MoneyBox/DensityAnalysis
Density Analysis of australian coinage
ie, how much value of a given coin can you fit inside, say, 1litre of space?
So what are we dealing with:
- 1litre = 1000cm^3 of volume = 1,000,000 cubic mm
Australian coin sizes: (see: http://www.worldmints.com/ccoin_ram.asp) (note that diameter is the specified, but thickness is the maximum legal allowed)
- 5c
- diameter: 19.41mm, thickness: 1.55mm
- 10c
- 23.6mm, 1.98mm
- 20c
- 28.52mm, 2.52mm
- 50c
- 31.51mm (across flats), 2.8mm
- $1
- 25mm, 2.8mm
- $2
- 20.5mm, 3mm
Contents |
How to calculate =
There are three estimates easily possible.
- Count of coins for maximum displacement within our 1litre limit (1litre divided by volume per coin)
- Same as before, but assume coins are square with edge length equal to diameter. Simulates stacks arranged in a grid
- Same as before, but assume coins are hexagonal and stacked in a hex lattice.
In the real world, coins are unlikely to be stacked, and in my estimate, are likely to be slightly more efficiently packed in than even the simulated hex lattice.
- Volume of coin
- (pi*r^2) * thickness
- Volume of squared coin
- d^2 * thickness
- Volume of hexed coin
- ((sqrt(3)*d^2)/2) * thickness
5c
real coins
- 1.55*pi*9.705^2 = 145.99*pi = 458.638 cubic mm
- This gives us 2180 coins to occupy 1litre of space.
Squared coins
- 19.41^2 * 1.55 = 583.96 cubicmm
- This gives us now only 1712 coins.
Hexed coins
- ((sqrt(3)*19.42^2)/2)*1.55 = 506.245 cubic mm
- This now gives us 1975 coins.
Conclusion
In the real world, you might get lucky to squeeze 2000 5c coins into your 1litre container - or just on $100
10c
real coins
- 1.98*pi*(11.8^2)= pi*275.7 = 866.12 cubic mm
- This gives us 1154 coins to occupy 1litre of space.
Squared coins
- 23.6^2*1.98 = 1102.8 cubic mm.
- This now gives us only 906 coins
Hexed coins
- ((sqrt(3)*23.6^2)/2)*1.98 = 955.036 cubic mm
- This gives us 1047 coins into our million cubic millimetre volume.
Conclusion
In the real world, you can probably get about 1000 10c coins into a 1litre container - or $100.
In an actual test however, 750 coins ($75) left little room available, and as coins become available, I doubt I'll get more than 800 in there.
20c
real coins
- 2.52*pi*(14.26^2)= pi*512.436 = 1609.86 cubic mm
- This gives us 621 coins to occupy 1litre of space.
Squared coins
- 28.52^2*2.52 = 2049.744 cubic mm.
- This now gives us only 487 coins
Hexed coins
- ((sqrt(3)*28.52^2)/2)*2.52 = 1775.13 cubic mm
- This gives us 563 coins into our million cubic millimetre volume.
Conclusion
In the real world, you might get lucky to squeeze 600 20c coins into your 1litre container - or $120
$1
real coins
- 2.8*pi*(12.5^2)= pi*437.5 = 1374.45 cubic mm
- This gives us 727 coins to occupy 1litre of space.
Squared coins
- 25^2*2.8 = 1750 cubic mm.
- This now gives us only 571 coins
Hexed coins
- ((sqrt(3)*25^2)/2)*2.8 = 1515.54 cubic mm
- This gives us 659 coins into our million cubic millimetre volume.
Conclusion
In the real world, you're gonna be looking at around 600-650 coins. I'm not gonna even pretend I need to work out the dollar value here.
$2
real coins
- 3*pi*(10.25^2)= pi*315.19 = 990.19 cubic mm
- This gives us 1009 coins to occupy 1litre of space.
Squared coins
- 20.5^2*3 = 1260.75 cubic mm.
- This now gives us only 793 coins
Hexed coins
- ((sqrt(3)*20.5^2)/2)*3 = 1091.84 cubic mm
- This gives us 915 coins into our million cubic millimetre volume.
Conclusion
- You're probably looking at the 950 coins mark if you're lucky, or $1900 work :)
