I've seen in an advertisement that Clothoid curves–also known as Euler Spirals–"transfer maximum energy" to a ball bearing that is rolled down it. Firstly, I was wondering if that might be true based on the information I've provided; second, if it is true, what is the intuition / mathematics behind it?

Thanks for your help!


1 Answer 1


The curves aren't "transferring" energy, they're preventing the most kinetic energy loss.

A Euler spiral is a curve along which a body will experience the smoothest changes in centripetal acceleration. Friction is directly related to centripetal acceleration, so the path with the least amount of centripetal acceleration integrated along the length of the curve would be the most energy efficient.


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