# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Azimith forumula for Great Circle sailings- having problems
From: Gary LaPook
Date: 2014 Dec 24, 15:56 -0800
By definition, LHA is measured only towards the west, from 0 to 360 degrees, so for any LHA between 0.0001 degrees and 179.99999 degrees the destination must have a longitude further to the west than the starting point. So your example has the destination about 10 minutes of longitude west of the starting position (about 7.5 NM at a 41 degree latitude) so the course must be to the west of straight north. In fact it is about 4 degrees to the west of north. The standard formula provides a -4 degrees that you add to 360 to find the initial course of about 356 degrees true.

In the olden days and using old formulas and tables, what we now call LHA today was known as "angle t" or "hour angle" and was measured both ways, both to the west and to the east, from 0 to only 180 degrees so perhaps you are having a problem with definitions, perhaps you are looking at one of those old usages.

To clear this up, give us the actual longitudes of the starting and finishing positions.

gl

To: garylapook---.net
Sent: Wednesday, December 24, 2014 12:11 PM
Subject: [NavList] Re: Azimith forumula for Great Circle sailings- having problems

Gary,
Unless I'm really, really, really wrong the Azimith is 3.917400689 and not -3.917400689. Forget about the places to the right of the decimal for the moment.
The coordinates of both positions were plotted on a UPS and gave the same result of +3.917d
Several online great circle sailings calculators gave the same result.
Peter Hakel's Sailings.xls spreadsheet gave the same result of +3.917d
I think the error occurs when the LHA (Difference in Longitude) isn't examined for a greater or less than 180d value. If a negative sign is applied to the LHA when using the formula then the answer comes out correctly.
I've read your lengthy comments but learn only by trail and error. Thus, if the GPS says such and such a figure and Gary says something contrary....for the moment I'm going to work with the GPS figures until study and practice shows otherwise. It's like the "rounding up or down" situation I had a few months ago.
Would you please show me how in the world you arrived at a negative Azimith?
Sam L.

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