dg50@daimlerchrysler.com wrote:
>
> Not that the Edelbrock system is immune to these errors either, but with the
> extra data channels, you at least get the opportunity to rectify them.
You would need some (interesting) software to build all of those
corrections into the analysis system; however, the result could
be a really accurate total system.
> For example, there's a section on one of my traces that shows a 1.3G braking
> zone over .68 seconds. However, in that same section, the speed line drops
> 15MPH. Doing a little math yields 15MPH=22ft/sec, and a change of 22ft/sec in
> .68 secs is an acceleration of 32.4 ft/sec^2 - or about 1G.
>
> That's roughly a 33% error from what I assume would be pitch/roll, and any
> incline of the racing surface.
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.
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.
Solving for theta given your example means solving a transcendental
equation, but for small angles (where cos{theta} is always close to 1)
you can get there with successive approximations using a calculator:
theta = arcsin(0.3) gives 17.5 degrees, and cos(17.5) says you only
measured 0.95G of the actual deceleration so 0.35G was due to gravity;
thus theta = arcsin(0.35), etc .... Final answer is that a nose drop
of 21.7 degrees explains a measurement of 1.3G as originating from
0.93G of the 1G deceleration and 0.37G from gravity.
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.
Jim Carr
BS 1993 Miata & Old Fartz physicist
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