1:1 with the motor attached directly to the wheel. I think the gearing would be the only losses in power.
I love this question.
But if the motor had a speed limit, wouldn't you want to want to gear it down as far as you could until you were at the motor's limit at the finish line?
Finish line wheel RPM = 2500
Electric motor max RPM = 10,000
Then gear ratio should be 4:1
That's my answer. You want to most leverage possible without blowing up the motor.
-kevin
Ignoring the maximum RPM issues, the answer is the elapsed time is minimized when the cars weight reflected through the gear box is the same as the rotational inertia of the motor.
It is pretty easy to show that a minimum time optimization is achieved when the two inertias are matched. And yes I am sure, I based a multi million $ design optimization based on the principle.
What that means is that 1:1 is only optimum if the inertia of turning the engine is equivalent of moving the car. If the car is 4 times the mass, then the GR is 2.
Now what does that have to do with a gasoline powered drag bike? I don't know
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