A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Tony Oz
Date: 2018 Apr 5, 06:07 -0700
Dear Lars, dear Robin!
Yes, it is great to have a formula always giving the azimuth value that does not need any further transformations.
But the good old one, where the azimuth may come out negative, also has its' own merits - if you are going to calculate the way-point coordinates. It is simpler to use the value stored in the register (on my Casio fx-85ES Plus it is the Y register).
My cheat sheet goes like this:
- the observer's position Lat and Lon are stored in the A and B registers respectively
- the destination's Lat and Lon are stored in the C and D registers respectively
- the angle t = B - D is stored in the E register
- the formula then: Pol(cos(A)·tan(C) - sin(A)·cos(E), -sin(E)); it returns the r and θ in the X and Y registers respectively
- the G.C. distance is then: arcsin(X·cos(C)), the initial azimuth is Y (may be negative)
- Now for the first way-point at distance Dst° along the Crs° course from the observer's position: I choose some reasonable value for the distance and store it in the register F, the course is already stored in the Y register from the first step
- Lat1 = arcsin(sin(A)·cos(F) + cos(A)·sin(F)·cos(Y)) which I store in the register A
- Lon1 = B + arcsin(sin(F)·sin(Y)/cos(A)) which I store in the register B
- then I update the angle t: B-D→E
- now I just recall the Pol() formula from the history of operations and re-execute it. I write down the current contents of the A, B and Y registers for the way-points' coordinates and next leg course value.