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## Main Question or Discussion Point

Hey everyone, i am trying to design a small and lightweight cvt (continiously variable transmission) for an electric car that can either be on or off, no variable speeds from the motor. I am having trouble representing the math of the transmission. I have to have the car complete a race of 312 inches, the motor has a top rpm of 4040rpm, and at that rpm torque approaches 0. the graph of the torque vs rpm is piecewise in 2 parts with the following equations when rpm<1248 then torque=-0.0019*rpm=23.3 and also when rpm>1248 then torque=-0.0075*rpm=30.3

anyway, my problem is that i dont know how to represent a smooth change between the infinite gear ratios and relate that to how much time it will take to cross the finish line (312 inches later). obviously i am starting at a velocity of 0, and an rpm of 0. this should give me a torque just as the motor starts to move of 23.3 ounce-inches. i know i want to minimize time, and maximize velocity. i think i have to use an integral to represent the cvt, but im really turning around in circles here. oh and by the way, the diameter of the drive wheels is 3 inches. please can anyone help me out here?

anyway, my problem is that i dont know how to represent a smooth change between the infinite gear ratios and relate that to how much time it will take to cross the finish line (312 inches later). obviously i am starting at a velocity of 0, and an rpm of 0. this should give me a torque just as the motor starts to move of 23.3 ounce-inches. i know i want to minimize time, and maximize velocity. i think i have to use an integral to represent the cvt, but im really turning around in circles here. oh and by the way, the diameter of the drive wheels is 3 inches. please can anyone help me out here?