Terrestrial navigation: How to determine your course without technology

Navigation series

• Episode 1: Taking stock of the terrestrial situation
• Episode 2: From map navigation to compass navigation and combined navigation
• Episode 3: The Taking wind and electricity into account
• Episode 4: GPS waypoint navigation – tips, tricks and common mistakes

GPS and chartplotters have long been standard equipment on board. However, the Current GNSS disruptions in the Baltic Sea show that satellite navigation is not reliably available in all conditions. Authorities and maritime organisations have been warning for months about increasing jamming and spoofing – that is, disrupted or deliberately falsified position signals.

If the electronic navigation system fails or displays an implausible position, traditional skills are crucial. With an up-to-date paper nautical chart, a compass, course calculations and thorough preparation, you can verify your position even without GPS and maintain a safe course to your destination.

But even in supposedly safe waters, circumstances may arise – such as water ingress or a lightning strike – which render the navigation electronics unusable, meaning one must fall back on traditional methods. Quite apart from that, there is always a certain appeal in determining one’s current position using simple means, just as the seafarers of old did.

Keep an eye out

To determine a position, objects with a known position must be within sight. This applies equally to satellite navigation, where the GNSS antenna must have a sufficient number of satellites within its field of view. In terrestrial navigation, these objects are earth-based, such as navigation marks and landmarks. They must also be marked on the nautical chart.

The first step, therefore, is to look out from the cockpit: what can be seen in the ship’s surroundings, and which of the objects spotted are also marked on the nautical chart? Is the distinctive church tower on the starboard side actually shown there? What about the radio mast visible further ahead? To identify features beyond any doubt, you need to have at least a rough idea of where you are – regular cross-referencing helps here.

Some nautical charts and local sailing guides feature drawings or photographs of distinctive landmarks to aid identification. The appearance of lighthouses is also described in the lighthouse directory. At night, lighthouses can be clearly identified by their colour, code and interval.

As a general rule, the more reference points are included in the positioning process, the more reliable the result will be. However, it is not always the case that several suitable objects will be in view at the same time. Especially as these must be objects with a fixed position. Buoys floating in the water are only of limited use. Ultimately, though, you have to make do with what’s available. Inaccuracies can be corrected when more suitable objects come into view.

Spot on

The simplest way to determine one’s position is by taking a bearing. If, for example, you take a bearing of 120 degrees towards a lighthouse, you must be situated somewhere along a line from which the lighthouse lies exactly in that direction. This is known as a ‘line of position’. It encompasses all possible positions of the vessel based on a previous measurement.

The bearing line is plotted on the nautical chart by drawing a line from the lighthouse’s location in the opposite direction to the bearing (bearing value ± 180°) – in our example, therefore, in the direction of 300 degrees (120° + 180° = 300°). This is because if the lighthouse is at 120 degrees as seen from my position, then, as seen from the lighthouse, I must be in the direction of 300 degrees.

It is important always to use a true bearing (rwP) when making entries on a nautical chart. This is because the nautical chart is oriented to true north (rwN). On motor yachts, however, bearings are usually taken using a magnetic compass, which is subject to so-called compass errors.

A magnetic compass bearing (MgP) must therefore first be corrected for deviation (Abl, also known as ‘Deviation’) and magnetic declination (MW), and converted into a true bearing.

Bearing conversion

In order to plot a bearing line on a nautical chart based on a magnetic compass bearing (MgP), the bearing must first be corrected for any compass errors – that is, for declination (Abl) and magnetic deviation (MW; more on these errors in the next instalment). A calculation method has proven effective for this, which many will likely recognise from their training for the recreational boat licence exam:

The direction of calculation is from top to bottom – from the ‘incorrect’ to the ‘correct’, the latter always being the direction of true north. The signs are set accordingly. When converting a bearing from a relative bearing to a magnetic bearing, the signs would be reversed.

The value for the deviation, including the sign, is taken from the deviation table for the steering compass when taking bearings with it (where available). Important: The magnetic compass bearing (MgK) prevailing at the time of the bearing is decisive, not the bearing (MgP). This is because, for the declination, it does not matter in which direction one takes a bearing using the steering compass – it depends solely on the direction in which the compass is currently aligned. Therefore, the declination value applicable is always that corresponding to the MgK prevailing at the time of the bearing.

As the deviation depends on the compass’s position on board, it remains unspecified when taking bearings with a portable compass (in the absence of better information, a deviation of 0° is assumed in such cases).

