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Passionate about Astro navigation and Ocean Sailing;

Image by andreas kretschmer

Mastering Ocean Navigation?
Why Bother!

According to my parents, I cannot stay away from water, they tell a story about me as a child, having driven from Derbyshire (Middle of England) to the Yorkshire coast with Grandparents for a day or so by the Sea. As the car door was opened, I leaped out and ran as fast as I could across the beach to the sea, my Mother in chase. Grandma calling out that she was sure I would not go into the sea in my best cloths . . . wrong, I ran straight into the sea fully dressed, even then the sea was all I wanted.

I started sailing in the mid 1960s, a Mirror Dingy owned by friends of my parents. Flash Dam is Cheshire was the place. I was less than enamoured, if the truth is to be known, there was no engine, lots of little bits of rope, non of which seemed to make any difference to our lack of progress across Flash lake.

My parents then moved to Southport, North West England and joined Southport Sailing Club (I suspect because of the cheap bar) but to a teenage boy with a love of water and lots of dinghies to be sailed (Mirrors, Enterprise, GP14, even a couple of Fireballs and 470s), the shallow water made things fairly safe but the competition in the Frostbite and Tuesday evening races was fierce.

Later in the Royal Air Force I was able to sail in Enterprises and later in bigger yachts. Upon leaving the RAF I was able to purchase my first Yacht, a Camper & Nicholson “Nic’30”, a wonderful ½ tonne, very fast to windward but rolling wildly on a dead run. A few other sailing yachts later and I found a glorious Schooner, designed around 1850 but built as a copy in the late 1970s. Talisman became home for both my Wife and I, our Daughter and Deefa the Boarder Terrier, for some 15 years.

It was around this time that I became a full time Instructor for the Royal Yachting Association, shore-based as I am Diabetic (Type 1).

I have been a busy Instructor during all of my time with the RYA. I am now a YachtMaster Examiner for both Sail and for Ocean. I have been navigating and teaching navigation since the early 1990s. Back than there was no GPS, if you were going any distance off-shore then the sextant was the instrument of choice.

Even today, if you are talking with almost any sailor, their desire will be to sail across an ocean, or even two. Some will want to sail around the world. This is a relatively simple thing to do from a basic navigation point of view. Assuming that you know where you want to go (most of us do) Just turn on the GPS (or chart-plotter), enter a few waypoints and then follow the course line (or bearing) shown on the screen. The problem with GPS is that it never invites you to look ahead, the GPS will show you where you are and where you are heading. It will even give you an ETA (Estimated Time of Arrival) for your destination, but GPS will not involve you in the development of the position, of the course lines or of your speed made good towards your destination. The modern GPS/Chart-plotter is a wonderful form of navigation and as a back-up to the more traditional forms of navigation. I am a great fan of GPS and it’s accuracy and even in it’s reliability. For any navigation system, these are the two corner stones, Accuracy and Reliability. GPS excels at both, accuracy down to around 15 meters and with differential GPS and or the new Galileo system a possibility of 2 to 3 meter accuracy (when the pencil lead is around 2 Miles wide on an Ocean chart, some 200 meters on a coastal chart and 20 meters on a large scale pilotage chart), yes ,15 meters is very good indeed. But GPS is boring, it is deadly dull, delivering a continual fix as a Lat & Long or the slowly moving ships symbol on the screen. At no point does the modern navigator get involved in the progress from one fix to the next, with the movement of the heavens or the progress of weather systems, GPS does not involve one in the way that the use of a Sextant and the observation of the heavens involves the classic Navigator.

Please do not get me wrong, I am a great believer in GPS and the modern Chart-Plotter, I just prefer to Navigate using the Sextant and the Celestial objects. Is this a more accurate or more reliable way of navigating . . . No, probably not. BUT, it is much more involving, more enjoyable and much more satisfying. I read recently (Yachting World, ARC crew survey) that the biggest problems for the crew on the latest ARC (Atlantic Rally for Cruisers) was that there were insufficient movies to watch! My reaction was “What!” How does anyone have any spare time on an Ocean passage, My experience is that with Astro Navigation and vessel Maintenance, the preparation of meals and the constant desire to sleep, I never have enough time to even open a book, let alone read one, time to watch a movie, WOW! 

