There is also a link to a simplified sight reduction worksheet for sun sights that I created a couple years ago for some of my own seminars. Feel free to download that in .pdf form, and email me any questions you might have. Enjoy!
Go to navsoft.com/downloads.html to get downloadable, free copies of the nautical almanac and increments and corrections tables. Get the PUB 249 sight reductions tables for free at the US Government website here. (By the way, that government website has oodles of excellent, free downloadable navigation stuff, including pilot charts, pilot books, etc. It's a wealth of information, and all free.)Celestial Navigation, Part I: Championing a Dying Art
Celestial Navigation, Part II: Predicting the Sun's Geographic Position
Celestial Navigation, Part III: Sight Reduction
Celestial Navigation, Part IV: Sight Reduction, Continued
Sun Sight Reduction Worksheet
So, sometimes these links don't work - you need a google account to access them. I'm posting the entire text of the articles and worksheet below, so at least the info is available to everyone. I'll be making a 'Celestial Nav.' page in the coming months with more detailed info, so watch for that.
--
Sun Sight Reduction
Worksheet
|
Date:
|
D.R.:
|
Time (GMT):
|
1.
Sextant
Observation & Corrections (Data from Sextant & Almanac Inside Cover)
|
Hs
|
à
Raw Sextant Data
|
|
|
|
|
|
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I.E.
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à
Index Error
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|
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Dip
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à
‘Height of Eye’
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|
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Alt.
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à
Altitude Correction
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|
|
|
|
|
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Total Corrections
|
|
|
|
|
|
|
|
Ho
|
à
Final ‘Observed’ Sextant
|
|
|
|
|
|
2.
Sun’s
Geographic Position (Data from the Nautical Almanac & Your Watch!)
|
Date:
|
D.R.:
|
Time (GMT):
|
|
|
|
|
|
|
|
Declination (N/S?)
|
à
Almanac Date Page
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|
|
|
GHA1(Hrs.)
|
à
Almanac Date Page
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|
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GHA2 (M/S)
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à
Almanac “Grey Pages”
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|
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|
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|
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|
GHA (Total Correction)
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à
GHA1 + GHA2
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Assumed Position
|
à
DR ®Lon. w/GHA Min.
|
Lat:
|
Lon.
|
|
|
|
|
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|
LHA
|
à
GHA ‘T’ – AP Long.
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**Steps to Entering the Sight Reduction Tables**
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1. Assumed Position Latitude (Whole Degrees)
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|
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2. Declination à Sun’s Latitude, North or South?
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3. Local Hour Angle (LHA)
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3.
H.O.
249 – Sight Reduction Table & Calculated Sextant Angle
|
Hc
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à
Calculated Sextant
|
|
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d
|
à
Declination “Factor”
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|
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Z
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à
“Azimuth”
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d Correction
|
à
HO249 Last Page
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Hc Final
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à
Hc – d Correction
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Ho
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à
Take From Sect. 1
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Intercept
|
à
Hc - Ho
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**Steps to Beginning the Plotting Sheet**
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1. D.R. Position à Where you ‘think’ you are
|
|
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2. Assumed Position à Start Plotting Here!
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|
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3. Azimuth (360-Z?) à Bearing to the Sun
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|
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4. Intercept (Towards or Away?) à Naut. Miles!
|
|
--
All at Sea July
2011
CELESTIAL PART I
by Andy Schell
Celestial is a lot like biathlon – men and women of the
sport ski around challenging cross-country courses and are asked to stop every
few miles and fire a rifle at a tiny target a few hundred meters away. Panting
and exhausted. And often while standing.
Celestial asks of the navigator to head offshore for a few
hundred miles, and from the deck of a rolling sailboat, aim a bronze
contraption at the sun without blinding yourself and measuring its angle off
the horizon. Then, the navigator is asked to log the precise time in Greenwich
that he took his reading – a mistake of only four seconds will cost him a mile
of accuracy. Celestial or biathlon – which, then, is harder?
Regarding celestial, what bogs people down is the theory.
