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Originally Posted by Dick Linn
... The only way you are going to get the robot going faster (top speed) is by putting more energy into it (such as some flywheel effect) or accelerating it to a higher speed within a certain limited time period (getting up to top speed within the confines of the game). Ultimately, you have only so much power so the beast can go only so fast. ...
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To understand the reason for using a multispeed transmission on a FIRST robot, you need to look at the torque vs RPM curve for the motors they give us.
like this one for the Chiaphua motors:
http://www2.usfirst.org/2004comp/Specs/Chiaphua.jpg
Unlike gas engines, which have their max HP at a high RPM, the electric motors have the max torque at zero RPM. HP is a function of torque and RPM -Im not sure off the top of my head where the max HP point is on the curve
but, to get the most power from the motors you want to keep them at the max HP RPM point - therefore, to get the most HP at different speeds, you need a multi speed transmission.
If you have a transmission that shifts at the right points on the curve, your robot will have the best acceleration, pushing power, and top speed possible from what we are given to work with.