I've been looking into rollercoaster track designs and wondered how they mathematically calculate the ideal curves to fit some specific layout without creating excessive Gs or other rider discomfort or for maximising speeds.
One thing I do know is they don't use perfect arcs, due to G forces especially on the loop-the-loop which is why they take on the tear-drop shape (do normal curves also there for not take perfect curves for the same reason?).
My current guess is they must be using some bezier type spline stuff, but there are many ways to design a bezier curve between two points. So what are they actually using to find optimal curves for rider safety / comfort and speed?
Are there special types of curves they use or do they shape the curves manually in 3D software then run simulations to see if its rideable?