Most books on the subject are incredibly dense – technical and uninspiring,
they don’t exactly make for pleasant reading. In reality, the theory is simple
– once you get a reasonable understanding of your spatial relationship with the
earth and your surroundings, celestial theory becomes intriguingly intuitive.
For now, we’ll focus on the ‘biathlon’ component of
celestial navigation, namely the physical act of taking a sight. As with a gun,
practice begets accuracy – it’s no coincidence that sailors before the GPS age
referred to ‘shooting’ the sun or stars. And just as biathletes must contend
with visibility, wind, snow and fatigue – making the job of hitting that tiny
target much more difficult than that of the shooter at an indoor range – the
sailor has to contend with wind, waves, clouds, a pitching deck and that same
fatigue.
A sextant, in simplest terms, is a device used to measure
angles. Steven Callahan famously navigated across the Atlantic in a life raft
using a crude sextant he cobbled together from two pencils and a piece of
string. A modern sextant is a precision instrument, often cast in bronze that
measures angles to the nearest minute in terms of arc distance. We refer to the
angle of any celestial body as its altitude.
You need only two things to get a good sight – a celestial
body and a clear horizon. Start with the sun – it’s the biggest celestial body
out there, and when it’s up, there is always a horizon visible. It’s easiest to
first estimate the height of your chosen celestial body and then pre-set the
sextant for that altitude. Thanks to biology, most people’s extended fist will
measure roughly ten degrees, regardless of the size of their hand – bigger
hands mean longer arms, and so from your eye their size appears the same. Using
that as a guide, estimate the altitude of the celestial body and pre-set the
sextant’s index arm.
With the sextant pre-set, aim the scope at the horizon in the direction of the sun – be sure to put some
shade on if you’re shooting the sun. What you’ll see is the horizon itself,
through the scope, and (hopefully) the sun as reflected through the index
mirror. Now, simply adjust the micrometer drum (the small wheel on the index
arm that is essentially the ‘fine’ adjustment on the angle you’re measuring) to
move the sun up or down. The object of the game is to get the bottom edge (lower limb) of the sun to ‘kiss’ the
horizon. By slightly rocking the sextant back and forth on it’s vertical axis
as you adjust the micrometer drum, the sun will appear to swing like a
pendulum. It’s at the bottom of this arc that you want the sun to ‘kiss’ the
horizon. Have a partner record the time in GMT, to the nearest second, the
instant you say ‘mark!’ Stop your adjustment and read the angle off of the
index arm, being careful to interpret the minutes correctly from the drum. Record
the time and the altitude. The prudent navigator will take a series of sights
(usually five) and use their average for the actual calculations.
It’s easiest to shoot the sun in the mid-morning or
mid-afternoon, when the sun is about 40-50 degrees above the horizon. Any
higher, and the angles get very large and cumbersome, any smaller and the
refraction from the atmosphere will interfere with your accuracy. Once
comfortable with the sun, try a trick Bernard Moitessier used on stars – go
through the same process of estimating altitude, but before aiming the sextant,
remove the scope. Peer through its bracket, and, with both eyes open, it will be much easier to locate your star. Where
the sun appears as a large disk, the stars appear as small pricks of light, and
are nearly impossible to find in the limited field of view of the scope.
Next issue we’ll follow up with what to do with your sight
data and how to actually plot a position from it (easier than you think). The
elegance and simplicity of the theory may surprise you.
--
All at Sea July 2011
CELESTIAL PART II – PREDICTING THE SUN’S
GEOGRAPHIC POSITION
by
Andy Schell
Understanding
celestial theory is best accomplished through a series of mental exercises that
puts your mind in the real world and gets your nose out of the books and off
the charts. It’s assumed that the reader will have a basic understanding of
latitude and longitude and coastal navigation.
We’ll
focus again on the sun. Imagine the sun and the earth suspended in space. Now
imagine a ray of the sun emanating from its core, and piercing the earth, right
through to its core. In celestial
nav. terms, the point where the sun’s ray pierces the surface of the earth is
called it’s geographic position (GP).
