NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Gary LaPook
Date: 2010 Dec 7, 12:44 -0800
Back in 1979 I programmed my TI-59 calculator to do in-flight celestial navigation. Since I was not up on sophisticated mathematical procedures, I came up with a way to approximate the fix near the center of the cocked hat. The program took the first two LOPs and calculated a fix for their intersection. I drew many different triangles and used the "bisecting the LOPs" method to determine the center of the triangles. I measured where these fixes were in relationship to the two body fixes. After looking at many sample triangles, I programmed the calculator to determine the azimuth of the bisector between the first two LOPs that was within 45° of the azimuth of the third LOP. I then moved along this bisector approximately two-thirds (I actually used .663)the length of the third intercept and used that spot as the fix. The program also displayed the length of the third intercept so that I would have an idea of the accuracy of the fix. Maybe not elegant for the purists but it provided reasonable results especially since you avoid using stars that have a very small "cut."
Using this program for your example, and assuming the third azimuth was between west and north and the intercept was 10 NM long, the fix would be determined to be 6.63 NM northwest of the two body fix.
gl
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