A sextant and the sun is all you need to find your position, says Tapio Lehtinen. It’s easier than messing around with stars and much more satisfying than GPS
When you read this, I will be somewhere in the depths of the Southern Ocean, bound for Cape Horn aboard the Swan 55 Galiana WithSecure. Supported by a crew of young Finnish sailors, I’m taking part in the Ocean Globe Race, a fully crewed roundtheworld race that eschews modern technology, including GPS, to recapture the spirit of adventure of some of the early offshore races.
I actually first started writing this article while aboard the m/v Darya Gayatri following my Southern Ocean rescue, initially by Kirsten Neuschäfer, when my beloved yacht Asteria sank suddenly during the Golden Globe Race last in 2022.
Modern technology is great, but there’s something about finding your position on the Earth’s surface without it that is immensely satisfying, and helps us know our place within the cosmos, rather than just on a digital screen.
While much as has been written about the noble art of astronavigation, I hope to set out, as simply as possible, how I have navigated my way round the world more than once using little more than the sun, a sextant, a watch and an almanac.
You certainly don’t have to mess around with the stars to establish your position to an accuracy of five to 20 miles, which is perfectly sufficient in the middle of an ocean and adequate even for most landfalls. You do not need to worry about finetuning your sextant or understanding the spherical trigonometry or astronomical theories behind the process.
The processes for forenoon and afternoon sights are fairly simple, not to mention the noon sight, which gives your latitude, which is very simple indeed. If you enjoy the process, you are free to go deeper into the theory and also to making the next step of taking sights of the moon, planets and stars.
Noon sights
The noon sight is a simple calculation and the result provides your exact latitude.
Calculating local noon time
This is based on the longitude of your rough dead reckoning position. The sun revolves around the earth, which means 360° of longitude in every 24 hours. That means the sun moves 15° of longitude per hour or four minutes of time for each degree of longitude. That’s one minute of time per 15 minutes of longitude. Figure these out with paper and pencil and remember them by heart – it will make the calculations easier.
The sun crosses the Greenwich Meridian (000º) roughly at 1200 each day. The exact time for each day is called Meridian Passage (MP), and the value is found at the lower righthand corner of each page of the Nautical Almanac (NP314, £44, UKHO), which covers three days per page.
For the local noon time at your longitude on a certain day you first check the Meridian Passage time for the day, e.g. 1146.
You then take your Dead Reckoning (DR) longitude, e.g. 62º 20’ E. As we are on eastern longitudes, our noon will be before London. The time difference will be 62º x 4 minutes per degree = 248 mins, which is four hours and eight minutes.
The additional 20 minutes of longitude make for roughly one more minute of time, so the local noon will be four hours and nine minutes before MP, which gives us a local noon time of 0737 UTC (=GMT).
Taking the noon sight
Next you get on deck with the sextant at least five minutes before the calculated local noon time and start taking sun sights once every 30 seconds. The sun will be slowly ascending, so you’ll keep getting slightly bigger values each time. The rate of increase slows down and at noon it will not change. A while later the lower limb of the sun will be below the horizon when you look at it through the sextant. Don’t adjust the sextant in the other direction, but instead read the last and highest value when the sun stopped going up. That is your Noon sextant height (H/s).
Calculating noon latitude
You’ll need to correct your Noon H/s for index error and height of eye, but these are the same every time, get Noon H/o (observed height). From the H/o we need the socalled Zenith Distance (ZD) for the calculation. Instead of the angle between the horizon and the sun, the ZD is the angle between the sun and the Zenith which is vertically above your head. This is easily calculated by subtracting the H/o from 90°. When you do the subtraction, instead of 90°, write 89° and 60 minutes (which is the same thing, but easier to work) and subtract yourH/o from that to work out the ZD.
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Next, you get the declination of the sun at the time of your local noon. Check it for the closest whole hour from the Nautical Almanac and add or subtract the minutes according to the d= value at the bottom of the declination column and the hourly increase or decrease according to the minutes of time of your local Noon time.
