Conference unifix::sailing

    Phew! People have written THICK books which answer these questions
    and the questions which arise from them. But I can summarize a few
    answers (and gladly accept corrections from the more expert).
    
    The basic operation of celestial navigation is to measure the altitude
    of a known body (sun, moon, planets, or one of the 57 navigational
    stars) above your horizon at a precisely known time. Then, knowing
    the time, to figure out the position of that body on the earth (the
    point it is 'directly above') at that time. It is then possible
    (usually using tables) to figure out your distance from that position.
    This establishes a 'line of position' - a line which is perpendicular
    to the great circle arc connecting your position and the body's
    position, and running through your position. This line is in fact
    a circle drawn on the earth's surface, but since its radius is usually
    enormous, it can be treated as a straight line in your local vicinity.
    If you can compute three such lines (from observations of three
    different bodies), then their intersection indicates your position.
    
    This simplifies the process. The details have been tabulated using
    several different systems in ways which aim to reduce either the
    amount of tabular space required, the difficulty of using the system,
    or both. The tables correct for the difference between sidereal
    (real rotational period) and statue days.
    
    The choice of what celestial bodies to shoot is one of the fun parts
    of celestial navigation. It depends on what will be visible, your
    abilities to find and take good altitudes of the bodies, and what
    we give good LOP intersections (three bodies close together give
    a poor position intersection, same as when taking RDF or hand bearing
    compass bearings). People are likely to use (always assuming visibility)
    	1. A noon sight of the sun - because it's easy and gives a latitude
    	   essentially directly. Traditionally very important - the
    	   day at see began with the noon sight. That was when local
    	   was changed to coincide with the sun (no standard times!)
    	2. A morning or evening twilight sight of as many celestial
    	   bodies as possible. Venus is real good if visible. There
    	   are some good stars, particularly if you have learned to
    	   identify them. The moon as a last resort, and the sun as
    	   a real last resort (both are changing altitude pretty fast,
    	   and other effects combine to give questionable sights unless
    	   you're pretty experienced).
    
    The last basic measurement required is a good value of time which
    can be converted to GMT. The chronometer has been supplying this
    for many years now, and modern yacht-oriented chronometers are,
    of course, digitized. Many use a combination of time signals and
    a good digital wristwatch. Converting time to distance, one second
    equals 1/4 nautical mile, so time accuracy is important.
    
    There's lots, lots more, and this summary is off the top of my head.
    More expert noters are invited to correct and expand.
    
    Ross Faneuf
    

A correction:

When you measure the altitude of a celestial body (in degrees and
usually with a sextant), you are determining how far you are from the
geographic position of that body. 

The line of position is actually a great circle drawn on the earth's
surface with the geographic position of the celestial body as the center
of the circle. Your position is anywhere on that circle. As was pointed
out in .1, the radius of the circle is usually so large that the line of
position may be treated as a straight line on the plotting sheet or
chart (this is not true when the celestial body is nearly overhead). 

Since finding position accurately depends on measuring the time of the 
sight to the nearest second, it doesn't really matter which celestial 
body you use for a sight. The sun and moon, being big, are a great deal 
easier to use, especially with a cheap sextant with poor optics and in 
bad weather, than a little star or planet. Besides, the sun and moon are 
easy to recognize, the stars and planets aren't.

Alan

	Re: .0
	
	The issue of how many bodies to use involves the desired degree
	of both precision and accuracy of (confidence in) the result.  As
	mentioned in .1 and .2, an altitude observation of a single body
	will yield a line of position.  This result is neither precise,
	since you could be anywhere along the line, nor of known
	accuracy.
	
	Simultaneous observations of two bodies will yield two lines of
	position which will (usually) cross at some point near your
	estimated position.  This is a two-body fix, and is a precise
	position but one of unknown accuracy.  If one or both of the
	observations is faulty, the lines will still cross but will do so
	at the wrong place.
	
	Three lines of position will form a triangle.  If your
	observations are good and your arithmetic is error free, then the
	triangle will be small and the center of it will represent your
	position.   A triangle a mile on a side is as good as most
	navigators ever get, even under ideal conditions.  This result is
	both precise and (probably) accurate.  If your observations are
	bad, the triangle will be large and you will know that the
	accuracy of the indicated position is doubtful.
	
	The more lines you have, the greater the precision (assuming
	random errors) of the (averaged) result and the greater the
	degree of confidence you can assume.  Overcome by a fit of
	swaggering bravado, I once shot a six body fix during evening
	twilight.  Unfortunately, I exhausted the batteries on my
	calculator trying to reduce all the data.
	
	What makes this celestial stuff something of an art form is that
	to measure the altitude of a celestial body you need to be able
	to see both the body and the horizon.  During the daytime, when
	the horizon is visible, it's rare to have more than one celestial
	body available.  During the night, when there are plenty of
	celestial bodies, you can't see the horizon.  Stars and planets
	are therefore only usable during a ten minute window each morning
	and evening twilight, and then only if the sky is clear, etc.,
	etc.

	Selection of which body(s) to use is largely a matter of
	availability and personal preference.  As a gentle correction to
	.1, they all (the Sun, the Moon, the four planets and the 57
	stars - nothing else exists) move around the Earth at about the
	same speed.  Some navigators avoid using the Moon since it is a
	lot closer than the others and reducing the sight requires a
	couple more steps to correct for hourly change in semi-diameter
	and parallax.
	
