Somehow – and I don’t know exactly how, you know how the internet is – I came across this odd but cute song by the ineffable Weird Al. It’s an almost seven-minute(!) ode to the roadside attraction that is the titular biggest ball of twine. The twine ball actually exists, and lives in Darwin, Minnesota.
Oh! What on earth would make a man decide to do that kind of thing!
Oh! Windin’ up twenty-one thousand, one hundred forty pounds of string!
You know, I bet if we unravelled that sucker,
It’d roll all the way down to Fargo, North Dakota
‘Cause it’s the biggest ball of twine in Minnesota
I’m talkin’ ’bout the biggest ball of twine in Minnesota
Hmm. Sounds like a Fermi problem to me. Eyeballing the twine ball, it looks like it’s about 10 feet in diameter (I could look it up, but that’s no fun). We’ll call it 3 meters for good measure. This is just over 7 cubic meters of twine. Converting units and dividing out, the twine ball has a density of about 1.4 grams per cubic centimeter. This is not wildly unreasonable – it’s a little denser than water – but I’m not sure loosely wound twine is that heavy. I think Al’s probably adjusted the actual mass a bit upward to fit the rhythm of the song.
What about the ball’s odds of rolling to Fargo? We need to figure out how much the string weighs per meter and then extrapolate out from the 21,140 lb mass postulated. As it happens, I have a pair of calipers and a round cross-sectional shoestring. It’s hard to measure precisely without squashing the string, but it appears to be about 4.5mm in diameter. Assuming the twine is similar, each meter of twine will have a volume of about 1.6e-5 cubic meters. We could just divide the 7 cubic meter twine ball volume by that and call it a day, but the twine probably isn’t so densely packed that the volume is entirely filled with the twine. There’s probably some air spacing between the windings. On the other hand, we have no good way to guess a correction factor, which is not likely to be large. So in the spirit of the Fermi problem, we’ll just scrap the mass factor entirely and just divide out volumes: 7 cubic meters divided by 1.6e-5 cubic meters per meter (how’s that for units!) is 437,500 meters, or 272 miles. And darned if it isn’t 204 miles from Darwin MN, to Fargo, ND.
Now our estimate is pretty rough, but that’s not half bad for a Weird Al song.
And yes, I know this is a ridiculous thing to write about, but I’m hoping it will finally get the song out of my head…