You get your Noon Latitude by either adding the ZD and declination or subtracting declination from your ZD. If the latitude and declination are the same name (both S or both N), you add the declination to the ZD. If they’re different, you subtract the declination from the ZD. One more thing: if the latitude is less than declination but the same name, then subtract the Zenith Distance from the declination. And voila! There’s your Noon Latitude!
Forenoon & afternoon sights – Shoot the sun
Using a sextant is said to be similar to using a shotgun to shoot a moving object – you don’t normally hit the bird with your first try. Practice makes perfect.
When taking the sight, set the index arm of the sextant at roughly the angle you expect the sun to be at the time. You seldom need the shades for the horizon, but select a shade for the index mirror and be careful looking so that you don’t hurt your eye staring straight into the sun without a shade.
When you get the sun into the view of the telescope, bring the image of the sun close above the horizon by adjusting the index arm. When you have both the sun and the horizon visible simultaneously in the telescope, adjust the telescope so that the image of both the horizon and the sun are sharp and make sure you use the best shade for the moment. The sun and horizon should be well visible and the sun should not be too bright to protect your eye and to enable you to stare at it to get an accurate sight.
The lower edge of the sun is called the lower limb. Now you swing the sextant slowly a bit from side to side. You will see, that the sun will move in an arc, being at it’s lowest at the middle of the swing. You now adjust the index arm so that the lower limb of the sun just kisses the horizon at the lowest point of the arc when you slowly swing the sextant from side to side.
When you are happy, check your watch to have the exact seconds of the sight. Next grab your notebook and write down the exact second, minute and hour of the sight. Then read the sextant and note down the degrees and minutes above the horizon.
Selecting an accurate sight
As you get into a routine and the conditions are smooth, one sight is enough. But in the beginning and if the conditions are rough, take five to seven sights, noting down the exact time and reading of the sextant for each one.
You then go down below, plot a graph of the readings on a squared paper with the height of the sun on the Y axis and time on the X axis. As a result you should get an ascending line in the forenoon and a descending line in the afternoon.
You will find that most of the sights land roughly on such a line and a couple are clearly erroneous. You then neglect the bad ones and calculate the average of the times and heights of the good ones, and use that as your value for time and angle when you proceed with the calculations. It’s a bit of a laborious process, but gives you better quality figures to base your calculations on.
After some time, when you plot the heights on paper, you will get a smooth line or curve without erroneous fixes – then you know your sights are accurate enough to rely on just one sight in the morning and afternoon. At noon, you will always need to take a number of sights as long as the sun keeps ascending to its highest position, which you then record.
At noon you don’t need to write down the time of the sight.
After getting the sextant height H/s you again convert that figure into observed height H/o by making the various corrections for index error, parallax, dip etc. These seem very complicated, but if you have a good instrument, there will not be many corrections, you just add everything up and use the same correction every time; that is accurate enough, for a yacht at least. My correction on Asteria was plus 13 minutes.
So H/s + 13 minutes = H/o.
Greenwich Hour Angle
As with any almanac, the Nautical Almanac is organised by dates. Take the right date, look at the column for the sun and take the row for the whole hour of your sight. It gives you two values, the ‘GHA’ and the ‘dec’. GHA is the Greenwich Hour Angle, which is the number of degrees and minutes that the sun is to the west of Greenwich on that date and hour. At every noon, it starts from zero and grows to 360° as the sun appears to be travelling around the earth from east to west.
In order to get the exact value of GHA for the time of your sight, you go to the back of the almanac, where you find a section printed on yellow paper under the title ‘Increments and corrections’. It contains two columns per page, one column for each additional minute on top of your whole hour value.
Each column features 60 separate rows, one for every second on top of the minute of your minutes of the sight.
So, if the time of your sight was 10 hrs 15 minutes and 27 seconds UTC (also called GMT), you go to the column for 15 minutes and the row of 27 seconds and find there a value of degrees and minutes, which you add to your GHA value for the whole hours.
You now have the exact GHA of the sun at the time of your sight, which is the longitude of the sun on the celestial sphere.
Declination
Next we want to find the latitude of the sun at the sky at the moment of your sight – the dec = declination. As the sun appears to be revolving around the earth, it moves straight above the equator in the spring during the spring equinox at the end of March and during the autumn equinox at the end of September.
