In Reply to: Oops, correction posted by Nelson on September 26, 1999 at 12:02:31:
: P=0.5*m*2*v*a, not P=0.5*m*2*a
: This however does not change the reasoning.
: : I've thought about this a little bit, and I still may be wrong, but this is how I see it.
: : The kinetic energy of the car is KE=0.5*m*v^2.
: : The power produced at the drive wheels is the first time derivative of the kinetic energy:
: : P=0.5*m*2*a.
: : Since the mass of the car (m) is constant, the acceleration is directly proportional to the power output. Therefore, you want the engine to be running in the range where the power output is highest.
: : So you might be asking, well doesn't F=ma, and isn't the Torque directly proportional to the force at the wheels (T=kF)? Well, yes, but the gearing defines this coefficient k, so if you're up shifting to bring the engine into peak torque, you're actually reducing the force at the wheels because of the longer gearing, and therefore, less acceleration.