In Reply to: THe Glossary for the above...... posted by gercar on September 26, 1999 at 11:24:34:
: : : 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.
: : Torque is a force, force does nothing except apply itself. Work is the distance an object is moved by that force. Power is the amount of work done in a period of time, therefore power is the torque applied over a distance in a period of time. The higher the power the greater the distance covered in a period of time. Example: 150 bhp will take twice as long to cover a distance as a car with 300 bhp (all else being equal of course). In conclusion you want to run in the best power band not torque band for max acceleration. Torque comes in handy when breaking the static friction in the cars drivetrain and between the road and tires. It takes a certain amount of force to overcome that friction, therefore the more torque you have the sooner you will overcome that static friction (this is the reason why torque monsters feel really quick off the line, even if they sometimes end up being slower in 1/4 mile and 0-60 times). Torque also helps to overcome the tendency of an object at rest to stay at rest (this again leads to friction, the evil enemy of all Mechanical Engineers). Take away friction and you need very little force to move the heaviest objects (like moving a frig with wheels or on ice).
: Static friction is the force that keeps things from sliding off the coffee table or you out of your seat under braking. Kinetic friction is the force required to keep an object in motion once the static friction is overcome (this force is actually much lower than the static friction). Kinda like breaking loose a real stuburn bolt. This static friction is why sometimes getting sticker tires actually slows down acceleration times, but increase lateral grip. Actually, with out friction the wheels on your car would slide not spin.
: End of lecture, any questions
Hey fellow mechanical engineers...this has probably become too technical for most on this board! lol.
A useful formula is, Power=torque x rpm, but the driving input is the torque vs rpm curve(and resulting power)for the engine. Power(and acceleration) for the 3 series peaks at 5500 rpm so unless someone had a good reason I would run out to redline at 6500 and then downshift and run through the "power band" rpms to 6500 again, etc.