From the spring equinox onwards the sun will travel around the earth further and further to the north so that during the summer solstice in June, it will be above the ca 20th parallel north, after which it will again start moving closer to the equator. After the autumn equinox it will start revolving the earth on southern latitudes, reaching again ca 20° S latitude by the time of the northern winter equinox in late December.
This latitude value is called the declination of the sun. It keeps changing hour after hour and the almanac gives you both the hourly value and the rate of the change below the column of the declination value, marked ‘d’.
You can also check the rate of change by comparing the value of declination at the hour of your sight to the next hour, then you also see whether the declination is growing or diminishing. For your calculations, you don’t need to have the value of declination as accurate as the GHA – it suffices that you have it roughly to the closest tenth of the minute which you can calculate in your head by looking at the two whole hour figures around the exact time of your sight – in reality the closest whole minute is enough, at least when navigating a small boat.
So, now we have the exact position of the sun at the exact time of your sight.
As an aside, a fun experience with the sextant is to take the noon sight when the latitude of the ship is the same or very close to the declination. This happened to us on the Darya Gayatri, as we approached the equator from the south and the declination is an S value. Then the noon height will be very close to 90°as the sun rises to the Zenith at noon. The closest I have got was 89° and 51 minutes in the 2018 GGR coming back over the Equator.
Calculating a position line
Next, based on GHA and declination, together with our rough dead reckoning position and the observed sextant height, we will work out not our exact position, but a position line along which we are. In order to fix our position, we’ll take another sight later during the day in order to get another position line, which, together with details about the direction and distance we have moved between the two sights will then allow us to fix our position.
Sight Reduction Tables
In order to get the information required for the position line, we enter the Sight Reduction Tables. On big ships, the Admiralty Tables, which have a separate volume for each 10 degrees of latitude, are being used. On smaller vessels, it is more convenient to use Sight Reduction Tables for Aerial Navigation, which only have three volumes, one for stars, another for latitudes 040 degrees, and the third one for 4089 degrees of latitudes. The second two are for the sun and other bodies in the solar system.
The Sight Reduction Tables are organised by whole degrees of latitude. There are double pages for each latitude, depending whether your estimated latitude is same or a different name as the sun’s current declination. Meaning, that if you are, for example, in the northern hemisphere in summer time, i.e. between the spring and autumn equinox, both your latitude and declination will be N, i.e. ‘same name’ and so on. This means you can now select the correct page.
Local hour angle
Next we need to know our Local Hour Angle (LHA) to pick the right row of the table. LHA is the amount of degrees that the sun is to the west of us at the time of our sight. It is calculated by adding (on dead reckoned easterly longitude ) or subtracting (on DR westerly longitude) our DR longitude value to or from the GHA.
As the Sight Reduction Tables are organised by whole degrees of LHA, we need to choose the closest whole figure of degrees of Local Hour Angle, as the result of the addition or the subtraction of your DR longitude from the GHA.
Now we’ve found the right page and the right row from the tables. The columns are for declination, so you should choose the column with the same value of declination you got from the Nautical Almanac.
Find your figures
With this information we find three figures from the Sight Reduction Tables. First one is H/c, which is the calculated height of the sun at the given LHA and declination. The next value (d) is used to find the value of correction (positive or negative) to the H/c based on the minutes of the declination, as we’ve only used whole degrees so far.
This correction is found on Table V at the end of the Sight Reduction Table; select the row according to the minutes of declination and the column by the value d, then take the correction and either add or subtract it to the H/c value to get the final H/c.
The third value you find next to the H/c and d is the z, which you either subtract from 180° or you add 180° to it. It may also be a straight right, depending whether you are in the southern or northern hemisphere and whether the LHA is bigger or smaller than 180 – the instructions for this calculation are to be found on top of each page of the tables for northern latitudes and on the bottom for southern latitudes.
After this calculation you get the value Z/n, which is called the azimuth. The azimuth is the compass bearing towards the sun from your estimated position at the time of the sight (chosen whole degree of latitude and the interpolated value of DR longitude used to get an whole LHA figure).
