Newsgroups: sci.aeronautics.airliners,misc.transport.air-industry,
	alt.disasters.aviation
Date: 22 Nov 96 05:48:07
From: Ed Hahn <ehahn@mitre.org>
Subject: Vertical Speed Measurement (was Re: Peruvian 757 crash -- possible 
	cause reported)

"David G. Davidson" <gerhard@onramp.net> writes:

> After looking this is up again I see this going to require somemore
> research.
>
> The ADCs feed:
>
> Altitude, Altitude Rate, True Airspeed
>
> to the IRS. The IRS in turn outputs:
>
> Attitude, Mag Heading, Vertical Speed, Angular Rates, Linear
> Acceleration
>
> Present Position, True Heading, Ground Track Vector, Wind Vector
>
> Whether the IRS uses any of the ADC info to calculate VS is unclear. The
> IRS should certainly be able to figure it out using the accelerometers.
> I do know that we've never fixed a VSI problem by changing the ADC, only
> the IRS has fixed this. I'm only talking about 757/767 here.

The IRS is unable to give an accurate position OR speed in the
*vertical* dimension due to an effect called the "Gravitational
Gradient".  (See Appendix below.)  Therefore, the primary source of VS
information will always be the static system.  So why feed the info
through the IRS?

The Air Data Computers measure Altitude Rate one of two ways: 1) by
taking the change-in-altitude over successive readings and dividing by
the change-in-time during those readings, or 2) by looking at the flow
rate in and out of the static system via a number of complex
mechanical/pneumatic devices.

Unfortunately, because of the nature of the altitude rate measurement
in EITHER case, the Altitude Rate will ALWAYS lag behind the actual
aircraft motion.

Now then, the reason the IRS supplies the Vertical Speed (VS) is
that, while the vertical accelerometer CANNOT provide raw VS output,
it CAN provide enough of a "smoothing" signal to the Altitude Rate
signal to allow the cockpit instrument to not lag behind the
aircraft.  (See Appendix below.)

Note that the cockpit instrument is most properly known as the
"Inertial-lead Vertical Speed Indicator", but is more commonly known
as the "Instantaneous Vertical Speed Indicator".

Hope this helps,

Ed Hahn

Appendix:  So what's the Gravitational Gradient?

Recall that the IRS uses a set of three accelerometers (one on each
axis) and three gyros to generate all of its information.  Basically,
the IRS uses the three accelerometers to determine linear changes in
motion, and uses the three gyros to measure rotational changes
(i.e. attitude changes).

Normally, you cannot build a device which measures linear speed
directly - Newton figured out a long time ago that any unaccelerated
motion feels identical - in other words, you can't tell without
looking at an external reference point whether you are standing still
or moving at hundreds of miles per hour, as long as you don't change
speed or direction.

However, accelerometers use the basic physics principle relating
acceration, velocity, and position. In other words, if you take the
accelerometer's reading and integrate it once, you get the velocity.
If you integrate that velocity once more, you get the position.  Of
course, you have to worry about constants - but the alignment
procedure takes care of that.  (The gyros, on the other hand, don't
have this limitation because motion in a rotating frame is easily
detectable.  The gyros can measure rotation rate directly.)

Unfortunately, while this works great for the two accelerometers in
the horizontal plane, the vertical axis has a problem:  in steady
level flight, the vertical accelerometer will still experience
gravitational accelertion (~1g). However, again thanks to Newton (and
Einstein), we know that the acceleration due to gravity falls off as
the aircraft climbs higher (f = Gmm'/r^2). There is, in other words, a
*gradient* to the gravitational acceleration with altitude.

So, if a small bias (error) exists in the vertical accelerometer
output, the IRS cannot tell whether this is due to the aircraft
changing altitude within the gravitational gradient, or whether this
is just a problem in the signal.  This leads to divergent behavior of
the output.

For example:

1) say the bias makes the accelerometer read slightly high
   (i.e. indicating a slightly greater vertical acceleration from
   gravity than is really present).

2) Since the IRS cannot detect this, it assumes the aircraft is
   accelerating upwards slightly (i.e. climbing).

3) Because the aircraft is moving away from the center of the earth,
   the IRS then *must* assume that the acceleration due to gravity
   should also decrease.  (The effect of the gravitational gradient.)

4) But the accelerometer output hasn't changed because it really
   hasn't moved vertically.

5) Since the output is the same, the IRS must assume that there is an
   additional real acceleration in the aircraft upwards.

This cycle (2-5) continues until the velocity and position solutions
blow-up divergently.  Note that if the bias was in the other
direction, the solutions would still diverge, but in a downward
direction.  Since you can't build a perfect accelerometer, you're out
of luck.

This effect is why barometric altitude rate is always the source of
the source of vertical speed, and is only smoothed by the IRS to
respond more quickly (i.e. you can use the presence of a change in
vertical acceleration to deflect the IVSI needle ahead of time,
countering the lag inherent in the baro system.).