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    Re: Coastal Plotting Sheets
    From: Michael Bradley
    Date: 2007 Mar 27, 23:19 +0100

    Peter Fogg wrote:
    'Michael, can you expand this section a little ?'
    > Furthermore, the horizontal sextant angle station
    > pointer type method itself is notorious for a poor
    > angle of cut built into its geometry, particularly >
    > the 'middle' object sighted is further away than the
    > two 'side' objects sighted.
    Gladly Peter, ...
    Given a known angle between two known objects viewed
    from the boat,
    it is possible to construct a circular LOP for the
    boat through the two objects.
    This is then repeated for another pair of objects to
    get another circular LOP. Where these
    circles cut is the boat's position. Because you save
    the geometric effort of drawing the circles when using
    a station pointer or similar, you get no indication of
    the angle of cut between the two circles, hence the
    potential danger.
    To do the geometry, you draw a 'base line' between the
    two known objects, take 90 deg minus the observed
    angle = x, draw a line from each object at angle x to
    the base line. Where these two lines meet is the
    centre of the circle, which you can then draw with
    your compasses. If your drawing is accurate, the
    circle passes through the fixed objects. The boat lies
    somewhere on the circle which I've called the circular
    LOP. Repeat for another pair of objects and their
    particular angular difference to construct the second
    circular LOP. The circular LOPs usually cross, but
    there's no certainty that they will...
    In the extreme case, if all three fixed objects lie on
    a position circle which also crosses the boat's
    position, the 'plotted' position circles will lay over
    each other, and the boat will get the same ambiguous
    horizontal angles wherever it lies on the joint
    position circle -  a major danger.
    The general advice to avoid these dangers is to ensure
    that the middle object used for the fixes is the one
    nearest to the boat. In that case there is no way the
    boat can be on a circular LOP which includes all three
    objects. Even so, that set up does not ensure a decent
    angle of cut.
    I couldn't find a detailed reference to this in the
    2002 Bowditch. The whole technique is counted, I
    guess, more than a little past its sell by date. Older
    navigation texts mention the technique and its
    dangers: Admiralty Navigation Manual Vol 3 1938
    edition page 176, M J Rantzen's 'Little Ship
    Navigation' 1970 fifth impression page 142, and
    Lecky's 'Wrinkles', 21st Edition, 1925, page 144 refer
    to the dangers after describing the geometry.
    Posibly other list members know web accessible
    references to the same topic. If nothing crops up on
    the list in the next few days, I'll crank up the
    boss's scanner and send you some copied material by a
    side email.
    All the best
    Michael Bradley
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