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
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.
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.
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.
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…
