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From: Peter Fogg (no email)
Date: Sat Jun 04 2005 - 23:06:20 EDT
At first glance this looks like an excellent post here by Frank:
seems simple, practical and eminently doable.
As he has added in a follow up posting:
" lat/lon by noon sun is something that can be learned and re-learned in an
afternoon. It's not quite as accurate (does that matter? depends on what
you're trying to achieve) as full-blown celestial navigation, but fewer and
fewer students are interested in toiling over the details of the Nautical
Almanac's interpolation tables and the tedious study of H.O. 229 or other
sight reduction tables. They wanna play with their sextants and figure out
where they are in the fewest possible steps (just in case something bad
happens to GPS)."
________________________________________
From: Navigation Mailing List [mailto:]
On Behalf Of Frank Reed
Sent: Sunday, 5 June 2005 9:54 AM
To:
Subject: Latitude and Longitude by "Noon Sun"
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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