Computing MPH

[steve ravet]

This algorithm is basically "drawing rectangles" under the curve to
estimate area.  Calc was a while back for me but I remember that for the
same number of points you could get better accuracy if you topped your
rectangle with an angled line to better match the curve.  That would be
something like (for 4 data points G1-G4)

V1=(G1+G2)/2*t
V2=(G2+G3)/2*t
V3=(G3+G4)/2*t

velocity at endpoint=V1+V2+V3

There was also an elliptical method that would fit an ellipse to the
data using a moving window of 3 adjacent points.

Neither is necessary for calculating trap speed BUT I would think that
if you were trying to attempt dead reckoning (integrating G twice to get
position) that you would want to use the most accurate integration
possible.

--steve

Greg Hermann wrote:
> 
> At 10:00 AM 8/27/01, steve ravet wrote:
> >You need Gs and time.  The first derivative of distance is velocity, and
> >the second is acceleration.  If you take the acceleration info,
> >numerically integrate w/ respect to time, you'll get velocity.
> >Integrate one more time and you'll get distance.  It's easy to do:
> >
> >Take each acceleration data point, multiply by the sampling interval.
> >Sum these up to get your velocity.  If Gs are in ft/sec^2, you'll get
> >velocity in ft/sec.  There are other methods of mumerical integration
> >that are more accurate, you could find them in a starter calculus book.
> >A faster sampling rate will improve the accuracy of this calculation but
> >it probably doesn't matter too much if you only want trap speed (vs
> >speed at other points on the track).
> >
> >--steve
> >
> This approach is as accurate as you are going to get for any given sampling
> rate. dt is actually approximated by delta t (the sampling interval),
> rather than being infinitely small, as is the "theory" in calculus--
> 
> Greg

-- 
Steve Ravet
steve.ravet at arm.com
ARM,Inc.
www.arm.com
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