[Gary Dillard]

OK - time to spill the beans a little more.....

Dennis - we measured 1.7 with the green BrekoFlex belts - under load on the robot by pulling against a spring scale (the traction pit we brought to Disney); 200# pull with a 115# robot. The belts were slipping on the carpet since we had plenty of motor power. We measured the same on team 144's robot with the same belts at stall (they were underpowered). We had measured 1.8-1.9 by just dragging the belts across the carpet before we built the robot.
Here's the big surprise from the pit results: Second best was pneumatic tires! 2 teams (457 and 121) pulled 180# or a u of about 1.4.

Gui - for your physics problem you need to start at the other end.

Say, hypothetically, you wanted to push rolling goals full of balls and other robots around. You want to maximize your pushing power (we'll address speed later), and you can assume the other team is doing the same. Only 2 things impact whether you will push or be pushed: friction factor between you and the carpet, and downward force. Take the friction factor times your weight plus any downward force from lifting up on the goal, and thats the most you can push.

Now, ignoring internal drive train friction losses for a moment, the maximum pushing force times the wheel radius divided by the total gear ratio through to the motor equals the torque that the motor will see at any point after the belt or wheel starts slipping (if you have multiple motors, divide by the number of motors). That tells you where you are on the motor curve. In design it works the other way around; you pick the point on the motor curve where you want to operate (generally either max efficiency or max power) and determine your gear ratio from the same equation.

Nothing about speed yet, right? That's a fallout of your chosen design point and the losses in the system. If you have a higher gear ratio than necessary you will drive slower but push the same (remember, the pushing force is limited at the carpet, not by the motor) - the tread will slip first. The motor operating curve times the gear ratio times the wheel radius gives you the speed.

So why a 2 speed gearbox? We were (and usually are) current limited. We have one gear ratio for speed (under no load) and a different gear ratio for pushing. Actually it turned out this year with the Chips that we had plenty of power to run in high gear most of the time. Finding the optimimum gear ratios is a lot of field testing, but the method above gets you in the ballpark.

Ooops - lunch is over; gotta get back to work. Hope this helps. Stay tuned for the full version.