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    Re: AP terminology, WAS: 2-Body Fix -- take three
    From: Jeremy C
    Date: 2009 Nov 13, 16:31 EST
    In a message dated 11/13/2009 3:33:56 P.M. Eastern Standard Time, jhkarl@att.net writes:

    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.)
    The simple reason is that sailors don't like math, especially equations, and anything we can do to avoid triple interpolating both variables of the tables is what we are going to do; even if it means plotting several other points on the chart.  If you use a calculator or computer, there is no need to do this, and you can certainly use the position of the ship (or at least what the black box is telling you it is) for your Celnav.

    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 we need to get at least 2 Sumner points, and preferably three to expose plotting and/or math errors. Sounds like at least as much work, if not more, than St. Hilaire.  I don't know, since I've never plotted Sumner lines.  As an aside, we use the same equations with different names in our Great Circle sailings.

    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??
    Why is Blu-Ray better than HD-DVD, or VHS better than Betamax?  It was adopted over time and tradition truly does rule the seas.

    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.

    I don't claim to be great at Math.  I have a decent understanding of the Trig and the Celestial triangles, but I am certainly no expert.  I am however, an excellent navigator and extremely proficient in finding position at sea under a myriad of conditions using any body I can find.  I always use some prime point (typically a GPS fix at the top or bottom of the hour) as a starting point for my navigation, no matter what method I use. 
    So here is my challenge.  I need a demonstration from you to try to understand how you are solving these triangles without the third point of the triangle.  I can even supply you with any amount of real world information you may require to demonstrate 1) how the Sumner line is easier/better than the St. Hilaire line; and 2) how you can easily draw an LOP on a mercator projection without the use of a prime point position (DR/AP whatever you want to call it). I only ask that you don't use a computer to do this because we all know that computers can do this easily.  I just want to know how we do this as simple sailors with tables a universal plotting sheet, and some plotting tools.
    Here's your chance:
    August 23, 2009
    Altair at Ho 22 deg 09.1'  shot at UTC 15h 11m 31 seconds
    Rigel Kentaurus Ho 57 deg 43.0'  shot at UTC 15h 07m 08 seconds
    Ship's course  245 deg true, speed 17.8 knots.
    Find position at 1500 UTC
    All altitudes are ready to go.
    I look forward to your reply.


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