August 25, 2016
How Many Ping-Pong Balls Can Fit in a Table Tennis Club?
Today's topic is scary. We're talking something that will leave many readers shaking with fear, sweating like David Sakai, and plucking their eyeballs out as they scream, "No! For God's sake, Stop!" Yes, today we're going to use math. (You have my permission to skip the math part and just read the paragraphs that give conclusions.)
How many ping-pong balls can you fit in your table tennis club? It's a simple matter of working out volume with the sphere packing formula. As we all know (after reading the Wikipedia entry I just linked to), as volume goes up and the size of the balls (sphere) goes down, the packing efficiency approaches the following density, which I'll call the Packing constant (P). (Hopefully, in my formulas below, the subscripts and superscripts will come through properly on your browser.)
P = π/[3x(2)^½] = ~0.74048
So how can we use this?
- Let Nd = number of balls of width d that will fit in your club.
- Let C = volume in cubic inches of your club.
- Let B = volume of the balls in cubic inches.
Then the number of spheres (N) you can fit inside a given volume approaches the following:
Nd = (C/B)xP = maximum number of spheres you can fit inside your club.
To get C, you simply get the volume in cubic inches of your club. This is easy if it is roughly rectangular shaped. (We're using inches and feet here, since I live in archaic America, which hasn't adopted the metric system.) Multiply your club's dimensions in feet – length x width x height – and then multiply by 1728 (number of cubic inches in a cubic foot) to get cubic inches for your club.
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