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Re: Haversine- how to derive it?
From: Samuel L
Date: 2015 May 18, 17:36 -0700

Hanno,

I tried a reduction using the Haversine method Greg lists (for Deneb) on his s/v Nightcap site  (http://gregrudzinski.blogspot.com/)

I deteremined Hc with not too much trouble but can't figure out how to calculate Zn. He shows 360d - 16d= 344

Would you, or Greg, please explain how to determine Zn....in very simple terms?

Thank you,

Sam L.

However, using the haversine G. Rudzinski and I can show you another,
very easy calculation of Hc. Only one table, 2 pages, is used and only one
multiplication is needed. There are no complicated sign rules
and special cases - it will work for all permutations of  L, d and LHA.

Given: L, d, LHA, find Hc. Execute these 6 elementary steps:

1. calculate                 n = hav ( L - d )
2. calculate                 p = hav (L + d )
3. calculate                 q = p + n

4. calculate                 n + ( 1 - q ) * hav ( LHA ); this yields hav ( ZD )
5. find in table             ZD  by looking up the table backwards

6. Finally                    Hc = 90 deg  - ZD

As can you see the steps are basic arithmetic - executable by hand in minutes.

We discussed all this on the list under the topic Longhand Sight Reduction.
For the azimuth we suggest using the azimuth table I published there, too.

H
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