From: jfh@cs.brown.edu (John F. Hughes)
Newsgroups: rec.boats
Subject: Re: Celestial Navigation Question
Date: 4 Jan 1993 14:21:16 GMT
Organization: Brown University Department of Computer Science
NNTP-Posting-Host: euclid.cs.brown.edu
Keywords: Celestial

In article <1993Jan3.215750.9831@phx.mcd.mot.com> teroach!dbk@phx.mcd.mot.com (Dave Kinzer) writes:
>   I read the post about getting sites to about 0.2 to 0.1 minute accuracy,
>but I'm not sure how this translates into actual accuracy of a fix.  For
>example, by my admittedly un-expert calculations, any fix you could make
>will be traveling due west (or east depending on how you think about it)
>at better than 11 nautical miles a minute (This assumes a 45 degree or
>less latitude, in other words most waters in which we recreationally go
>boating.)

Uh...two problems with this. (1) The fix isn't going to move at all. The
geographical position of the star on which you based the fix will move, at
about the rate you describe. This means that 4 seconds elapsed time <-> about
1 nm error in the "line of position". That's why navigators get all excited
about accurate timepieces. (2) The typical sight reduction is based on repeated
sights of the several bodies, so that I might take 5 observations of the sun in
a row, then 5 more or the moon. For each of these, I make some error in
recording the time. The random errors should (and do) average out pretty
rapidly to near 0. The systematic errors (I always take 1/2 second to look
at my watch) do not, but by practicing at a known location for a long time,
you get a pretty good estimate of what your systematic errors are.

>  I recall several months ago of one poster being thrilled to get a fix   
>less than a mile from his actual position.  Note: A fix.  This doesn't
>mean average, root mean squared, three sigma accuracy, or any meaningful
>measure of how well this kind of navigation would keep you off a reef in
>the Bahamas.  

Anyone who uses celestial alone to determine a position within a mile is 
loony. The function of celestial navigation is to get you about to where 
you're going. When you get to where you're going, that's when *piloting* 
takes over. 

The problem here is that GPS performs both functions, and so folks begin to
think that a sextant should, too. The error modes for sextant and GPS
are interesting, though. GPS errors tend to be large (e.g. the 85 knot
speeds that someone reported recently.) If the GPS reading sounds reasonable,
they are likely to be right. Celestial errors come in all forms, and it's
quite possible to get reasonable-sounding results that are just plain wrong,
because of errors in computation, timepieces, sextant, etc. 

>   Anyone care to venture the average error of their last 20 fixes as
>compared to their GPS or LORAN location at the same time?

Well, I'l bet that my father-in-law's last 20 fixes were a *whole* lot better
than his Loran readings. He was navigating from the Chesapeake down to the
Virgin Islands. Within about 10 minutes of the time he predicted, the landfall
showed up just where he predicted. At the same time, his Loran was saying, 
very accurately, "BLINK....BLINK....BLINK" :-). 
>
>   Don't worry, no one will be able to judge your errors absolutely by this,
>since everyone who reads this newsgroup KNOWS how crummy GPS and LORAN
>positions are.  8^)

Sometimes they are, sometimes they're not. 
They *really* stink when the battery is dead. Celestial fixes stink
when it's overcast. 

-John
Newsgroups: rec.boats