Although, I have only once crossed an Ocean by GPS, it is true to say that the daily position fixing took only a few minutes compared to the probable two hours  per day required for Astro position fixing, It also true to say that I only fixed position 4 times a day by GPS, whilst by Sextant and Astro I would aim to fix position 6 times a day. This is to allow for the need to project my course and speed through the night (for Astro to work one needs to be able to see the horizon, not normally possible on a Moonless night). I am not suggesting that Astro is a means to waste time, I am suggesting that Astro is a great way to become more involved with the passage, the weather and the ship-board routines. 

It is the Seaman like method.

Mastering Ocean Navigation Part 2

It is the Seaman-like method . . .

There is nothing saltier than navigation by Sextant. Very little else speaks of the ability, knowledge, and experience of the Blue water sailor than navigating by the Sun, Moon, Stars and Planets. It is the ultimate sign of the Master Seafarer.

The use of the Sextant and it’s associated tables to find ones position is a complex, involving task. 

For Astro to work the Navigator needs to be able to see both the horizon and the celestial object. This means that there must be enough light to see the Horizon, easy when the Sun is visible but much harder during the night hours. It is because of this that the Ocean Navigator needs to be able to project the ship's course for extended periods of time. Most navigators are comfortable enough when projecting an Estimated Position or a Course to Steer for a couple of hours when involved in Coastal Navigation, however, the thought of projecting a course for some 10 hours through the night and across the surface of an Ocean subject to unknown currents is something else altogether. We call this projection “Dead Reckoning”.

The art of “Dead Reckoning” is a fast-disappearing art form. It is being killed by the pervasive use of GPS onboard vessels of all sizes. The modern navigator is uncomfortable being removed from the re-assurance of the screen giving the constant image of the vessel and its immediate location. When crossing an Ocean we know that there are no rocks to run into, no tides to push us off course, yet we are still assailed by doubts about our position and our course. The little ship shown on the Chart-Plotter screen gives the reassurance we crave. This constant reassurance does not exist with Astro. The nearest we get is a past and future course line drawn onto a plotting sheet or chart. Often during the long Oceanic night, some 12, or more hours with no Sun to illuminate the horizon (even on the longest Day, on the Equator there is only 13 hours of Daylight) the best navigator feels as if the predicted course is being lost to the wind and waves. When calculating one's course, the navigator needs to consider the wind, waves, probable Ocean currents, leeway, and the ability of the vessel and crew to hold the required course and speed through the water. This is a lot of variables, the use of the “autopilot”, be it a windvane or electronic, will make things much, much better. Slow the boat down a little bit, it is easier to maintain a lower speed rather than the fastest possible speed. Be aware of your vessel's windward abilities, spend some time calculating it's leeway for each point of sail and for each set of sails along with each wind force (see the annex on Leeway).

Why this obsession with the antique art of maintaining a Dead-Reckoned position? When crossing any body of water using Astro, the means of position-keeping used is that of the “Running Fix”. The running fix uses two or more position lines to establish a fix, in normal coastal use the running fix is used to establish a fix when there is only one point of reference, a single Lighthouse at night, for instance. When using Astro as our means of position fixing, there is usually only one object available at any one time (we will consider multiple Star sights elsewhere), the fact that we have only one object available means that we have to use the Running Fix. 

In the figure below is an example of a running fix, this is probably the sort of explanation you are familiar with. It is based on a vessel on a coastal passage using a lighthouse as it’s single point of reference. For more information on Running Fix, please see the annex “Running Fix”


1, first position line, drawn from the lighthouse, a note is made of both time and log

2, from anywhere on position line 1, start to draw the Water Track, This is your Dead Reckoning

3, After a period of time and or a distance travelled, i.e. 20 minutes and 2 Miles mark the D.R. position along the Water Track

4, Draw the second position line from the Light House, your position fix will be somewhere along this line

5, Draw a “Transferred Position Line” This is PARALLEL to your first position line and also passes through the D.R. on your water track, Where this Transferred position line crosses your second position line is your FIX.

