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    Sextant precision
    From: George Huxtable
    Date: 2004 Sep 29, 21:04 +0100

    Alex Eremenko asked about the precision of sextants and sextant measurements.
    This is a matter which surfaces from time to time on Nav-L, but hasn't come
    up for a little while. And now we have several new and active members, so
    perhaps it's a good time to revive it, and exchange some prejudices around
    the list, which may have been rehearsed before. Here are my own views, with
    apologies to the list members who have seen them before; they can turn away
    I speak, not as an ocean navigator, but as a small-boat sailor who is never
    out of sight of land for more than a day or two at a time; so my life has
    never depended on my astro observations, though I have made quite a few of
    them in my time.
    Sextant observations could be divided into two categories; those that
    involve the horizon, and those that don't.
    Let's consider first those that don't. They comprise measurement of lunar
    distances, and altitudes measured on-land using an artificial horizon.
    Because the sea-horizon, with all its defects, isn't involved, the
    observation is capable of high accuracy. For a lunar, in particular, high
    accuracy is called for, because the resulting error in longitude, in
    minutes, is roughly 30 times the error in measuring lunar distance, in
    minutes. That is why the brass Vernier sextant was developed, in the
    mid-1700s, and later the micrometer sextant, in the 1900s. In capable
    hands, it became an instrument capable of reading to about 0.1', and
    calibrated to a corresponding precision.
    These were superb instruments, many of them; the ultimate expression of the
    instrument-maker's art and skill. They were cossetted, treasured, and
    prized; rightly so. They became the "badge of office" of the real
    navigator; a totem of his craft.
    For altitudes above the sea-horizon, the resulting error in position is
    only one mile for every minute of error in altitude. Few mariners ask for,
    or really need, better accuracy than a few miles: an exception would be for
    marine surveyors. For ordinary navigation, the wooden "Hadley" quadrant was
    quite adequate, when fitted with a vernier, as long as its index error was
    checked at regular intervals. If lunar distances had never appeared on the
    scene, I suggest that such simple instruments might have been acceptable,
    even to this day.
    The problem with all altitude measurements, up from the horizon, is the
    quality of the horizon itself as an indicator of the horizontal, especially
    on a small boat.
    To start with, the horizon, except under calm conditions, consists of a
    series of wave-peaks or swell-peaks. When observed from a small vessel,
    heaving up and down on those same waves, the best it's possible to do is to
    time an observation when the boat is on the top of a similar wave, so as to
    cancel these elevations to some extent, but it's a chancy business. Who can
    estimate the effective distance, and the angle, of the horizon in such
    Even in still conditions, there's the problem of anomalous dip. That's the
    effect caused by refraction due to temperature gradients within a few feet
    of the sea, which causes the dip to deviate (one way or the other) from its
    nominal predicted value, by (commonly) 1', (occasionally) 2', (rarely) 3'
    or more, depending on local atmospherics. There's no way of knowing whether
    anomalous dip is perturbing the horizon, without special instruments.
    Applying corrections to the refraction for non-standard atmosphere doesn't
    help in this case.
    So (for those that don't take lunars) is there any point in using an
    instrument capable of measuring to 0.1', for measuring an altitude, above a
    horizon that's only determined to 1' or so?
    And yet, on this list, the finer points of calibration of these expensive
    and exotic instruments, ancient and modern, are discussed in detail, by
    many navigators who will never use them for anything but an altitude above
    the horizon. There's another list which is devoted to sextants and nothing
    else. I suspect that many of these instruments are treated as trophies, as
    possessions to cherish, or even as investments, rather than as tools to do
    a job.
    I use a plastic sextant, which has, for me, acceptable accuracy appropriate
    to the rough measurements I can make on my 26-foot boat. If I drop it, it
    bounces. It has defects, particularly in the optics, which I put up with.
    It wouldn't do for lunars, though, not by a long way.
    Don't get me wrong; I would love to own a precise brass sextant (preferably
    Vernier type). But if I had one, it would live on my mantelpiece, and the
    plastic one would remain in use on my boat.
    If Alex is planning to measure lunar distances, then he is asking all the
    right questions. But if he plans to navigate a small boat by measuring
    altitudes, then any old sextant will do that job as well as any other.
    Those are some of my prejudices, anyway.
    I hope Alex will go ahead with his checks on sextant accuracy, and inform
    us of his results.
    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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