The following applies to the MW: an eastern value generally has a positive (+) sign, whilst a western MW has a negative (-) sign.

Suitable sounding tool

As the deviation depends on the compass’s position on board, a table of corresponding values usually exists – if at all – only for the steering compass. This actually makes it the preferred navigation tool.

In practice, however, it is usually of limited use, if any at all. For example, with compasses mounted on the steering column, the compass cover and superstructure often get in the way when taking bearings ahead. With a bulkhead compass, taking bearings astern is impossible – unless you alter course to take the bearing.

You can also try to align the yacht’s keel line precisely with the object being sighted, and then use the resulting magnetic compass bearing (MgK) as the bearing value. This method also works with an electronic compass, which can be compensated for relatively easily to eliminate the declination entirely. GPS, on the other hand, is not suitable for this purpose, as it has no reference to the true heading.

If you do not wish to alter your course whilst taking a bearing, a hand-held bearing compass or a pair of marine binoculars with a built-in compass are suitable options. These are also subject to deviation, the extent of which, however, is unknown. You will therefore have to accept a corresponding margin of error in the bearing.

A bearing disc offers an alternative solution. It is used to take lateral bearings (SP). The angle read off the disc therefore refers to the yacht’s true heading (bow direction). It is added to the current heading to give a north-referenced value (MgK + SP = MgP; if the bearing is to port, the value must be subtracted). This enables bearings to be taken in all directions whilst taking into account the deviation of the steering compass.

Cross or triangle

Once we have plotted the position line on the nautical chart, we know that we are somewhere along that line. To determine our exact position, we need at least one more position line – ideally from a second bearing object. The ship’s position is at the point where these lines intersect.

For this type of cross-bearing, the two bearing objects should not be too close together; otherwise, the lines will overlap, meaning that a clear point of intersection can no longer be identified. This is referred to as ‘sliding intersections’, which can also occur when the bearing objects are opposite one another. The angle between the two bearing lines should, if possible, be greater than 30 degrees and less than 150 degrees.

The bearings must also be taken at the same time. In practice, it is advisable to take bearings on objects in the forward or aft directions first – as the object being bearings will not move out of the way so quickly in these directions. And, of course, all bearings should be taken before you start working on the nautical chart.

If there are more than two bearing targets, the lines of sight may no longer all intersect at a single point, but instead form what is known as an ‘error triangle’. However, sometimes not all bearings are of the same quality – perhaps the observer’s position was unstable during one bearing. In the case of a cross-bearing, this would distort the point of intersection – but with multiple lines of sight, there is at least a chance of determining where a realistic location might lie.

Completely sealed

It is possible to determine one’s position even with just one bearing object – although this is less reliable than a cross-bearing. In what is known as a ‘double bearing’, the same object is sighted twice at a certain interval. By the time of the second bearing, the reference mark should have moved significantly. At the same time, the yacht must maintain its exact course between the two bearings and travel as steadily as possible.

The position lines from both bearings will, of course, not intersect on the nautical chart – after all, they originate from the same object. To obtain a point of intersection, the position line from the first bearing is shifted in parallel – or ‘sailed’ – by the distance the yacht has covered in the meantime.

There are various methods for plotting the seal. One involves shifting the position of the object being beared on the nautical chart by the distance travelled by the yacht. From this point, one then plots the bearing line from the first bearing. Alternatively, instead of moving the position of the object being sighted, you can shift any point on the first bearing line accordingly and then shift the first bearing line parallel to the position reached by the yacht.

This method of ‘reusing’ a bearing is also useful if another landmark appears later on, whilst the first bearing object has since disappeared behind a headland. In that case, the second bearing object is taken in the usual way and the first bearing is then sealed again – this is known as a truncated double bearing.

The accuracy of a double bearing depends heavily on the reliability of the assumed movement of the yacht between the two bearings. If, for example, the values from the log and the steering compass are used to calculate the course, this merely describes the distance travelled through the water – not over ground. Any current drift or steering inaccuracies are not taken into account.

Four dashes further on

A four-line bearing is also sufficient when there is only one bearing object. The name derives from the former division of the compass rose – in pirate films, the captain often has the course corrected by a few lines. One line corresponds to one 32nd of a circle, i.e. 11.25 degrees. Here we are talking about 4 lines, i.e. 45 degrees. However, these 45 degrees refer to the bearing (a side bearing).

