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    Re: Position lines, crossing.
    From: Robert Eno
    Date: 2006 Dec 10, 20:47 -0500

    George wrote:
    
    > Already, three have put their heads up in defence of their cherished
    > illusions;
    
    Robert responds,
    
    Really George, that response strikes me as somewhat harsh and pedantic. In
    fact I did not disagree with your assertion regarding the inaccuracy of
    assuming that one's fix is within the cocked hat.  I think we -- at least I
    did anyway -- all agreed with you.
    
    That you overlooked the thrust of my argument may have been due to it being
    lost within my usual long-winded response.
    
    So here is my question: for purposes of practical navigation at sea, does
    one really have to take into account the statistical probabilities of the
    actual location of the fix, as so eloquently outlined by George, or is it
    sufficient enough to do what countless navigators have done for generations:
    take the fix from the centre of the cocked hat and/or the centre of the
    "smudge"?
    
    I believe that the latter it is good enough for practical purposes.
    
    George wrote :
    >
    > Well, he [Robert] makes two proposals there, that are quite contradictory.
    > If
    > he "assumes he is in the centre of the cocked hat", then what's the
    > purpose of the "big circle or ellipse"? And I suspect that Robert is
    > really advocating something a bit different. That a navigator plots a
    > point on the chart at the centre of the cocked hat (where else, after
    > all?) but without any assumption that he is exactly there; then draws
    > a smudge around it, either on the chart or at least in his head, and
    > accepts that he will be somewhere within that. If that represents
    > Robert's view, then we agree.
    >
    > ==========================
    Robert responds,
    
    Not quite George. I was talking about two different situations: the cocked
    that results from the intersection of 3 LOPs, in which case, I would take my
    fix from the centre of that cocked hat, recognizing that I will likely be in
    error.
    
    An ellipse, circle, smudge that one would scrawl around the general area of
    intersection of more than 4, 5, 6, 7 or more LOPs is merely a graphic tool
    that one would use in an attempt to eyeball the centre of mass in order to
    pick spot from which to commence a new course. Of course one can assume that
    one is somewhere within that smudge but for practical purposes, one must
    pick a point within that smudge from which to draw a new course line.
    
    I think we are discussing two different aspects of navigation here:
    navigation as practiced a sea and navigation/mathematical theory. I maintain
    that for the former, one need not concern oneself with a statistical
    analysis
    of the error of the fix, unless one has lots and lots time on one's hand.
    Even at that, if one is on the move, in a sea of currents and wind, it would
    be a waste of time.
    
    In terms of nearshore navigation where one is likely to encounter dangerous
    reefs, astro navigation is the last thing I would want to employ. Shore
    bearings would be a more accurate means of keeping one's distance from
    dangerous ground and better yet, radar.
    
    I remember hearing a little chestnut about how, mathematically, it is
    impossible to close a door. The theory goes like this: in order to close the
    door, one must move the door from point A to point B. In order to do this,
    the door must pass through the halfway point -- let us call it HP1 --
    between A and B; once the door has reached HP1, in order for it to get from
    there to Point B, the door must pass through the halfway point between HP1
    and B, which we call HP2 and in order for the door to get to point B
    from HP2......you get the picture. It is a tunnel of mirrors. But people
    close doors all of the time.
    
    I am not attempting to dismiss what George stated about errors in fix -- in
    fact I agree with him. I am only questioning the practical need to consider
    these errors for everyday navigation at sea.
    
    Robert
    
    
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