<1> correct horsepower formula:
HP = ( Torque * RPM ) / 5250
Please note that this is a linear relationship, not geometric
as previously stated.
So, what are we to do to increase the power of our cars by a factor
of say 20% for example? Well, you could either (a) increase the
torque by 20% at the same rpm (for example, by upping the boost),
or (b) increase the rpm by 20% with the same torque (power peak
@ 7800, up from 6500), or (c) increase both torque and rpm by about
9.5% (yes, 9.5% : do the math ... 1.095 * 1.095 = 1.199). or you
could get really crazy and increase both rpm and torque by 20% (1.2
* 1.2 = zoom!) for a 44% power gain ... isn't turbo rotary power
fun?
Historical note: Horsepower was "invented" by james
watt, way back when. mr watt, an engineer, and a damned good one
at that, was in the business of building steam engines (very cutting
edge tech at the time) and he had a problem: his steam engines were
not selling. Coal mine owners (target market) came to his demo,
watched the engine perform, nodded their heads as he explained the
engines capabilities, and wenttheir way without buying. Discrete
questioning brought forth
the reason for this sad state of affairs: the mine owners simply
did not understand physics or the engineering of the engines. So,
Mr. Watt toned down his talk a bit, but still no sales. Stepping
back from his problem, Watt reconsidered the competition and his
marketing. The competition was draft animals, most usually horses.
Hmmmm. The solution to his marketing problem, Watt decided, was
that he was not really selling steam engines, he was selling a replacement
for horses. Thus did Mr. Watt undertake a study of the draft animals
used in industry, and determined that the average horse could lift
550 pounds 1 foot every second. Thus 550 lbft/sec = 1 HP. Watt
revamped his presentation, making little mention of physics, and
instead stressed greatly the number of draft animals that could
be replaced by each steam engine. Sales soared. Other engine manufactures
took note of this success, and quickly copied watts rating method
and sales tactics.
Thus was the horsepower born to its ascendant position as THE
universal measure of engine output. The moral of this story: horsepower
was invented as a marketing tool. (Torque is what determines performance.
See below.)
<2> Basic physics lesson for the day: F = ma
The mass of the car is constant, so the above equation may be
simplified to: a ~ F
In plain language, the acceleration of the vehicle is directly
proportional to the force applied. To belabor the obvious, the force
is applied by the driven wheel(s) to
the ground. PLEASE NOTE that force is measured in POUNDS, not in
horsepower!!!
So, we wish to maximize the acceleration of the vehicle by selecting
the most advantageous shift rpms. Some simple physics (above) and
little algebra (spreadsheet of you choice) will show us how to obtain
maximum acceleration. I will not explain formulas in any real detail,
but the math is simple: (trans ratio) * (torque @ rpm) ==> plot
vs. speed for each gear examine the graph ... where the lines cross
is the optimum shift point (simple linear interpolation).
At the drag strip in the real world, one may need to deviate from
this slightly to obtain the best time. for example, in a bone stock
RX7, the above analysis would have you to shift to 4th at about
97MPH. This would produce the best overall acceleration (if we were
interested ingetting to 130) but in fact this shift occurs just
shy of the finish line and hurts ET. The better plan for the RX7
is to hold 3rd all the way to the finish line, winding to 8000 rpm.
This will sacrifice speed to save ET.
Footnote for the "horsepower" crowd ... if one follows
the "equal horsepower after the shift" strategy at the
strip, you will see a faster (higher) trap speed and a slower (higher)
ET ... this has some usage in pro drag racing, where there is often
a $$$ prize pay out for the car that posts the highest trap speed,
and another $$$ pay out for the quickest ET in the class. If you
want to pocket the speed prize, you will have to adopt the "equal
horsepower after the shift" method. Always remember: Drag racing
is about getting to the other end of the strip FIRST !!! Its not
about getting there quicker or getting there going faster, but getting
there first. So while the HP method will get you there going faster,
it will not get you into the next round if the other fellow got
there first.
barry