In other words, if you were standing on the GP, the sun would be directly
overhead. Of course, this position is not fixed, as the earth is always
spinning. Hence the importance of keeping accurate time when taking sights –
you must ‘fix’ the sun’s GP to a specific time in order to make sense of it. We
express GP in terms of latitude and longitude, called declination and Greenwich
Hour Angle (GHA), respectively.
The
sun’s declination defines the tropics – they lie at 23 ½º north and south,
representing the furthest from the equator the sun’s GP will travel from season
to season. On an imaginary picture of the globe then, over the course of a
year, the sun’s declination will trace a sine curve between the Tropic of
Cancer and the Tropic of Capricorn (at the summer and winter solstices),
crossing the equator twice, during the autumnal and vernal equinoxes. In the
course of a day, the sun’s GHA will always travel from east to west, from
sunrise to sunset. Hence the 24 time zones on the planet, and the 24 hours in a
day; 360º of longitude, divided by the 015º per hour of the sun’s westwardly
march, equals an even 24. Here then – and this is one of the ‘Ah ha!’ moments
of celestial nav. – time and longitude are one in the same and easily
convertible.
It’s fun and intuitive to predict the GP of the sun at any
given time – for example, I’m writing from a café in Stockholm. The date is 30 May
and the local time is 1430. My approximate longitude is 018º East. I know the
sun is to my west (it’s past noon here), and it’s a ways south of me, as
Stockholm sits at 59º north latitude. How far west? Two and a half hours, or about
037 ½º of longitude (recall the sun travels 015º per hour). I can therefore
guess that the sun’s GHA is about 019 ½º, somewhere in the western hemisphere.
In reality, the GHA is closer to 022 ½º, which I’d discover in the Nautical Almanac. Why? Because Stockholm
sits a full three degrees east of the
center of it’s time zone, 1430 on my watch in Stockholm is slightly inaccurate
in terms of the sun. Time zones are spread E-W over 015º of longitude (for
modern convenience), and unless you are positioned exactly over the center of a
time zone, the sun will be a bit ahead of or behind your watch. In the
Stockholm example, the sun is 003º ahead
of my watch, or approximately 12 minutes. Knowing the center of your particular
time zone is also how you compute actual local
noon, the time when the sun is directly overhead. All this confusion over
time also underscores why it’s imperative to keep accurate GMT when taking real
sights. The sun’s GHA, by the way, is always
measured west, through 360º, unlike longitude, which is divided into two
hemispheres, with 180º in each. The sun, after all, cannot travel east.
Now
for declination – it’s past April but before June 21, so I know the sun is
somewhere north of the equator and south of the Tropic of Cancer, though closer
to the latter. I can also predict in which general direction the sun bears on
the compass – about SW from Stockholm. Make sense? Do this exercise several
times over, in different imaginary places on the globe for practice.
Making
these mental predictions is often as far as one needs to go to make practical
use of celestial nav. Offshore, during a winter passage from Tortola to
Bermuda, say, I’d know that in the mid-morning, the sun should be off my
starboard quarter (it’s GHA is east of me – not yet noon – and it’s declination
is somewhere in the southern hemisphere, as its winter. Therefore, its GP must
bear to the SE). If I wake up a little groggy, a quick look out a portlight is
all I need to confirm the watchkeeper’s course. Not once would I have to
consult a chart, GPS or even the compass, and the sextant would never have left
it’s box, yet I’m still using celestial navigation.
Next month we’ll look at finding an accurate position using
celestial, and delve into the books to reduce an actual sun sight, step by
step.
--
All at Sea November 2011
CELESTIAL PART III – SIGHT REDUCTION
by
Andy Schell
Most
books on celestial will offer a ‘simple’ sight
reduction form. Don’t use it. Most of these forms are standardized for use
with any celestial body, and will contain information not applicable to a sun
sight. They will confuse you to no end. Make your own forms instead (or use the
one in the photo, which I devised, available for free download on allatsea.net).
The form is in three parts, one for each stage of the sight reduction.
