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Comment by Animats | Hacker News Reader

Railroad curves are usually splines. That was the original physical application. You need a curve that minimizes jerk as the radius changes.

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Now I'm wondering how the steel tracks get bent- I figure it's done on site rather than at the factory. Dunno what sort of equipment they use to bend them though. Maybe they can just use bigger "spline weights" and pin the bend points to scale from the drawing! Hmmmmmmmmm probably not but I want it to be true

I would guess in a ring roller.

Basically a roller on top pressing down and 2 rollers on the bottom and you wind the metal through tightening the top roller to increase the curve.

Sorry to disappoint you.

If it makes you feel better though, the whales used to set the curves on boats used to be real whales.

But a ring roller produces curves of constant radius, and for the railway application it would have to be absolutely enormous.

From a quick DuckDuckGo search, it looks like they basically are just laid out the same way the "splines" from the article are: the curves are gentle enough that the steel is not very hard to bend.

Talking of ducks, some think that the spline weight 'ducks' could be the origin of the expression 'have your ducks in a row'.

https://www.arema.org/files/roadmasters/1995/1995_STRINGLINI...

Railroad tracks are pretty flexible, there's no need to bend them separately, you just put them in the sleepers and can fine tune them in there.

You can see how much they bend in this video: https://www.youtube.com/watch?v=CpP6ar63Qxw (1:40). In this case they get delivered as 200m sections on normal rail cars, so they hava to withstand normal curves during transport.

Interesting, do you have a source where I can get deeper into the application of splines to reilroads? Specifically, how to arrive at the jerk minimization problem. All things railroads are too descriptive with little engineering/physics formulas.

chapter 3.2 has a good explanation of it all. https://nap.nationalacademies.org/read/22800/chapter/3

There are tons of papers and research on this topic. Here's just one review of some of the various approaches that have been used.

https://www.researchgate.net/publication/341476435_Railway_T...

i think - but am not sure - they use clothoid definitions to characterize jerk, as it is more restrictive regarding the maximum rate of turn change. you can make quite a sharp turn with a mathematical spline. but i can see how they would use the physical spline to solve this…

Googling “railroad spline clothoid” got some intriguing hits — and this HN comment. https://news.ycombinator.com/item?id=10446154

semi-relatedly, this is a fun watch. https://youtu.be/aVwxzDHniEw

even less relatedly, here is a drawing i did by torturing a clothoid optimizer https://www.instagram.com/p/CSe40DTp-WW/?igshid=YmMyMTA2M2Y=

before ships ?

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