Navigation by bearing: From the chart bearing to the correct compass bearing
Navigation series
As explained in the previous episode, determining one’s position without satellite navigation systems such as GPS first requires an approximate starting point. From there, the route travelled can be traced by continuously cross-referencing data. For centuries, this method was the only way in seafaring to determine a ship’s current position, albeit approximately.
Course-based navigation is a simple method of determining position. The yacht’s anticipated route is plotted on the nautical chart using the course steered and the speed travelled. The starting point is the last known position. From there, the course steered since the last position fix is plotted. The distance covered during this period is then measured along this course line. This gives the yacht’s calculated position at the relevant point in time. Its distance travelled is calculated from the logged speed in relation to the elapsed time (see formulas).
Calculate distance and arrival time
The result is what is known as a ‘plotted position’. It is generally marked with a cross on the course line and the abbreviation ‘OK’ (an observed position, on the other hand, is marked with the abbreviation ‘OB’ and circled). In addition, the current time is recorded so that further connections can be made later on the basis of this information.
The methods and formulae used for route planning are equally suitable for making predictions. For example, by planning the route in advance, it is possible to work out when you will arrive at your destination or the next waypoint. This Estimated Time of Arrival, or ETA for short, is calculated from the distance to the destination in relation to the yacht’s speed.
If you divide the distance between two known positions of the yacht by the time elapsed between those positions, you obtain the yacht’s average speed over that distance. In long-distance sailing, for example, the average daily speed can be calculated using the daily mileage (the distance covered in 24 hours).
The uncertainties
Unlike a observed position, which is based on a measurement such as a cross-bearing, a radar range measurement or GPS, position determination by means of coupling is subject to a wide range of factors of uncertainty.
Firstly, there is the speed, which may have fluctuated somewhat along the route. Furthermore, when read from the log, this refers to the speed through the water (STW) – not the speed over ground (SOG). However, the yacht’s movement over the bottom is crucial for determining its accurate position on the map. When travelling with the current, the vessel moves faster over the bottom than through the water; when travelling against the current, it moves more slowly.
Similar uncertainties arise with regard to the direction in which the yacht has been travelling: apart from any steering inaccuracies, wind drift and tidal drift can cause the course over ground (COG) to deviate significantly from the intended course.
Mooring always represents a target situation rather than the actual situation: the yacht should be at the mooring point – but it does not have to be.
Key formulas for link navigation
- Distance: d (sm) = (v (kn) • t (min.))/60 or d (sm) = v (kn) • t (hr)
- Journey time (ETA): t (min) = (d (sm) × 60) / (v (kn))
- Speed: v (kn) = (d (sm) • 60)/(t (min.)) or v (kn) = d (sm) : t (h)
If the linking location and the observed location differ
If there is once again an opportunity to determine the position of an observed location, this position may differ significantly from the assumed coupling location for the same point in time. This deviation is known as a bearing displacement (BV). It is expressed as the direction and distance from the OK to the OB (from the ‘incorrect’ to the ‘correct’ position; for example: BV = 155°/1.5 sm).
The shift in the cutlery provides valuable clues for identifying an unexpected current shift or increased wind drift, and for considering how far ahead of the wind and/or current on the windward side one should sail in future. If the vessel is making significantly slower headway over ground than expected, the route may need to be adjusted to ensure that the destination is reached whilst it is still light.
How the Earth’s magnetic field affects the compass bearing
In order to achieve useful results when pairing, one should aim to keep the cutlery offset as small as possible. This requires careful course design, taking into account all conceivable influencing factors.
This applies to wind drift and the prevailing current just as much as it does to typical compass errors. The latter mean that the course read from the steering compass does not correspond to the yacht’s actual movement over ground, even in still waters and without any significant wind drift.
One reason for this is magnetic declination: whilst the nautical chart is oriented towards true north (rwN) – that is, the direction towards the geographic North Pole, where the meridians (lines of longitude) converge – a magnetic compass is oriented towards the Earth’s magnetic field.
To put it simply, one could also say that it aligns with the magnetic North Pole, where the field lines of the Earth’s magnetic field enter the Earth’s surface vertically (although, strictly speaking, the north needle of a magnetic compass aligns with the South Magnetic Pole, which is therefore actually located there – but we shall stick to the usual terminology here). This direction is known as magnetic north (mwN).
