NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Tables vs. Calculators
From: Dan Allen
Date: 2002 Sep 20, 14:51 -0700
From: Dan Allen
Date: 2002 Sep 20, 14:51 -0700
On Friday, September 20, 2002, at 11:32 AM, Chuck Taylor wrote: > I could even reproduce the sines and cosines if I wanted to trouble > myself with going through a Taylor series expansion. You're lucky: you've got a series expansion named after yourself, but the rest of us (except for Maclaurins) are just out of luck... ;-)Seriously, I totally agree with Chuck. I can and do have the basic formula for great circle nav and sight reduction memorized because it is so simple: cos(a)*cos(b) + sin(a)*sin(b)*cos(ab) = cos(c) Many of our nav problems boil down to using this simple formula. For example, for great circle problems with arguments in degrees IF a = 90 - lat1 & b = 90 - Lat2 & ab = Lon2 - Lon1 THEN c = GC Distance in degrees, or multiply it by 60 for nautical miles or for sight reduction with arguments in degrees IF a = 90 - estimated latitude & b = 90 - declination & ab = LHA = GHA - estimated longitude THEN 90 - c = altitude This formula is easy to program into calculators, or easy to write down on a piece of paper and do by hand with a basic scientific calculator. This is the essence of self-reliant navigation. Dan
