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Unread 06-01-2011, 23:44
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Re: 6WD vs 8WD

The final speed, as well as the acceleration are functions of the angular velocity and acceleration of the drive shaft (respectively), as well as the wheel radius.
Think about a wheel with radius = r and a driveshaft with some torque T. We then sum the torques about the center of the wheel and get Fa*r < Fsfmax*r (theta is ninety so it goes away sin(90)=1). Cancel the r, plug in uFn for Fsfmax, and you have your max Fa to not slip. Use T = F * rsin(theta) and you get the max torque from the driveshaft to be traction limited. From there it's just some basic ratios back to the torque output of the motor and that ratio is your desired gear ratio.
Now, this assumes that you have a perfectly efficient gearing system, and that your wheel has no mass and therefore no moment of inertia to slow the acceleration, but it gets you close.
For speed based, do the same basic thing only with rpm instead of torque.
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