Correcting the Sextant
Correct
the sextant reading for index error, dip (height of eye) and observed altitude. Read your sextant’s instructions on how to correct index
error – a properly maintained sextant should not have any. If it does, it will
reveal itself when the sextant is set on 0º 0’ – when pointed towards the
horizon, the reflected horizon will appear slightly above or below the actual
horizon. Adjust the micrometer drum until both horizons appear as one – the
amount of adjustment is your index error; ‘-’ if it’s ‘on the arc,’ ‘+’ if it’s
‘off the arc.’ Height of eye is simply how far off the water
you were when you took the sight.
Inside
the front cover of the Almanac you’ll find a table giving minutes of correction
corresponding to various dip measurements, in feet and meters. Refer to this,
but note that on most cruising sailboats, the dip (your height of eye) will be
about six feet, the corresponding correction about 3’. The altitude correction
table is found on the same page. This correction accounts for the thickness of
the atmosphere that the sun’s light must travel through, and its being
refracted because of it. Think of the grade-school pencil-in-a-glass-of-water
example. Find the corresponding range of
observed altitude, and record the correction on the form. Note the different
tables for different times of the year. Some corrections may be negative, so
always put a ‘+’ or ‘-’ sign before each number to avoid confusion. Total the
three corrections, and record the resulting Ho
– the observed sextant angle – on
the highlighted line. You’ll need this number later.
The Sun’s GP: Your Watch & The Almanac
Perusing
the Nautical Almanac, you’ll find all kinds of useful information, from the
rise and set of the sun and the moon, to information on the 57 most useful
navigational stars as well as the best times of the year to view the different
planets. All of this information is useful to the navigator. What we need to
get started is information on the GP of our celestial body – the sun in this
case. Find the page corresponding to the date the sight was taken. Each date
consists of two full pages of information – stars and planets on the left page,
sun and moon on the right. Find the sun column. You’ll see two columns of
information, labeled d (declination)
and GHA (Greenwich Hour Angle) at the
top, and a column of numbers down the side, corresponding to whole hours of
GMT. Locate the hour of GMT when you took the sight, and record the values for d and GHA in their appropriate places on the form. There are two GHA slots on the form – since the ‘date page’ only
includes information for the whole hour of GMT, you’ll refer to the ‘grey
pages’ (at the back of the Almanac), which give figures for the minutes and
seconds of GMT. Add these figures to the hourly GHA to arrive at the total GHA (recall that the sun travels a
full 15º of longitude each hour – and always
to the west – so the minutes and seconds make a huge difference). Declination
changes only negligibly from hour to hour, so one figure here is sufficient.
Next,
record your assumed position (AP). This
figure is simply the closest whole degree
of latitude from your dead reckoning, plus your DR longitude degrees, but
with the same minutes as your total GHA.
The goal is to end up with a Local Hour
Angle (LHA), expressed in whole degrees. Get this figure by subtracting
your AP longitude from the total GHA (by making the minutes of your AP longitude
the same as the minutes of GHA, the subtraction will cancel them out, leaving a
whole number). Where GHA is the sun’s position relative to Greenwich (and 000º
longitude), LHA is the sun’s position relative to you (almost anyway – you
in this case is an assumed position (AP),
near to your DR but a spot on the globe with whole degrees of latitude and
longitude. The sight reduction tables have been computed to include information
on the bearing to the sun (azimuth), as well as what an imaginary sextant would have read based on these whole
numbers. The navigator then gets his line of position by comparing this
imaginary sextant reading to his own, and plotting the difference). Next month,
we’ll describe exactly how to do that, and bring the celestial series to a
close.
--
All at Sea
December 2011
CELESTIAL PART IV:
by
Andy Schell
Pub. 249.
Imagine
coming across a bell buoy in mid-ocean. Your radar tells you the buoy is a mile
away; your other instruments are dead. You cannot determine the buoys bearing.
What are your possible positions? If plotted on a chart, you would draw a
circle around that buoy, with a one-mile radius – you could be anywhere on that
circle of position. Remember this.
