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    Re: sight reduction tables
    From: Peter Fogg
    Date: 2007 Oct 5, 20:56 +1000

    Five days ago I somewhat flippantly answered Lu's:
      It's also my
    understanding (at least as of a decade ago or so) that most of the long
    distance voyagers that still practicing celestial navigation use Ho249

    with:
    As if it was a question of one or the other, Lu!  There are other methods ...

    I'm a little bit surprised that so many people, who are in other ways so well informed about matters navigational, seem to think that when it comes to sight reduction then the choice is limited to choosing between HO 249 and HO214.

    Quoting from: New Sight Reduction Tables

    "The two most popular tabular techniques were using either the DR position or a chosen position; the latter based on an integral degree of latitude and local hour angle. This method required six volumes of tables to cover all possible latitudes ...

    On the other hand, tables using the DR position require multiple interpolated entry points. The Ageton Tables (H.O.211) have proved popular and consist of 49 pages of log secants and log cosecants at 0.5 minute intervals. The solution is accomplished in ten steps, with an extra four steps if an azimuth solution is required. Because the DR position is used, the intercepts are usually short, whereas using a chosen position the intercepts are often long and it may not be known until after plotting that a mistake has been made in the sight reduction procedure.

    In 1979, P F Pfab of the Honorable Cross-Staff Society of Sweden published his so-called PET Tables (reviewed in the US and British Journals of Navigation) which were based on the cosine-haversine formula, as adapted by  Radler de Aquino, but only after a detailed investigation of tabular methods had been made. His analysis took into account such things as accuracy, rules, book openings, DR versus assumed position etc. The PET Tables have been modified and adopted here. They are extremely simple to use."

    In this way does the author of The Complete On-Board Celestial Navigator explain the reasoning behind, and the history of, the sight reduction tables contained in his book. They consist there of 20 quarto pages and are tabulated for 1 minute of arc intervals, adequate for the purpose of the book (practical celestial navigation from a small craft).

    They would seem to constitute a useful alternative to the HO family.

    Relatively recently George Bennett has revisited and expanded these sight reduction tables, with the aim of making them suitable for use with the increased requirement for precision associated with lunar distances. Two versions were devised: Six figure tables (in place of the original 5 digits) in half minute intervals, and then six figure tables with minute intervals.

    The latter are freely available on the author's site:
    http://gbennett.customer.netspace.net.au/
    under:
    New Sight Reduction Tables

    I find them (the six figure tables) a little more fussy to use, although not much different to the original tables in the book. A table of Proportional Parts and a Sum Search Values is included to assist interpolation. They appear to address the lack of precision of the original tables.

    They consist of (or rather, can be printed out as) 20 A4 pages, which I have slid into plastic sleeves between more substantial plastic covers. Hardly one volume, let alone multiple volumes that need replacing at regular intervals ...

    The quotes above come from an explanatory note offered with the tables, which includes a worked example.




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