Sunday, May 11, 2014

Ask Santos: Scrooge McDuck Diving

This one is for my buddy Carolyn and her wife Heather.  They ask,

How much money would you have to have to be able to pull off swimming around in it Scrooge McDuck-style?

An Olympic-size swimming pool is 50 meters long, 25 meters wide, and one to three meters deep, giving a total volume of roughly 2500 cubic meters. Swimming in gold coins is a lot more expensive than swimming in pennies. To make this more cost effective, I'm first going to assume he's swimming in pennies rather than gold. A penny has a volume of 0.349 cubic centimeters, meaning you'd need roughly 7.2 million dollars to fill an Olympic-sized swimming pool with pennies.1 Even a smaller non-Olympic pool would require over one million dollars.

If money is no option, you could instead fill the pool with gold coins. Given that one cubic centimeter of gold costs about 80 dollars, a gold-filled swimming pool would require roughly 2.0 trillion dollars, or about 12% of the national debt. This is certainly a hefty amount of coin, but I would contend the sheer dollar amount is not the main obstacle to swimming around in a swimming pool Scrooge McDuck-style. Once again, Family Guy does a pretty good job illustrating the practical difficulties of the matter,

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions. Follow him on Twitter at @aarontsantos.

[1] You need slightly less money if you take into account the packing fraction of pennies.