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    Checking a sextant calibration.
    From: George Huxtable
    Date: 2003 Oct 5, 11:55 +0100

    This relates to Jared Sherman's recent mailing with the complex thread name-
    .Re: [NAV-L] CEKCTAH  SNO-T [Re: lack of manufacturer's non-adjustable
    In reply to a question from Courtney Thomas, as follows-
    "Once those sights were taken, how would you  suggest then
    differentiating instrument error from observer error ?"
    Jared replied-
    > I don't know that you can differentiate the two readily. Let's suppose
    >the instrument is made with +-20" of error throughout the arc, like
    >Celestaire's new Chinese models are. Take your sights, reduce them by the
    >means of your choice. let's suppose that position comes up 1-1/2 miles off
    >from reality.
    > Now run a couple of the sight reductions again, using an observation that
    >is +20" off, and then -20" off.
    > You may find that the +-20" change reflects in a 2 mile change in your
    >position...If it brackets reality by that much in either direction, you
    >might assume that the "instrument+observer" has less of an overall error
    >than 20". But if your reading, regardless of the +-20", is still five
    >miles away from reality, then you can assume the greater error is coming
    >from something you are doing--not from the instrument's arc error.
    > I know that's still vague, ...
    Remarks from George-
    Well, to me, it's vague indeed. I really can't see what Jared is proposing
    to do. When he says " You may find that the +-20" change reflects in a 2
    mile change in your position...", why should that be so? Perhaps he is
    crossing two altitude observations of bodies at different azimuths to
    obtain a fix, then comparing his result, North and West coordinates, with
    the given coordinates of his trig point.
    But a much simpler and more accurate process would be to take the position
    of the trig point in lat and long, and simply work out the altitude of a
    single observed body from that spot, and compare that with its (corrected)
    altitude observed by the sextant. In that case a 20" change in observed
    altitude will result in a 20" discrepancy, no more, no less. That's the
    best that can be done.
    Nor do I understand the next sentence-
    "If it brackets reality by that much in either direction, you might assume
    that the "instrument+observer" has less of an overall error than 20". I
    don't follow the logic here. Perhaps I am being dim. I wonder if Jared can
    offer an example.
    To discern a sextant error of 20", the errors in measuring the altitude of
    the body, and in predicting that altitude, must when combined be
    significantly less than 20". That's a rather tall order. Do any of us claim
    to be able to meet it? Here is a list of some errors in that chain.
    1. Nautical almanac predictions are given to the nearest 0.1 minutes, but
    on page 261 (para 24) it's stated that the maximum error for Sun GHA may
    reach 0.25'. Maybe more accurate predictions from computer calculations or
    tables, aimed at astronomers or surveyors, can be used.
    2. Sight reduction tables have limited accuracy, which can be avoided by
    using computers or calculators with many digits.
    3. Refraction due to the shades can occur and needs to be checked for each
    4. The inherent resolution of the human eye is of the order of 1 minute,
    but may be somewhat better for those with particularly sharp eyesight. This
    effect can be improved if a high-magnification telescope is fitted to the
    sextant, but often only a mag of 2.5 or 3 is available.
    5. The effects of irradiation (which inflates the boundary of a bright
    object as seen in the eye) are rather unpredictable, and variable between
    observers, but can reach a significant fraction of a minute.
    6. Refraction in the view of the object in the sky can vary in an
    unpredictable way from the predicted value, as can be seen sometimes in the
    squashed appearance of a lowish Sun. It can be limited by restricting
    observations to bodies well up in the sky, but not when checking a sextant,
    when a wide range of altitudes has to be covered. Refraction can be
    corrected to some extent for changes in sea-level temperature and pressure,
    but this is only partially effective.
    7. A still day must be chosen so that the horizon as seen is the same as
    the mean sea level, rather than a collection of wave-tops. Similarly, the
    observation should be made from the shoreline or from a vessel in quiet
    surroundings with no heave. And to achieve sufficient accuracy,
    height-of-eye needs to be known to a few inches.
    8. The tabulated dip includes a correction for refraction of light at is
    skims past the horizon and travels close to the sea surface to reach the
    observer's eye. This is highly dependent on the temperature of air layers
    within a few feet of the surface and can vary considerably (anomalous dip).
    Variations from the tabulated dip by 1 arc-minute are common, and 2 or 3
    minute errors, though unusual, are not rare. In mirage conditions, dip
    errors of many minutes can occur. Refraction correction tables don't help
    here. Anomalous dip is one of the most intractable problems in accurate
    sextant observation, because it isn't apparent when it's happening.
    9. There's only a certain precision with which even the most skilled
    observer can read a sextant's micrometer (and there are two readings
    involved, because the index error must be subtracted). And his readings can
    be perturbed by tilt error, particularly.
    I may have left some out, but with as many possible errors as I've listed,
    how many of us could put his hand on his heart and declare that he could
    detect a sextant error of, say, 20" from altitude measurements?
    If anyone seriously wishes to pursue the best possible accuracy for a
    sextant calibration, I suggest an on-land programmme of measuring angles
    between suitable pairs of stars, choosing stars that are rather high in the
    sky. It's a demanding job calling for much skill, rather like measuring
    lunar distances (only harder). I wouldn't like to take it on. The
    calculation is similar to that of a lunar, but simpler because it's only
    for the two refractions, there being no parallax.
    With modern sextants designed the way they are, it seems unlikely that even
    a drop to the floor is likely to degrade the precision of its
    scale-division noticeably, without the damage being sufficient as to cause
    the index arm to bind somewhere on the arc. The most likely thing to
    suffer, in my view, is collimation error due to the telescope becoming
    misaligned. Any mirror derangements can normally be adjusted out.
    I have seen many pious exhortations in textbooks about never using a
    sextant unless it has a recent calibration certificate. This must have
    provided plenty of business for Kew laboratory (NPL) and others.
    I wonder how many list members have managed to check on their sextants and
    discover any real reproducible scale error? I refer to reputable modern
    makes: not Pakistani backyard jobs, nor antiques with hand-divided scales.
    My bet is that not one has discovered any such errors.
    Let's be realistic about all this: Sextants were designed to measure lunar
    distances, a measurement that demands (but seldom obtains) 30 times the
    accuracy of a normal altitude sight. That degree of accuracy is no longer
    needed, except for the "lunartics" among us. Except for such lunar
    observations, if your sextant can give you position lines within 3 or 4
    arc-minutes, that's as good as a small-boat sailor normally needs. And as
    much as a small boat sailor can usually expect, with the motion of a small
    craft in a turbulent sea.
    So should a small-craft navigator be worried if his sextant has no
    calibration certificate from its maker? I doubt it. It's almost certainly
    good enough for his needs. He should relax and enjoy using it - but always
    keep his eyes open for signs of any serious discrepancy, as applies to any
    instrument, new or old.
    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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