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Peter,



Thank you very much for establishing this contact! The postings in this
e-mail list made me realise that I still have to do some more homework
before contacting an authority in the field of refraction.



With homework I mean TRYING to calculate refraction for negative altitudes
using the following approach:



1) Calculating for an observer at a given elevation (a.s.l.), a given
(negative) altitude (but e.g. still above the apparent horizon), a given
temperature and given pressure the tangent point on a line above and
parallel to the earth's curvature at sea level, this using calculation of
terrestrial refraction.



2) Calculating for this tangent point the local temperature and pressure,
this using the standard atmosphere model.



3) Adding to the terrestrial refraction the astronomical refraction for an
altitude of 0? corrected with temperature and pressure at the tangent point.



Comparing the results obtained this way with table 6 of the Air Almanac may
lead to further, but now more specific questions. I think at this point it
will be really helpful to use the contact which you, Peter, did establish.



Again, thank you.



Marcel

----- Original Message -----
From: "Peter Fogg" 
To: 
Sent: Sunday, August 07, 2005 1:16 PM
Subject: Re: Refraction


>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:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM]
> On Behalf Of jcs
> Sent: Friday, 5 August 2005 7:26 AM
> To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM
> 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 
> 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: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM
> 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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