NavList:

   

Reply

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.

   

Reply