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    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.
    ----- Original Message -----
    Sent: Thursday, August 04, 2005 11:48 AM
    Subject: Refraction



    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.


    Thank you for any input to my problem.



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