--> Introduction & Abstract
You may recall from a year ago that I was conducting an experiment to
maximize the savings of my piggy bank, and had calculated the value-
density of the 7 circulating US coins. Please accept this re****t of the
experiment's first trial completion. The result suggests using coins of
greater value-density in constant-volume collection vessels.
--> Background.
Here's a link to the original post, from 2002/09/11:
http://tinyurl.com/mav6
Message-ID: <MPG.17e9cfaa60251e4e989695%40news.seanet.com>
--> Method.
Vaguely proposed in that thread was the experiment which I have now
completed: I would fill the piggy bank only with the three coins of
common value-density, but with random pro****tions that match my pocket
change, which will hopefully reflect the circulation of the coins
themselves though I won't think too hard on that.
--> Data.
Now it is very nearly 1 year later and as of 2003/08/31 I have filled to
the brim my piggy bank with dimes and quarters primarily, and while I
got wishy-washy[1] about half-dollars (the same value-density as dimes
and quarters) -- much larger and presumably less stackable than dimes
and quarters, and Sacagawea "golden" dollars -- which are quarter-sized
but thicker, and much denser.
I was going to sort and count the coins myself, but then my employer, a
non-profit, received as a donation a old 1980's sorting machine, a
***mins Jetsort. Here's a link to the modern equivalent model; ***mins
is now ***mins-Allison, and the Jetsort interface has grown up quite a
bit, but I prefer the Reagan-era buttons and 2-line LCD display to this
modern version:
http://www.***minscurrency.com/sort_4000.htm
I'm not going to miss a chance to use a new gadget, even if it meant
hauling 12.8 pounds (calculated weight) of coins to work (a 20-minute
walk). And the sorter only bags the coins (how often do you get to see
actual bags of money with dollar signs on the side?), so after the very
rapid count (less than 2 minutes) I walked home with 12.8 pounds of
coins in 2 bags and a pocket, to be rolled. Here's the count, absent
coins omitted:
--> Chart A: Coins Recovered from Sample Vessel
2*# pennies $ 0.02
599 dimes $ 59.90
2* nickels $ 0.10
769 quarters $192.25
4# Kennedy half-dollars $ 2.00
4# Sacagawea dollars $ 4.00
-------
For a grand total of $258.27
* The pennies and nickels I recall putting in there by mistake, but
there wasn't a good way at the time to get them out, and it was only two
coins.
# manually counted
--> Qualification of results and measurement of an independent data
point.
As in the last post, I'm using the US Mint figures from
http://www.usmint.gov/about_the_mint/index.cfm?
action=coin_specifications
for thickness, diameter, and weight of the coins. You may recall that
this produced some discrepancies in the value-density of dimes,
quarters, and Kennedies, because of the reeds or notches cut into the
edges of those coins. A poster from rec.collecting.coins informed us
that the reason for this common value density is that when initially
minted, they were given the volume of an equivalent amount of silver for
their value, or something like that.
Here's what the Mint has to say on the topic of reeds:
http://www.usmint.gov/about_the_mint/fun_facts/index.cfm?
action=fun_facts10
Back to the experimental data, we have it that the total volume used by
coins in the piggy bank come to 837.9 ccs. I filled the bank with
measured amounts of water[2] (because it's easier than measuring water
poured out of the bank), as prescribed in the previous thread. I came
up with 5 cups 11 tablespoons, which is 91 tablespoons, which in turn is
1345.6 cubic centimeters according to Google Calculator.
--> Calculations:
So the experimental result for packing density is p=0.623: the coins
used 62.3% of the available volume. At this point I should remind the
reader that our own Eb Oesch investigated the theoretical elements of
ideal coin-packing in this thread from October of last year, which makes
for brief and interesting reading, unlike my posts in either respect:
http://tinyurl.com/mav7
Message-ID: <903f6dfe.0210131441.3d65e5fb@[EMAIL PROTECTED]
>
--> Chart B, The Value of Bank Volume Filled With Different Coins
Coin Value/volume Volume Value Value
($/cc) used (cc) Full Packed
Penny 0.023 0.884 $30.46 $18.99
Nickel 0.073 1.378 $97.65 $60.87
Dime 0.294 203.724 $395.64 $246.63
Quarter 0.309 622.065 $415.86 $259.23
Half-Dollar 0.316 6.329 $425.24 $265.08
Dollar 0.907 4.412 $1,219.84 $760.40
--> Notes on Chart B:
Volume used is the amount of room in the bank taken by coins in the
experiment.
Value Full is the value of a piggy-bank full of coin homogenate for each
particular coin filling 100% of the measured volume set. Value Packed
is the same result if the homogenate fills only 62.3% of the volume.
Round down to the coins increment for a number that makes sense.
Obviously each coin will fill a different percentage of the ellipsoidal
cavity in the piggy bank, so from left to right, the numbers get
increasingly meaningless.
--> Some More Number Fudging.
Note that the experimental result of $258.25 comes in right where it's
supposed to, just below the quarter value, and just a little above the
average value (packed) of dimes-quarters-half-dollars, $256.83, as
expected, since the dollar coins' concentrations of value outweigh the
dilution of value due to the nickels.
--> Sample Handling.
It only took about an hour to roll the 1362 coins that made up 12 rolls
of dimes (added one dime) and 19 rolls of quarters (7 remained). The
easy way is to make stacks of 25 dimes or 20 quarters, and then just
make stacks of coins with the same height. I watched David Byrne's
movie "True Stories" while I did this. Now I've just gotta haul those
to the bank, or sell them to people who need them for laundry, phone
calls, newspapers, flathead screwdrivers, shotgun ammunition, arcade
games, etc.
--> Future Research.
I'm considering running another trial, as it's sure nice to find
yourself in possession of a spare $250, just before gaming season.
Homeworld 2, Half-Life 2, and Halo PC are all coming out in the next
couple of months[3], and those'll be $50 a hit. I'm almost inclined to
try an all-quarters trial or an all-dimes trial, but dimes are less
common in my pocket change, and I feel like a doofus (as I have twice
already) bringing rolls of coins to the bank and asking for rolls of
coins in return. I don't even bother angling for the cute teller when
that's all I've got for them to do.
I could probably use some money to register some of the software I use
all of the time, for example the editor I'm using right this minute,
Textpad. (I know, I know, get a vim, get an emacs, get a life, I've
heard it all.)
--> A Proposal.
Also, I'd like to note that SCIENCE! should look into finding more
research op****tunities like this, which are composed and fueled by
waste-money, pocket change, and therefore is not only self-funding, but
actually produces real money from the dregs of currency known as small
coins.
Your in Science,
-LAN3
[1] I put some in, I left some out, thereby further contaminating both
this experiment and the less substantial one, which was "how long does
it take to fill the bank with all of my coins" (which was why I would
save my nickels and pennies and when possible exchange them for dimes
and quarters)-- but I'd have to go through my bank records to find the
other three times I'd filled my bank with the random assortments of
coins. Between 2002/09/11 and 2002/08/31, in addition to the above, I
collected $5.56 in pennies, nickels, half-dollars and dollars.
[2] I regret that I did not have enough rice around to use a solid-
measure estimation technique that I thought of. I'd like to be able to
tell people, in Ranjit's words, that I "rice[d] my pig"
[3] Remember: Gamers Have Two Jobs.
http://www.penny-arcade.com/view.php3?date=2001-11-14
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