Jim Carr sez:
> Exactly. Tilting the accelerometer causes two errors. A
component
> of the acceleration of gravity will now be along that axis of
the
> accelerometer and be interpreted as a change in velocity, and
the
> actual acceleration of the vehicle will no longer be parallel
to the
> axis of the accelerometer and part will get missed. The
properties
> of the trig functions make the first effect big and the second
small.
This is also a problem in a car with no pitch or roll going up or
down a grade or cornering on a curve with camber. The best you
can do using only acceleromters is to resolve accelerations in
the plane of the pavement. This is why the g-analyst has 3
accelerometers on orthogonal axes. The others all make do with
2-axis accelerometer systems.
> Specifically, when the car is nose down (as when under braking)
by
> an angle theta, the device will only see a*cos{theta} of the
actual
> (de)acceleration and will see an additional g*sin{theta} of
forward
> acceleration on the test mass from gravity that it interprets
as
> additional deceleration.
Not only that, but any inclination error due to the installation
in the car - you need to get the longitudinal accelerometer
perfectly level when the car is on level ground - will contribute
to the same tpye of error. Again, the g-analyst accounts for
that.
> Solving for theta given your example means solving a
transcendental
> equation,
The g-analyst has a calibration setup that includes estimates of
roll and pitch in degrees/g. There's a table in the manual giving
typical values of these parameters for different types of cars
ranging from large family sedans to formula cars. It's not
perfect, but you can account for pitch angle and resolve the
actual deceleration to a new axis that isn't necessarily
coincident with any of the accelerometer axes through relatively
simple rotation of axes mathematics.
> Since the sine function rises rapidly, seemingly small pitch or
roll
> angles produce a significant error in the measured
accelerations.
> Integrating these errors produces the direction and distance
errors
> that result in a bad map -- hence the option to fix the map
within
> GEEZ!. They would also throw off the speed. Using GEEZ! to
study
> relative changes (e.g. full use of friction circle) due to
driving
> inputs is unaffected by these kinds of errors, but evaluating
changes
> in the suspension (which *will* alter roll and pitch angles for
the
> same maneuver) requires awareness of them.
I prefer the g-analyst no-shortcut transducer approach, although,
since it's been discontinued, that point is moot. The ideal
system would also include a gyroscope-stabilized horizon
indicator as well, so pitch/roll angles wouldn't have to be
estimated, but I don't think anyone's likely to go that far.
=8<0
Jay Mitchell
ASP Lotus Europa
Pretty old myself (relatively speaking ;<), and a physicist too
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