Podoboo on Tracks Math
This kinda is a bit nerdy r/theydidthemath question.
I saw this video https://youtu.be/y5P7T8Xk6YQ?si=SaNJ4wPB3_A-z6U-&t=810
At 13:30 you can see this setup where a slow podoboo goes on a small circle, while a winged podoboo goes around it on a faster track.
-regular podoboo: a quarter is one curved track tile
-winged podoboo: a quarter is 2 straight track tiles and a diagonal one.
They seem to line up perfectly, so that for both it takes the same amount of time to go a full circle. Which I find to be kinda remarkable as both track lengths should contain different irrational numbers. (Pi and Squareroot of 2)
How do a curved tile line up so nicely with 2 straight and 1 diagonal tile? And by how much do wings affect speed, is it just a factor of 2?
Curved tiles are not curved all the way, they consist of a curved and a straight part. If the speed multiplier for wings was 2, you could do math on how much of the curved tile is really curved, and how much of it needs to be straight to make sure that the a curved tile is exactly half as long as 2 tiles and a diagonal one.