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    Re: Position lines, crossing.
    From: Peter Fogg
    Date: 2006 Dec 10, 11:36 +1100

    Geoffrey wrote:
    "Now you have three amalgamation position lines all crossing at the
    same point�"
    By bisecting roughly parallel position lines, the 6 have been reduced to 3.
    
    Guy wrote:
    "I highlighted my position lines with a orange highlighter and BINGO I
    could see the
    convergance of the lines."
    
    With the exception of Rasalhague, this broad line convergence of 5
    LOPs is only just to the west of the centre of the small triangle
    indicated by Geoffrey's 3 LOPs (the difference is half of the effect
    of Rasalhague; as one body out of six).
    
    As to George's insistence that the ACTUAL position is not necessarily
    located at the centre of a triangle, or other intersecting LOPs, this
    does not seem especially helpful. As an example of how unhelpful it
    is, Lu is now worrying about the precise statistical improbability
    involved. Will this knowledge enable the calculation of a more
    accurate position?
    
    The value of the nominated position at the centre of position lines is
    that it is the only possible CALCULABLE position. Saying that the
    actual position could be somewhere else doesn't change this, or assist
    the goal of position finding in any way that I can see.
    
    Why do we want to define a position, anyway? Usually it is not to know
    where we are, since after sight reduction and plotting in any sort of
    moving craft we are no longer back there any more. Usually the
    calculated position is then used to run forward our track since then,
    a process largely beyond precision.
    
    Moving this calculated position closer to identified danger seems like
    simple common sense.
    
    As Guy has found, 6 LOPs are potentially confusing when it comes to
    deriving a position from them*. Geoffrey's solution has the appeal of
    simplicity, although there seems to be little point in doubling the
    sight reduction needed to produce 6 LOPs only to reduce them back to 3
    in this rather arbitrary fashion.
    
    What I would suggest as a better approach is to make sight reductions
    from only three bodies with a wide spread of azimuths, but only after
    comparing a number of observations from each body over a 5 minute
    period with the slope of the bodies' rise or fall. This should
    eliminate 'blunder' sights and lead to a more accurate position line,
    which then leads to a more accurate position, although it will not
    identify or eliminate systematic error.
    
    
    [* Like so much else in nav, this is very much a case of 'horses for
    courses'. If a land explorer or surveyor was seeking to establish as
    precise a position as possible, perhaps using a theodolite, then 6 or
    more position lines would not be redundant, and this and other data
    could then undergo statistical and other analysis to enable the most
    accurate position to eventually be established from them. Once again;
    for position finding from a moving platform there is usually not much
    point.]
    
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