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George:

Your simulated data has thrown me for a loop. I expected to learn, but
not to find that what I proposed is not what I expected. I started with
your first example, not expecting to do any more. First, I had to convert
your decimal data, which is what the computer needs, to that which is
what is commonly used with the sextant and the almanac.Degrees, minutes
and tenths. A bit of work, but no big deal. All of my programs input and
output data in that format. The conversion to decimal and back is done
out of sight. My first computer lessons stressed that, "The computer
should work for you and never vice versa." Alas, grossly violated these
days.

The results of that first try were not good. The altitude-time slopes
looked fine, and the ascending slope was flatter than the descending one,
which is what would be expected from the northward motion. But the time
from highest altitude to LAN was only three minutes, and I knew it should
be about five. So, I reluctantly tried the second set. Worse! I was
surprised to find that the slopes for that example were significantly
flatter than for the first. Giant difference! Astonishingly, the ratio
looked okay--the ascending slope was flatter than the descending one. So,
I had to sit back and think. My method is dependent on determining the
slope of the altitude-time lines, and therefore it is vulnerable to
factors that distort those. But I never expected to see such a huge
variation.

As I wondered what I would do if this were a real situation, I realized
that I would have to start taking sights earlier. The standard quoted is
twenty to thirty minutes before maximum altitude. Your example started
twenty-five minutes before. But with such a low altitude, I should start
earlier. Hindsight, but that's what I would do faced with the situation.
That intensifies errors due to changes in course and speed, but it's the
only way out.

I make my students plot their sigths, and they reluctantly do so at
first. But they have increased confidence in them when they see that they
fall on a straight line. The idea there is to help them select the best
sight for reduction. Now, I once was invited to introduce a boatload of
scouts to celestial navigation on one of the LA Maritime Institute's
brigantines. I instructed them as to how to hold and use my sextant, and
how to take readings. Then I turned them loose. I gave each one a single
opportunity, and recorded the time and altitude. I couldn't reduce the
sights, but I did plot them as they took them. I was pleased that they
all fell on a straight line. That meant that they were doing it right.
Their first sights ever, and they were all good. Except for my
granddaugher's. Anyway, I'm a believer in plotting runs of sights. Too
see such an extreme variation in your simulated data shakes my
confidence.

So, I need a run of sights starting earlier. Maybe forty minutes before
maximum altitude. Sorry to make more work for you, but if we're trying to
simulate real life, it's necessary. The idea of the double altitudes
method is to take sights far enough away from LAN to get a reasonable
attempt at determing it. At higher latitudes, starting earlier is the
only way to do that.

Hoping for better results next time.

Jim Wilson
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