> > >
> > > > Think of it as a flat ramp instead of a pipe. The ball rolls down the ramp (without slipping). If I ask for the optimal shape of the ramp, does that clear it up?
> > > >
>
> I think it's a cycloid.

Yeah, it's a cycloid.

For those of you who don't know what a cycloid is, imagine you have a circle (or a cylinder) rolling on a flat surface. Stick a pencil to a point on the outside of the circle. In true Spirograph fashion, as the circle rolls, the pencil will trace out a cycloid.

Another interesting thing about a cycloid-shaped ramp is that no matter how high up the ramp you let a ball go from, it will take the same amount of time to get from that point to the bottom.

^v^:)^v^
FB