(1) a typical coin measures slightly more than 1" in diameter, 1/10" thick.
(2) a cubic foot holds approx 12,000 stacked coins (stacked, not loose)
(3) a cubic foot of loose coins fills approx 5 feet x 5 feet x 1/2" depth, or 3 feet x 3 feet by 1".
Working backwards;
(3) is OK:
One cu ft has 1728 cu in;
5 ft x 5 ft x 0.5 in
60 in x 60 in x 0.5 in
1800 cu in
3 ft x 3 ft x 1.0 in
36 in x 36 in x 1.0 in
1300 cu in
The first figure is probably close enough for gov't work;
it's a little low once you throw in the packing density.
The second figure is somewhat low, expecially when packing
is thrown in (a depth of 1.5 in probably is more correct,
with packing), but still close enough.
(2) is a bit off -- for stacked coins:
Working from the coin volume:
pi * (0.5 in) ^ 2 * 0.10 in
yields
0.075 cu in / coin
As a side note, based on this, a 75% packing should easily be
possible for stacked coins.
One cu ft has 1728 cu in; 0.075 cu in / coin gives us:
23,000 coins / cu ft [1.00 pack]
17,000 coins / cu ft [0.75 pack] (about)
That's with a simple rectangular stack, which is less dense than a
hexagonal pack.
(1) Doesn't jive with the figure of 50 coins / lb:
Working from 18 ct yellow gold @ 1000 lbs / sq ft:
1000 lbs / (12 in) ^ 3
1000 lbs / 1728 cu in
Or,
0.58 lb / cu in
1.72 cu in / lb
Coin densities work out to:
13.3 coins / cu in [1.00 pack]
10.0 coins / cu in [0.75 pack]
That is:
17.2 coins / lb (18 ct yellow gold)
For silver, one has:
Silver SG: 10.5 gm / cc
However, this example doesn't use pure gold; instead,
"18 ct yellow gold" is used, with about 5/6 the density
of pure gold:
Gold SG: 19.3 gm / cc
18 CT Gold SG: 16.1 gm /cc
That gives:
26.4 coins / lb (Silver)
There is a little improvement with tin, copper, and electrum:
Tin SG: 7.3 gm /cc
Electrum SG: 8.5 gm /cc
Copper SG: 8.9 gm / cc
Giving coin yields:
38.0 coins / lb (Tin)
32.6 coins / lb (Electrum)
31.1 coins / lb (Copper)
Allowing for further adulteration of the gold, the following
seem reasonable:
gold: 20 coins / lb [orig: 17.2]
silver: 30 coins / lb [orig: 26.4]
copper: 35 coins / lb [orig: 31.1]
tin: 40 coins / lb [orig: 38.0]
I've deliberately asjusted the counts high to allow for alloys
with lighter, lesser value metals.
