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    Re: It Works.
    From: Arthur Pearson
    Date: 2002 Apr 7, 12:29 -0400

    I have been puzzling on this for the week since Bruce made his initial
    posting.  Like George, I am still struggling.  I am convinced of the
    utility of a method for deriving GMT using calculated altitudes.  My
    struggle is to understand the method of minimizing the errors resulting
    from uncertain time AND position that. Here is where I stand.
    I am intrigued by Bruce's description of using "SHA meridian", but I
    don't quite understand it. The key phrase from his posting is: "I'd
    taken a time sight of the sun the afternoon before the lunar
    observation, so knew the error of the watch on local apparent time. By
    subtracting local apparent time SINCE NOON (converted to arc) from SHA
    sun I got SHA meridian. That nailed my east-west position in the
    celestial sphere at the moment of observation."  I just can't master
    what is going on here, I probably need a diagram.
    Here is what I think I understand about the general procedure. Like
    George, I welcome corrections and challenges.
    1. During the day, one establishes latitude by a noon sight.
    2. The same sight that is used to determine latitude is used to
    establish the Watch Time of Local Apparent Noon.
    3. Using DR Longitude, WT of LAN, and the equation of time we can come
    up with an Estimated GMT.
    eliminated error in Latitude.  In addition, my error in Est. GMT and DR
    CELESTIAL SPHERE. Somehow this seems important though I can't put my
    finger on exactly why.
    5. We now need to keep a good DR and trust the rate of our watch up to
    the moment that we take our lunar distances and need to use position and
    est. GMT to come up with calculated altitudes.
    6. Because the error in position is minimized (Latitude is correct) and
    the error in est. GMT and DR Longitude are consistent, the need for
    iterative solutions of GMT by observation is minimized. In Bruce's
    examples (under extreme conditions) two iterations were adequate.
    Again, I suspect if I can diagram how Bruce "nailed my east-west
    position on the celestial sphere at the moment of observation", perhaps
    the scales will fall from my eyes. Perhaps a more detailed description
    of the sequence of his almanac look-ups and calculations would also make
    things more clear.  This is a particularly interesting discussion and I
    hope others will weigh in as we find our way to a common understanding.
    -----Original Message-----
    From: Navigation Mailing List
    Sent: Sunday, April 07, 2002 5:22 PM
    Subject: Re: It Works.
    From George Huxtable-
    I've been "off-watch" for a few days, as far as Nav-L is concerned,
    my boat "Christina" into a seaworthy state after her winter lay-up. Even
    poked her head out into Poole Bay, but the weather in the English
    being pretty thick, turned tail again straight back into harbour.
    Now back home to find a helpful contribution from Bill Noyce, about what
    navigator has to do if he needs to work a lunar using altitudes that
    been calculated rather than measured. Here's what he said-
    >George Huxtable says
    >> 1. For a lunar that uses altitudes that are calculated rather than
    >> measured, it is necessary to make a measurement for local apparent
    >> This should be done within a day or so of the moment of taking the
    >> depending on how well the timepiece can be trusted over such a
    >> :
    >> 4. The local apparent time, so derived, and corrected by the equation
    >> time to give local mean time, can be checked against the ship's
    >> and can now be used with the Almanac to establish precise altitudes
    >> both the bodies used in a lunar observation, even though the GMT and
    >> longitude are both still uncertain.
    >I don't think you need to make any special "local apparent time"
    >observations or calculations.  Assuming the navigator has been
    >using celestial observations all along, but has an incorrect clock,
    >he will have determined a celestial "fix" whose longitude is off by
    >almost exactly 15' for every minute of time error.  These two errors
    >will cancel out to reduce errors in computed altitudes, the same way
    >as Bruce Stark's procedure using local time.  The remaining errors
    >are come from the change in declination (pretty fast for the moon),
    >and the difference in rate of change of GHA between the sun, planets,
    >and stars.
