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From: Peter Fogg (no email)
Date: Sun Aug 07 2005 - 06:16:26 EDT
I thought these mentions of his work on refraction might be of interest to
George Bennett, and so passed them along. His comment:
"The evaluation of Astronomical Refraction is an interesting subject. I see
that Marcel Tschudin has chosen one of the empirical formulas that I derived
when I was working at Greenwich. In my article I confined the apparent
altitudes to range of zero to ninety degrees. I would be interested to know
the result of any investigation into the validity of my formulas at small
negative altitudes. As a lead you might write to HM Nautical Almanac Office
who in turn could direct any enquiries to Dr A T Sinclair. He is an expert
on the subject and although retired now he may offer some helpful
information. Cheers, George."
________________________________________
From: Navigation Mailing List [mailto:]
On Behalf Of jcs
Sent: Friday, 5 August 2005 7:26 AM
To:
Subject: Re: Refraction
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. Tschudin
To:
Sent: Thursday, August 04, 2005 11:48 AM
Subject: Refraction
Hello
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.
Marcel
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