We now have two values for the height of the sun (the angle between the horizon and the sun), the observed altitude H/o and the calculated altitude from the Sight Reduction Table H/c. You now subtract the smaller from the bigger. The difference between the two is the length of the Intercept, which we will use when plotting down the sight – one minute of height equalling one nautical mile.
Plotting position
Now we are ready to proceed to the plotting sheet. On my boat, I use a navigation log book with squared pages, and make life easy for myself by making my plotting sheets on the book, this way everything is nicely documented and can be checked by the organisers of the races in which I participate.
My approximation for a plotting sheet is that every square is five minutes of latitude, so 12 squares up or down equal 1° of latitude. Between latitudes 0º–20°, the longitudes are on the same scale. Between latitudes 20º–35º I use one square for six minutes, which means 10 squares for one degree of longitude. For latitudes higher than 35° I use the scale of 7.5 minutes per square, which means eight squares per one degree of longitude. With my accuracy of sextant use, I have found this sufficient, though perhaps not precise enough if you want more accuracy.
Setting up the plotting sheet
You first plot the morning sight. When you entered the Sight Reduction Tables, you chose an estimated latitude of whole degrees, the one closest to your DR position. Now you mark that latitude at mid height of your plotting sheet. On the vertical scale mark 10 minutes of latitude per two squares, both north and south.
Then mark the closest whole degree of your DR longitude in the middle of the horizontal scale and, depending on your latitude, mark either 10, 12 or 15 minutes per two squares of the sheet to the left and right (west and east).
Estimated position
Then you start by marking down your Estimated Position (EP) on the sheet. As you entered the Sight Reduction Tables using an whole degree figure for latitude, that is your estimated latitude. Your estimated longitude is the interpolated value of longitude, which you used in order to get a whole number of degrees when you calculated the LHA.
After getting the EP1 (for the forenoon sight) on the plotting sheet, you now take the chart protractor and draw a line across the EP1 at the angle of the azimuth z/n with an arrowhead at the end towards the sun and the line continuing also across the EP1 away from the sun. Mark the number of minutes of the Z/n next to the arrowhead, so it will be easy to check everything afterwards.
Next you will mark the length of the Intercept on the line of azimuth, which is the difference of H/o and H/c measured in nautical miles. If H/o is greater than H/c, the Intercept will be drawn towards the sun (where the arrow is pointing at), if H/o is less than the H/c, the Intercept will be away from the sun. When you make the subtraction in your calculations, write either towards or away right away next to the answer, so you remember to mark it correctly.
Noon position
As we are finding our position at local noon time, the next step is to take the movement and heading of the vessel between the time of the sight and the local noon into consideration. You draw a vector (arrow) from the end of the Intercept in the direction which equals the true heading of the vessel and the length equals the distance travelled between the forenoon sight and local noon.
Then remains only the marking of the forenoon position line, which is a line perpendicular to the azimuth and going through the end of the DR vector you just marked from the end of the Intercept.
Afternoon sight
The plotting process for the afternoon sight is the same, except that the DR vector is drawn at an opposite (+/ 180°) of the heading of the ship to bring back the afternoon position line to our noon position. If you take the forenoon sight 2.5 to 1.5 hrs before the noon sight, and the afternoon sight a similar time after the noon, the lines will cross each other in a nice, almost 90° angle, giving you a fairly exact position.
Noon latitude
The Noon Latitude is the last thing you plot and it will be your third position line. These three lines will form a triangle on the plotting sheet, the so called ‘cocked hat’. The smoother the sea and the more accurate your sextant sights are, the smaller the hat will be.
If conditions are rough, the horizon isn’t clear or the sun is only visible through clouds, the hat becomes bigger and you have to take a measured guess where your position is within the ‘hat’.
However, the more often you run through the process the more accurate your plotting will become, and in fair conditions you’ll be able to plot your position accurately.
Conclusion
After going through this process a few times and getting used to the routine, you’ll discover that it is actually relatively simple.
For me, the biggest challenge is to stay focused and avoid making stupid mistakes when making my calculations. That’s the reason for marking down the calculation process neatly and in the same way every time. Doing this should make it easy to check and locate possible errors before they ruin your workings.
Knowing you can find your position without the aid of any modern technology is extremely satisfying, so good luck and enjoy the process!
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