	As a matter of practicality, most modern navigators just shoot
	the Sun at different times during the day and advance the lines
	of position along the Dead Reckoning track to obtain a running
	fix.  Purists consider such practice a reprehensible cop-out but
	we're a dying breed.  In any case, the increased possibility of
	error is acceptable since if you need to know your position
	closer than 10 miles it's usually because you're trying to hit
	something or you're trying to miss something and, in either case,
	once you're within 10 miles of whatever it is, you should be able
	to *see* it so you don't need the sextant at all.
	
	There are exceptions to all of this - one is that you can take a
	series of measurements on a single body during it's meridian
	transit (when it passes due North or South of you) which is when
	it reaches maximum altitude, stops rising and begins to set.
	Plot all the altitudes versus time, strike a curve through the
	points, and try to interpolate the peak altitude and the time at
	which it occurred.  The observed altitude can be converted to
	your latitude and the time can be converted to your longitude.
	Presto!  Unfortunately, the curve is likely to be pretty flat, so
	the exact time of the transit will be hard to pick out.
	
	... and yes, a Sidereal day is 4 minutes shorter than a Solar
	day.  However, none of us navigators believe that Copernican
	fantasy about the Earth revolving around the Sun (Indeed! - the
	man must have spent his life in a cave) so the Nautical almanac
	is keyed to the Mean Sun, that is, where the Sun would be if it
	revolved around the Earth (which it does, as anyone can plainly
	see) at an even rate (which it doesn't).  The common name for
	this is Coordinated Universal Time (abbreviated UTC as a
	concession to the French) which replaced the older term Greenwich
	Mean Time (GMT).

    I thought I'd revive this note with a question on Celestrial Navigation
    tables....
    
    I am currently teaching myself Celestrial Navigation using the HO229
    tables for sight reduction. I was given a book, printed in 1975
    on using HO208 for sight reductions. In reviewing the book, it looks a
    bit easier and ALL the tables are in one fairly thin book. Wondering if
    it would ever become outdated, I began searching through the tables for
    a correction table with dates on it. The only one I can find is one for
    the Planet Jupiter, with corrections from 1975-2000. From this, I am
    deducing that the table may work until the year 2000 and then become a
    paperweight.
    
    From a curiosity standpoint though, I'm wondering if anyone has any
    info on HO208 and if it is still viable? Does Bowditch have any
    reference to it? I figure I'll stick with the 228 tables for now,
    primarily because I've got a great book I'm using that makes sense to
    me and it uses them. But once I understand what I'm doing, I can see
    where learning the 208 method would sure cut down on the poundage of
    tables required for sight reduction in absence of a nav calculator.
    
    Comments anyone?
    Robert

    correction to .4..
    Please read HO229 everytime you see HO228. Confusion from a neophyte...

The sight reduction tables are good forever (unless a calculation 
mistake is found) as they are nothing more than solutions to the 
spherical trigonometry used in celestial navigation. What does change 
yearly is the Nautical Almanac. 

If you are willing to trust electronics a bit, it is quite simple to 
program a Hewlett Packard calculator to do sight reductions without the 
need for hand arithmetic or the interpolations needed to use the tables. 
I wrote such a program for a HP 32S (<$100) that works quite nicely and 
is, I think, much easier than the tables. I keep all the input data in 
registers so I can check that I entered it correctly. Still, not quite
failsafe, so I carry the tables, too. 

Alan

PS If anyone is interested, I'll post the program.

    By all means post the program.


    Also note that the formulas can be fairly easily used with any
    scientific calculator. The more adressable memories the better.

    The new Nautical Almanacs have their own tables in them such that you
    don't need external reduction tables. The method is more difficult than
    HO249 but probably easier than HO209. Also i think Reeds has a reduced
    almanac and reduction tables too.

    My personal choice would be a programmable (and programmed) caculator
    and a few backup normal scientific calculators. Plus a Nautical
    Almanac.
    
    paul

    The "selected stars" is only valid for 5 years.
    
    Peter

    
    Robert,
    
    You might want to keep your eyes open for a copy of Self-Contained
    Celestial Navigation with H.O 208 by John Letcher, Jr.  It contains 
    H.O. 208 as an appendix as a bonus.
    
    H.O. 208 is a handy volume to have in your abandon ship (scramble)
    bag.  It sure takes up less room than H.O. 214, 229, or 249.
    
    Steve

    Steve,
    
    This is precisely the book I am referring to! As I mentioned, my volume
    was copywrited in 1975, so I was curious about it's continued long-term
    usefullness. What I am reading from the replies are that it is still
    viable, minus the "selected stars" section.
    
    Alan, please post your program. I've got an HP 95LX that I'd like to
    program with your offer. 
    
    The goal is to learn Celestrial well and understand why/how the steps
    are done manually to get the proper results. I then would feel a lot
    more comfortable using a calculator to do the same if I knew that the
    first time it fell off the nav station and broke, I could still
    navigate my way home with tables and sight reduction tables.
    
    Robert

    Alan never did publicly post his program but I would guess that it is
    based on the Law of Cosines...
    
    I am very much interested in celestial navigation and would like to
    discuss it further (e.g. I am trying to apply the Spline function to a
    meridian transit).
    
    Is anyone interested in a pregrammable calculater that has navigational 
    algorithms? Original cost $274. Offered for $150/obo.
    
    I am always interested in any text dealing with CN.
    
    bernie