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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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