Regarding Gerhard Wiederholl's formula for HP as a function of top speed,
Ray W. James wrote:
> Very interesting; but why isn't this HP at the rear wheels, not at the
> flywheel...? Has the loss in the drive train been built into the
formula?
>
> Where does the formula come from? The only way I could imagine to develop
> such a formula is by getting dynomometer results on a series of cars and
> then document their top speeds, and develop an emperical curve of
HP.vs.speed.
>
> If done in this way, then it is a measure of power as the dyno measures
it,
> (at the rear wheels, right?)
The formula is, I suspect, merely a specific application of the fact that
wind resistance varies as the cube of speed. There are, of course, other
factors besides wind resistance that affect top speed - like drag
coefficient, frontal area, friction from the tires, gearbox, universal
joints, rear end, hubs and the like.
But if one assumes that all other factors are constant (not unreasonable
within a narrow speed range) then the horsepower required to produce a given
top speed varies as the cube of the speed. The actual horsepower required
can then be calculated as:
Horsepower = [speed]^3 divided by [some constant]^3
or, as in the formula given:
HP = (top speed in kph)^3 / (37)^3
Since the horsepower at the rear wheels is generally assumed to be some
percentage of the brake or clutch horsepower, that percentage can simply be
a part of the [constant] for purposes of this calculation. In a similar
fashion Gerhard's formula can be converted from KPH to MPH simply by
adjusting the constant (from 37 to 22.94).
If you accept the basic concept, you can calculate the constant from
published figures for engine HP and top speed of a similarly equipped (and
geared) automobile.
Note, however, that the horsepower figure you get will be the horsepower
rating at the RPM reached at top speed. If you're going as fast as you can
and you're not at the red line, there's probably more power left.
Of course with a Triumph, you have to factor in the weight reduction as
parts begin to fall off the car at high speeds . . .
Jim Hill
Amici Triumphi
Madison WI
PS: Wait a minute . . . YOU're the "P.E., Ph.D.", why aren't you explaining
this to ME?
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