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From: Frank Reed (no email)
Date: Sat Jun 04 2005 - 19:54:15 EDT
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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