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Doug Royer said-

>A year ago I downloaded a tutorial about useing alternative methods to
>calculate differant navigational problems.I started reading through the
>pages and came to a chapter (chapter 7) that dealt with useing Lunar
>observations to find time and longitude.The proceedure is called "Finding
>Time and Longitude useing Lunar Distances by the Intercept Method".It has
>half the number of calculations and corrections as does the method used by
>Thompson (and others) and doesn't require the actual measurement of the
>distance angle between the bodies involved.Have any of you heard of or used
>this method?Would it be a topic of discussion that would interest
>you?Unfortunately I only saved the hard copies of the download and can't
>remember where I downloaded it from.If someone is interested I will research
>and find where I got it and post the site on list because I don't have the
>skill or time to draw the diagrams used to illistrate the proceedure and
>send them to the list.
>For my part I am going to study the proceedure closely the next few days and
>try it useing the data I got from the Lunars I observed in May.

Doug, that looks like a really intersting tutorial you have unearthed, and
I would enjoy reading the whole thing. Please rack your brain to discover
where it came from. It would be interesting to discover the author and open
a dialogue with him.

As for the method under discussion, which involves finding a time which
reconciles altitudes measured for the Moon and two other bodies, it does
come up on this list from time to time, probably before you joined.

It has certain snags, as follows-

1. However you calculate time, and longitude, from the postion of the Moon
in the sky relative to other bodies, that position has to be measured as
precisely as possible, because every minute of error results in a longitude
error of about 30 minutes. Precision is all. Anything that dilutes that
precision spoils the result.

The method described in chapter 7 uses altitudes measured, for the Moon and
stars, above the horizon. The horizon introduces by far the biggest errors
in celestial navigation. In rough weather, it's not a straight flat line,
but a series of wave-tops or swell-tops. The height-of-eye is very doubtful
because the vessel is heaving up and down. These effects are much worse for
a small craft than a merchantman, of course. Even in calm waters, there's
always the unknown effect of anomalous dip, in which light skimming past
the horizon is bent in an abnormal way on its path to the observer's eye,
because of low-level layers of air, near the sea surface, with an
unexpected temperature gradient.

In the chapter 7 method, these errors in the horizon can combine to add,
very significantly, to the errors in the result (though sometimes they can
partially cancel). The traditional lunar-distance method doesn't involve
the horizon at all (except in measuring the moon and other-body altitudes,
which are not needed to any accuracy), so it maintains all the
reading-precision that the observer can give it. That's why it was chosen
by Maskelyne in the 18th century. If the horizon was involved, the
precision would be so degraded that it just wouldn't be worthwhile as a
navigation technique.

2. The procedure described gives an "improved longitude" from an initial
estimate. Is that enough, or is another "iteration" needed, when you start
from the "improved" longitude and arrive at a still-better one? If so, that
extra calculation would destroy much of its simplicity.

3. The lunar parallax plays an important part in finding a position-line
for the Moon, and I have doubts as to whether the method takes this fully
into account when reassessing the new position after a time delta-T. But I
haven't gone into the details fully enough to be sure about that.

4. The idea that it was necessary to have three or four observers to
measure a lunar is an old red-herring from the Navy, that was thoroughly
discredited by many merchant officers and by Joshua Slocum, who were
perfectly able to do the job single-handed.

5. However, it's perfectly true that the traditional method of measuring a
slant-angle across the sky is unfamiliar, tricky, and needs a lot of skill
to get a good answer. If it were possible to do as well by measuring
altitudes "straight up" from the horizon, that would be welcome.
Unfortunately, it doesn't really work. It would be more convincing if
Chapter 7 had included some actual numerical examples. It will be
interesting to discover how Doug gets on.

George.



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