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Re: Haversine- how to derive it?
From: Hanno Ix
Date: 2015 May 17, 21:14 -0700

John,

I humbly admit an error I made in my last email: I read your formula wrong, therefore please forget my discussion

of step 4. However, the rest still applies.

:( H

On Sun, May 17, 2015 at 8:51 PM, Hanno Ix <hannoix@gmail.com> wrote:

John,

there is no need to divide the versine but it is nice to have it normalized. This make things
easier at times. Example:

Step 4 of the procedure I described in my prior email was:

4. calculate n + ( 1 - q ) * hav ( LHA ); this yields hav ( ZD )

Had I used the versine I'd write:

4. calculate n + ( 1 - q ) * vers( LHA )/2 ; this yields hav ( ZD )

and therefore would need an extra operation, a division by 2. Not a big issue, but a small one of many.

You notice, of course, that your version of the ZD formula demands two trig functions: cos and vers
and therefore two tables. Also, you'd regress to the need for certain sign rules with the cos, two
multiplications and the mentioned division by 2.

Why would you want to do that?

H

On Sun, May 17, 2015 at 8:11 PM, John Brown <NoReply_JohnBrown@navlist.net> wrote:
Hanno
Your list of virtues of the haversine are IDENTICAL to those of the versine, so why do we need to divide by 2?
For example the formula: vers ZD = vers LHA. cos lat. cos dec + vers (lat +/~ dec) works just as well as the traditional formula, substituting versines for the haversines and using both natural and log functions.
Could a mathematician or a navigation historian on this list please explain why the versine is the poor relation of its half-size parent??
Regards
John

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