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    Direct Sight Reduction
    From: Chuck Taylor
    Date: 1996 Aug 23, 12:08 EDT

    Celestial navigation as currently practiced relies on two concepts:
    1. The celestial line of position, developed by Sumner, ca. 1830
    2. The altitude-intercept method, developed by St. Hilaire, ca. 1870
    We compute azimuth and intercept for each sight, then plot lines of
    position from our DR or assumed position, and where the lines of
    position come together is our fix. Sight reduction can be via various
    tables or by calculator/computer using the Law of Cosines. We can think
    of these methods as "indirect sight reduction": we get our latitude and
    longitude indirectly by first computing azimuths and intercepts.
    "Direct sight reduction" means we compute latitude and longitude
    directly without computing azimuths or intercepts, without using DR or
    AP, and without any plotting. A GPS does direct "sight" reduction.
    Direct sight reduction has not been widely used to date because it has
    been considered "too hard". It appears that this may no longer be the
    The newest issue of Ocean Navigator (September/October) has an extremely
    interesting article on page 110 about a new direct sight reduction
    method being developed by Tony DiCambio and a company called Triangle
    Navigation, Inc., of Rye, NY. They call it the Evening Star Astronomic
    Ephemeris (ESAE) system of Direct Sight Reduction. The company has
    apparently been working on the method for 8 years and intends to sell
    computer programs using the method for a profit. So far, they have a
    version that works only for the sun, runs on MS-DOS, and sells for
    $240. They are working on versions that work for stars and that also run
    on Windows and Macintosh. The programs have built-in almanacs.
    The idea is to harness the power of a personal computer to grind out the
    arithmetic. They claim that you can get an accurate fix from two sun
    sights taken 5 minutes apart. Ocean Navigator's tests confirmed that
    claim. Applying the method to stars, you would enter two star sights
    taken a few minutes apart and get out your lat/lon at the time of the
    second sight, without any need to adjust for the difference in time
    between the two sights.
    The method works by solving 3 celestial triangles in succession:
    Triangle	Vertices
    --------	--------
    1		Star 1, Star 2, and the observer's zenith
    2		Star 1, Star 2, and the elevated pole
    3		Star 2, the elevated pole, and the observer's zenith
    The article (by Andrew Howe) omits some details, which the company deems
    "proprietary". Aparently the algorithm has a number of branches
    depending on the relative positions of the stars (east or west of the
    observer, north or south declination), which adds to the
    complexity. Also not explained is how the method allows for the
    difference in time and the motion of the observer between observations.
    As mentioned, the programs being developed by Triangle Navigation
    include built-in almanacs. It would be interesting to see how well the
    method could work using look-ups from a paper almanac and doing
    calculations with a programmable calculator.
    For more information, please see the article in Ocean Navigator, or
    contact Triangle Navigation at (914)-381-9210, triangle@XXX.XXX or
    http://home.sprynet.com/sprynet/triangle/. Triangle will happily send
    you a reprint of the article.
    Chuck Taylor
    Everett, WA, USA
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