Horsepower and Torque - a Primer (part 1)

[Bruce Augenstein <Bruce.Augenstein@xxxxxxxxxxx>]

There's been a certain amount of discussion, in this and other files, about
the concepts of horsepower and torque, how they relate to each other, and
how they apply in terms of automobile performance. I have observed that,
although nearly everyone participating has a passion for automobiles, there
is a huge variance in knowledge. It's clear that a bunch of folks have
strong opinions (about this topic, and other things), but that has generally
led to more heat than light, if you get my drift :-). This is meant to be a
primer on the subject.

OK. Here's the deal, in moderately plain English. 

Force, Work and Time

If you have a one pound weight bolted to the floor, and try to lift it with
one pound of force (or 10, or 50 pounds), you will have applied force and
exerted energy, but no work will have been done. If you unbolt the weight,
and apply a force sufficient to lift the weight one foot, then one foot
pound of work will have been done. If that event takes a minute to
accomplish, then you will be doing work at the rate of one foot pound per
minute. If it takes one second to accomplish the task, then work will be
done at the rate of 60 foot pounds per minute, and so on. 

In order to apply these measurements to automobiles and their performance
(whether you're speaking of torque, horsepower, newton meters, watts, or any
other terms), you need to address the three variables of force, work and
time. 

Awhile back, a gentleman by the name of Watt (the same gent who did all that
neat stuff with steam engines) made some observations, and concluded that
the average horse of the time could lift a 550 pound weight one foot in one
second, thereby performing work at the rate of 550 foot pounds per second,
or 33,000 foot pounds per minute, for an eight hour shift, more or less. He
then published those observations, and stated that 33,000 foot pounds per
minute of work was equivalent to the power of one horse, or, one horsepower.


Everybody else said OK. :-) 

For purposes of this discussion, we need to measure units of force from
rotating objects such as crankshafts, so we'll use terms which define a
*twisting* force, such as foot pounds of torque. A foot pound of torque is
the twisting force necessary to support a one pound weight on a weightless
horizontal bar, one foot from the fulcrum. 

Now, it's important to understand that nobody on the planet ever actually
measures horsepower from a running engine on a standard dynomometer. What we
actually measure is torque, expressed in foot pounds (in the U.S.), and then
we *calculate* actual horsepower by converting the twisting force of torque
into the work units of horsepower. 

Visualize that one pound weight we mentioned, one foot from the fulcrum on
its weightless bar. If we rotate that weight for one full revolution against
a one pound resistance, we have moved it a total of 6.2832 feet (Pi * a two
foot circle), and, incidently, we have done 6.2832 foot pounds of work. 

OK. Remember Watt? He said that 33,000 foot pounds of work per minute was
equivalent to one horsepower. If we divide the 6.2832 foot pounds of work
we've done per revolution of that weight into 33,000 foot pounds, we come up
with the fact that one foot pound of torque at 5252 rpm is equal to 33,000
foot pounds per minute of work, and is the equivalent of one horsepower. If
we only move that weight at the rate of 2626 rpm, it's the equivalent of 1/2
horsepower (16,500 foot pounds per minute), and so on.
Therefore, the following formula applies for calculating horsepower from a
torque measurement: 


                                	Torque * RPM
        Horsepower      =       ------------
                                          5252


This is not a debatable item. It's the way it's done. Period. 

The Case For Torque

Now, what does all this mean in carland? 

First of all, from a driver's perspective, torque, to use the vernacular,
RULES :-). Any given car, in any given gear, will accelerate at a rate that
*exactly* matches its torque curve (allowing for increased air and rolling
resistance as speeds climb). Another way of saying this is that a car will
accelerate hardest at its torque peak in any given gear, and will not
accelerate as hard below that peak, or above it. Torque is the only thing
that a driver feels, and horsepower is just sort of an esoteric measurement
in that context. 300 foot pounds of torque will accelerate you just as hard
at 2000 rpm as it would if you were making that torque at 4000 rpm in the
same gear, yet, per the formula, the horsepower would be *double* at 4000
rpm. Therefore, horsepower isn't particularly meaningful from a driver's
perspective, and the two numbers only get friendly at 5252 rpm, where
horsepower and torque always come out the same. 

In contrast to a torque curve (and the matching pushback into your seat),
horsepower rises rapidly with rpm, especially when torque values are also
climbing. Horsepower will continue to climb, however, until well past the
torque peak, and will continue to rise as engine speed climbs, until the
torque curve really begins to plummet, faster than engine rpm is rising.
However, as I said, horsepower has nothing to do with what a driver *feels*.


You don't believe all this? 

Fine. Take your non turbo car (turbo lag muddles the results) to its torque
peak in first gear, and punch it. Notice the belt in the back? Now take it
to the power peak, and punch it. Notice that the belt in the back is a bit
weaker? Fine. Can we go on, now? :-) 
(part two follows)

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End of bmw-digest V9 #943
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