# NavList:

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

**Re: Refraction**

**From:**Clive Sutherland

**Date:**2005 Aug 4, 22:25 +0100

Hi Marcel Welcome to the
list;

Be careful there are nearly as many different
formula for refraction as there are members of the list. There is not to
my knowledge a definitive formula. Almost all of them will work well
at sextant altitudes above about 15 deg but begin to fail at low
angles, particularly negative angles, due to the unpredictable behaviour of the
atmosphere close to the sea or ground.

G.G.Bennet wrote a short article in the
(UK) Journal of the Institute of Navigation.Vol 35 No 2. in which he
compared several calculator programs with a Fortran program written by G
Garfinkel, described in The Astronomical Journal,Vol 72,No 2 (1967),
However it is not an easy method to use. I believe his program was
written for the benefit of Nasa space program but I may be wrong about this.
.

The following is one I use,

Ref = Tan (90-Altitude - 0.999139 * Altitude
- (7.31 / (Altitude + 4.4)))

between -20 < Air Temp < +40, and 970
<air pressure mbs < 1050

or else use the correction below for abnormal
temperature and Pressure

Abn = (( Baro Pressure - 80 ) / 930) * (1 / ( 1 +
0.00008 * (Refraction + 39) * (Temperature - 10))),

using mbs,deg celsius and deg
Altitude.

Refraction = Ref * Abn and True
Altitude = Observed Altitude - Refraction

I have compared several formula using Excel for
angles below zero altitude and all them diverge dramatically from each
other at altitudes below -1/2 deg. Also I think that all the simple
formula are based on an empirical value of about -34 minutes for zero
altitude but how this number has been obtained I dont know. Perhaps
someone on the list could enlighten me.

The table at the back of the Air almanac are
the only tables I know that are for use in aircraft etc above ground
level. but they don't lend themselves very well for calculator or computer
programs.

Clive.

----- Original Message -----From:Marcel E. TschudinSent:Thursday, August 04, 2005 11:48 AMSubject:RefractionHello

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 Bennetts 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.

Thank you for any input to my problem.

Marcel