Built on Facts

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…

Comments

#1 ppnl
March 25, 2010

The best way to get that song out of your head is to listen to this song:
#2 VJBinCT
March 25, 2010

This song is perhaps my favorite among Weird Al’s impressive oeuvre. Another is ‘Frank’s 2000 Inch TV’. These are original for him, but he is better known for his parodies, all better by far than the original songs. But he is an original himself.
#3 Dave
March 25, 2010

Al’s no jerk although the does play the fool,i’ll bet he did the math..also,someone should do a core sample on that thing.
the old farmer who did that took years and years and not a fast one shot thing to make a record book.the dirt,chemicals,pollen,whatever,bound into that binders twine would be a good record of changes in the local ecology.
having that in a town called Darwin is a nice touch.
#4 Benjamin Geiger
March 26, 2010

I’m a tour guide on the Jungle Cruise ride
Skipper Dan is the name
And I’m doing thirty-four shows every day
And every time it’s the same
Look at those hippos, they’re wiggling their ears
Just like they’ve done for the last fifty years
Now I’m laughing at my own jokes but I’m crying inside
‘Cause I’m working on the Jungle Cruise ride
#5 lordaxil
March 29, 2010

Another way to interpret your answer is to back-calculate the correction factor (packing fraction) of twine ball: 204/272 = 0.75. This also seems very reasonable, since the maximum packing fraction (0.91) is given for hexagonally close-packed rows of parallel twine.
#6 Andrew
March 30, 2010

There was a sign at 3:29 on the video that says the ball is 17,400 pounds, and approx 40′ in circumference. Can’t be bothered doing the calcs again for these numbers as it’s late here.
Love this video, and really enjoy the blog.
Many thanks, from NZ
Andrew
#7 Luke Shingles
April 15, 2010

“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.”

(4/3) pi (1.5 m)^3 = 14.1 m^3. By your result of 7 I’d guess you accidentally used the formula for area instead of volume.
#8 Matt Springer
April 21, 2010

I have no idea in the world how I could have done that, but it looks like I might have. Fortunately by coincidence the numbers are still in the right vicinity.
#9 ball valves
March 27, 2011

The unveiling truth about this article is, that it spoke to me deeply. Thank you for sharing your thoughts and concerns.
#10 Sohbet Arkadaslik
March 27, 2011

Bu yüzden Fermi problemi ruhu içinde, sadece ve tamamen kitle faktör hurda olacak sadece hacimleri dışarı bölmek: 7 metreküp metrede 1.6e-5 metreküp bölü (! That’s nasıl üniteler için), 437.500 metre veya 272 mil. o Fargo, ND Darwin MN, 204 kilometre değilse Ve belâ.
#11 altın çilek
March 30, 2011

This also seems very reasonable, since the maximum packing fraction (0.91) is given for hexagonally close-packed rows of parallel twine.