JX,
You've come to the right place - I think maybe we can straighten this
misunderstanding out. There is really no need to do an experiment, I think
Newton has already done sufficient experimentation and would have been
easily able to answer this question - although I wouldn't want to cheat the
good Dr. Moonstone out of some fun.
It's certainly true that in the same moderate rpm range, the BMW will out
accelerate the Honda - but it isn't a question of torque versus horsepower,
it's horsepower versus horsepower. The BMW simply makes more horsepower at
say 3800 rpm than the Honda does at anywhere near the same rpm. What you
have given us is what is sometimes called an 'ill-posed' question.
Let me attempt to explain. I'm sure you will agree that fundamentally it's
really force that accelerates your car, be it Honda or BMW. We've all known
since Newton that F=ma or a=F/m. That's fine and dandy, but how do we know
how much force a particular engine will exert? Well, torque is equal to
force times distance, or T=Fr, where r is the radius of the rear wheel. OK,
so combine the two equations and we have a=T/rm. Good, now we see that
acceleration is proportional to torque at the rear wheels, but we have that
troubling wheel radius (and mass) in the denominator. Looks like the smaller
your wheels, the faster you accelerate - and of course the lighter the car
the faster you accelerate too.
If we stopped right here, we could start arguing over whether it's really
force or torque that accelerates the car, but that's as silly as arguing
whether it's really torque or horsepower. It's not a matter of which it is,
but which way of looking at it serves us best. We usually don't know F and
we also don't usually know T at the rear wheels either, just at the engine.
But if we have torque and horsepower numbers for the engine, then we can
work from the engine back to the rear wheels. The torque at the rear axle is
the torque at the engine times the combined gear ratio (transmission plus
differential). For example, take the BMW full throttle at 3800 rpm and
assume a combined gear ratio of 10:1. Then the torque at the rear axle,
neglecting friction losses, is 10x 236=2360 lb-ft. Does this tell us what
the acceleration is? Nope, not quite - we also need to factor in the wheel
radius to get the force where the rubber actually meets the road. This makes
a comparison of two engines in two cars on the basis of torque a bit
complicated, because to be able to know which one accelerates best, we need
to measure tire radius and factor in the total gearing, and if they aren't
the same, then we're comparing the cars at two different speeds, which is a
major foul ball, as I'll explain below. But it should be clear at this point
that engine torque alone won't tell you which car accelerates best, even two
cars of identical weights. It depends on total gearing including wheel
radius. But, it turns out if you work through the numbers that the torque
times rpm at the engine is equal to the torque times rpm at the rear wheels
(which happily conserves energy too). Thus, engine horsepower is a much more
useful indicator of acceleration than torque since you don't have to factor
in gearing and wheel radius.
But that's not quite the whole story - as I said above, you can't compare
acceleration at different speeds, even neglecting wind resistance and
friction. That's because power is force times speed, P=FV. That's right, it
takes twice as much horsepower at 60 mph to get the same acceleration as at
30 mph, etc. And that's not including the added wind resistance. But
horsepower is still more useful that torque for judging acceleration,
because you just need to compare cars of equal weight at the same speed, or
at least factor them in proportionately.
So, which car, the Honda or BMW, is quickest? Both cars have their maximum
acceleration at their maximum horsepower of 240; i.e., at 6,000 rpm for the
Beemer and 8,300 rpm for the Honda. To a first approximation, the BMW is 10%
heavier, so it will accelerate 10% less. But, this neglects the power curve,
and since the engine changes rpm between shifts, it's really the time
averaged horsepower between shifts that counts. The Honda probably has a
narrower horsepower curve that the Beemer, so my money is on the BMW. Let's
say both cars have trannies with 0.75 ratios between gear changes; then the
Honda needs to shift at around 9,500 rpm (rpms drop from 9,500 to
0.75x9500=7,125 rpm) and the BMW needs to shift at about 6,900 rpm (rpms
drop from 6,900 to 5,175 rpm). One needs to take the average horsepower
between those rpms in order to figure which one actually has the overall
horsepower advantage. Odds are, it's the BMW, but without comparing the two
horsepower curves you can't be sure. And besides, the Honda engine may blow
up at 9,500 rpm.
Any questions? ;-)
Bob Palmer
rpalmer@ucsd.edu
rpalmerbob@adelphia.net
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