Originally Posted by
Walter
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Whatever size you choose for the biggest "pebble", make the next size 1/5 the size/diameter. If you consider the pebbles as perfect spheres, the smaller one will just fit in the gap in a tetrahedral packing.
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You didn't tell us how much of the smaller size to use. My math tells me that it is a very small amount. If there is one gap for each pebble in the larger size, then there will be one grain of the smaller size for each pebble. Assuming that the pebbles and the smaller grains have the same density, the weight will go as the cube of the diameter. So for each pound of the pebbles, you will need (1/5)*(1/5)*(1/5) pounds of the smaller size. That's 1/125 of a pound, which isn't very much.
Assuming we use a third size, how big should that be? I believe it is *larger* than 1/5 of the smaller size. Also, how much of it should be used? I would guess that my calculation above would still be correct.
So much for the math. In fact, though, because you cannot hope to get perfect tetrahedral packing, the numbers are probably way off.
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Does anyone know what the "right" numbers are?
Ken
Kenneth Lerman
55 Main Street
Newtown, CT 06470