--
There
are three figures needed to enter Pub. 249 – AP latitude, declination and LHA. Each
whole degree of AP latitude has several corresponding pages. AP latitude is not
distinguished between north and south – in celestial they are symmetrical. It
is declination that must be
distinguished. Pub. 249 does this by listing “same” or “contrary”. Use the
“same” page if declination and your AP are both in the same hemisphere. Likewise, use the “contrary” page if declination
and your position are in contrary
hemispheres. Find your exact declination, and move down that column to the
corresponding LHA. You will find three numbers – Hc, the calculated sextant angle; d, the declination factor;
and Z, azimuth, the angle to the GP from geographic north. On the back
page of Pub. 249, you will find corrections for the d number. Apply this correction (+/-) to the Hc to arrive at HcFinal (HcF).
HcF
can be thought of as an imaginary sextant reading – it is precisely what the
sextant would read if an imaginary man were standing exactly on the AP at the
same moment of your sight. Comparing your sight at an unknown position, to that of the imaginary man’s – at a known position – is how we derive lines
of position (LOPs). This comparison is called the intercept. Since it would be impossible to calculate this imaginary
reading at every single point on earth, the tables allow for only whole degrees
of latitude, hence the necessity for an assumed
position.
This
intercept is calculated from the
difference between Ho and HcF. Subtract the lower reading from the
higher one so your answer is always a positive number. If your actual reading
(Ho) is smaller than the calculated reading (HcF), then you must be further from the sun. Conversely,
an Ho higher than HcF would mean the opposite. This towards the sun or away from
the sun (from the AP) distinction is essential.
The Universal
Plotting Sheet.
Set
up the plotting sheet for the correct latitude – lines of longitude converge
towards the poles, so that the distance between them changes dramatically as
you head north or south of the equator. The plotting sheet accounts for this
with the scale on the bottom right corner. Record DR, AP, azimuth and intercept
(towards or away).
Plot
your DR position. Then plot your AP. Plot the azimuth as a dotted line drawn
through the AP. Label the correct end with a small sun (be careful not to plot
the reciprocal bearing). Starting at the AP, measure the intercept towards or away from the sun and
make a mark. The beauty of measuring in arc (degrees and minutes) is that the
scale from the sextant exactly corresponds to degrees and minutes of latitude,
and therefore distance. An intercept of 24’ away,
for example, means that your sextant altitude was taken 24 nautical miles further from
the sun than the calculated altitude (another ‘Aha!’ moment in celestial).
Finally, plot your LOP as a solid line through the intercept and exactly
perpendicular to the azimuth. This LOP represents but a tiny tangent to a much
larger circle of position around the
GP of the sun.
The
sextant, in effect, is like the radar from the example above, giving a range
(through trigonometry) but not a bearing – forming a circle of position
centered on the sun’s GP. The azimuth represents that needed bearing. Almost.
What is imperative – and this is the final ‘Aha!’ moment – is understanding
that the azimuth is calculated from the
AP and not from your actual position. While you can know precisely the
distance you are from your AP (the intercept), you cannot know if you are
actually in line with it. Plotting an LOP perpendicular to it accounts for that
unknown. So in truth, the azimuth-as-bearing analogy is not entirely accurate.
The azimuth merely puts you on the correct side of the circle of position, gets
you close – giving an LOP. It takes another sight and another LOP to actually
get a fix.
Celestial
then requires a big commitment. At dawn and dusk, during twilight, the
navigator will get the most accurate fixes, as likely three, four or even five
stars can be shot within minutes of each other. As the sun rises, he will be
ready around 1000, to get a good morning sight. He will advance and cross his
morning LOP with the noonsight, and further advance the noonsight to cross with
his PM sight. Again at dusk he will repeat the procedure with the evening
stars. Safe landfalls are dependent upon the navigator’s accuracy, which over
the course of a long offshore passage, may not be truly known for weeks. When
an island finally appears over the horizon when and where it should be, only
then can the navigator relax.
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