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Re: Making an impact with hav-Doniol (collection of prior posts)
From: Hanno Ix
Date: 2015 Jun 22, 04:41 -0700

Gary, Ken

the hav - Doniol story is even older yet:

1.
fer3.com/arc/m2.aspx/g27982

In June 2014, Greg found an existing version of Doniol, one that one could call sine-Doniol.

As he noted in this posting :
R. Daniol (1955) formula :
Sin h = n - (n+m)a
n = Cos(L-d)
m = Cos(L+d)
a = haversine LHA

It still required at least two tables, if not three, but still had sign complications in the trig functions. However it was mathematically strictly applicable to all permutations of L, d and LHA and needed only one multiplication. So it was a very welcome simplification of the Hc formula for sight reduction. Greg went through several examples that demonstrated these advantages very clearly.

2.
fer3.com/arc/m2.aspx/g29121
fer3.com/arc/m2.aspx/g29126

In Nov 6, 2014 I re-wrote the sine-Doniol formula into a haversine - only version and compared it with the sine - Doniol in the first of these postings addressed to Greg:

hav(s2s) = hav(L-d) - [ hav(L-d) + hav(L+d) - 1 ]* hav(LHA).

where I used s2s for ZD for my own convenience, and I included an example. This, then, is the oldest hav - Doniol version. Greg and I were very happy about this discovery.

3.
fer3.com/arc/m2.aspx/g29138

Greg is very practical: he prefers to proceed in well defined steps as his hav - Doniol examples in this posting show. With these examples he compacted hav - Doniol into a form similar to the step-by-step procedure of the original sine - Doniol:

n = hav (L- d)

p = hav (L+d)

q = n + p

hav(ZD) = n + (1 - q) * hav( LHA )

which has become the preferred version. It easily can be executed on an index card as Greg likes to do on his RIC's = "Rudzinski Index Cards".

4.

My 2-page haversine table was introduced several days later:fer3.com/arc/m2.aspx/g29172

and the azimuth diagram almost 2 years before.fer3.com/arc/m2.aspx/g20982
Some other proposals I made in this context, for instance the Vedic multiplication scheme, did certainly not find approval at all.

5.

Comment: there was no particular mathematical ingenuity on my part involved - just certain insights into the needs of the navigator which are mainly issues of dis-ambiguity and simplitiy. The decisive steps were 1. and 2. above and perhaps my azimuth diagram. Since we discovered hav - Doniol Greg spread the word in a tireless effort.

Strangely enough, there were authors ( e,g, Willis ) who developed a very similar formula but did not recognize the advantages.

On Sun, Jun 21, 2015 at 11:11 AM, Gary LaPook <NoReply_LaPook@fer3.com> wrote:

Ken, look at these posts to bring you up to speed on the Hanno Ix-Greg Rudzinski Hav-Doniol invention. (In no particular order.)
gl
http://fer3.com/arc/m2.aspx/Doniol-Longhand-Sight-Reduction-Summary-Rudzinski-dec-2014-g29725
http://fer3.com/arc/m2.aspx/Doniol-Longhand-Sight-Reduction-Summary-Rudzinski-dec-2014-g29733
http://fer3.com/arc/m2.aspx/Gregs-article-havDoniol-Ocean-Navigator-FrankReed-jun-2015-g31625
http://fer3.com/arc/m2.aspx/Gregs-article-havDoniol-Ocean-Navigator-Rudzinski-jun-2015-g31634
http://fer3.com/arc/m2.aspx/HavDoniol-Rudzinski-jun-2015-g31685
http://fer3.com/arc/m2.aspx/HavDoniol-LaPook-jun-2015-g31684
http://fer3.com/arc/m2.aspx/HavDoniol-LaPook-jun-2015-g31695
http://fer3.com/arc/m2.aspx/Making-an-impact-with-havDoniol-Rudzinski-jun-2015-g31804
http://fer3.com/arc/m2.aspx/Making-an-impact-with-havDoniol-LaPook-jun-2015-g31805
http://fer3.com/arc/m2.aspx/Gregs-article-havDoniol-Ocean-Navigator-LaPook-jun-2015-g31698
http://fer3.com/arc/m2.aspx/Doniol-Longhand-Sight-Reduction-Summary-HannoIx-jan-2015-g30027
http://fer3.com/arc/m2.aspx/Gregs-article-havDoniol-Ocean-Navigator-HannoIx-jun-2015-g31689

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