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Re: Haversine- how to derive it?
From: Hanno Ix
Date: 2015 May 17, 09:45 -0700
John, Ed, Samuel,
hav (x) is
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:
4. calculate n + ( 1 - q ) * hav ( LHA ); this yields hav ( ZD )
From: Hanno Ix
Date: 2015 May 17, 09:45 -0700
John, Ed, Samuel,
as I outlined the virtues of the haversine to Frank yesterday,
hav (x) is
(i) always positive,
(ii) no matter the sign of the angles x
(ii) no matter the sign of the angles x
(iii) never goes to infinity which I forgot to mention.
Contrast this to sin(x), cos(x), tan(x) etc. and their logarithms!
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.
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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