# NavList:

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

**Re: Refraction**

**From:**George Huxtable

**Date:**2005 Aug 5, 22:37 +0100

Marcel Tschudin posed an interesting question-- >While searching with Google, I came across this mail list. May be some one >out here may be able to help me answering the following question: > > > >How do refraction values for negative elevations have to be calculated, >such as e.g. the horizon from a plane? (I am interested in the range of 0? >to approx. ?5?.) > > > >Is Bennett?s approximation also valid for negative elevations? If not, >what other approximation formulae should be used, or, where can one find >some benchmark values? > > > >I am interested in formulae for both, refraction from apparent position >and from physical position. =============== Following that, there have been several resposes from the Nav-l community. By the way, several of those responses from Roibert Ene were misdated to have a September date rather than an August one. I hope he will correct his calender, because my email reader, which puts correspondence into strict date order, keeps mis-sorting Robert's contributions. ============== Marcel's question puzzled me considerably, until it emerged that was referring to bubble-sextant observations, with respect to the true horizontal, not altitudes measured up from the observed horizon with an ordinary sextant. It's not a question I am familiar with, nor is the table HO249, so I have little to offer in the way of a positive contribution. I've been reading the correspondence with interest, and have some comments to make about suggestions made earlier. Marcel wrote- >I also was wandering whether the approximate formulae could be used by >calculating the Refraction R for e.g. -2? the follwing way: > >R(-2?) = R(0?) + ( R(0?) - R(+2?) ) > >If this would be correct then one would not need separate formula for >negative elevations. I am sure that suggestion would not work. It would be true only if the refraction was linear with altitude, which is VERY far from being the case. ================== Fred Hebard wrote- >I assume you have Meeus' formula for normal observations. >Meeus' formula, as transcribed by G. Huxtable, is: >tan(90-0.99914*S-(7.31/(S+4.4)), where S is the sextant altitude in >degrees. I don't know whether this formula blows up at 0, but you >could try it and see whether it gives the same results as HO249's Table >6. No, it doesn't blow up at 0 degrees, but it does at -4.4 degrees: This empirical formula doesn't pretend to give even an approximate answer for negative altitudes. By the way, that formula wasn't "transcribed" by me from Meeus, but tinkered-with slightly. This was to avoid an infinity arising during the calculation of tan, for an angle of 89.92 degrees (which is in the 'useful' range). The coefficient of S is adjusted to 0.99914 rather than 1.0, just to ensure that refraction goes to zero at an altitude of 90 degrees, as symmetry says it must. ================= Robert Eno wrote- >If I had a scanner, I could scan the table for you. Here are a few examples: > >Height of observer: 0 feet >Sextant Altitude: minus 1 degree >Correction: minus 35 minutes > >Observed Altitude = minus 1 degree 35 minutes. That seems a bit odd, and unphysical. From a height of 0 feet, how can a sextant altitude possibly be -1degree? Also, the quoted value for the correction, at -35 minutes, is rather a surprise, considering that the adopted value for refraction at 0 degrees altitude is -34 minutes, and refraction increases very quickly as the altitude decreases towards zero. ================== I can suggest a useful analysis of such low-level refractions by Andrew T Yoiung and George W Kattawar, titled "Sunset Science 2. A useful diagram", in Applied Optics , vol 37 no 18 (20 June 1998), pages 3785 to 3792. Andy Young is an acknowledged authority on such atmospheric optics, including mirages. 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.