I'm looking for a derivation of the following aviation formula. I found this on one or two other sites as well but no explanation.
http://www.edwilliams.org/avform147.htm#LL
I took a stab at this myself. The destination latitude comes directly from the cosine rule for sides applied to the colatitude using two great circles through the North Pole and a third great circle through the origination and destination.
I tried using the same technique to get the angle at the North Pole, opposite the line of longitude. What I came up with was the following.
cos(dlon) = (cos(d/R) - cos(colat1)*cos(colat2)) / (sin(colat1)*sin(colat2))
Colat1 and colat2 are the origination and destination colatitudes, respectively. D/R is the angular length. If I plug in small random numbers, I get the same result as in the link above. But I can't see how to get to either of the two formulas starting from what I have here.
