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    Re: Position lines, crossing.
    From: Robert Eno
    Date: 2006 Dec 10, 00:35 -0500

    I have to agree with Bill and Peter Fogg on some of their assertions
    regarding the cocked hat.
    Certainly, I am not attempting to argue the point as to whether or not the
    fix lies within or outside of the cocked hat and I have no intention of
    going toe to toe with George or any of the other learned folks on this list.
    You know the old saying: better to keep your mouth shut and be thought of as
    a fool than open your mouth and have those suspicions confirmed. I
    acknowledge my relative ignorance about the finer mathematical aspects of
    astro-nav. I accept what George has said regarding the probable locations of
    one's actual position when presented with several LOPs. I have read about it
    numerous times in such respected tomes as the American Practical Navigator.
    And, rightly or wrongly, promptly ignored it.
    What I would like to distill this discussion down to is this: in the absence
    of GPS and assuming that astro-nav is one's primary means of fixing a
    position at sea, how would the practical seaman approach this problem?
    Would he conduct a statistical analysis of each and every set of
    observations?  I think not, unless he has the luxury of time to do so. I
    suggest that he would simply assume he is in the centre of the cocked hat
    and/or he would draw a big circle or ellipse or whatever, around the
    profusion of criss-crossing lines and aim for the centre of mass; then he
    would carry on as normal.
    I further suggest that the individuals who wrote the texts and lesson plans
    regarding placing the position within the cocked hat formed by three
    intersecting lines of position, likely knew all about statistical
    probabilities and other such forms of mathematical black magic, but they
    also knew their audience: the ordinary seaman who hasn't the time nor the
    inclination to worry about such matters. The latter want something simple,
    quick and reasonably accurate.
    In the end, the quickest, easiest and most expedient course of action would
    be to place one's position in the centre of the cocked hat. One might be
    dead wrong but in the middle of the ocean, using a relatively coarse
    measuring device such as a sextant (I will have to say three Hail Mary's and
    an Act of Contrition to atone for uttering such blasphemy), does it really
    matter if one ignores mathematical reality and instead, opts for the
    simplest solution to determining one's fix?
    I offer this as a genuine question rather than a statement of fact.
    It would be interesting to hear from some older old timers (if there are any
    in this group) who sailed -- professionally and/or personally -- during the
    era when astro nav was the only game in town.  What did you folks do?  Does
    anyone know of any disasters, near disasters, groundings, accidents or
    otherwise that resulted from navigators erroneously assuming that their
    position lay within the cocked hat?
    Interesting discussion as always.
    ----- Original Message -----
    From: "Bill" 
    Sent: Saturday, December 09, 2006 9:58 PM
    Subject: [NavList 1857] Re: Position lines, crossing.
    > Peter wrote:
    >> 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?
    > It is indeed a guessing game and to some degree frustration IMHO.  No
    > systematic errors or personal bias, you are *probably* in the cocked hat.
    > No one-in-four statistics as related in my texts.  With systematic errors,
    > then you may well be outside the cocked hat according to my texts.
    > I am well aware George is far better read an educated on the topic than I
    > will probably ever be, but it still seems a bit hit or miss in any case.
    > If
    > I have done my homework before a long voyage and do not find personal or
    > systematic problems, or instrument error, then I might tend to believe
    > that
    > after a month at sea that would remain true and trust a position within
    > the
    > cocked hat within certain limitations.
    > That's an assumption. How do you know--really--unless you are comparing to
    > a
    > GPS?
    > I recall a chapter in a book a friend loaned me--I don't recall the
    > title--recounting of a month-long blue-water voyage by some yachtsmen.
    > The
    > author pointed out that such-and-such was their best day yet. They covered
    > 192 miles where yesterday they covered 190 miles.  This was done with cel
    > nav and running fixes. No GPS.  I had to laugh.
    > Thankfully the sextant can be a bit more precise for coastal navigation,
    > so
    > it serves both purposes very well if taken with a grain of salt and dose
    > of
    > common sense.
    > In the digital age where operating system and application interfaces must
    > be
    > relearned with each upgrade, it is comforting to have a tool in the
    > sextant
    > that meets my classic definition of a tool--a handle on one end and a use
    > on
    > the other. It measures angles well enough for the purpose at hand.
    > The big plus being there are so many uses those angles can be put to.  For
    > some tangential reason, UNIX comes to mind.  Referring to the various
    > flavors of UNIX, one wag commented decades ago, "A good operating system
    > needs standards, and the beauty of UNIX is there are so many to choose
    > from." 
    > Bill
    > >
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