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    Re: Latitude and Longitude by "Noon Sun"
    From: George Huxtable
    Date: 2005 Jun 13, 12:10 +0100

    Frank Reed wrote:
    >By the way, in another post you commented on the  fact that you need speed
    >over the ground which means you would need to correct  for any current. That's
    >true, of course, and it applies to ALL running fixes.  One recent post pointed
    >out that many people using standard celestial at sea  just shoot a couple of
    >sun sights during the day, likely separated by quite a  few hours, and then
    >bring them together as a running fix. If they're in a 2 knot  current, and the
    >two sun sights are separated by six hours, this could easily  lead to an error
    >of 12 miles in the fix. That's standard LOP navigation. That  there is a
    >moderate error from ignorance of current in the lat/lon by noon sun
    >technique that
    >I have described is not a problem of this method per se.
    That's all true, of course. That effect puts your crossing position lines
    out because the run between them hasn't accounted properly for current, and
    shifts them in the direction of that current.
    What's rather different about "Frank's method" for longitude is in its
    unexpected nature: that it's a North-South velocity that gives rise to an
    East-West displacement of the longitude result.
    There's another phenomenon that a navigator might not expect when sailing
    in gusty/squally conditions in a North or South direction near noon. If his
    vessel is speeding up in the puffs, then slowing in the lulls, then so will
    his rate of change of Sun altitude due to those changes in speed. That
    changing slope has to be added to the expected parabolic change in Sun
    altitude caused by the Sun's transit through the meridian. And the end
    result is a wavering of the curve of altitude with time, about its peak. In
    an extreme case, the Sun could show more than one maximum altitude.
    I don't suggest that that's going to be a cause of serious error. The
    effects on the resultant wavering parabola can be averaged out, rather
    well, by the proposed folding of the graph, particularly if the series of
    measurements extends well away from noon (the further, the better.
    On 7 June, in "Northing correction to noon latitude", I wrote-
    we seem to agree that choosing a different zero-point for the corrections
    will not shift the timing of the corrected peak, which depends on the slope
    of the corrections, but not their amount.
    Then I went on to-
    >"However, it looks to me as if an error in
    >that initial  presumption of noon would give rise to an error in the deduced
    >maximum  altitude, and so in the latitude. Perhaps Frank will comment."
    Frank did, as follows-
    "Nope. No  error. See above."
    However, I urge Frank to rethink his flippant dismissal of the point that I
    have made. What's needed, to calculate latitude simply, is the Sun's
    altitude AT MERIDIAN PASSAGE, and not at any other time. To obtain that,
    Frank tells us to take the altitude from the peak value of the corrected
    Sun-altitude curve, at his "folding" point, which will be at meridian
    passage. But that's not the observed altitude, it's the corrected altitude,
    at meridian passage. The correction that's been made to observed altitude,
    at that moment, depends on how far it is away in time from the zero-point
    of his corrections, and that zero-moment was chosen quite arbitrarily. Only
    if the zero-point of the corrections happened to be at the moment of
    meridian passage, would the peak of the corrected-altitude curve correspond
    to the observed altitude at that moment.
    So I suggest that Frank's proposed method should be somewhat modified. Yes,
    certainly, use the corrected-altitude curve to determine, from its
    symmetry, the moment of meridian passage. But then, read off, corresponding
    to that moment of meridian passage, the UNCORRECTED value of altitude,
    which will NOT in general be its peak value.
    I haven't seen any response from Frank to this suggestion, and wonder if he
    thinks that it is perhaps wrong, or negligible.
    contact George Huxtable by email at george---.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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