Reading and applying directional information correctly
As the geographic pole and the magnetic pole are not in the same place, there is an angle of varying magnitude between the two north directions, depending on the location – this is known as magnetic declination (MW).
So, if our yacht is sailing on a true north course according to the compass, we cannot be certain that we are also moving northwards on the nautical chart exactly parallel to the meridians.
This angular difference must be taken into account. And as it is not the same everywhere on Earth, the extent of magnetic declination depends on the sea area in which we are currently sailing – particularly as the Earth’s magnetic field is not entirely uniform either.
Information on local magnetic declination can be found on the nautical chart. It is usually shown on a printed compass rose. Sometimes there are also framed boxes containing details of magnetic declination. If there are several such entries on a chart, you should use the nearest one as a guide.
The figures always refer to a specific year, as the magnetic North Pole is on the move. Whilst it was located in northern Canada towards the end of the 20th century, it is now heading towards Siberia. Therefore, the magnetic declination figure may need to be adjusted to reflect the current year (see below).
Why every yacht has its own deviation
In fact, the navigation compass is not aligned with true north, but with magnetic north (MgN). This direction is only available to us on board. This is because there are also numerous on-board magnetic influences at play here that cause the compass to deviate – for example, metal components and, in particular, iron parts, but also electrical wiring.
The vessel-specific deviation of the steering compass from true north is referred to as ‘deviation’ (Abl). It is naturally particularly high on steel yachts, but on GRP boats too, the engine block and alternator, the steering gear, the navigation electronics, the radio, external loudspeakers, metal objects stored in the locker and even the helmsman’s mobile phone in their pocket can cause the compass to drift off course without this being noticed.
The deviation also varies depending on the ship’s course. Sometimes the ship’s heading causes the ship’s magnetism and the Earth’s magnetism to reinforce one another; in other cases, it causes them to cancel each other out – to put it simply. And depending on the direction in which the deviation then occurs, it has either a positive or a negative sign.
To keep deviation under control, all magnetic objects that could affect the compass should, as a general rule, be kept away from it. The influence of components permanently installed on board can be determined by carrying out a compass check (see box on page 30).
Ideally, a deviation table for the steering compass would be drawn up on this basis, showing the applicable deviation value for the vessel for each magnetic compass bearing.
In some cases, there is also a so-called steering table with adjusted deviation values for when a chart course taken from the nautical chart needs to be converted into a steering course.
How exchange rate conversion works
That brings us to the correct course conversion. Much like the bearing conversion ((see the previous episode on terrestrial positioning) A calculation method has proved effective here, in which calculations are carried out from top to bottom – from the ‘wrong’ to the ‘right’, the latter being the direction that leads to the correct answer:
The signs to be used are also determined by this direction of calculation. If an rwK is to be converted into an MgK, the calculation must be carried out from bottom to top with the signs reversed. The sign for the deviation is taken from the deviation table or the navigation table, together with the relevant degree value. The following applies to magnetic declination: an easterly magnetic declination generally has a positive sign, whilst a westerly magnetic declination has a negative sign.
With this calculation, we have at least already ruled out the so-called misdirection (Fw) – the sum of Abl and MW – as the cause of a possible shift in the survey line. What remains are wind drift and current offset – how these are taken into account will be explained in the next instalment of this series.
Pre-coupling and co-coupling
In practice, plotting can prove useful in many ways. For example, pre-plotting – that is, entering all planned courses along the route, including their bearing and distance, onto the nautical chart in advance – provides a good means of checking the plausibility of the data output by the navigation electronics. This allows errors in programming or within the system to be identified quickly.
To ensure continuous cross-referencing, it has proved useful to regularly record the course settings and logged speeds in the logbook. As a reliable reference point depends on the reliability of the motion data, it is advisable to make a corresponding entry in the logbook and on the nautical chart at least whenever there is a change in course or speed – for example, when the wind dies down or picks up. If frequent manoeuvres are required, navigation in the waters being sailed
If the area is particularly challenging or if conditions are very changeable, it is advisable to use shorter intervals than you would for a long, straight leg with a steady breeze out on the open sea.
Just give it a go. Pairing is fun and leaves impressive patterns on the nautical chart. I like to use these charts as wrapping paper later on, which is always well received. And should the electronics on board ever fail, your conscientious planning and plotting will also prove to be a welcome gift.
