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[About half a second before my reply went out, too late to stop it, I
saw that it was going to Jared Sherman only. Since he did ask the
question on the Navigation list and it's on-topic, I will repost my
reply to the whole list.]

Jared Sherman wrote:
>
> Paul, how did your position fixes agree with where you actually were?

I didn't take any fixes, just shot the Sun when convenient. There was
no attempt to plot LOPs or cross them for a fix.

Since I shot from a known position, the observed altitudes should have
matched the calculated ones obtained from the USNO Web page. Any
discrepancy would be due to nonstandard refraction, personal error
(i.e., systematic tendency to position the body off center with
respect to the bubble), instrumental error, or random error.

Refraction I'm disregarding, so that leaves the last three. The
personal and instrumental errors can't be distinguished by any simple
test I know, and since I'm the sole user of these instruments, there's
really no reason to do so. I simply took the mean discrepancy (Ho - Hc
for all observations) and called it "index error". That was +12
minutes for the A-12 and -1.4 for the Kollsman. These are the amounts
my observations were offset (on average) from the expected values.

After subtracting this bias, the individual observations will still
have random plus and minus discrepancies with respect to the expected
values. The size of these is expressed by the standard deviation: 1.8'
for the A-12, 1.7' for the Kollsman. What this means is that after I
subtract 12' to remove the index error, 2/3 (practically) of my A-12
LOPs would lie within 1.8 miles of my position, if I plotted the
observations. And that is the bottom line.

It's surprising a near-novice can do so well, since my A-12 requires
centering a 30' solar disk in a bubble image, the inner ring of which
is about 120' in diameter, and doing it without the aid of any
magnification. Furthermore, the Sun and bubble don't move together as
in a marine sextant. The Sun moves around with respect the bubble, so
you must mentally average out the wobbles.

I made a special effort to work fast, terminating each observation as
soon as the coincidence looked correct. "Miss 'em quick" was the
saying among the old U.S. Coast & Geodetic Survey triangulation
observers. They found that fussing with the theodolite added no
accuracy, wasted time, and tired the observer.

Of course when using the Kollsman's averager you do have to sustain
the coincidence. But on the other hand it runs for two minutes so any
given instant is not critical. You just maintain a good overall
picture and trust the pluses and minuses to cancel.

   

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