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From the archives for June 4, 2005:

"Latitude and Longitude by "Noon Sun"
From: FrankReedCT---COM
Date: 4 Jun 2005 19:54


First things first: I've put the phrase "Noon Sun" in quotes here because the 
set of sights required for this system goes a little beyond the standard 
procedure for shooting the Noon Sun for latitude only.
 
This short method of celestial navigation will get you latitude and longitude 
to about +/-2 miles and +/-5 miles respectively --more than adequate for any 
conceivable modern practical purpose. You can cross oceans safely and 
reliably for years on end using this technique if it suits you to do so. Its 
enormous advantage is simplicity. It's easy to teach, easy to demonstrate, 
easy to learn, and also easy to re-learn if necessary. I mention this because 
most people who are learning celestial navigation today will quickly forget 
it. What's the point of learning something if you can't reconstruct your 
knowledge of it quickly when and if the need actually arises to use it? It's 
tough to resurrect an understanding of the tools of standard celestial 
navigation on short notice, but easy with this lat/lon at noon method. 
Additionally, this method does not require learning all the details of using 
a Nautical Almanac (you don't need one at all --only a short table of 
declination and equation of time, possibly graphed as an "analemma") and it 
needs no cumbersome sight reduction tables. 
 
Here's how it's done:
 
Start 20 or 30 minutes before estimated local noon. Shoot the Sun's altitude 
with your sextant every five or ten minutes (or more often if you're so 
inclined) and record the altitudes and times by your watch (true GMT). 
Continue shooting until 20 or 30 minutes after local noon. [note the 
difference from a noon latitude sight --we're recording sights leading up to 
and following noon-- usually these are thrown away]
 
Next you need to correct for your speed towards or away from the Sun. For 
example, if we're sailing south and the Sun is to the south of us, then each 
altitude that we have measured will be a little higher as we get closer to 
the latitude where the Sun is straight up. We need to 'back out' this effect 
so that the data can be used to get a fix at a specific point and time. This 
isn't hard. First, we need the fraction of our speed that is in the 
north-south direction. If I'm sailing SW at 10 knots, then the portion 
southbound (in the Sun's direction) is about 7.1 knots. You can get this 
fraction by simple plotting or an easy calculation. Next we need the Sun's 
speed. The position where the Sun is straight overhead is moving north in  
spring, stops around June 21, then heads south in fall, bottoming out around 
December 21 (season names are northern hemisphere biased here). It is 
sufficient for the purposes of this method to say that the Sun's speed is 1 
knot northbound in late winter through mid spring, 1 knot southbound from 
late summer through mid autumn, and 0 for a month or two around both 
solstices (it's easy to prepare a monthly table if you want a little more 
accuracy). Add these speeds up to find out how much you're moving towards or 
away from the Sun. If you're moving towards the Sun, then for every six 
minutes away from noon, add 0.1 minutes of arc for every knot of speed to the 
altitudes before noon and subtract 0.1 minutes of arc for every knot of speed 
to the altitudes after noon. Reverse the rules if you're moving away from the 
Sun. Spelled out verbally like this, this speed correction can sound tedious 
but the concept is really very simple and it's very easy to do. 
[Incidentally, George Huxtable deserves credit for emphasizing the importance 
of dealing with this issue (although I don't think he ever spelled out how to 
do it)]
 
Now graph the altitudes (use proper graph paper here if at all possible): 
Sun's altitude on the y-axis versus GMT on the x-axis. The size of the graph 
should be roughly square, maybe 6 inches by 6 inches so that you can clearly 
see the rise and fall of altitude. For longitude, you will need to determine 
the axis of symmetry of the parabolic arch of points that you've plotted. 
There is a simple way to do this: make an eyeball estimate of the center and 
lightly fold the graph paper in half along this vertical (don't "hard crease" 
the fold yet). Now hold it up to the light. You can see the data points 
preceding noon superimposed over the data points following noon which are 
visible through the paper. Slide the paper back and forth until all of the 
points, before and after, make the best possible smooth arch (half a 
parabola). Now crease the paper. Unfold and the crease line will mark the 
center of symmetry of the measured points with considerable accuracy. Reading 
down along this crease to the x-axis, you can now read off the GMT of Local 
Apparent Noon. Reading back up the crease to the data, you can pick off the 
Sun's maximum noon altitude (which is probably already recorded but if you 
missed the exact moment of LAN you can get it this way).
 
Next we need two pieces of almanac data: the Sun's declination for this 
approximate GMT on this date and the Equation of Time for the same date and 
time. You do NOT need a current Nautical Almanac for this. The exact value of 
declination and Equation of Time varies in a four-year cycle depending on 
whether this year is a leap year or the first, second, or third year after. 
So we don't need an almanac for this. A simple table will do (where to get 
one? Today, they're very easy to generate on-the-fly... or you could use an 
old Nautical Almanac... or you could also use an analemma drawn on a 
sufficiently large scale).
 
Apply the Equation of Time to the GMT of Local Apparent Noon that you found 
above. You now have the Local Mean Time at LAN, and you already know the 
Greenwich Mean Time. The difference between those two times is your 
longitude. Convert this to degrees at the rate of 1 degree of longitude for 
every four minutes of time difference. Done. We've got our longitude.
 
Now for latitude. Notice that we didn't correct any of our altitudes for index 
correction or dip or refraction or the Sun's semi-diameter. These corrections 
are totally unnecessary for the longitude determination. But we need them for 
latitude. Take the Sun's altitude at the time of LAN (read off the "crease" 
or actually observed by watching the Sun "hang" at the moment of LAN). 
Correct it for index correction, dip, refraction and semi-diameter as usual. 
This gives you the Sun's corrected observed altitude. Subtract from 90 
degrees. This "noon zenith distance" tells us how many degrees and minutes we 
are away from the latitude where the Sun is straight up. The latitude where 
the Sun is straight is, by definition, the "declination" that we have looked 
up previously from our tables. So if the Sun is north of us at noon, then we 
are south of the Sun's declination (latitude) by exactly the number of 
degrees and minutes in the noon zenith distance. If the Sun is south of us at 
noon, then we are north of the Sun's declination by the same amount. A simple 
addition or subtraction yields the required latitude. Done.
 
We've spent about ten minutes making and recording observations of the Sun's 
altitude over the course of 45 minutes to an hour, and reduced those 
observations to get our latitude and longitude at noon with about five 
minutes of paperwork. Not bad!
 
Again, the overwhelming advantage of this "short celestial" is that it can be 
taught easily, learned quickly, and RE-learned quickly on the spot if 
necessary. An additional advantage is that it requires an absolute minimum of 
materials. You need a sextant (metal if at all possible, but plastic will 
do), a decent, cheap watch or small clock, tables of refraction and dip (one 
sheet of paper), a four-year revolving almanac of the Sun's declination and 
equation of time (another sheet or two of paper), and some graph paper and a 
pencil. You could even print out these (or equivalent) instructions and throw 
everything in the case with your sextant.
 
As for disadvantages, they really depend on the student and his or her 
expectations. What is it that we want to do with celestial navigation? Why 
study any method? And for a thousand students, you will get a thousand 
answers. The days are gone when celestial navigation was essential and fixed 
curricula could be dictated for students to either take in their entirety or 
leave. This field has moved on to the stage of "a la carte" learning. It can 
be a pain in the neck for instructors accustomed to doing things the same way 
year after year but it's a real liberation for students and possibly also for 
more creative teachers and "information publishers".
 
-FER
42.0N 87.7W, or 41.4N 72.1W.
www.HistoricalAtlas.com/lunars"





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