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"There are no stupid
questions, only inquisitive idiots." Gregory House
Rick Asks:
<<over time,shouldn't the rotation of the earth cause the gyro to
indicate a change
(error) relative to earth's horizon. >>
Yes it would if it were not for the fact that most gyroscopic aircraft
instruments, including AHRS, have some form of gravity vector aiding.
Mechanical attitude gyroscopes have the equivalent of a pendulum that,
during level flight, points towards the center of the earth. The
coupling of the aiding is weak so that it takes several minutes for
the gyroscopic frame of reference to erect normal to the local earth
plane. You can see this if you put your plane into a shallow turn for
several minutes and then roll level. Your instrument should then have a
bank offset that takes several minutes to self correct. What is
happening is that the centripetal vector, due to the turn, which is
parallel to the earths surface is added to the gravity vector producing
a new vector that everything in the airplane feels as gravity. If you
are in a 1G (horizontal) turn you would "feel" 1.4 Gs (vector sum) and
have a bank angle of approximately 45 degrees. If you held this turn
long enough the gyro would erect and show you in level flight. In
theory, you could hold a 45 degree indicated bank and "chase" the
vector to structural failure or a 90 degree bank, which ever occurs
first.
Directional Gyroscopes doe not have gravity aiding and DG precession is an example of
earth rotation induced error. Remember that at the mid latitudes your
velocity while "standing still" is about 700 mph due to earth's
rotation and the earth turns "under" you at 15 degrees per hour.
In practice the erecting effect is weak enough so that it reasonably
averages all flight maneuvers and stays acceptably close to earth
normal. Most MEMS AHRS can be upset easier than your typical mechanical
artificial horizon and there is usually a flight maneuver, such as a
climbing low rate turn, that will cause a MEMS AHRS to lose its
reference. This is the major "gotcha" that you can only find out about
during flight testing as it is very difficult to replicate in an lab.
An AHRS, in theory, could be configured so that once referenced to the
earth it would maintain an accurate indication regardless of the
duration and rate of the turn. If you know your velocity and yaw rate
you can calculate your instantaneous centripetal vector and then
subtract that from the measured "gravity" vector. Viola! Sounds easy
but in practice there are many secondary effects that conspire to make
things difficult. You are fighting sensor accuracy, calibration
accuracy, hysteresis, vibration, temperature drift, sensor noise,
induced noise, non linearity, rounding errors, aliasing, algorithm
approximations, gain drift, sensor aging, mechanical tolerances and
production variances to achieve the highest levels of performance. You
also need to get your math and algorithms right and implement them in
code accurately and efficiently. (Caution: Shameless boasting follows)
I know this because these are all the things we had to overcome in
order for the Chelton ADAHRS performance to match that of the flight
reference system, a Collins AHR-3000, typically used in a Pro Line 21
system.
Any idiot can take some cheap sensors and build an AHRS that works fine
on the ground. Many have. Take the thing into the air and your problems
increase exponentially. The bad news is that flight testing is
expensive and the faster your airplane the more AHRS performance you
need. An "inexpensive, high performance AHRS" is an oxymoron as
engineering and flight testing costs to develop same can run well into
7 figures. Allocate those costs over a few hundred systems and you are
into your "cheap AHRS" a couple of grand before you even add in the
bill of material costs, assembly costs, overhead and margin.
One point of clarification. I do NOT think Rick is an idiot,
inquisitive or otherwise. I just couldn't resist the opportunity to
include a funny quote.
Regards
Brent Regan
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