    >I think, George, that if you go back to your example where you assumed
    >the watch was 30 minutes fast, and simply change the assumed longitude
    >to be 7.5 degrees east of the true position, then you'll come up with
    >results that match Bruce's.  This assumed longitude is what a navigator
    >would have concluded with traditional celestial observations, if he
    >were misled by a watch that is 30 minutes fast.
    Later, Bill Noyce corrected this as follows-
    >I wrote:
    >> I think, George, that if you go back to your example where you
    >> the watch was 30 minutes fast, and simply change the assumed
    >> to be 7.5 degrees east of the true position, ...
    >Of course I got this backwards -- the assumed longitude would
    >be west of the true position in this case (unless I've confused
    >myself even more).
    >Then simply use the (erroneous) watch time as if it were GMT
    >for looking things up in the almanac.  You'll end up with nearly
    >the same LHA for most bodies, except of course the moon (which
    >is the point of the exercise).
    Well, those comments were most useful, and I am grateful to Bill for
    clearing matters up. However, I am still having rather a struggle to get
    the concepts clear in my mind. I hope others on the list will bear with
    while I try to thrash the matter out a bit further, perhaps with the
    of Bill and Bruce, and maybe others. I am anxious to get to the bottom
    it, being aware that the final part 5 of "About Lunars" awaits
    and this will become part of it.
    Below is my summary of the matter as I now see it, assembled rather
    tentatively, with an invitation to knock it down.
    If a lunar distance has been measured, together with measured altitudes
    the Moon and the other-body at the same time, then that provides a
    straightforward measure of GMT that stands on its own and needs no other
    observations. If the azimuths of those bodies are such as to give a
    reasonable "cut", then position lines of the bodies, taken by comparing
    observed altitudes with those predicted at that GMT from the Almanac,
    give the ship's latitude and longitude directly.
    However, if only the lunar distance has been measured, and the altitudes
    the two bodies must instead be calculated from the predictions of the
    Almanac, then matters are somewhat different. Neither the GMT (needed
    looking up the positions of the bodies in the Almanac) nor the
    position (needed for calculating the altitudes of the bodies as seen by
    him) is known.
    In that case, it is necessary to combine the lunar with additional
    measurements of altitudes, which could be made before or after the
    of the lunar, and very likely, made of different bodies. An important
    requirement is that these additional measurements are made at a time
    is not widely separated from that of the lunar (within 12 hours,
    preferably). The aim is that any contribution arising from errors in the
    rate of the clock, or in the dead-reckoning of the vessel's travel
    the elapsed interval, will be small.
    There are occasions when this might be a more satisfactory procedure
    direct measurement of altitudes with the lunar. Particularly, if the
    distance had been measured in the night, in the absence of a visible
    horizon, then it could be combined with altitude measurements made in
    previous, or the following, daytime, when the horizon is clear: perhaps
    measurements of the Sun.
    It may not be necessary to make special observations for this purpose.
    will be made regularly by the navigator during the course of the voyage,
    even if he was then uncertain about the accuracy of his clock. Although
    observation may be of the Sun's meridian altitude (to provide latitude
    directly), one should be in a direction well toward the East or West of
    meridian, to be sensitive to the longitude. The ship's position, deduced
    from that (uncertain) clock, but with allowance then made by
    to the moment of the lunar, together with the GMT indicated on that same
    (uncertain) clock, are used to calculate the altitudes of the Moon and
    other-body at the moment of lunar observation. Although the longitude of
    the ship, and the GMT itself, may not be known individually, because of
    clock error, their combination will be known well enough to provide
    accurate altitudes.
    Once the altitudes of the Moon and other-body have been calculated, a
    precise measurement of the lunar distance should provide GMT to within a
    minute or two. This allows the ship's position, which until that moment
    been based on an uncertain clock, to be reassessed on the basis of the
    newly known time from the lunar.
    I would welcome any comments on this matter. I have not only found it
    difficult to put across, but also difficult to grasp myself. Have I got
    right? Could it be expressed more clearly, or more simply? Over to the
    George Huxtable.
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.

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