# NavList:

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

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Re: Very Small Altitude-Accurate Results
From: Stan K
Date: 2015 Aug 16, 13:16 -0400
Not important, but the 1.002' in Eqn. 1 is still really 1', as in Eqn. 2.  Both come from 0.0167º as shown in the Almanac, which is really 0.016666....º.  But the Bennett formula, either in its original form or as modified, does not agree perfectly with Table A3, or, in fact, even with Table A2.  Neither formula was used to create these refraction tables.  The formula is shown in the Almanac because it is a relatively simple single formula that gives fairly good results for all altitudes.  The Bennett formula was published in 1982.  In 1985 HMNAO Technical Note No. 63, "The Computation of Angular Atmospheric Refraction at Large Zenith Angles", was published.  This may or may not match the tables better than the Bennett formula, but Table 2 in the publication is entitled "Comparison with Garfinkel's program (as used in Nautical Almanac)".  Garfinkel's article was published in 1967.  My Nautical Almanac collection jumps from 1962 to 1991, so I am not sure when the Bennett formula or any other formula actually appeared, but the earlier years did not even have a "Sight Reduction Procedures" section.

Stan

-----Original Message-----
To: slk1000 <slk1000@aol.com>
Sent: Sun, Aug 16, 2015 12:57 am
Subject: [NavList] Re: Very Small Altitude-Accurate Results

Since 2004 the Nautical Almanac has used the formula Ro' = 1.002'/tan(Ha +7.32/(Ha+4.32))      Eqn. 1
Prior to 2004 the Nautical Almanac used the formula    Ro' = 1'/tan(Ha +7.31/(Ha+4.4))                 Eqn. 2
The most significant difference in the two formulas occurs for values of Ha less than 2°
See attached PDF,   the Ro values shown in the green column were calculated using Eqn. 1 and the Ro values in the grey column were calculated using Eqn. 2

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