# NavList:

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

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Refraction correction
From: Peter Hakel
Date: 2009 Jun 20, 06:59 -0700
That formula came from the 2009 Nautical Almanac.  The 2009 Astronomical Almanac says:

---- begin quote ------
[altitudes a greater than 15 degrees]
R = 0.00452 * P / ( ( 273 + T ) * tan a )

[...] This formula is usually accurate to about 0.1' for altitudes above 15 degrees, but the error increases rapidly at lower altitudes, especially in abnormal meteorological conditions. For observed apparent altitudes below 15 degrees use the approximate formula:

R = P * (0.1594 + 0.0196*a + 0.00002*a^2 ) / [ (273 + T) * (1 + 0.505*a + 0.0845*a^2) ]

where the altitude a is in degrees.
------ end quote -------

Frank,

In the NavList archives I found an extensive discussion of refraction dating back to August 2005, long before I joined this list.  The debate includes references to "Pulkovo data", humidity...  Do I understand correctly that these formulas are not accurate enough for body-body distance calculations but OK otherwise?

Many thanks.

Peter Hakel

From: "frankreed{at}HistoricalAtlas.com" <frankreed{at}HistoricalAtlas.com>
To: NavList@fer3.com
Sent: Friday, June 19, 2009 11:07:22 PM
Subject: [NavList 8745] Re: Star-star distances for arc error

Peter, you wrote:
"Yes, that's the one.  My edition says:
R = 0.0167 / tan( H + 7.32/(H+4.32))"

Yeah, that would explain it then. That formula is an empirical fit to the refraction table. It's close enough for most navigational calculations. That particular formula (an earlier variant of it) was originally published in the 1980s, I think, by George Bennett. Back then when computing devices had very limited memory and slow processors, this was a great thing: a nice compact equation for refraction at any altitude. But these days??

-FER

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