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    Re: Fwd: Principles and Being Practical
    From: Geoffrey Kolbe
    Date: 2003 Sep 7, 08:21 +0100

    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
    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.
    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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