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    Re: Sight reduction using a calculator's POL (arctan2) key
    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(Atan(C) - sin(Acos(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(Acos(F) + cos(Asin(Fcos(Y)) which I store in the register A
    • Lon1 = B + arcsin(sin(Fsin(Y)/cos(A)) which I store in the register B
    • then I update the angle t: B-DE
    • 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.

    Please comment.

    Warm regards,

    Tony

       
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