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    Re: AP terminology
    From: Peter Hakel
    Date: 2009 Nov 13, 15:16 -0800
    Since LOPs are one-dimensional objects, you need precisely one parameter to characterize them.  It is this parametrization that amounts to "calculating the LOP directly" (answer to Geoffrey Kolbe's question).  Sumner used longitude as the parameter.  The parameter doesn't have to be longitude and in the case of LOP=meridian, it is in fact unsuitable.

    The LOP is what it is, based on the Ho and GP, independent of any AP.  As I said in an earlier post, you need to have a coordinate system to do anything practical.  The AP is the origin of such a convenient local coordinate system.  We have some freedom in choosing where to place this AP=origin.  The computed intercept distance then tells us how far the chosen AP is from the LOP, and the computed azimuth tells us the orientation/direction.  That is what the solution of the celestial triangle AP-GP-Pole is about; it gives the relative position of the (independently existing and fixed) LOP and our arbitrarily chosen AP.  In practice St. Hilaire proceeds in reverse; we choose the AP first, solve the triangle, and then we construct the LOP at the appropriate distance from the AP and orientation with respect to true North.

    On a Mercator plotting chart LOPs look like straight lines (for not too high Hs's).  A straight line lying in a plane can be defined by two points, or by one point and one direction.  Sumner uses the former; St. Hilaire uses the latter.  St. Hilaire is less work because one detail regarding the direction part is automatic; it is the angle between the LOP and the azimuth line toward the GP, which is always 90 degrees.  We can therefore plot the LOP at the right angle to the azimuth line (at the intercept distance) because Mercator mapping used in plotting charts is conformal, i.e. it preserves angles.


    Peter Hakel



    From: John Karl <jhkarl---.net>
    To: NavList <navlist@fer3.com>
    Sent: Fri, November 13, 2009 12:33:27 PM
    Subject: [NavList 10635] Re: AP terminology, WAS: 2-Body Fix -- take three


    No one has addressed my question of why the St Hilaire method
    calculates an altitude at a location our ship is NOT at, when we've
    just measured the altitude where our ship IS at.  (For politically
    correct reasons, I'm not using the name of this location.)

    Now lets go back to Sumner's 1837 calculation, where he picked three
    different longitudes and calculated three points on the circular LOP.
    This calculation is exact, and the equation for each point is the same
    as the one of the two necessary in the St Hilaire method (thus each
    Sumner point is half the work of a St Hilaire reduction).  And he
    could calculate as many exact points as he wished.

    So I'll put my question yet another way:  Why is the St Hilaire method
    superior to Sumner's and consequently the only one used today??

    I claim that the answer to this question has been made confusing
    because of the conventional name (names?) used for the location of the
    St Hilaire altitude calculation.  As evidence of this confusion I note
    that some authors write that we need to assume some point because the
    distance between the GP and the LOP is too great to plot, that there's
    insufficient information to plot the LOP, or that iterations are
    required to get exact points on the LOP.  The Sumner calculation
    demonstrates that none of this is correct.

    JK




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