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

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Re: Modelization of Refraction
From: George Huxtable
Date: 2010 Mar 15, 13:47 -0000

```Andres offered the Bennett approximation for refraction-

"If R is the refraction for standard conditions, (10ºC and 1010 hPa), Ha is
the apparent altitude and h = Ha-R, then:

Bennett, G.G.: 1982, The calculation of astronomical refraction in marine
navigation, en Journal of the Institute of Navigation, 35,
255.
R = 1/60 / TAN( Ha+7.31/(Ha+4.4) )"

which gives the refraction in degrees.
==============

This provides a remarkably good, and simple, empirical fit to refraction observations.

However, it shows two minor difficulties.

1. It doesn't, quite, give a refraction of zero at an altitude of 90 degrees,
as symmetry tells us that it must, so it's a bit
unphysical.
2. There's an altitude of 89.92º, at which the denominator becomes infinite,
and so some computers / calculators would fail.

So I usually use a slightly tinkered version, which avoids both those
problems, but is indistinguishable elsewhere.

This is best expressed as-

R in arc-minutes = tan (90 - Ha + .000861Ha - 7.31 / (Ha + 4.4) ))

George.
contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
----- Original Message -----
From: "Andres Ruiz"
To:
Sent: Monday, March 15, 2010 11:28 AM
Subject: [NavList] Modelization of Refraction

| If R is the refraction for standard conditions, (10ºC and 1010 hPa), Ha is
the apparent altitude and h = Ha-R, then:
|
|
|
| Bennett, G.G.: 1982, The calculation of astronomical refraction in marine
navigation, en Journal of the Institute of Navigation,
35, 255.
|
| R = 1/60 / TAN( Ha+7.31/(Ha+4.4) )
|
|
|
| Meeus:
|
| R = (58.294*TAN(90-Ha) - 0.0668*pow(TAN(90-Ha),3))/3600
|
| R = (58.276*TAN(90-h) - 0.0824*pow(TAN(90-h),3))/3600
|
|
|
| Saemunndsson:
|
| R = (1.02/(TAN(h+10.3/(h+5.11))))/60.0;
|
|
|
| Chauvenet Vol I, chapter IV gives a very good view of the general law of refraction.
|
|
|
| …
|
| Answering to Brad, yes the iterative process will be something like:
|
|
|
|      for( dH = 0, iter = 0;  iter < 255;  iter++ ) {
|
|            Hs = Hs + dH;
|
|            Ha = AlturaAparente( Hs,  ie,  Dip );
|
|            R = Refraccion( Ha, T, P );
|
|            dH = Hc - ( Ha - R );
|
|            if( fabs(dH) < 1E-8 ) break;
|
|            }
|
|
|
| It is more complicated if parallax, for Moon and Sun, it will be taken into account.
|
|
|
| Regards.
|
| ---
|
| Andrés Ruiz
|
|

|
|
|
| ________________________________
|
| De: navlist-bounce@fer3.com [mailto:navlist-bounce@fer3.com] En nombre de Antoine Couette
| Enviado el: viernes, 12 de marzo de 2010 17:20
| Para: NavList@fer3.com
| Asunto: [NavList] Re: Star - Star Observations
|
| Hello to all,
|
| There is an EXCELLENT refraction formula which gives refraction as function
of unrefracted topocentric altitude.
|
| Its use would simply avoid the requirement for the "loop computation" you have explined.
|
|
| This formula is the so-called Saemundsson's formula which can be found on
the Internet. Its accuracy is well under 6 arc-seconds.
|
| It is also quoted in M. Jean Meeus's most celebrated book "ASTRONOMICAL
ALGORITMS" in its Chapter on atmospheric refraction.
|
| Best Regards to you all
|
|
| Antoine M. Couëtte
|
|
|
|
|
|

```
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