Several weeks ago our team put together a spreadsheet that made it easy to determine the optimum wheel diameter once we knew the robot's mass.
(This exercise is left to the student.
)
After a couple of iterations, we achieved a climb rate of 1.17 seconds, just about what the laws of physics had predicted.
The only variable in our equation that we didn't know for sure was the overall efficiency of the drive train. We assumed ~ 90%, as we had tossed out the gearbox. The timed result suggests that it was more like 85%.