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    Re: Long and Time at Sea
    From: George Huxtable
    Date: 2005 Jun 5, 00:54 +0100

    Lu Abel wrote-
    
    >I don't know how many on this list have actually taken a noon sight.  I
    >have.
    
    But from on-land, it seems, when he says later "I also freely confess this
    sight was taken on dry land, so I wasn't dealing with trying to bring down
    the sun on a heaving ship's deck."
    
    It's quite a lot harder, and less accurate, when you observe a Sun altitude
    in real-life, at sea, above a real sea-horizon. Is an observation from
    on-land considered adequate by the US Power Squadron?
    
    >A noon sight is part of the requirements for US Power Squadron's
    >Navigation course (advanced celestial nav) which I have taken.  I found
    >(at ~40N Lat, sight taken during the early summer) that not only did I
    >get a spot-on latitude value, but by graphing a series of sights over
    >about 10 minutes (5 min on either side of LAN) I got quite an excellent
    >value for longitude.
    
    I would expect a "spot-on" latitude value, just as Lu claims. But notice,
    he doesn't quote any actual figures for his "quite an excellent value" for
    longitude. I hope he will dig out his observation log and give us some real
    numbers.
    
    I have recalculated what Lu's observations should have been, taking an
    observer at 40 deg North, 0 deg West, and as an example of "early Summer",
    today's date of 4 June 05. The following altitudes include no correction
    for refraction, dip, semidiameter.
    
    Noon-by-the Sun occurred at 11h 58m 18s, when Sun alt. was at its maximum
    of 72deg 28.6'
    
    5 minutes earlier, and also 5 minutes later, the Sun alt was 1.9' less, at
    72deg 26.7'
    
    At those two times, 10 minutes apart, for which Lu will have to split the
    difference to find his moment-of-noon, the Sun is first rising, then
    falling, at 0.75 arc-minutes for each minute of time.
    
    How accurate are Lu's altitudes going to be, if measured in real-life at
    sea? I wonder if any one of us can put his hand on his heart and claim to
    be able to measure the altitude of a real Sun above a real horizon AT SEA
    within a scatter of, say, ?1 arc-minute. Here, I am referring to the
    small-craft situation; I accept that on a big-ship, in millpond conditions,
    somewhat less scatter than that might perhaps be achievable.
    
    If the altitude is changing at only 0.75 arc-minutes, each minute of time,
    at the extremes of Lu's time-range, and with a presumed scatter of ? 1
    minute in each observation, I really can't see how, with the most careful
    graph-plotting over those 10 minutes, a navigator will find the
    centre-of-symmetry of the resulting curve to better than, say ?1 minute of
    time. Not a very precise result then, when he might expect his chronometer
    to be good to a second. A scatter of ?1 minute of time corresponds to a
    longitude error of ?15'.
    
    Those error estimates seem fair to me, but I would be happy to argue the
    matter out if anyone thinks otherwise.
    
    Compare that with a time-sight measurement made several hours away from
    noon. If the Sun is on a path to pass overhead, then its altitude will
    change by 15 arc-minutes for every minute of time. From higher latitudes,
    the rate of rise will be less, but a properly chosen moment for a
    time-sight will normally involve the altitude changing by at least 7.5
    arc-minutes per time-minute (except in arctic latitudes). This is ten times
    faster than the rate-of-change that Lu observed, so given the same accuracy
    in observing altitude, the scatter in deduced time will be reduced by a
    factor of 10, to be 6 seconds of time. And that would correspond to a
    longitude error of 1.5 miles, not 15 miles: a substantial improvement,
    obtained by using the traditional time-sight technique.
    
    So if Lu really did get his unspecified "quite excellent value for
    longitude", I wonder if it was perhaps obtained by some sort of fluke.
    
    I don't deny that a noon Sun longitude can be made to work, to some extent.
    One distinct improvement would be to extend the period of observation, to
    be significantly longer than the 10 minutes around noon that Lu allowed
    himself. But if the time interval between the rising Sun and the falling
    Sun becomes great enough, the question then arises: can you call it a "noon
    observation" any more?
    
    Of course, from a moving ship, with any Northing or Southing in her course,
    there's another factor to consider, that didn't come into Lu's on-land
    observations. That motion gives rise to a displacement in time between the
    moment of maximum altitude (which is what's observed) and the moment of the
    Sun's meridian passage (which is what's needed). It isn't hard to correct
    for, but that correction should not be neglected. There's an additional,
    smaller, correction to make to allow for the Sun's changing declination,
    being greatest near the equinoxes, but that's usually small enough to
    neglect.
    
    George.
    
    ================================================================
    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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