# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**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. > >