Determining speed without a log
As the log generally relies on a functioning on-board electrical and electronic system, an alternative method of measuring speed must be used in the event of a technical failure. This is where the so-called ‘railing log’ can come in handy. To do this, you throw something buoyant – such as an apple – over the side at the bow of the yacht and time how long it takes for the object to reach the stern. A vessel travelling at a speed through the water (STW) of one knot (kn) travels 0.514 metres in one second (1 kn = 1 nm/hr = 1,852 m/hr = 1,852 m/3,600 sec = 0.514 m/sec). This distance is referred to as the meridian tert (MT), which in practice can also be rounded to 0.5 metres. As a general rule: MT per second = nautical miles per hour (= kn).
Now we just need to work out the distance the apple has travelled from the bow to the stern. If the yacht is 12 metres long, this corresponds to 24 MT (12 m ÷ 0.5 m = 24). If the apple took 6 seconds to do this, the yacht is travelling through the water at 4 knots: 24 MT in 6 sec. = 4 MT per sec., which is 4 kn.
Calculate the current magnetic declination
Magnetic declination (MW) describes the angle between true north (rwN) and magnetic north (mwN). Details of the local MW are given as the corresponding angle in degrees and minutes on the nautical chart. In addition, there is the direction: E (East) for an easterly magnetic declination and W for a westerly magnetic declination.
In addition, the reference year is given, along with the annual change in brackets. If the change is in the same direction, it is added; otherwise, it is subtracted.
An example: The specification 3° 16’ E 2022 (12’ W) indicates a mean longitude of 3° 16’ East in the year 2022, with an annual shift of 12’ West (W). For the year 2026, this gives: 3° 16’ E – 4 × 12’ W = 2° 28’ E. However, when entering the course, the figure is always rounded to whole degrees, i.e. to 2° E.
Check compass deviation
In order to take deviation (Abl) into account when setting a course, the navigation compass must be checked accordingly. A compass check is particularly advisable if the ship’s magnetism has changed – for example, due to additional equipment, alterations or technical installations.
The simplest method is to check against a verified bearing line (see previous instalment). For example, if I am positioned with my yacht exactly on a leading light line for which the nautical chart specifies a bearing of 151°, and I point the bow in that direction, then my true course (rwK) corresponds exactly to this value. The true heading (rwK) must now be converted into a magnetic heading (mwK) by applying the local magnetic declination (MW) (rwKMW = mwK). This is then compared with the magnetic compass bearing (MgK). If the steering compass indicates a different value, the following applies: mwK – MgK = deviation.
As an alternative to such a deck bearing, one could also take a bearing on the fires in the line of fire using the steering compass, without aligning the bow with them. In this case, the following applies: mwP – MgP = Abl (where mwP again corresponds to 151°, corrected for MW, and MgP is the magnetic compass bearing). This method also works when taking a bearing on an object with a known position from a secure location, such as directly next to a navigational mark shown on the chart.
This is also the procedure followed when drawing up a deviation table for a deviation dolphin. As the dolphin’s position is known, a reliable true bearing (rwP) can be determined for each landmark also marked on the chart, which is then converted into a magnetic bearing (mwP). The yacht is then turned around the dolphin, and after each 10-degree change of course, a bearing to the landmark is taken using the steering compass. This allows the deviation to be determined for each course – at least in 10-degree increments; for intermediate values, interpolation may be necessary. Alternatively, a bearing disc could be used, the lateral bearing of which is then added to the current compass course to give a MgP.
The values are entered into a suitable table. Some people also draw up a deviation curve and an additional control chart – but we don’t want to overcomplicate things here. It is also possible to have the compass compensated by a qualified specialist.
Book recommendations
Stress-free navigation explains the basics of determining your position using a nautical chart, compass and GPS in clear, step-by-step instructions. The book thus complements the topics of courses, drift and anchorage by covering their practical application on board. Particularly useful are the clearly presented explanations on trip planning, weather, tides and visual navigation.
Seamanship incorporates traditional course and chart work into a significantly broader reference work for cruising sailors. As well as terrestrial, electronic and astronomical navigation, the book also covers weather, tides, maritime law, safety issues and boat handling. It is therefore particularly suitable for readers who do not wish to learn navigation in isolation, but rather to deepen their understanding of it within the context of seamanship as a whole.
How do you check your electronic position indicator whilst on the move – and what role does traditional chart-based navigation still play for you on board?
Sven M. Rutter
Freier Mitarbeiter