If this is your first visit, be sure to check out the FAQ by clicking the link above. You may have to register before you can post: click the register link above to proceed. To start viewing messages, select the forum that you want to visit from the selection below. |
|
|
Thread Tools | Display Modes |
#1
|
|||
|
|||
Maximizing the Piggy Bank: RESULTS
-- 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 report 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 proportions 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 Cummins Jetsort. Here's a link to the modern equivalent model; Cummins is now Cummins-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.cumminscurrency.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 $258.27 * The pennies and nickels I recall putting in there by mistake, but there wasn't a good way at the time to get them out, and it was only two coins. # manually counted -- Qualification of results and measurement of an independent data point. As in the last post, I'm using the US Mint figures from http://www.usmint.gov/about_the_mint/index.cfm? action=coin_specifications for thickness, diameter, and weight of the coins. You may recall that this produced some discrepancies in the value-density of dimes, quarters, and Kennedies, because of the reeds or notches cut into the edges of those coins. A poster from rec.collecting.coins informed us that the reason for this common value density is that when initially minted, they were given the volume of an equivalent amount of silver for their value, or something like that. Here's what the Mint has to say on the topic of reeds: http://www.usmint.gov/about_the_mint...cts/index.cfm? action=fun_facts10 Back to the experimental data, we have it that the total volume used by coins in the piggy bank come to 837.9 ccs. I filled the bank with measured amounts of water[2] (because it's easier than measuring water poured out of the bank), as prescribed in the previous thread. I came up with 5 cups 11 tablespoons, which is 91 tablespoons, which in turn is 1345.6 cubic centimeters according to Google Calculator. -- Calculations: So the experimental result for packing density is p=0.623: the coins used 62.3% of the available volume. At this point I should remind the reader that our own Eb Oesch investigated the theoretical elements of ideal coin-packing in this thread from October of last year, which makes for brief and interesting reading, unlike my posts in either respect: http://tinyurl.com/mav7 Message-ID: -- Chart B, The Value of Bank Volume Filled With Different Coins Coin Value/volume Volume Value Value ($/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 opportunities 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 |
Ads |
#2
|
|||
|
|||
Chart B was pretty good.
But in the section "-- Conclusions", did you forget the part where it's time to discontinue cents and nickels, and start using dollar coins?? ;-) --Dave Louis Nick III wrote: -- 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 report 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 proportions 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 Cummins Jetsort. Here's a link to the modern equivalent model; Cummins is now Cummins-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.cumminscurrency.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 $258.27 * The pennies and nickels I recall putting in there by mistake, but there wasn't a good way at the time to get them out, and it was only two coins. # manually counted -- Qualification of results and measurement of an independent data point. As in the last post, I'm using the US Mint figures from http://www.usmint.gov/about_the_mint/index.cfm? action=coin_specifications for thickness, diameter, and weight of the coins. You may recall that this produced some discrepancies in the value-density of dimes, quarters, and Kennedies, because of the reeds or notches cut into the edges of those coins. A poster from rec.collecting.coins informed us that the reason for this common value density is that when initially minted, they were given the volume of an equivalent amount of silver for their value, or something like that. Here's what the Mint has to say on the topic of reeds: http://www.usmint.gov/about_the_mint...cts/index.cfm? action=fun_facts10 Back to the experimental data, we have it that the total volume used by coins in the piggy bank come to 837.9 ccs. I filled the bank with measured amounts of water[2] (because it's easier than measuring water poured out of the bank), as prescribed in the previous thread. I came up with 5 cups 11 tablespoons, which is 91 tablespoons, which in turn is 1345.6 cubic centimeters according to Google Calculator. -- Calculations: So the experimental result for packing density is p=0.623: the coins used 62.3% of the available volume. At this point I should remind the reader that our own Eb Oesch investigated the theoretical elements of ideal coin-packing in this thread from October of last year, which makes for brief and interesting reading, unlike my posts in either respect: http://tinyurl.com/mav7 Message-ID: -- Chart B, The Value of Bank Volume Filled With Different Coins Coin Value/volume Volume Value Value ($/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 opportunities 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 |
Thread Tools | |
Display Modes | |
|
|
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
FA: Terrific Ceramic Piggy Bank | Liz@Mamie's Rich Memories | General | 0 | March 8th 04 12:39 AM |
Bank charges for rolled coin deposits | Ric Burney | Coins | 16 | August 23rd 03 07:45 PM |
Bank money bag - any value? | Scottishmoney | Coins | 1 | August 18th 03 04:53 AM |
Bank wrapped rolls | Bill Krummel | Coins | 11 | August 12th 03 02:03 AM |
MS69 1982 George Washington Halves TeleTrade results and population trivia.. | Harv | Coins | 24 | July 29th 03 08:47 PM |