>
> 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

Aw heck, I was getting ready to say an oval cross section with the long axis horizonal, but I guess that is ruled out.

Let me put some numbers on it and see how that works. Assume a horizonal distance of 20 meters, and a vertical distance of two meters. I'd want the first two meters (horizonal) to be quite steep to get the ball moving fast, and after that just enough gradient to maintain speed. The steep grade and the shallow grade would be connected by a curve with a radius of about half a meter. Any drag racer knows that a slow start will likely get you too far behind to catch up.

In the scooter game, the beginnng of the pipe is about four feet off the ground and the lower end, some 12 feet away, is about three feet. The ball rolls rather slowly, which requires the contestant to ride very slowly. Motor scooters get really unstable at very low speeds. So the rider has to concentrate on keeping the scooter steady while arriving at the end of the pipe at just the right time. He also must take one hand off the handle bar and catch the ball while keeping his balance. It ain't easy.

My wife likes the "blindfolded driver" game. This one envolves three-wheeled Cushmans such as Trucksters or Golfsters. Yes, the driver is really blindfolded, but someone sitting next to him (usually his wife) is giving him directions as he weaves in and out through a zigzag course between plastic cones. Running over or knocking down a cone adds points to your time. Each second is also a point and the lowest score wins. It's usually good for a few laughs.
Howard