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    Re: St Hilaire not Iterative was: Finding The Symmedian
    From: Gary LaPook
    Date: 2010 Dec 29, 16:48 -0800
    I am attaching the second table of offsets from HO 229 (the first table is identical to Table 4 of Bowditch) which covers greater distances out along the LOP.

    gl

    --- On Wed, 12/29/10, George Huxtable <george@hux.me.uk> wrote:

    From: George Huxtable <george@hux.me.uk>
    Subject: [NavList] Re: St Hilaire not Iterative was: Finding The Symmedian
    To: NavList@fer3.com
    Date: Wednesday, December 29, 2010, 4:07 PM

    On 25 Dec, Andrew Nikitin explained why he though it would be unproductive
    for a navigator using graphical techiques to reiterate a fix of LOPs, as
    follows-

    "A navigator using plotting techniques introduces greater errors
    which stem from these techniques (placing a ruler, drawing line along its
    edge are not exact operations, especially on a small cluttered badly lit
    table which rocks back and forth). Assuming your AP is within a degree,
    the error introduced by Hilaire method would be smaller then the errors
    introduced by the act of plotting lines. Doing second iteration would be
    a waste of time."

    ===================

    That is a fair comment, but it needs a bit of qualifying. It depends. It
    depends on the altitude, the geometrical errors getting worse at high
    altitides. It depend on angle-of-cut between the azimuths of observed
    bodies. It depends on the accuracy of the Assumed Position, on which Andrew
    sets an upper limit of 1 degree, but that in turn depends on how good is
    the dead-reckoning. In the heyday of celestial navigation, how good was the
    DR of a sailing vessel which had spent a week battling adverse weather,
    without a sight of the Sun or anything else? Such conditions were not
    unusual, especially in the Atlantic, in Winter.

    I attach Table 4 from vol.2 of my 1981 Bowditch. This is a table of
    offsets, showing how to bend a straight-line approximation to an LOP, to
    make it sufficiently curvaceous to be an accurate position line. It also
    shows the error that remains if, as usually happens, no such adjustment is
    made.

    The maximum such discrepancy in AP that the table contemplates is 45', and
    because the resulting errors go as the square of that , then Andrew's
    assumption, that the AP was within a degree, could result in errors that
    are nearly double those in the 45' column. Those errors can then be
    considerably greater than a competent plotter  would accept on a
    plotting-sheet.

    The careful navigator can disregard the need for reiterating if his
    altitudes are all low ones (less than 60º, say), at a good angle of cut,
    and his Assumed Positions are known to be close to the truth. Or if he uses
    table 4 to bend his position lines suitably. Or if, being in mid-ocean, he
    doesn't really care about his position being a few miles out. But
    otherwise, reiteration may need to be considered seriously.

    George.

    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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