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From: Dr. Geoffrey Kolbe (no email)
Date: Sun Sep 07 2003 - 03:21:39 EDT
George Huxtable has pointed up a potential problem with the azimuth tables
in George Bennett's book "The Complete On-board Celestial Navigator". He
has shown that there can be errors in computed azimuth of (at least) 15
degrees where the celestial body is that sort of distance away from the
prime vertical.
Peter Fogg tells us that this is "nit-picking" and that in any case, the
book tells us that, "In extreme cases the table should be interpolated when
observations have been made in the vicinity of the prime vertical."
I do not have the second edition, only the 1999-2003 edition where this
phrase is not present. Perhaps Peter can tell us just what "extreme" means
in this context? When do we know we are in an extreme case? George also
posed some other pertinent questions to Peter and I too would be interested
to see the answers...
I also wonder just how much of a problem it would cause having your
near-prime-vertical azimuths off by around 15 degrees? For a cluster of
star sights, say, a prudent navigator would also be taking sights from
objects far away from the prime vertical (to get useful angular separation)
and this would tend to mitigate any problems due to bad near-prime-vertical
azimuths. The inaccuracy of the tables near the prime vertical are also
mitigated by being able to assess independently (in many cases) in which
azimuth quadrant the celestial object sits.
If your estimated position is pretty close (say, within 10 nautical miles)
to your actual position then I cannot think of any circumstances where it
would significantly affect the sort of accuracy we would expect from CN in
a small boat at sea, which is the sort of user the book was aimed at in the
first place. I have not thought deeply on this problem and I would
appreciate the thoughts of other listers who will have greater insight on
this problem than I.
The "short" method of sight reduction used by Bennett is popular because
the computed altitude can be arrived at quite quickly. But a different
procedure is required to calculate an azimuth and this rather takes the
gilt off this method. Ageton's method, by contrast, requires more steps to
get to the calculated altitude, but the azimuth then drops out very quickly
and is accurate. Azimuth quadrant ambiguities are also easily resolved.
Too, only one set of tables is required for the Ageton method.
Geoffrey Kolbe
-------------------8<---------------------
From: George Huxtable
The problem with these azimuth tables ...
is not in their ambiguity, but in their inaccuracy, and that inaccuracy is
exactly what I have complained about. And there is not one word, not even a
hint, in the book that major errors in azimuth can occur, for certain
observations in a VERY wide swathe around East or West.
-------------------8<---------------------
From Peter Fogg
Inserted in second edition is . "In extreme cases the table should be
interpolated when observations have been made in the vicinity of the prime
vertical and/or LHA, declination and latitude require substantial rounding
off before using the table. When in doubt use the Weir diagrams.
In practice you could happily sail across an ocean and never notice this
supposed problem, particularly by following the common sense approach
outlined previously. With nav. it it often a case of one system checking
another. In fact taking sights and working out a fix is a check on the
basic tool of running a DR.
If the whole book has been subjected to the same searching criticism and
this rather inconsequential nit-pick is the only flaw found, then it is
really a back-handed compliment to the book as a whole. A ferocious critic
seems to think the rest works just fine.
Border Barrels Ltd., Newcastleton, Roxburghshire, TD9 0SN, Scotland.
Tel. +44 (0)13873 76253 Fax. +44 (0)13873 76214.
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