A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Sean C
Date: 2021 Jun 29, 22:16 -0700
Gary LaPook wrote:
"If you want to check the accuracy of the result you can use the formula from AFPAM 11-216. There are typos, you need to add one more set of parenthesis to the formula."
I'll add that you can use any sight reduction method to do great circle calculations. All you have to do is substitute the departure latitude for the DR latitude, substitute the destination latitude for the declination and substitute the difference in longitude for the LHA. That's because it's the same problem. With sight reduction, you're trying to find the direction and [difference in] distance from the DR to the G.P. of a celestial body. Great circle calculations simply swap the departure for the DR and the destination for the G.P. The only real difference is that you need to subtract the calculated "altitude" from 90 to get the distance in degrees.
My personal favorite method is the formulae found in the back of the Nautical Almanac, which would look like this when used for great circle calculations:
- sin(Dest. Lat.) = S
- cos(Dest. Lat) · cos(δLong.) = C
- asin(S · sin(Dep. Lat) + C · cos(Dep. Lat)) = Hc
- (90 - Hc) · 60 = great circle distance in NM
- acos((S · cos(Dep. Lat.) - C · sin(Dep. Lat.)) / cos(Hc)) = X
- Common sense shoult tell you whether to subtract X from 360 to get the initial course angle
If I'm using my TI-30X IIS which has five variable memory slots, I simply store the variables and all I have to enter is:
- asin(sin(D)sin(B) + cos(D)cos(A)cos(B)) → C (where "→" is a "store as" command)
- (90 - ans)60
- acos((sin(D)cos(B) - cos(D)cos(A)sin(B))/cos(C))
I have developed an algorithm to find the rhumb line course, but I've forgotten it. o.O
That's okay, though, because it's in my spreadsheet. I just have to go digging and figure out what I did to make it work. I'll try and post that soon.