That we are constantly looking at the motion of the yacht, the sea state, leeway, boat speed, helm control, and anything else that affects the yacht, means that we are very much in touch with the Ocean and with the condition of the yacht. To get a good feel for Dead Reckoning we need to be aware of these things. You will soon recognise that at this wind speed, in this sea state your yacht will travel at XX Speed through the water. In the same conditions, your yacht will suffer from X degrees of leeway. I fully understand that often, when sailing in coastal waters, the effects of leeway may be ignored for short distances, when Ocean sailing, especially to windward or across the wind, we must assess and apply leeway to our course. Failure to do this may add many miles and possibly days to your Ocean voyage.

It is when we take all of this into account that we really start to understand why we like to sail, or motor, with the wind and Ocean current. We always try to arrange the time of our passage so that we have an easier time of things. We use Ocean Planning Charts to find the best time of year for our crossing, to help us get the best winds and currents, the least opportunity for calms and storms. Once we have arrived at a time for our passage, the yacht is prepared and we are ready to depart.

The first few hours will probably be spent getting used to how a more heavily loaded yacht moves, time spent watching the land slowly sink below the horizon, getting the crew ready for the first night at sea. Before the land disappears, fix your position using traditional methods, a three-point fix, range and bearing, GPS Lat & Long, whatever works for you at the time. It is from this fix that you will start your Dead Reckoning, go below, plot your fix, and draw your Compass Course onto the chart, remember to correct your Compass Course for Deviation, Variation, and leeway (TVMDC) (see Annex 2 Compass Correction). Dependant upon the time you departed your first Sextant sight may be a Sun sight, a Meridian passage, or even a sight of the Moon, Stars or Planets. Usually, the first sight of the passage is a Sun or Mer Pass (Meridian Passage, NOON Sight). Set the Sextant box somewhere safe, open the box, and allow the Sextant to gradually come up to ambient temperature, give it an hour or so, then you can take it out on deck and go through the checks to ensure that the Sextant is in good shape. Start with Perpendicularity, followed by side and index error (see Annex 4 - Sextant Errors & Care), make a note of the index error in your deck log (or whatever notebook you will be using for your Sextant sights. Check your chosen timepiece for error, and note the “going rate”. Be aware of your anticipated Height of Eye at your chosen safe and stable position.

Find a safe, stable position on the deck of the yacht, re-check Index Error against the horizon away from the Sun, better contrast, won’t hurt your eyes. 

Now you are ready for your first sight, make a couple of practice swings, bring the Sun down to the horizon, remember that you want the bottom of the Sun, the Lower limb, to be tangential to the Horizon. Now swing the Sextant so that the image of the Sun moves in a short arc, where the image of the Sun is closest to the Horizon, this is where the Sextant is vertical and is the altitude you want to record. If you are unfamiliar with the Sextant then take a few sights (5 or 7 sights work well for an average Sextant Altitude and Average Time)

Work through your sight form, plot the sight on a plotting sheet, compare it to your D.R., and correct the D.R. to the sights position line. From this “corrected” D.R. redraw your water track line and aim to take a further sight 3 to 4 hours later (the Sun moves around 15° per hour, so 3 Hours = 45 degrees of movement, this gives a reasonable amount of angular change between the position lines of the first and second sights, obviously 4 hours would give a better angle of cut at 60°)

In an ideal world, we would like to take our first sight of the day at morning twilight, Stars, Planet, Moon, something to either give a Fix, like 3 Stars, or to use with a Transferred position line from yesterday to give a reasonable fix this morning. Some 3 to 4 Hours later, mid-morning 09:00 or thereabouts a Sun Sight followed by a Mer Pass (Noon Sight) at around 12:00 Local Mean Time. At around 15:30 we will take a further Sun Sight and a final set of Sights at evening Twilight, 3 Stars or a combination of Stars, Planets, and Moon to give a 3-line Fix. 

