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    Re: AP terminology
    From: Peter Hakel
    Date: 2009 Nov 15, 10:23 -0800
    I agree that misunderstandings often occur simply because of different interpretations of key words, not necessarily because anyone has a factually wrong idea.

    The universal plotting charts that I have show five parallels of latitude and a compass rose in the middle.  By putting numbers on those parallels and drawing the corresponding meridians, we are automatically "assuming" that this is where the ship is, somewhere in that region.  Then, within this "assumed region" (AR) we choose an "assumed position," draw a straight-line LOP, etc.

    Since the question was about how to compute the LOP "directly" without any AP, we have to consider the LOP in its entirety.  That is a circle and not just the relevant section approximable by a straight line.  The only "natural" reference point, independent of navigator's choice, is the GP which will be at the root of the parametrization of the entire LOP.

    I believe that computing an LOP "directly without an AP" and yet "within the context of the St Hilaire method" is an oxymoron and thus this question cannot be answered.  Indeed, John Karl calls this section of his book "Position without St. Hilaire" in which he writes (p. 79): "Note that this is a sight reduction in its own right, completely avoiding the St. Hilaire intercept method."

    BTW, Problem 5.9 in his book (p. 192) does find the fix using the St. Hilaire method, but with equations of planar analytical geometry instead of actual plotting.  There the (straight-line!) LOP's are necessarily parametrized.  John chose relative azimuth angles as parameters and used the common AP as a reference location.

    Peter Hakel

    PS. I used the term "compass rose" above.  Is that the correct term, or is it properly called "azimuth rose" or something different altogether?  Well, "a rose by any other name…" right?   :-)

    From: Geoffrey Kolbe <geoffreykolbe---.com>
    To: navlist@fer3.com
    Sent: Sun, November 15, 2009 12:07:18 AM
    Subject: [NavList 10688] Re: AP terminology

    Frank, Peter H and Peter F.

    The confusion comes from a loose (I hesitate to say incorrect) use of
    terminology. Peter Fogg is right, I think, that because the tables
    generally used for sight reduction require an Assumed Position, this
    term has degenerated into a generic term for the starting position
    when using the St Hilaire method - but that does not make it the
    "correct" term.

    Frank has a point, that we bring the baggage of our backgrounds with
    us when getting to grips with new concepts and problems and this can
    cause confusion. Peter Hakel tells us that his background is as a
    "theoretical and computational physicist (in the area of radiative
    properties of plasmas)".  As I did my Ph.D. in the radiative
    properties of (atoms in) plasmas, there is no excuse there ;-).

    My problem was the term 'LOP'. To me, an LOP (or position line as we
    call it over here) is a straight line. We must remember that the St.
    Hilaire method is essentially a graphical method where a fix is
    generated by drawing lines on a chart. The LOP's drawn on the chart
    are lines which are tangential to a circle of position, centered on
    the Geographical Position of the celestial object of
    interest.  Looking at Bowditch, there is some fuzziness in the
    definition of a line of position. "Circular lines of position" are
    synonymous with "circles of position" and lines of position, it
    seems, can be circles. But when discussing the St Hilaire method,
    Bowditch (article 1703 in my 1984 edition) describes the LOP as a
    straight line drawn to be tangential to the circle of position.

    In his post [NavList 10683], Peter Hakel finally tells us that...
    "The LOP's are circles", so now we know where he is coming from and
    his single parameter to describe a circle of position makes more
    sense. But since we are talking about LOPs in the context of the St
    Hilaire method, where LOPs are straight lines, I could not see what
    John Karl was getting at when he talked about "calculating the LOP
    directly" and I suspect he, too, was talking about the circle of
    position, not the LOP as (usually) drawn on a chart.


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