and see where I'm at haha.



If you measure carefully (as in caliper) you could likely scale from a smaller size of tight pack.
You just will not be able to not later the length/width ratio from your smaller 'test' section. 


Originally Posted By rcb1586:
That is correct if you place them in a simple square pattern like they come in factory boxes. It gets more complicated if you stack them in a hexagonal pattern such as this. I came up with a over 7000 for 45. I didn't do the calculations for 9mm. http://upload.wikimedia.org/wikipedia/commons/6/69/Circle_packing_%28hexagonal%29.svg View Quote View All Quotes View All Quotes Originally Posted By rcb1586:
Originally Posted By InfiniteGrim:
.45 ACP close to 6200 9mm close to 9300 That is correct if you place them in a simple square pattern like they come in factory boxes. It gets more complicated if you stack them in a hexagonal pattern such as this. I came up with a over 7000 for 45. I didn't do the calculations for 9mm. http://upload.wikimedia.org/wikipedia/commons/6/69/Circle_packing_%28hexagonal%29.svg Yeah maybe I should have said mine was an estimate, basically an absolute minimum needed number. 


Originally Posted By brickeyee: Depends on the length to width ratio of the rectangle. If it does not match the hexagon dimensions you run into problems. The best method is probably to arrange the cases and THEN decide on the table dimensions, not the other way around. View Quote View All Quotes View All Quotes Originally Posted By brickeyee: Originally Posted By rcb1586: Originally Posted By InfiniteGrim: .45 ACP close to 6200 9mm close to 9300 That is correct if you place them in a simple square pattern like they come in factory boxes. It gets more complicated if you stack them in a hexagonal pattern such as this. I came up with a over 7000 for 45. I didn't do the calculations for 9mm. http://upload.wikimedia.org/wikipedia/commons/6/69/Circle_packing_%28hexagonal%29.svg Depends on the length to width ratio of the rectangle. If it does not match the hexagon dimensions you run into problems. The best method is probably to arrange the cases and THEN decide on the table dimensions, not the other way around. I agree. That's how I would do it as well.


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Originally Posted By Dascarecrow72:
.45ACP Calculate how many circles of diameter .480" can fit into a 48" x 30" rectangle. 9mm Calculate how many circles of diameter .392" can fit into a 48" x 30" rectangle. The math is way beyond me. I'm a .45 fan, but was thinking a smaller round like 9mm would give me more detail on the design. Going to be making a glass covered coffee table, with a sort of mural design done with spent casings under the glass. View Quote So the 48 inch side can hold .48/.48=100 rounds the 30 inch side can hold 30/.48=62.5 rounds No 62.5*100=6250 rounds For 9mm 48/.392=122 30/.392=76 122*76=9272 rounds 


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