This is 5 Fixes each day, with this amount of data it is relatively easy to gain a good insight into the efficiency of the yacht, Speed over the ground, course over the ground, Ocean Current, Leeway, helm control, all of these are equal to the difference between your D.R. position and the actual “true position” of your Astro fixes. As you get better at D.R.s, better with the ship's log, better at holding a compass course then the distance between your D.R. and your fix will also reduce. 

One of the keys to gaining a reliable fix by Astro is in the angle of “cut” of the position lines. You will recall from coastal sailing that the optimal angle of cut is 60° between the position lines, and 60° is the internal angle of an Isosceles triangle, the most stable of geometric functions. Therefore if we wanted a 3-point fix then we would attempt to use objects that would produce position lines close to 60° apart. However we will probably only have two position lines the Transferred position line from the previous sight and the position line from the current sight, we would like these two lines to cross (cut) at close to 90°, not easy but well worth bearing in mind when planning the timing of your sights. As discussed the Sun moves 15° per hour, 6 hours then is equal to 90°, this is rather too long between sights, better to try for 3 or 4 hours and take the lesser angle of cut.

If you happen to be sailing in the Tropics, one of the local phenomena that can cause some problems is that on a couple of occasions a year, it is possible for the Sun’s declination to equal your latitude, this means that at (or close too) Noon the Sun will be directly overhead, when you work through your Mer Pass sights the TRUE ALT will equal 90°, if this is the case there a couple of things to be aware of.

If the Sun is at 90°, it does not matter what horizon you use 

All of the Sun sights you take on that Latitude will have position lines that run North/South this is because the Sun (Zn) is either due East or due West of you and the position lines are drawn at 90° to the Zn.

Because of this, your position lines will never cross, they cannot and will not result in a fix

If you want to use the Sun then you will need to either Transfer the Mer Pass position line from the day before or wait until Noon and then transfer your Mer Pass position line backward to your first Sun Sight of the day and use that as your first fix then work you likely position from this point

Who said Astro was not fun?

The way around this is to take a few Star sights at morning Twilight, If you plot say 4 Stars, then you will have a selection of position lines each at a different angle of cut to choose from. Just select the one that works best and use that one.

Whilst writing this I am on the Island of St Helena in the South Atlantic Ocean, the date is Sunday 30/01/2022, and on Saturday 05/02/2022 the Declination of the Sun will be S15°50’.6 at 12:00 UT. The Latitude of Longwood, St Helena is 15°56.6 S. On this date little ‘d’ is 0.8, increments and corrections gives a value of 0.4 for little d at 26’. This means that the Declination of the Sun will be equal to Latitude at 07:16 on the morning of 05/02/2022.

Even on the 30/01/2022 at Noon when I took a Mer Pass the resultant True Alt was 

87°40’.9, LHA 358, and the Z = 90°, Latitude Rule states LHA greater than 180° then Zn = 180° - Z so the Zn is still 90°

I will take sights as close to every hour of this day to prove that there cannot be a fix.


I will break Astro / Ocean Navigation down into a series of shorter sections. I have given these names, such as "How Astro" or "How Sextant" the general idea is that you can simply go to the section of interest and find the information you require

How Astro?
Here you will find some history, background, and possibly some interesting facts about Astro Nav

That we can navigate by the light from the Sun, some 93 million miles away, is quite incredible. That we do this with a device invented in the time of Sir Christopher Wren (it seems that an American named Thomas Godfrey and an Englishman named Thomas Hadley both seem to have invented a very similar device at about the same time in history (1730 -/+)) is even more incredible. All we really need is the Sextant, Time and 4 books.

