I got some of the W739083 Tetrix motors (12V, 152 RPM marking) to test in my lab. We performed dynamometer tests to measure the output mechanical power vs. torque, for two types of electrical source: (1) a regulated 12V laboratory bench supply, and (2) a standard 12V (marked) W739057 Tetrix NiMH battery pack. We did not measure the battery voltage; however, the (unloaded) initial motor speed when fed from the battery probably indicates variation of its voltage due to the previous test. Some charging was done between tests.
We repeated the power curve measurements for four sample motors. Three showed consistent performance, and one was slightly lower. Results follow:
With regulated 12V dc supply:
Motor 1: 10.8 Watts peak output mechanical power at ~75 RPM, 145 RPM initial motor speed
Motor 2: 10.8 Watts peak output mechanical power at ~75 RPM, 145 RPM initial motor speed
Motor 3: 10.1 Watts peak output mechanical power at ~75 RPM, 143 RPM initial motor speed
Motor 4: 10.9 Watts peak output mechanical power at ~75 RPM, 148 RPM initial motor speed
With Tetrix battery: (voltage > 14V)
Motor 1: 16.5 Watts peak output mechanical power at ~90 RPM, 178 RPM initial motor speed
Motor 2: 16.0 Watts peak output mechanical power at ~90 RPM, 173 RPM initial motor speed
Motor 3: 14.2 Watts peak output mechanical power at ~90 RPM, 172 RPM initial motor speed
Motor 4: 15.2 Watts peak output mechanical power at ~90 RPM, 176 RPM initial motor speed
Based on the above, my calculations for climbing time and gear ratio would yield a recommendation for 4" wheels and 2:1 gearing, for a (theoretical) climbing time of about 3 sec if we assume the minibot mass is 5 lb, two motors are used, and the mechanical efficiency (motor shafts to pole) is 75%. That mechanical efficiency might be about right, considering that my dynomometer measurements did not include any side loading on the motor shaft, which will certainly be present in the minibot.
Of course your motors may vary from the ones we tested. However, two general conclusions are still valid:
(1) Battery state of charge will be a very significant factor for minimizing climbing time. So will mechanical losses in the power train from motor shafts to pole.
(2) Design calculations based on the published motor data are likely to be too conservative; my calculations using the published data would yield a recommendation for 3" wheels, while the test data above suggests that 4" wheels are a better choice.
NOTE: I wanted to include the raw data and plots of speed and power vs. torque; however, they cannot be attached to this post because the file size is too large (>101.8 kB).
Test Temperature: Ambient (22 degrees C)
Software: M-Test 5.0
Dynamometer: Magtrol HD 705-6N (Calibrated 01/12/2011 by NT)
Dyno Controller: Magtrol 4629B (ML144)
Power Supply: Sorensen XG 150-11.2