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First off I would like to congratulate Frank for coming up with a new tool
for the navigator's toolbox. It is not often that that happens and I think
it is fair to say that this is one of the most significant contributions to
traditional celestial navigation since Marcq St.- Hilaire had his epiphany.
I hope Frank takes the time to write it up in the "Navigator's Newsletter"
or one of the other more formal forums for the discussion of celestial
navigation matters. He certainly should.

However, I think it is also right to talk about the practicalities of this
method. Frank's quip that if you want practical, then get a GPS, is quite
true - but suppose you are at sea in a small boat. It has been blowing a
gale for a week and the GPS fell overboard days ago. You have no idea where
you are, but the clouds finally part so you can see the moon, high in the
sky and some stars - but no horizon. Is it better to use Frank's method and
a marine sextant, or reach for the bubble sextant?

Like George, I have been worried about the accuracy which Frank claims for
his method. Frank has given a theoretical ultimate accuracy, with the
assumption that a good standard marine sextant is being used and is the
principal source of error. But George is right to point out that the data
source available to the likely user of this method will most likely be the
Nautical Almanac.

The average error for the GHA of the moon in the NA would appear to be
about 0.1' (The NA quotes 0.3' as the maximum error likely to be
encountered for the GHA of the moon, so assuming that this is three
standard deviations is, I think, reasonable.) Note that this is +/- 0.1'.

I also have deep reservations on the inherent errors of even "good"
sextants. We assume good sextants, coming as they do with certificates
saying that the maximum error is 0.1' , mean what they say and that sextant
will contribute no more than 0.1' to the error of the observation. But as
Alexandre Eremenko discovered when trying to get his SNOT calibrated, it is
hard to get accurate numbers when looking for errors at the level of
seconds of arc. Measuring angles to an accuracy of six seconds of arc (the
height of a man standing 20 kilometres away) is not easy. Sextants may have
this precision, but I question that even good ones will have this accuracy
across the whole arc.

Assuming a resolution of the human visual system to be 1' of arc, (0.5' of
arc has been quoted, but this is in ideal circumstances,) then to get the
observer's error down to the 0.1' level would need a telescope of at least
10x magnification. A stable platform starts to become a necessary condition.

If we use 0.1' as the error for the moon's GHA and throw into George's
calculation an error of 0.1' for the sextant error and 0.1' for
observational error, we get something closer to 0.25' as the best the
practical navigator (using a watch, Nautical Almanac and a marine sextant)
could hope for. Now we are up to 15 nautical miles as the best expected error.

On land, there is no doubt that it would be better to use a bubble sextant,
or put a bubble attachment on a marine sextant. At sea, pitching about in a
small boat, observational error for a moon-star distance would go up. Say
it went up to 1'. This is equivalent to not being able to measure altitudes
to much better than a degree with a bubble sextant in such circumstances. I
have no experience using a bubble sextant in a small boat, but I would
guess this is about right. I would be interested to hear the experiences of
anyone who has used a bubble sextant in a small boat.

For the scenario given above, it may be actually be better to leave the
bubble sextant in the box and use Frank's method with a marine sextant.
Then we can say that Frank's method is not only original, new, interesting
and significant - but also useful!

Well done Frank!

Geoffrey Kolbe





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