Firstly, you need to wait for the moment when a target is exactly at a bearing of 45 degrees to port or starboard. A compass bearing is then taken. From this point onwards, the course and speed must be maintained precisely until the object is exactly abeam (cross-bearing = 90°). It has now drifted by 4 marks. The second compass bearing is then taken.

With the four-point bearing method, an isosceles – or, more precisely, a right-angled – triangle is formed on the nautical chart. The angle between the course line and the first bearing is 45 degrees, as is the angle between the two standlines. As an isosceles triangle has two sides of equal length, the distance logged between the two bearings must correspond to the distance to the object being sighted at the second bearing. You can then plot the logged distance on the baseline of the second bearing, and you’re done. It sounds simple, but in practice it requires a great deal of attention and care when steering and taking bearings.

There are also uncertainties here regarding the sealing. That said, the principle of the four-point bearing can also be varied – the result need only be an isosceles triangle, though it does not necessarily have to be a right-angled triangle. This is always the case when the angle of the second side bearing is twice the angle of the first side bearing. The method is generally known as the doubled side bearing or as the distance from a double bearing.

Keep your distance

Determining the distance to an object also yields a line of position – in the form of a circle centred on the object’s location, with a radius equal to the distance measured. If the object is also bearinged, the ship’s position lies at the point where the circle of distance intersects the line of position derived from the bearing.

However, measuring distances without technical equipment, such as a radar system or a laser rangefinder, is not easy to achieve. We shall also leave aside angle measurements using a sextant for the moment. Without resorting to sophisticated technology, the visibility range of objects offers a starting point.

At sea, a distinction is made between meteorological and geographical visibility. The following applies to geographical visibility: the higher I stand, the further I can see – in other words, the further away the optical horizon is from my position. Added to this is the height of the target: a high target can be seen on the horizon earlier – even from a greater distance – than a low one.

As the degree of the Earth’s curvature is known, it is possible to calculate the distance at which a target of known elevation will appear ‘on the horizon’. The following formula applies: D = 2.075 × (√Ah + √Zh). ‘D’ stands for the distance in nautical miles (sm), ‘Ah’ for the eye level, and ‘Zh’ for the target height, all in metres (m). Anyone wishing to avoid doing the calculations will find relevant tables in nautical publications, such as textbooks and lighthouse lists.

In practice, for example, at night you can keep an out look to see when a leading beacon appears on the horizon, and then determine its distance at that moment. This method is known as ‘beacon on the horizon’. The beacon elevation (= target elevation) can be found on nautical charts and in beacon lists. The same method also works with other objects of known height. Incidentally, the reticle in a pair of marine binoculars can also provide a guide to distance. We shall, however, refrain from going into trigonometric calculations at this point.

Everything’s fine

There are also reference lines that are already marked on the nautical chart – for example, leading-light lines. If, as seen from on board, the upper and lower lights are directly one above the other, the yacht is positioned exactly on that line.

The line-of-sight measurements obtained from such deck bearings are more reliable than compass bearings, although the method also works with other reference points that are perfectly aligned.

Added to this are depth contours: if my depth sounder shows a water depth of 20 metres whilst I am taking a bearing on an object on land, I must be at the point where the line of bearing intersects with the 20-metre depth contour. At least in theory – in practice, there are a few more sticking points to bear in mind when taking soundings.

Firstly, there are water-level fluctuations in tidal waters. This is particularly true as the current tidal height cannot be calculated precisely for every point on the chart. Added to this are wind-induced changes in water level, which can also occur in non-tidal waters. Furthermore, the echo sounder must be functioning correctly and be properly calibrated; for example, the transducer depth must be set correctly. On top of that, a seabed with as distinct a profile as possible and a clear depth gradient is advantageous.

In practice, it is advisable to follow the depth contour for a while to be on the safe side. And, of course, you will need a nautical chart with the most up-to-date survey data possible, as well as a suitable scale. The latter is, however, absolutely essential for reliable positioning and navigation.

Book recommendations

Stress-free navigation It fits in perfectly with the topic of terrestrial navigation. The guide provides a clear overview of how to determine your position using nautical charts, a compass and visual navigation. Readers will also find basic information on navigation marks, the weather, tides and trip planning.

Exercises and tasks: Navigation is aimed at anyone who would like to practise the procedures shown on the chart step by step. The focus is on, amongst other things, taking bearings and setting a course, determining one’s position, and working with nautical charts.

How well are you prepared for a failure of your GPS and chart plotter, and which traditional navigation method are you confident in using?