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Originally Posted by Rod
The gears used are a 55 tooth 3/8 face 20 DP for output and a 5 tooth stem pinion on the end of the Cim motor.
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I just realized; you've got an 11:1 reduction there, meaning that your quoted speed numbers are sort of conservative (I'd say you estimated 3000 rpm from the CIMs). With any luck, under normal loading (no pushing), your motors will tend to spin closer to their free speeds (5342 rpm) than their max. power speeds (2671 rpm).
Actually (using free speed), your top speed would be closer to 11.6 ft/s. I've found that free speeds of motors provide a better approximation of robot top speeds than anything else--with the extra voltage from a full battery
roughly accounting for the load on the motors from normal driving, and allowing an estimate of free speed = operating speed. (This varies, depending on the drivetrain, and is clearly not the product of rigourous calculation! If anything, it overestimates the speed.) The 6.5 ft/s @ 3000 rpm figure seems more consistent with assuming that the robot will run most of the time at full power. That's not a realistic number to work with, because you'll never know what your power output actually is, when pushing something around--you certainly can't hope to be at max. power in any given pushing match. If anything, when pushing another robot, you'll be on the slow side of max. power (that is, the high-torque side).
And one more note: I was using the max power figure earlier in the chain calculations, while quoting free speeds. In reality, since max. power occurs at 50% free speed, you should (if you want to be rigourous about it) divide the speed I gave above by 2, and use the corresponding power figure on the chart. With some rough interpolation, and the #25 14-tooth instead of the 13-tooth sprocket, you're at about 0.12 HP rated. But I think that these compounding safety factors are getting a little absurd. I wouldn't bother with this last step, if only because this is a mere robot, and we don't need to overbuild it to last forever without failing. As long as it lasts the season intact....