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    Re: Refraction
    From: Marcel Tschudin
    Date: 2005 Aug 16, 17:33 +0300

    I just received the follwing information from USNO, refering to the table 6
    Pub 249 is indeed a publication of NGA, not USNO.  It is regrettable
    that they are unable to support their own product.  I will answer this
    question as best as I can, but be aware that I am working from an old
    (epoch 1995.0) copy of Pub 249.  It does appear that the refraction
    table in Pub 249 was derived from the more detailed refraction table
    published annually in the Air Almanac.  The Air Almanac table first
    appeared in the AA for 1953. The scientific underpinnings of the Air
    Almanac table were published in a paper, "The Refraction Table in the
    Air Almanac," by D.H. Sadler, former Superintendent of H.M. Nautical
    Almanac Office (UK).  The paper likely appeared during the first half of
    the 1950s in the (British) journal, Navigation (may have been called the
    Journal of the Institute of Navigation).  That's the best I can do
    regarding the reference.  Perhaps a good library can help with the
    literature search.
    Astronomical Applications Dept.
    US Naval Observatory
    Does anyone of you know more about the mentioned paper from D.H. Sadler or
    the journal where it was published?
    ----- Original Message -----
    From: "Gary J. LaPook" 
    Sent: Tuesday, August 16, 2005 9:05 AM
    Subject: Re: Refraction
    > Any idea how the refraction tables in the Air Almanac and HO 249 were
    > computed? They show values for altitudes down to 3?53' below the
    > horizon, from a height of eye of 55,000 feet at which point the
    > refraction is 60'. The refraction is also listed as 60' for -2?53' when
    > observed from 30,000 feet. It should be noted that for altitudes below
    > about 1? the refraction correction is only listed by 5' intervals.
    > Gary LaPook
    > george huxtable wrote:
    >> This is the second attempt to send this message to nav-l. Previously,
    >> on 14
    >> August, I had a bounce message. Don't know why.
    >> ==============================================
    >> Marcel Tschudin wrote- further about refraction.
    >> Unfortunately, there is no TRUE value for refraction at low angles of
    >> altitude, close above the horizon. Pulkova observatory near St Petersburg
    >> has been running a programme of measurements over many years, that as far
    >> as I'm aware still continues. Every now and then, a revised publication
    >> emerges with improved and updated results. Because refraction  at low
    >> angles varies with the local weather (and not just the air density at the
    >> observer), quoted values are average results, over a long time. On any
    >> day
    >> the actual refraction can differ, as distortions in the apparent disc
    >> of a
    >> low Sun clearly indicate.. Correcting for local temperature and pressure
    >> will do something to iron out those variations, but significant
    >> differences
    >> will remain.
    >> Bennet has provided a  formula which is an empirical attempt to fit that
    >> averaged data. At large angles of altitude, it becomes proportion to the
    >> tan of the zenith angle, as Snell's law requires. Near the horizon, where
    >> refraction rises sharply, the divergence from Snell's law shows up in
    >> correction terms which turn out to be remarkably simple. However,  I
    >> doubt
    >> whether those terms have any backing in terms of the physics of the
    >> refraction process; more likely, they are just empirical attempts to
    >> get as
    >> good a fit as possible, compatible with a simple calculation. It was
    >> devised in the days before everyone had a computer / calculator.
    >> So it's no surprise that tabulated refraction values agree well with
    >> Bennett. His formula was devised to replicate those values. In some
    >> publications, such as the Nautical Almanac, it appears that Bennett's
    >> formula itself is used as the basis for the refraction tables (though the
    >> constants have recently been tinkered-with a bit to improve the fit to
    >> recent Pulkova data) so it's not surprising that it shows good agreement.
    >> The almanac wisely states that-"the actual values of the dip and of the
    >> refraction at low altitudes may, in extreme atmospheric conditions,
    >> differ
    >> considerably from the mean values used in the tables".
    >> Bennett's empirical formula was, presumably, optimised to achieve an
    >> acceptable fit for positive angles of altitude and took no account of
    >> negative angles, and there's no reason to expect it to fit the observed
    >> refraction in that region.
    >> What I would conclude from all this is that there's no point in seeking
    >> extreme accuracy for such low-angle refraction predictions, positive or
    >> negative.. Where Marcel says-
    >>> In the mean time I also found the source code of a BASIC program to
    >>> calculate refraction by integration. The program was described in Sky &
    >>> Telescope of March 1989. Without having the original article, I
    >>> transcribed
    >>> the program into the language with which I am working at the moment,
    >>> i.e. in
    >>> Pascal/Delphi. A comparison of the refraction values, either from the
    >>> table
    >>> 6 or those from Bennett, with those of the program show that those
    >>> depend
    >>> substantially of the selected refraction index of air. The problem of
    >>> calculating the refraction becomes now a problem of calculating a
    >>> realistic
    >>> refraction index for air,  which depends on the wavelength, temperature,
    >>> humidity.
    >> It strikes me that (as Fred Hebard has indicated) such corrections for
    >> wavelength and humidity are sufficiently small to be neglected, and to be
    >> overwhelmed, at low angles of altitude, by the unpredictable layering of
    >> temperature gradients in the air. Any such integration is only as good as
    >> the data that is available to feed into it, varying from one day to
    >> the next.
    >> Marcel added-
    >>> All this investigations done so far are for refraction values for
    >>> APPARENT
    >>> negative altitudes. For my program I need however also the "inverse",
    >>> i.e.
    >>> the calculation of the refraction for physical, TRUE negative
    >>> altitudes,which has not been tuched so far.
    >> Well, I touched on it, in my last posting, in quoting the refraction
    >> at the
    >> tangent point (which corresponds to zero degrees true altitude) to be, at
    >> sea level, about 29 minutes, and not 34 minutes (which is the adopted
    >> mean
    >> value for refraction at zero degrees apparent altitude).
    >> George.
    >> ===============================================================
    >> Contact George at george@huxtable.u-net.com ,or by phone +44 1865 820222,
    >> or from within UK 01865 820222.
    >> Or by post- George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13
    >> 5HX, UK.

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