travelgirl sends this in: “I understand what a catenary is, but have no idea what that has to do with the punchline… guess my retirement years are catching up to me :) “
Mouseover text: “Some tires are marketed as all-shape tires, but if driven in a climate with both inverted catenary falls and triangle falls they wear out really fast.”
Comics I Don't Understand 
Square wheels can roll smoothly over inverted catenaries. Not sure I can post links so I’ll reference a Youtube video from Texas A&M titled “Square Wheeled Tricycle” here and try to post the URL separately.
What Consul said. The whole thing is to point out how weird and cool it is that square tires would be preferable to round ones if you drove over a surface shaped like that.
Youtube link to Square Wheeled Tricycle (skipping intro fluff):
Link post failed but technical details are available in the “Square Wheels – Reinventing the Wheel” video on the Mostly Mental Youtube challenge. It’s actually better than the other video which is mostly filler.
Oh… looks like it did post, after all. I’ll push my luck and post the other video:
Also, “challenge” <– “channel” in 4)
Maxima culpa
It seems to me that you’d need square wheels of a fairly specific size, otherwise you’d just get stuck in a valley. I should point out that, while I appreciated the explanations (many thanks) the cartoon still didn’t make me laugh.
Yes, the problem with making roads out of inverted catenaries is that everyone’s wheels would need to be the same size.
Thanks, Consul!
I had “cheated” by looking at the “Explain XKCD” site, which made the basic point that a square wheel can roll smoothly over a series of catenary humps, but didn’t go into it in any detail. Which the Mo Math video certainly did!
Here’s the link for “Explain XKCD”, btw. I’m proud of myself when I don’t have to look at it to get the joke. http://www.explainxkcd.com/wiki/index.php/Main_Page
I was fine with the comic once I could convince my brain to stop seeing the falling ones as coat hangers.
Powers (7): They call them cobblestone wtreets.
… streets.
another point I haven’t seen mentioned, the phrase “catenary fall” also means that a power line fell down (or something)
harder to search for since the cartoon came out, but here are 3 pages that mention it (if you are curious)
forum.trains.com/t/third-rail-electrification/107958/15
personal.math.ubc.ca/~njb/Research/plat.pdf
section 2.4.2. “Later times” on page 4
http://www.morssmitt.com/products/400865/catenergy-dc
under “Insulation”
XKCD tends to be a rather niche comic.
Rammy, I think the page you were looking for is: https://en.wikipedia.org/wiki/Overhead_line
Catenary lines are overhead, low-tension lines, used to power vehicles. They’re “catenary” because they hang a little loose, forming a curve. A catenary curve.
Millar(15): yes, but that page doesn’t specifically say “catenary fall”, which can be just if it breaks, or if it hangs too low (eg due to heat) and touches the ground, or a passing vehicle (etc)
But I couldn’t find a page that explicitly says “the term catenary fall refers to …”
So, it is a thing, but don’t quote me on the definition.
@Powers (7), the other problem with catenary-and-square-wheel roads is that you can’t turn easily, because it makes the squares not fit exactly with the length of the catenary curve.