From: lc2b+@andrew.cmu.edu (Lawrence Curcio)
Newsgroups: rec.models.rockets
Subject: 3-Observer Tracking (Long)
Date: 8 Sep 92 03:27:10 GMT
Organization: Doctoral student, Urban and Public Affairs, Carnegie Mellon, Pittsburgh, PA

I tried out the 3-observer trajectory analysis procedure over the
weekend. We tracked six flights of two different rockets, the ESTES
SKYHAWK and CHEROKEE upper stage. All launches were as vertical as
possible, and we used a plumb bob to make them so. The weather was
overcast with a 15 mph wind, higher in gusts, so strictly vertical
filghts were impossible. (I would have scrubbed the launch but it's
hard getting enough people together to do something like this.)

The trackers were 135 feet apart from each other, arranged along a
straight line. The center observer was approximately 300 feet from
the launch rod. Each (elevation-only) tracking instrument was made
from a protractor, a yardstick, a string and a weight. A BASIC
program is included in a separate post to reduce the three
elevation angles to X, Y, and Z(altitude) measurements in a
coordinate system with the center observer as the origin. 

^    |-End Tracker
|    |
|    |
|    |         ~300 feet      
135' |----------------------- <>   (Launch Pad)
     |\Middle Tracker         
     |
     |
     |-End Tracker



Of the six flights, two had impossible data, and a third gave an
absurd altitude. It turned out that the particular combination of
angles on the absurd flight was very sensitive. A single degree
more for the center observer would have given a reading about 600
feet lower. Another degree more would have given a flight 700 feet
lower. (The combination was 68, 64, and 60 degrees for the left,
middle and right observer respectively.) 

With the limited area we had to work with, most altitude estimates
would have varied about 100 feet for a single degree of one
observer or another. My instruments were not accurate to 1-degree.
Larger tracking lines and distances from the launch pad would have
helped matters. I did find that, for vertical flights, I had an
error check that was at least as powerful as the redundant
altitudes from the 2-observer azimuth/elevation method. Since I
knew the approximate coordinates of the launch rod, and since the
flights were fairly vertical, I could compare the estimated X and
Y (horizontal) coordinates of the rocket at apogee with these. If
they were approximately equal, I knew the data were approximately
correct. This procedure compares tracking data to known quantities,
albeit approximately known ones that will vary somewhat in
practice. The same procedure does not work in the 2-observer method
because the horizontal coordinates are obtained from the azimuth
angles alone; the elevation measurements are left untested. In the
3-observer method, all coordinates use all elevation angles, so if
2 coordinates of 3 are correct, then so is the last. (Unless all
trackers shoot the wrong point, an event more likely with the 2-
observer method.)

Of the 3 flights I accepted, the Y coordinates were 323, 302 and
163 feet. The X coordinates were -131, -35.3, and -31 feet (The
launch pad was to the negative side of the middle observer by about
100 feet. Launch pad coordinates were known only roughly.)

SUMMARY:
My impression of the method, then, is that it requires a lot of
room for good precision, and that error sensitivity checks must be
performed before a track is accepted. ** In the context of near-
vertical ascents with a launch rod at known coordinates, the lack
of a redundant altitude reading is not a loss. ** Finally,
impossible angle combinations are common in practice.
Newsgroups: rec.models.rockets