If we look at this in very general terms for a minute. We will probably use the Sun (it is big, bright and I know I can find it in the sky). If I raise my arm so that I am pointing at the Sun, I now have an idea about where I am, I am somewhere on the circumference of a large circle where the angle to the Sun is the same as the angle of my arm. If I can keep my arm at the same angle and keep it pointing at the Sun then I am somewhere on that circle, we call this a Position Line. Now this is a BIG line. Possibly thousands of Miles in radius and entered on the surface of the Earth directly below the centre of the Sun. this position is known as the Geographical Position (GP) of the Sun. It is the position at which I would throw no shadow were I stood there. This position the GP (Geographical Position) could be referred to in terms of Latitude and Longitude, however in Astro terminology it has a different name. The Celestial equivalent of Latitude is known as Declination (Dec) and the Celestial equivalent of Longitude is known as the Greenwich Hour Angle (GHA). So the Geographical Position (GP) of the Sun would be referred to as the Dec and GHA of the Sun.

If I can know where the G.P.of the Sun is, then I can also know how far my position is from the G.P. and in what direction is the G.P. from my position. 

To achieve this I need to use either some complex mathematics or a couple of pre-written tables to solve the mathematical equation for me, I would choose the tables every time. The mathematical equation is complex and time consuming and looks something like this:

 Hc = sin-1[sin(declination) x sin(Latitude) + (cos(Latitude) x cos(declination) x cos(LHA)]

Followed by this:

Z  = cos-1[(sin(declination) – sin(Latitude) x sin(Hc)) / (cos(Latitude) x cos(Hc))]



A suitable scientific calculator will do the job. For most of us the use  of a calculator at sea is not what we are looking for and so we choose to use the books and tables instead. These are known as Sight Reduction Tables (SRTs), typically we will use the Tables for Air Navigation often called the “Sight Reduction Tables for Rapid Navigation” such as this one by the UK Hydrographic Office. In these books you will find comprehensive solutions for fixing position by the Sun, Planets, Moon and Stars for all Latitudes both North and South of the equator.

When we are beginning Astro Navigation we need to understand where the objects (Sun, Moon, Planets & Stars) exist with relation to our own planet Earth. As far as we are concerned they all exist on the surface of the “Celestial Sphere”. The Celestial Sphere may be visualised as an infinitely distant sphere upon the surface of which all the celestial object exist, it has the Earth as it’s centre. The Celestial Sphere has an Equator, Poles and a line of Zero degrees Longitude. Unsurprisingly these are named the Celestial Equator, Celestial North/South Pole and the Celestial Prime Meridian.

The Sun’s motion around the Celestial Sphere follows an orbit angled at 23.6° to the Equator, this is known as the “Sun’s Ecliptic”. It is this Ecliptic angle (23.6°) that give the planet Earth it’s seasons. You may have also noted that I stated that the Sun follows an orbit “around” the celestial sphere, this is odd, don’t you think? Surely the Earth and the other planets orbit the Sun? The reason that when we are involved with Astro Navigation we use this ancient Earth-centric model, is because when Astro Navigation came into being this was the model that was accepted back then. It is also the only model that makes working sense from the deck of a small craft at sea or a 4x4 in the middle of the desert. As the saying goes “You know it makes sense (Rodders?*)”, the Sun rises in the East and Sets in the West, you that the Sun moves across our skies, as do the Moon and the Planets. All of the Planets and their associated Moons orbit have an elliptical orbit, the closest point on this elliptical orbit is named “Perihelion” and the most distant point is named Aphelion. So the Earth's Moon has an Elliptical orbit around the Earth and the Earth has an Elliptical orbit around the Sun, BUT, We see both the Sun and the Moon as orbiting the Earth.

Whilst the Moon and the Planets move around the celestial sphere, the Stars are pretty much fixed upon the inside of the Celestial Sphere. We do know that the positions of the stars are not fixed, due to the lasting effects of the “Big Bang” the stars are always on the move. It is because of this movement that Volume 1 of the Sight Reduction Tables is only published for an Epoch, an Epoch is 10 years. Thus Volume 1 published for the Epoch 2020 would be valid from 2015 until 2025, for the middle one or two years the values provided for each of the 57 Navigational stars (HC & ZN) may be used directly, the other years will need to be corrected for Precession & Nutation. Whilst all of the celestial objects can be worked using Volumes 2&3 of the Sight Reduction Tables, Volume 1 makes the stars much faster and easier.


