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    Marq St. Hilaire - Altitude intercept method
    From: Andrés Ruiz
    Date: 2007 Oct 24, 11:14 +0200
    Marq St. Hilaire - Altitude intercept method

    I have changed the subject Poor St. Hilaire to Marq St. Hilaire - Altitude intercept method.

    Poor?, Sumner and St. Hilaire are the fathers of the modern celestial navigation.

    Some remarks:

    The true celestial line of position is the circle of equal altitude or circle of position: CoP

    Any point (B,L) of the CoP satisfied the equation:

    sin H  = cos B cos Dec cos ( GHA-L ) + sin B sin Dec

    where

    ·       B  - Latitude (-S/+N)
    ·       L - Longitude (-W/+E)
    ·       GHA - Greenwich Hour Angle of the observed celestial body
    ·       Dec - Declination
    ·       H Altitude of the body from the horizon

    The Marq St. Hilaire Altitude intercept method in Celestial Navigation, use the tangent line to the circle of equal altitude close to the estimated position of the observer. This line is called Line of Position: LoP

    ·       The method reduces the problem to that of the intersection of LoPs in a plane in order to obtain the fix.
    ·       It is necessary to know the estimated position (DR). Other position near the DR can be used with no appreciable error

    ·       This method is approximate. The only point in common with the CoP is the tangent one, defined by the intercept (p, Z)

    The coordinates of such a point, (assuming p small enough), common to the Cop and the LoP are:

            p = (HO-HC)

            x = p*SIN( Z )

            y = p*COS( Z )

            B = Be + y

            Bm = (Be + B)/2.0

            L = Le + x/COS(Bm)

    Any other point in the LoP differs to the matching one in the CoP by the following amount:

            Bowditch Table 19 Offsets

            h Altitude [º]

            D Distance along the LoP from intercept [nm]

            R = (60*180/PI) / TAN(H)

            theta = ASIN(D/R)

    Offset = R*(1.0-COS(theta))

    Having said that, the intersection of two LoPs, the fix in St. Hilaire method, is a point that not belongs to the Cops, but is close to the true fix, (defined by the intersection of the CoPs).

    Now take the St. Hilaire fix and use it as the new estimated position in order to obtain another fix by this method, (doing this in a paper could help to understanding), the result is a point closest to the true fix.

    Usually in the practice only one plot on a Mercator chart is used.


    Good drawings are at the Ecole Marine Marchande  de Marseille web site:

    http://dept.navigation.enmm.free.fr/droite_hauteur.swf

    Andrés Ruiz

    Navigational Algorithms

    http://www.geocities.com/andresruizgonzalez


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