NavList:

I am absolutely amazed at what an improvement you guys have found for using the haversine tables. As I wrote in 2008, the standard haversine method:

"The Haversine method required referring to nine different pages in the log tables 
including interpolating three times (I used Nories Air Tables). It 
required subtracting Dec from Lat;  adding three five digit numbers 
twice; adding two five digit numbers one time; and finally subtracting 
ZD from 90º."

Greg's and Hanno's method needs only 4 entries into the tables, 3 additions, 3 subtractions, and 1 multiplication and produces one minute of arc accuracy with an abreivated haversine table covering only two pages. When you think of how many great minds over the centuries worked to develop celestial computation methods and it ends up with our two guys besting all of them! (Unfortunately, Greg and Hanno were each born about two centuries too late.)

The shortest computation is with Weem's Line of Position book, which requires only 3 table entries and two additions, but the table is 54 pages long. See:

http://fer3.com/arc/m2.aspx/Fw-Chichesters-Calculations-SineCosinemethod-LaPook-dec-2008-g6745

In December 2008 I wrote a series of posts illustrating all the standard tabular methods of computing Hc See "Chichester's computations." 

http://www.fer3.com/arc/sort2.aspx?y=200812&sort=au&y2=200812&author=&subject=

http://fer3.com/arc/m2.aspx/Comparison-tabular-sight-reduction-methods-LaPook-jun-2011-g16648

http://fer3.com/arc/m2.aspx/Question-Position-Calculation-LaPook-jan-2014-g26214

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