To make this book work we will need to know a few things about our Dead Reckoned position and the G.P. of the Sun (or other celestial object). The SRTs only work in whole numbers of Degrees, they do not understand minutes and/or decimals. For this, we need to change all of our data into these whole numbers. Some of this is easy, we can simply round our D.R. Latitude to the nearest whole number, 38º41.5N would become 39ºN for instance. We need to know the Declination (Dec) of the Sun also, but initially, we will only use the whole degrees of Dec (without rounding the minutes and /or decimals, we will use those later). So a Dec of 11º53.6S would become 11º only. The final number we require is named LHA, in the same way that GHA is how far West of Greenwich the Sun is, LHA (Local Hour Angle) is how far West of our D.R. the Sun is, but always in whole numbers. Please see the section on Geographical Position for details on calculating the LHA. . . .

How Sextant?

In this section I will cover the care and use of the Sextant, you will find a description of the Sextant and an explanation of it's use.


The sextant is a relatively simple device that allows us to look in two directions at the same time. it is also capable of measuring the angle (we call this the Sextant Altitude) between those two directions very accurately and to a 1/10 of a minute of arc.

This means that the Sextant is capable of measuring altitudes to 1/600th of a Degree.

1º = 60 Minutes 

So a minute is 1/60th of a degree

1’ = 10 decimals of a minute

So a decimal is 1/10th of a minute

10 (decimals of a minute) multiplied by 60 (minutes in a Degree) = 600 (ths of a Degree)

The modern Sextant is a marvel of design and engineering. The Sextant is designed such that the Index Arc is graduated to a little over 120 degrees but only takes 60 degrees of Arc (hence Sextant) of a circle to do so. It is the use of the two glasses (mirrors) and the precise angles that they are set to that allow for this ( the mirrors effectively double the visual angle).  The Index arm is pivoted at the apex of the frame and is located upon the bottom of the arc in such a way that it may be moved back and forth across the arc. This is frequently performed by a worm screw and a clamp that will secure the arm to the arc. 


To be able to measure these altitudes 

To use the Sextant we need something to measure the altitude against, the most convenient thing to use at sea is the horizon. As long as we can see the horizon then we can use the Sextant (see the appendix for “Artificial Horizons”).

The Sextant is made up of a relatively small number of parts, these comprise:

The Frame 

The Handle

The Telescope

The Index Arm

The Index ARC, (degree scale)

The Minute and Decimal scale

There are other parts (pivot bearing, legs, worm screw etc) to the Sextant, but these are of lesser interest to you and I as the users of the Sextant.


The Frame,

This is the basic structure of the Sextant, all other parts are attached to it. It is essential that the frame is true. If there is any bending or twisting of the frame it will make the Sextant unusable. It is extremely difficult to straighten or repair a bent or twisted frame.

Usually, the Index Arc is fixed across the bottom of the frame, it is graduated from a few degrees below 0º to a few degrees above 120º degrees, these are to allow for over or under reading due to Sextant error (see Sextant Error, Index Error). Some of the plastic Sextants, such as the excellent Davies range of Sextants, have Arc scales from -15º to 130º 


The Index arm has a mark placed upon it to indicate the number of degrees of the arc being measured by the Sextant, it will also have a secondary marker, often a “Micrometer” Drum that further allows for the measurement of minutes and decimals of arc. These two measurements are equated to the Altitude of the celestial body being observed through the telescope or eye-piece.

The Index arm also has a Glass (mirror) attached to it and mounted across the center of the pivot. This glass is angled such that whatever is reflected is projected to the Horizon glass.

The Horizon Glass is so called because it is through this glass that we see the horizon. This glass is fixed to the frame of the Sextant and is angled such that it will always reflect the image projected by the Index glass, and will in turn project this image onto the telescope or eye-piece. The Horizon glass is usually “half-mirrored”. The side of the glass closest to the frame (usually the Right side) is mirrored and the left side is clear. It is this half-mirroring that allows the user to see both the horizon and the reflected celestial object at the same time.

It is essential that these two glasses are aligned with one another and are perpendicular to the frame (see Sextant adjustment)

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