Ok, I'm a smart guy, but math is where is stops. I need the help of a numbers wizard here. In my setting coins are roughly the size of a US 25 cent piece (Diameter 24.26 mm and Thickness 1.75 mm). Approximately how many of these would fit in a chalice of, let's say, two litres in volume?
Well, you need to consider a packing factor, as coins are not just stacked neatly inside the chalice. I believe there was a study that found the packing factor for many objects randomly packed was about 0.6.
2 liters is a large volume, but my estimate is around 1400 coins.
But since some of the coins are likely to stack, the packing factor is probably closer to 1, so lets go with .85.
That would give you 2100 coins.
Each of the coins you described has a volume of just over 800 cubic millimeters. There being a million cubic millimeters in a liter -- sorry, American education -- that would be just under 2500 coins in 2 liters if they could be packed perfectly with no wastage.
This is unlikely. Flat-packed in neat columns, the densest packing you can get is about 90%, which would be about 2200 coins in that chalice. If as is more likely, you just have someone dump coins by the handful, you get closer to 50-60% packing density, which would be about 1250-1500 coins.
So, anywhere from 1250-2200 coins, depending upon how carefully you put them in.
ETA: Sorry, just re-checked my math. The densest possible packing for circular coins is 78.5% (pi over 4) efficient, so that's the absolute top. Both my 90% estimate and Claxon's 85% are thus overestimates, and we're down to a max of about 1900 coins.
These numbers work just fine. Thanks, everyone!!! One of the legends of Vlad the Impaler was the he kept a chalice filled with gold coins on a stump in the center of the impoverished village below his castle. If any of the villagers were to take so much as one coin, he would have executed every single citizen. I'm going to run an adventure based on this legend and was needing an estimate about the number of coins it might contain.
Paizonians for the win!
2 liters: 100mm x 100mm x 200mm
Coin diameter: 25mm
Coins per layer: (100mm / 25mm)^2 = 16
Coin thickness: 1.75 mm
Number of layers: 200mm / 1.75mm = 115
Total coins: 115 layers x 16 coins per layer = 1840 coins
Triple edit: corrected my math error, now my results match everyone else's.
Disclaimer: this calculation was based of both conservative and un-conserative assumptions. Off personal experience of material behavior and consolidation I would expect values ranging from 60% to 110% of the calculated result, with a median value of 80% for a 1470 coin total.
Well, offhand, I'd just handwave the difference between coins and spheres and assume that they achieve the same packing density as random close packed spheres (63.4%) and use that to decide. At .809 mL per quarter, you'd need 2472 of them to equal 2 litres. Multiplying that by the 63.4%, I'd say you'd have ~1567 coins in the chalice. Keep in mind though; that's a big chalice - it's the size of a large soda bottle.
Oh, and just offhand, given that we know the weight of coins in Pathfinder, we can determine their size easily enough.
1/50 lb of platinum = .423 mL per platinum piece
1/50 lb of gold = .47 mL per gold piece
1/50 lb of silver = .865 mL per silver piece
1/50 lb of copper = 1.01 mL per copper piece
Canadian $2 coin = 1.11 mL
Canadian $1 coin = .965 mL
US quarter = .809 mL (Canadian ones are .7076 mL)
US dime = .3401 mL (Canadian .3115 mL)
US nickel = .689 mL (Canadian .621 mL)
US penny =.4332 mL (Canadian .4133 mL)
So the PP is between the US and Canadian pennies (which are close enough in size that most people don't notice the difference unless they're looking for it)
The GP is between a penny and a nickel in size.
The SP is between a quarter and loonie.
The CP is nearly as big as a twonie.
In my setting, silver is the standard of exchange. This much gold would keep that little village solvent for years, but they cannot touch it and are forced to march by it every day to look at it, knowing it is only inches from their starving hands.
ETA: Sorry, just re-checked my math. The densest possible packing for circular coins is 78.5% (pi over 4) efficient, so that's the absolute top. Both my 90% estimate and Claxon's 85% are thus overestimates, and we're down to a max of about 1900 coins.
Per Circle Packing, the maximum packing density is hexagonal, at 0.9069.
Per 2 Liter Soda Bottle is 12.25" High x 4" in diameter.Per Quarter is 0.955 inches in diameter by 0.069 inches thick.
I would guess you get about 10 coins per layer, and 177 coins high, giving 1770 coins. Packing the open space on the two sides can probably up that to 1900-2000 coins.
/cevah