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    Re: Long and Time at Sea
    From: Lu Abel
    Date: 2005 Jun 6, 11:54 -0700

    I took this course more than a dozen years ago and was writing from
    memory rather than having the actual sights in front of me.  You are
    quite right to point out that my assertions about the ease of finding Lo
    during a noon sight may have been a bit aggressive.  I recently moved
    and my sights are buried somewhere in a large collection of as-yet
    unpacked boxes.  I value the integrity and expertise of this list and
    I'm going to withdraw my claim until I can resurrect my sights and
    confirm my experience.
    BTW, the US Power Squadrons standards for acceptable sights for their
    courses are +/- 3 miles if taken on land, +/- 5 miles if taken at sea.
    A bit of background on USPS for people unfamiliar with it -- it's the
    largest public service group devoted to recreational boating safety in
    the US.  Has about 60K members in 450 chapters throughout the country.
    Does everything from vessel safety checks to teaching 11 different
    courses, the latter running from simple deck seamanship through advanced
    I'm a USPS member and have to admire our volunteer sight folder checkers
    -- in both our basic and advanced celestial courses, each student is
    required to submit a sight folder (roughly six different types of sights
    per course) which must then be examined in detail and approved by a
    member volunteer before the student can pass the course.  Since each
    sight is unique to time, body, and sight location, there are no answer
    sheets the volunteer can refer to, he/she must start with the student's
    sight data and go through the full reduction using (a) the Nautical
    Almanac data (including all interpolation, ugh, because NA interpolation
    may give slightly different answers for GP than a computer program that
    solves the GP equations for the exact time specified) and (b) the
    reduction method specified (calculators for the basic course, sight
    reduction tables (to give experience with those) in the advanced
    course).  Before submitting the sight folders to the official grader
    they must be locally checked.   I've done this several times for my
    local chapter and it's quite a task (and I've then gotten folders back
    with things I missed marked off!)
    Oh, and the oddball name "Power Squadron" (which I desperately hope they
    will someday change since we're neither exclusively powerboaters nor a
    quasi-military organization)?  It relates to pre WW I days when the
    group started as the "power[boat] squadron" (vs "steam yacht") of the
    Boston Yacht Club.
    Lu Abel
    George Huxtable wrote:
    > Lu Abel wrote-
    >>I don't know how many on this list have actually taken a noon sight.  I
    > 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@huxtable.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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