Going off this file here: https://pcop.wikispaces.com/file/view/rec3.19f_project_tractor.pdf
Traction is the name of the game here, and that depends on how much torque your motors can effectively convert to traction. So is speed.
For a given motor power output, there is an inverse relationship between speed and torque, as given from one of the mathmetical definitions for power:
P(rot) = torque * angular speed
(derived for rotational motion from P = Force * speed)
What that means is, you can’t have both speed and torque. It either has to be geared for speed or for torque, and you need to find that perfect balance.
The motors also need to be able to torque against the weight of the robot and the weight. The surface is also a factor, because a rougher surface will make it harder for your robot to pull your robot. However, since you and your classmates are competing on the same surface, this wouldn’t affect the relative results. Another thing is that the hardest time for your motors is the start up, where they have to both provide torque to get the robot rolling up to speed, and to keep it rolling. It’s not as bad once it gets up to speed because the robot’s weight will naturally carry itself on. Your robot’s no good if the motors can’t survive the start-up. Don’t burn out the motors in the start.
Per your project rules, you can’t augment the motors with rubberbands, so it really boils down to three variables:
-The gear ratio
-The weight of the robot, the weight, and the latter’s rig.
-The size of your wheels (Bigger size = more speed. Smaller size = more torque)
So what I suggest is that you first try to remove as much weight as possible from your robot, then find that optimal gear ratio and wheel size. Also, see if distributing your weight across multiple wheels will help increase speed. The point here is to get your motors to run the wheels as fast as possible without tripping the internal PTC (burning them out).
I really can’t tell you how far it’ll go without knowing specifics about your robot, but my perspective is that 10 pounds is a lot for two motors.