3176: Inverted Catenaries
| Inverted Catenaries |
 Title 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. |
Explanation
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This is one of 52 incomplete explanations: This page was created BY A TRAPEZOIDAL WHEEL. Don't remove this notice too soon. If you can fix this issue, edit the page! |
During the winter, in snowy areas, people need to replace their typical, all-season tires with snow tires made specifically for the slick environment. In this comic, instead of snow, rounded shapes called inverted catenaries fall from the skies. On a plane covered in inverted catenaries all the same size, square wheels whose side length matches the arc length of the catenary are capable of rolling smoothly, contrary to how they would act on a normal road. Regular wheels would cause a significantly bumpier ride on this terrain, so Cueball plans to swap them out with square wheels to better suit the season.
Mathematicians have found what types of roads would suit weird wheels the most, and inverted catenary is best suited shape for the square. People make made real tracks demonstrating this.
The title text mentions all-shape tires (as a play on all-terrain tire), which is advertised to supposedly fit any shape road. However, different shapes would require very different wheels; for example, falling triangles would form a sawtooth road, for which one would optimally require wheels pasted together from pieces of an equiangular spiral. Any hypothetical all-shape wheel would wear out very quickly on most surfaces.
Transcript
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This is one of 27 incomplete transcripts: Don't remove this notice too soon. If you can fix this issue, edit the page! |
- [Megan and Cueball are walking as inverted catenaries fall from the sky. A few have landed in a regular formation, all flat-side down and next to each other.]
- Cueball: Oh wow, the first inverted catenary fall of the year!
- Cueball: Time to swap out my all-season tires for square ones.
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Hoookay ... am I nutz, or shouldn't a physical object with the shape of an inverted catenary (2D or 3D) fall and land with the rounded side down? And shouldn't such a "catenary fall" (if 3D objects) produce a flat-ish, unstable surface that would be [ahem] very interesting to drive (or walk or yada) on, and on which square tires would be useless? 2605:59C8:160:DB08:216D:5149:ACEB:AD1C 03:42, 4 December 2025 (UTC)
- Not necessarily. Depends on how catenary is weighted, it doesn't have to be of uniform density.--Trimutius (talk) 04:23, 4 December 2025 (UTC)
- If inverted catenaries flip, during their fall, then they become "inverted inverted catenaries", instead, which some might say are 'just catenaries' (or, indeed, be best observed as the catenary-chord, utmost). So, by definition, they don't. ;) 82.132.239.140 13:03, 4 December 2025 (UTC)
- The comic itself is 2D, so if this were a 3D scenario it might be that the inverted catenaries are actually extended, like a series of speed bumps aligned with roads. That may be likely since I'm pretty sure xkcd has more 3D cars than 2D throughout the comics R128 (talk) 14:14, 4 December 2025 (UTC)
A caternary curve is that of a tethered chain hanging loose in gravity, so defined as one with the curve pointed downward. this requires its inversion to curve up. Semantics, but in this case important ones. 50.37.102.15 (talk) 07:24, 4 December 2025 (UTC) (please sign your comments with ~~~~)
Coming from a snowy country, we don't use all-season tyres. We have summer tyres (useless on snow and ice, very well suited for dry and wet surfaces) and winter tyres. Winter tyres without studs can legally be used all year round, but are ill-suited for summer conditions. 109.247.36.180 08:32, 4 December 2025 (UTC)
- Well in Canada many people never use summer tires at all. They would drive all-season and then switch to winter tires. Cold snaps are sometimes so sudden in Canada, that many people don't want to risk driving on summer tires as it can come to bite you in Spring or Fall.--Trimutius (talk) 15:31, 4 December 2025 (UTC)
Although square wheels on inverted catenaries have no practical use, non-circular wheels on non-smooth tracks are used in rack railways, which are an application of a rack-and-pinion mechanism. 85.228.125.118 (talk) 11:41, 4 December 2025 (UTC) (please sign your comments with ~~~~)
Did Randall move to canada? 206.193.5.5 16:40, 4 December 2025 (UTC)
- I reckon he's been tempted, like many of us. But if we tried it, all we'd be likely to find was Randy Bachman singing his new song "The Ghost of Stephen Harper". We have all been here before ... 205.175.118.102 20:20, 4 December 2025 (UTC)
- Northern parts of USA get a lot of snow too. Some select cities in the North of US might even get more snow than southern Canadian cities.--Trimutius (talk) 16:48, 4 December 2025
- Pretty sure Randall lives near Boston MA (https://xkcd.com/3081/), and we had a significant storm on Tuesday (the day before this was posted). Plenty of people here (myself included) switch to snow tires around this time. 130.64.22.2 17:30, 4 December 2025 (UTC)
- I was referring to South Park featuring Canadian vehicles having square tires, not anything related to climate. 206.193.5.5 20:38, 4 December 2025 (UTC)
Has there actually been any research into a wheel shape that’s the best on average over any given terrain pattern, or is that just Randall having a laugh? KelOfTheStars! (talk) 21:37, 4 December 2025 (UTC)
- I'm guessing that, on average, the best general wheel shape is... round... (But with one or other tread, as a detail, of course.) But I'll admit that this is without actually doing the suggested research... 78.144.255.82 21:51, 4 December 2025 (UTC)
- Morphorcular on Youtube has a great video series where he finds the "best" wheel for a given road (defined in the series as one where the axle stays at a constant height.) I know this isn't what you asked but I'd recommend checking it out!
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