Funny Penny Math - Coin Community Forum

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Author	Replies: 14 / Views: 2,481
shadz Pillar of the Community 1325 Posts	Posted 09/28/2015 11:55 am So we have all heard it "blahblahblah remove the penny and maybe the nickel...." I have said many times "blahblahblah keep the penny and make it a better/cheaper way..." Well in my interest to do such I started with the idea to make a dime sized penny, and a penny sized nickel with existing material only changing the size. Well that worked and the coins seemed they would be cheaper, but the nickel sized dime went wonky. The cost of the dime was increased such that it would cost more to make coins of higher denominations to be larger in size (diameter only) but made of the same stuff. So I thought I would perform some mental metallurgy olympics and see what the costs would be at current to not only change the sized, but the contents to aluminum for the lower "silver" coins. First working with the penny with the information provided. now metal weighs more based on something called "specific gravity", "specific density", or more recently it seems just "density" since they are elements on the periodic table. Well I was working with just the sizes, not the mass and to come up with if the new coin was viable you would need to know if it will be heavy enough as a coin. For those that don't like all the math and since, its TOO LATE TO TURN BACK NOW CAUSE HERE IT IS! Scroll down while you still have a chance to the next part! Copper has a density of 8.96 Zinc has a density of 7.14 Aluminum has a density of 2.7 this means that aluminum is the lightest/less dense of the 3. If you have 1 square inch cube of each copper will weigh slightly more than zinc, and zinc would weigh almost 3 times that of aluminum! So in preparing to continue the math anyway even though it could make the 2.5 gram penny weigh only 0.8 grams relatively, I started preparing the spreadsheet for calculations. First I started with the volume of material based on US Mint provided information. Now, those that don't like math, I am going to spare you a bit and not show everything but give everyone the same tools to work with for those that may want to play with the math. US Mint says about the penny: 2.5 grams 19.05 mm diameter 1.52 mm thickness 2.5% copper 97.5% (inferred) zinc So to make sure my math is correct I try to find the grams based on the volume and the above density. The resulting volume of a cylinder with those percentages of those elements yields a coin with the mass of: 3.11 grams I quickly run to CCF US Coin Facts to look up a pre-1982 penny specs. Anyone want to guess what I find? Quote: Lincoln Memorial cent 1959 - 2008 Weight: 3.11 grams At this point my brain explodes. I spend an hour walking around and cleaning up the mess and getting a replacement installed and come back to double check the modern penny here to see if it matches US Mint weights. Quote: 2010 - Present Lincoln Shield Cent Weight: 2.5 grams But wait (no pun intended) what is this? Quote: Content: Core: 99.2% Zinc, .8% Copper - Plating: 100% Copper - Overall: 97.5% Zinc, 2.5% Copper Well that's news to me! But to prepare my math to make sure I have it right so I can arrive at 2.5 grahams, I am missing info and so is everyone else it seems. I searched the web for the missing info: How much of the coin is the core? How much of the copper is in the core? this bronze of zinc and copper will have a new density and therefore a new weight (read mass) to change it from 3.11 to 2.5 grams. Where is this at? Nobody had it that I could find....until now! the core of a penny is 98.28629% of the coin, bronze the plating is 1.71371% of the coin, "pure copper" the copper in the core is .0078629% of the coin we already knew the amount of zinc in the core (all of it) 97.5% of the coin now it becomes 2.5 grams for the whole coin! Anyone want any other figures maybe for teaching or entertainment purposes? How funny would it have been if it was pure copper plating and pure zinc core so that they were 3.11 grams as every penny before it. Why isn't it 3.11 grams like every one before it? Edited by shadz 09/28/2015 11:58 am Report this Post to the Staff

ChildOfTheWheat Pillar of the Community United States 5828 Posts	Posted 09/28/2015 4:20 pm Interesting.. Food for thought that was put into my fridge! Report this Post to the Staff
sel_69l Bedrock of the Community Australia 21786 Posts	Posted 09/28/2015 8:38 pm I love to have some simple fun with a calculator like that! I am no good at crosswords but I am OK with simple applied calculator arithmetic. Report this Post to the Staff
OldSkoolMadSkilz Pillar of the Community United States 2077 Posts	Posted 09/30/2015 12:49 am Quote: Why isn't it 3.11 grams like every one before it? Because the only way to make it as massive with a less dense material would be to make it thicker. Lots of equipment depends on the thickness not changing. Report this Post to the Staff
shadz Pillar of the Community 1325 Posts	Posted 09/30/2015 03:43 am Actually as I said, if the core were only zinc and the shell copper with what the Mint gives, the volume of the coin would be the same as they state, but pure zinc core and pure copper plating would yield the 3.11 grams coins. Only when they make the 99.2% zinc/0.8% copper bronze alloy does the density drop the mass to 2.5 grams. That is what caused me to go through the process to find the other numbers. 2.5 % copper and 97.5% zinc coin of pure materials (well as pure as you can expect) would be 3.11 grams just like the pre-1982 cents. Pi(9.525mm)(9.525mm)1.52mm of (2.5% copper + 97.5% zinc) = 3.11 grams; when no alloy is present. Report this Post to the Staff
OldSkoolMadSkilz Pillar of the Community United States 2077 Posts	Posted 09/30/2015 04:00 am I think what you're missing is that 1.52 is the nominal thickness. Actual average thickness is about 1.2 mm. Report this Post to the Staff
shadz Pillar of the Community 1325 Posts	Posted 09/30/2015 12:39 pm No official information provides "nominal" as a definition or reason, nor the 1.2mm. I thought initially it was planchet/blank thickness, but used the information provided. Report this Post to the Staff
