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Subject: Re: Tables vs. Calculators
From: Dan Allen (danallen46@XXX.XXX)
Date: Fri Sep 20 2002 - 17:51:37 EDT
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... ;-)
<grin>
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
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