NavList:

Recently, Hanno Ix said:

Bygrave needs consideration of special cases, whereas the sin-cos SR yields valid results for all combinations of L, D, t. 

What are the special cases for Bygrave, and what are the principles for addressing them?

Greg has helped me sort out how to make the equations work, as framed below.  I have been able to use them so far, and get the results to agree with the same problem solved with Pub. 249. 

But Hanno's allusion to "special cases" tells me that if I have been able to make all my problems work out so far, it is because none of my problems so far involve a scenario where I need to tweak my approach.

Here is what I am using:

Where...

d = declination of the GP
t = meridian angle
L = latitude of AP
Az = azimuth angle
X & Y = intermediate values
 

1. tan(d) ÷ cos(t) = tan(X)
           arctan(X) = _____°
2. 90° - X + L = Y
           If Y > 90° then Y = 180° - Y
           Y = _____°
3. (tan(t) * cos(X)) ÷ cos(Y) = tan(Az)
           arctan(Az) = _____°

4. cos(Az) * tan(Y) = tan(Hc)
           arctan(Hc) = _____°

5.  "Translating" Az into Z

                                             ___  (Az)° ___
                               N/S        E/W
                            Use N if GP is N of AP
                            Use E if GP is E of AP

 

I am pretty sure that there is an implied set of "other conditions" in my step 2 above.  I would appreciate feedback on that, as well as on any mistakes I may have made above.

Thank you!

Bob