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    Re: Cocked hats, again.
    From: Jackie Ferrari
    Date: 2007 Mar 17, 17:10 -0000

    I am a relative beginner and have been following this interesting
    discussion. I looked in the Royal Air Force Navigation manual 1944, and on p
    116 it says,
    " If the errors of the bearings, from which the position lines are obtained,
    are all of the same sign...the actual position of the aircraft may be
    outside the cocked hat. It is more often the case that errors in measurement
    are quite haphazard, and hence the navigator cannot tell which of the seven
    positions (refers to a diagram) contain the actual position of the aircraft.
    For this reason the centre of the cocked hat is assumed for all practical
    purposes to represent the fix, provided the sides of the cocked hat are not
    excessively long."
     Jackie Ferrari.
    ----- Original Message -----
    From: "George Huxtable" 
    Sent: Saturday, March 17, 2007 4:49 PM
    Subject: [NavList 2393] Re: Cocked hats, again.
    >  Gary has written, in Navlist 2353,
    >  Regarding your other post today, I too learned that your position
    > was
    >  always inside the triangle with the most likely point being the
    > center.
    >  We now know that was bad information.
    > And has been asked, by Peter Fogg, rather aggressively and
    > persistently-
    > Are you sure someone said those words: "always inside the triangle"? I
    > have never come across such a statement.  Could the statement have
    > been more along the lines of the calculable fix lying at the centre of
    > the position lines? In which case it wasn't bad info at all.
    > Gary was referring to what he had been taught, not quoting from a
    > book, so none of us is in a position to question his recollection, or
    > demand evidence. However, it corresponds exactly to what I had been
    > taught, and to the recollection of several others I have asked, and I
    > have no doubt that Gary described his teaching correctly..
    > Peter's admission, that he had never read such a statement, indicates
    > the limits to Peter's reading, and does not put Gary's account into
    > question.
    > Over the years, I have acquired an assortment of texts on navigation,
    > some of questionable merit, and am able to quote the chapter and verse
    > that Peter Fogg demanded, as shown below.
    > No attempt has been made to distinguish between references to cocked
    > hats arising from compass bearings to three landmarks, and those
    > arising from three astro position lines. Any reference to the
    > possibility of the true position being outside the triangle is indeed
    > hard to find.
    > Here goes-
    > Little Ship Navigation, Rantzen, 1961, page 122. "...The crossing
    > lines define a triangle, known as a cocked hat. ...The position of the
    > ship is somewhere in this triangle..."
    > Sea Navigation, Gates, 1968, page 51. "Rarely, of course, will the
    > three position lines intersect at a common point, and more usually
    > they will form a small triangle or 'cocked hat'.... The ship's
    > position is then assumed to be at the centre of the triangle. If the
    > triangle is a large one (even after checking the observations), then
    > the position of the ship is taken as the apex of the triangle nearest
    > to danger."
    > Learn to Navigate, Mosenthal, 1998, page 42. "Your are more likely to
    > end up with a cocked hat like this [diagram shown here]. You normally
    > take the middle of the cocked hat as your position. Unless you are
    > near a danger, when you take the 'worst' position- the point nearest
    > the danger."
    > Navigation for yachtsmen, Blewitt, 1973, page 52. "When your cocked
    > hat is small, you can put yourself in the middle of it. This is not
    > necessarily logical, but in practice is the best you can do." If the
    > cocked hat is larger she suggests a position at a point marked X on
    > one of the sides of the triangle, corresponding to the bearing of
    > which you have most confidence. No suggestion that the true position
    > might possibly be outside the triangle.
    > Dutton's navigation and pilotage, 1969, [highly reliable on most
    > matters] art. 2016. Referring to LOPs, "In practice they will seldom
    > intersect at a point but will produce a small polygon, which usually
    > contains the position of the ship." However, in the case of a
    > triangle, if we agree on the 1 in 4 probability, that's far from
    > "usually".
    > Admiraly Manual of Navigation, vol 3, 1938, page 166, states- "...
    > when a cocked hat is obtained, it is customary to place the ship's
    > position in the most dangerous position that can be derived from the
    > observations..." However, in the previous paragraph, an interesting,
    > and somewhat contradictory statement is made "... it can be seen that
    > the chance of F's falling inside the cocked hat is only 1 in 4". Here
    > then, is the first official backing for the 1 in 4 figure that I have
    > come across.
    > And here we should give credit to Cotter, better known for his
    > "History of Nautical Astronomy". In "The complete Coastal Navigator",
    > 1964, page 187, he writes- "In the general case, where the errors e1,
    > e2, and e3 are not known either in magnitude or sign, the possibility
    > or chance of P lying within the cocked hat is only 1 in 4."
    > On that evidence, perhaps Peter Fogg will retract.
    > George
    > contact George Huxtable at george@huxtable.u-net.com
    > or at +44 1865 820222 (from UK, 01865 820222)
    > or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    > >
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