What ways has everybody thought of for chucking
these things?! The medieval method for throwing boulders is obviously a catapult. Given that you can only control one boulder at a time this method could be viable.
From the prototypes we (The GreenHorns) have done I can say that a wheeled shooter is incredibly effective (so far). We have scuffed up our boulder pretty badly though. Currently we have mini cims in a versaplanetary gearbox at a 1:1 ratio direct driving some 4" high grip wheels from AndyMark. We've found that 3"-4" of compression is getting us the type of launch we want. I'd tell you how far we're launching it, but it keeps hitting the ceiling/walls in our shop (it launches far).
Also, how far do you think a high goal scoring robot should be able to launch a ball? Most boulders will probably be scored from right underneath the tower... is a launcher even necessary?!