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    Re: Refraction
    From: Gary LaPook
    Date: 2005 Aug 15, 23:05 -0700

    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---.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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