G-Tech meter

[Bruce Bowling]

>Correct me if I'm wrong but this device is just measuring the
>acceleration of itself (the G-Tech meter & its chassis) relative to a
>factory calibration (presumably while static).  Therefore it doesn't
>matter what 'environment' it is in at any given time.  For example, it
>will work in my hand while running as well as in my car while driving. 
>For that matter - in my spaceship while cruising through the stars
>(read: not on earth!)  Its just simple physics: Force = Mass x
>Acceleration.  The only other equation anyone needs to build such a
>device is the definition of one horsepower.

>Shane

The correction I am talking about is the environmental effects on air density,
which will affect produced power. Using the simple physics F = mA, the force
is a function of test environment, and is not a constant. G-tech does
not account for this (as well as aero/friction/rolling/inertial losses) so
any absolute number is meaningless. This is why HP and torque numbers are
published (most of the time) at "standard correction (29.92 Inches Hg Barometric
pressure at sea-level, 0% relative humidity,and 60 degrees F) or "SAE correction"
(29.38 Inches Hg Barometer at sea-level, 0% relative humidity, and a test temperature
of 77 degrees F).


>me three .... didn't I see such on Bowling's page or
>somewhere's ???  torque/hp vs weight & accel ???

Yes, you did. The equation I used for a "road" dyno program is the following:

       Horsepower = (Weight(Lbs) * Acceleration (g) * MPH)/375.0

The inputs to the program are environment, vehicle weight, aerodynamic and tire info,
and correlated pairs of MPH and time which one measures. The program then fits a piecewise
cubic spline (of the form y=a + bx + cx**2 + dx**3) which joins each time/MPH segment.
I could have used a least-squares fit polynomial instead of a spline, but the spline has
a deterministic order (fitting with a high-order polynomial can often end up with a
wildly-oscillating curve) with the drawback with the spline being that one now has to handle
different coefficient values depending on which set of pairs of HP/time points I bracket.

To compute acceleration, one simply takes the derivative of the spline (Y'=b + 2*c*x + 3*c*x**2)
and converts units to G's. Now stick into the above equation. To generate the RPM numbers, the
RPM values are back-propagated using the supplied gear ratios. Also, the HP number is then
corrected for environment/aero/rolling/friction.

See:

    http://devserve.cebaf.gov/~bowling/dyno.html

G-Tech uses the reverse: it has acceleration, and generates speed by taking a numeric integral:

   V = (V + Acceleration * DeltaTime) * UnitsCorrection

To do this, one has to have (or assume) an initial V. 

Which method is better? As it can be seen, having acceleration numbers mean one does an integral,
where with speed, one does a derivative. Generally, numeric integration is easier and more stable
than numeric differentiation. Having both (a device with an accelerometer AND a way of measuring
MPH) means that one can do both methods to cross-check results.

- Bruce


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                 Bruce A. Bowling
                 Staff Scientist
   Thomas Jefferson National Accelerator Facility
    12000 Jefferson Ave - Newport News, VA 23602
                 (804) 249-7240
bowling at cebaf.gov  http://devserve.cebaf.gov/~bowling
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