Parklane64 Rest in Peace United States 2668 Posts	Posted 09/30/2015 3:35 pm Make them out of plastic. Report this Post to the Staff
n9jig Pillar of the Community United States 997 Posts	Posted 09/30/2015 9:29 pm No matter what you make them of they will still cost more than a cent to make. Even if you give the material to the Mint for free. While I am all for reimagining the coinage in the US in some fashion there are way too many powerful lobbies out there to change things other than perhaps the elimination of the cent. Beyond that coins will become obsolete before they are changed in weight, size, composition or design. They might make some changes to one side of a coin here or there but the basic designs of circulation coins are unlikely to change before they are no longer used in commerce. Report this Post to the Staff
Conder101 Bedrock of the Community United States 17884 Posts	Posted 09/30/2015 10:16 pm The 1.52 mm thickness is more like a maximun thickness at the rim of a fully struck coin. The BLANK thickness is less than that. Take the weight and diameter and work it backward to determine what the blank thickness would be. Cent weighs 2.5 grams 2.7% or .0625 grams of that is copper and the other 2.4375 grams is zinc. Copper is 8.96 grams per cubic centimeter so there is .0625/8.96 = .007 cc of copper Zinc is 7.14 grams per cc so 2.437/7.14 = .341 cc of zinc total volume is .348 cc volume is pi * R^2 thickness So thickness = .348/(3.14(.95cm^2)) Or .348/2.83 = .122 cm or 1.22 mm thick for the blank. Edited by Conder101 09/30/2015 10:17 pm Report this Post to the Staff
jbuck Moderator United States 188213 Posts	Posted 09/30/2015 11:28 pm Stop making cents. Coin Collector Since 1978 Avatar Old Avatar 7070 Eisenhower Australia Canada World CCF Members on eBay CCF eBay Search Engine Report this Post to the Staff
shadz Pillar of the Community 1325 Posts	Posted 10/01/2015 05:21 am @Condor, you aren't including the metallurgy also. when you combine copper and zinc to make bronze the density is neither that of copper nor zinc, but of the resulting bronze. you cannot use the weight in order to find the dimensions with pure copper and zinc. In any event, my above calculations use neither the volume nor mass of the coin to find the percentage of the coins that is pure copper. you have 8 parts per thousand of the core that is copper and 992 parts per thousand that is zinc making the bronze core. so the density of the core will be slightly higher than that of zinc, and the overall copper mass will be reduced. so if the rim is 1.52 thickness, the Mint should be stating that and that the coin is 1.2 as you say PRIOR to upsetting the rim. Edited by shadz 10/01/2015 05:22 am Report this Post to the Staff
Conder101 Bedrock of the Community United States 17884 Posts	Posted 10/01/2015 2:22 pm Well I'm not a metallurgist, but what I remember from my chemistry and physics courses the SG of an alloy can be determined by the sum of the weight percentages of the component elements times their respective SG. As for a 90% siler 10% copper coin you get (10.5 * .9) + (8.96 * .1) = 10.34 Which just so happens to be the SG of our 90% silver coinage. (8.96 * .75) + (8.90 * .25) = 8.94 which almost exactly matches the specs for out copper nickel coins (8.96 * .95) + (7.13 * .05) = 8.86 which is very close to the official 8.84 for the shell case and 1963 - 82 cents) (8.96 * .027) + (7.13 * .973) = 7.18 and the official figure for the copper plated zinc cent is 7.17 In general this holds true for most alloys. A gold and copper alloy being an exception. I think the estimates are close enough to ignore any metallugical variance. It seems to be within 1 - 2% so my thickness estimate could be off +/- .001 mm. Report this Post to the Staff
shadz Pillar of the Community 1325 Posts	Posted 10/01/2015 3:13 pm But What I am saying is the US Mint SHOULD SAY 1.2 if that is what they mean, that isn't what they said We can infer that the coins are relatively the same because they reverse engineered the silver coins to have the new material be the same weight as much as possible and keep the same relative volume. But why doesn't the mint say the 1.2? what good is the 1.52? I am suspecting someone hit both the 5 and 2 when trying to type it on a keypad and nobody bothered to check. Had it not been for that error I probably wouldn't have so soon went the find the percentage of the coin that was in the core and the percentage or the coin that was pure copper. Where do you get your .027 number when this site says the copper is 0.8% in the core? should be: (8.96 * 0.08) + (7.14 * 0.992) = 7.15456 Again, not saying your 1.2 is wrong, I just find nothing from the mint to support it or give reason for the 1.52mm other than the typo reason. So I can only work with the numbers provided as I don't have a perfect coin form the mint to check, they are all circulated. Is there some sort of vendor info about coins that might be more precise for all the contraptions used to check electromagnetism, weight, mass, size of a coin from the Mint? I saw a design from some UK "How It's Made" type program on Youtube talking about the Euro coins that had what appeared to be micrometers measuring the coins as they go into vending machines as well as checking many other things at the same time because of the ring on the bimetallic coins. With better and more precise (or correct) info from the source. I will be more than happy to redo any math it seems someone needs me to do on the findings I made in the first post. Report this Post to the Staff
OldSkoolMadSkilz Pillar of the Community United States 2077 Posts	Posted 10/02/2015 01:21 am They only publish the nominal thickness because from a practical standpoint, that's all that really matters. Take a penny to the auto parts store and borrow their brake micrometers. You'll see that it's considerably thinner at the field. Report this Post to the Staff
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