[ecchorobotics]

Team 75 succssfully used a belted shooter last year. Its performance is highly comperable to the one wheel+curved wall design, although some aspects proved to be serious problems. Things like belt inefficieny/stretching/grip/wear and overal mechanism complexity made the shooter somewhat troublesome. However, there is no "physics" reason (that I can come up with at least) to say that a shooter with belts is any less functional than a shooter with a curved wall and one wheel. The principle is the acceleration period, which depends on the required change in momentum of the projectile. The larger the change in momentum is, the longer the wall or belt is required to be to reach the target speed.

I should also add that a curved wall and wheel is no differet in terms of friction from a belt and a wall; using belts is simply "unrolling" the wheel into a flat surface. I'll try to explain as best I can by saying that 2*pi*r would be the belt+wall length required to achieve the same performance as a wheel with that same r plus a curved wall. Unless you take into account other factors such as ceptripetal force and angular acceleration, then things change slightly.