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# Re: spherical geometry

Regarding Carl's rearrangement of his formula:

First let me simplify my formula to:

tan(B) = sin(T) * cot(P-P0)

Are you happier with this? It allows negative values, although of
course it still can't distinguish quadrants I/IV from II/III.

At least twice as happy as before. Actually, the ambiguity your
result still now has is *supposed* to be there. This is because
there are 2 geodesic paths connecting two arbitrary fixed points
on a sphere going in opposite directions. Your formula now gives
both the short way *and* the long way around the sphere from the
same formula.

If you want another spherical geometry exercise,
rederive Clairaut's formula.
http://williams.best.vwh.net/avform.htm#Clairaut

Heck, I'm never going to get anything else done, but it's fun.
Equation (3) divided by (2) in my PDF gives:

tan(A) = tan(T)/sin(P-P0)

Solve this for (P-P0) and substitute into my bearing formula above
to get:

cos(T) * cos(B) = cos(A) = constant

which is Clairaut's formula, and certainly looks like a nice way to
satisfy Hugh's request for a simple method of correcting course
enroute. Swap cos(B) for sin(H) for Brian's desire to get headings
relative to north. -Carl

Good work!

David Bowman