To shoot from our starting tile, what would the approximate gear ratio need to be?
At this point of the season, can you please attempt to do the math? Gonna make you work for it.
You can start by assuming no loss of energy at transfer or to spin and no air effects. Then once you prototype you can refine it upwards once you build.
You will be compounding gears though…
If you are thinking of doing a flywheel launcher, then you might have a look at this:
From the ball velocities discussed there, you can work out the math for the gearing for whatever criteria you might be interested in (angle and distance of the shot, etc.). Of course there are various ways to gear it, so probably you want to keep in mind what parts you already have on hand.
Hope that helps get you started.