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    Re: Q: how to calculate refraction at higher altitudes on land?
    From: George Huxtable
    Date: 2002 Feb 28, 11:49 +0000

    Dan Allen said-
    >...the question is, how does one calculate refraction at higher >altitudes
    >on land?  Do I just use the actual barometric
    >pressure or do I somehow factor in elevation explicitly?
    >It is my understanding that the more atmosphere, the more refraction,
    >>hence higher elevations have less pressure and thus less
    >refraction.  Bowditch and other sources do not say much about >refraction
    >as a function of elevation above sea level.  I did notice
    >one comment about Air Almanacs having extra columns in their refraction
    >>tables to allow an elevation to be entered, but I do not
    >have an Air Almanac to check on this.
    >My guess is that if refraction is stricly due to atmospheric thickness,
    >>the barometric pressure is sufficient, but if there are
    >geometrical aspects to refraction (which I know there are since there >is
    >no refraction for a body directly overhead), then elevation
    >much above sea level needs to be accounted for separately from >barometric
    >pressure.  The question then is, by how much?
    George Huxtable responds-
    As I understand it, refraction is, rather strictly, proportional to
    atmospheric pressure. So all that Dan has to do is to reduce his
    refraction, from the standard tables, by an (off-the-cuff) amount of about
    3% for every 1000 ft of elevation. So at 1000 ft the refraction at 10 deg
    angular altitude would be reduced from 5.25 minutes to about 5.1 minutes.
    For greater angles of altitude the reduction would be correspondingly less.
    So not very significant, unless the observer is working to a very high
    level of accuracy.
    As Dan points out, refraction varies with the angle of altitude, becoming
    zero when straight overhead. But that doesn't complicate the allowance for
    altitude as above. Whatever the sea-level refraction was, just reduce it in
    proportion to the pressure.
    Presumably a reflective pool is being used as an artificial horizon, in
    which case high accuracy is indeed possible. Several errors, that are
    inseparable from using the real horizon as a reference, vanish in this
    The only other effect that Dan would need to keep an eye on is that of
    temperature, because in his mountain retreat Dan may experience abnormally
    cool air.
    Elevation is not normally a concern of mariners, so its effects are not
    considered in the navigation textbooks. I wonder if astro-navigation ever
    played an important role in navigation on the North American Great Lakes?
    Even there, the elevations don't exceed 600 feet, so the impact on
    navigation was negligible.
    In another mailing, Dan asks the inverse question-
    Does anyone have any clever ideas about determining one's elevation above
    sea level using a sextant?  What if one knows one's
    latitude and longitude exactly -- would that help?
    Comment from George-
    I have no clever ideas about this. Dan doesn't say if he has a view of the
    sea from his mountain. If so, that would make a big difference.
    Because the elevation has so little effect on the observed position of
    objects in the sky, then presumably such observations are a very bad way to
    determine elevation. An aneroid barometer would do the job much better. But
    if latitude and longitude are accurately known, surely a map would give a
    good answer. Here, I am thinking of the UK, every square inch of which has
    been surveyed to death. Perhaps things are different in the vast expanses
    of the American NorthWest.
    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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