> > I'd think one with a flat bottom surface, to minimalize contact with it, and a high ceiling, to prevent any brushing against it. As for the sides, I'd go with ones that are spaced slightly further apart than the diameter of the ball to keep it on a course similar to a straight line. I don't think that the frequent impacts would slow it down significantly, but I could be wrong.
>
> What about a pipe like the one you described, but with wider sides and a groove down the bottom, a sort of track for the ball to roll in. That would eliminate the extra friction from the ball hitting the sides of the tube.

I didn't mean cross sectional shape. I meant what path the ball follows to get from height H to height 0 while travelling a horizontal distance L.

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?

Think of it as a problem in two dimensions.

^v^:)^v^
FB