So, thanks to those of you who attended my seminar today. Below are links to the four-part article series I originally wrote for All at Sea Caribbean magazine. The goal of the series was that after reading through them, the reader should be able to take and reduce a sun-sight - not the noon sight (which is unnecessary if you really know celestial), but an out and out sun sight taken at any time of the day.

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):

Sextant Observation & Corrections (Data from Sextant & Almanac Inside Cover)

Raw Sextant Data

I.E.

Index Error

Dip

‘Height of Eye’

Alt.

Altitude Correction

Total Corrections

Final ‘Observed’ Sextant

Sun’s Geographic Position (Data from the Nautical Almanac & Your Watch!)

Date:

D.R.:

Time (GMT):

Declination (N/S?)

Almanac Date Page

GHA1(Hrs.)

Almanac Date Page

GHA2 (M/S)

Almanac “Grey Pages”

GHA (Total Correction)

GHA1 + GHA2

Assumed Position

DR ®Lon. w/GHA Min.

Lat:

Lon.

LHA

GHA ‘T’ – AP Long.

**Steps to Entering the Sight Reduction Tables**

Assumed Position Latitude (Whole Degrees)

Declination

Sun’s Latitude, North or South?

Local Hour Angle (LHA)

H.O. 249 – Sight Reduction Table & Calculated Sextant Angle

Calculated Sextant

Declination “Factor”

“Azimuth”

d Correction

HO249 Last Page

Hc Final

Hc – d Correction

Take From Sect. 1

Intercept

Hc - Ho

**Steps to Beginning the Plotting Sheet**

D.R. Position

Where you ‘think’ you are

Assumed Position

Start Plotting Here!

Azimuth (360-Z?)

Bearing to the Sun

Intercept (Towards or Away?)

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.