Originally Posted by Epstein
I'll save you the trouble...
F (at the wheel) = M (of car) * A (of car)
If the mass stays the same (if it doesn't you're in trouble), then the max Acceleration happens at max wheel Force.
If wheel Force = wheel Torque / wheel radius, and the wheel radius is constant, then max Force happens at max wheel Torque.
Max wheel Torque happens at max engine torque with the most mechanical advantage, ie. lowest gear (highest gear ratio).
So max acceleration happens at max engine torque in 1st gear. Of course this assumes that the acceleration is in the forward direction....
yup. except that first gear is the anamoly here. after that you will get better mechanical advantage by remaining near the POWER peak because you stay in the lower gear.
this is why i say peak acceleration at ANY GIVEN SPEED is at the power peak.
in first gear at peak torque you are going to slow to be at your power peak because you don't have a numerically higher gear ratio available.
yeah you could artificially put your engine at power peak by slipping the clutch, but much the extra energy is spent producing heat (burning up the clutch) rather than moving the car.
a car with a CVT holding the engine at the POWER peak will produce the most possible overall acceleration out of any engine.
i could go REALLY mathematical by going into the calculus describing it all, but i'll spare the people who don't understand differentiation and integration
F = m*a is a GROSS, GROSS oversimplification of it because F and hence a are CONSTANTLY changing. you need to start delving into integral and differential calculus to REALLY explain why peak acceleration occurs at the power peak.
but i'd practically prepare you people for an A in a college classical mechanics course with calculus to explain this to you all.