See the **previous chapter… **

**Course overview: goals and introduction****Positions: latitude, longitude, nautical mile, scale, knots****Nautical chart: coordinates, positions, courses, chart symbols, projections**

**Compass: variation, deviation, true • magnetic • compass courses****Plotting and piloting: LOPs, (running) fix, dead reckoning, leeway, CTS, CTW, COG****Advanced piloting: double angle on the bow • four point • special angle fix, distance of horizon, dipping range, vertical sextant angle, radians, estimation of distances****Astronomical origin of tides: diurnal, semi-diurnal, sysygy, spring, neap, axial tilt Earth, apsidal • nodal precession, declination Moon and Sun, elliptical orbits, lunar nodes****Tides: tidal height prediction, chart datums, tidal curves, secondary ports****Tidal streams and currents: diamonds, Course to Steer, Estimated Position****Aids to navigation: buoys, leading lights, ranges, characteristics, visibility****Lights and shapes: vessels sailing, anchoring, towing, fishing, NUC, RAM, dredging**

# Compass navigation

## Marine compass

In **China** compasses have been in use since the Han dynasty (2nd century **BCE** to 2nd century CE) when they were referred to as “south-pointers”. However, at first these magnets were only employed for **geomancy** much like Feng Shui.

Eventually, during the Sung dynasty (1000 CE) many trading ships were then able to sail as far as Saudi Arabia applying compasses for actual *marine navigation*.
As a direct result, between 1405 and 1433, Emperor Chu Ti's Treasure Fleet of the Dragon Throne ruled the entire South Pacific and the Indian Ocean; a territory that ranges from Korea and Japan to the eastern coast of Africa.

At this time Western mariners were still rather incognizant of the navigational application of the magnet. The first treatise on the magnet itself was written by **Petrus Peregrinus de Maricourt** : “De Magnete” (1269). And though its nautical use was already mentioned in 1187 by the English monk Alexander Neckham, the use onboard only came about around the 13th and 14th century in the Mediterranean Sea.

In 1545 **Pedro de Medina** (Sevilla 1493-1567) wrote the Spanish standard work “Arte de Navegar” on marine compass navigation. This masterpiece was first translated in Dutch (1580) and was – O Irony – put into practice by Jacob van Heemskerk when the Dutch destroyed the Spanish fleet near Gibraltar in 1607. A drawback, obviously, was Van Heemskerk's own death during this victory.

## Magnetic Variation

In the fin-de-siècle of the 16th century mariners believed that the magnetic north pole coincided with the geographic north pole. Any suggestion otherwise had been denied by Pedro de Medina.

Magnetic observations made by explorers in subsequent decades showed however that these suggestions were true.

But it took until the early nineteenth century, to pinpoint the magnetic north pole somewhere in Arctic Canada (78° N 104° W). From then on the angle between the true north and the **magnetic north** could be precisely corrected for. This correction angle is called **magnetic variation** or **magnetic declination**.

2011 3° 59' W

2012 3° 51' W

2013 3° 43' W

2014 3° 35' W

2015 3° 27' W

2016 3° 19' W

2017 3° 11' W

2018 3° 03' W

2019 2° 55' W

2020 2° 47' W

2021 2° 39' W

2022 2° 31' W

2023 2° 23' W

2024 2° 15' W

2025 2° 07' W

2026 2° 01' W

It is believed that the Earth's magnetic field is produced by electrical currents that originate in the hot, liquid, outer core of the rotating Earth. The flow of electric currents in this core is continually changing, so the magnetic field produced by those currents also changes. This means that at the surface of the earth, both the strength and direction of the magnetic field will vary over the years. This gradual change is called the **secular variation** of the magnetic field.
Therefore, the encountered magnetic variation not only changes with location, but also varies over time.

The correction for magnetic variation for your location is shown on the *nearest* **nautical chart's compass rose****nautical chart's compass rose**.
In this example we find a variation of 4° 15' W in 2009, with an indicated annual correction of 0° 08' E. Hence, in 2011 this variation is estimated to be 3° 59' (almost 4° west), and for 2020 the estimate is 2° 47' W.

This means that if we sail 90° on the chart i.e. the “true course”, the steering compass would read 94° in 2009, and almost 93° in 2020 (and e.g. 92° in 2026, see the list on the right).

Note that the “true course” is often shown as COG “Course over Ground” or CMG “Course Made Good” on your GPS plotter.

Another example: let's say the compass rose on the nautical chart gives a variation of 2° 50' E in 2022, with a correction of 0° 04' E per year. In 2024 this variation is estimated to be 2° 58', nearly 3° east; if we sail 90° on the chart, the steering compass would read 87°.

A paper or digitized nautical chart can feature multiple compass roses: use the nearest ^{ } one to obtain the magnetic variation.

## Correcting for variation

The overlayed compass roses aboveon the right illustrate the difference between true north and magnetic north when the magnetic variation “**var**” is 10° west.

From the image we find: **tc = cc + var**

in which “**cc**” and “**tc**” stand for “compass course” and “true course”, respectively.

To convert a **true course into a compass course** we need first assign a “ **−** ” to a western and a “ **+** ” to an eastern variation. Note that this makes *sense* because of the clockwise ↻ direction of the compass rose.

Here, the inner circle is turned 10° anticlockwise, hence −10°.
Which is the same as 350° clockwise [cc = 225° − (+350°) = −125° and + 360° = 235°].

Now, use the same but re-written equation:

**cc = tc − var**

**235° = 225° − (−10°)**

So, to sail a true course of 225°, the helmsperson has to steer a compass course of 235°.

To convert a **compass course into a true course** we can use the original equation. If we have steered a compass course of 200°, we have to plot a true course of 203° in the chart if the variation is 3° east [tc = cc + var = 200° + (+3°) = 203°],
or a true course of 190° if the variation is 10° west [tc = cc + var = 200° + (−10°) = 190°].

## Magnetic deviation

Magnetic deviation is the second commonly correctable error – this time *within* the ship – which is caused by magnetic forces brought on by pieces of metal, such as an engine or an anchor. Moreover, cockpit plotters and other electric equipment or wiring – if too close to the compass – can also introduce a compass error.

Pertinently, the deviation varies with the ship's heading (HDG), the angle of the yacht's centre line with the true north, resulting in a deviation table / chart as shown below.

The vertical axis states the correction “**dev**” in degrees west or east, where east is again positive.

The horizontal axis states the ship's heading “**cc**” in degrees divided by ten. Thus, when steering a compass course of 220°, the deviation will be 4° W.

Note, that on most modern sailing yachts the deviation will be less than ±3°.

When a steering compass is newly installed it often shows larger deviations than this and will require compensation by carefully placing small magnets around the compass. It is the remaining error that is shown in your deviation table.

You should check the table every now and then by placing the yacht in the line of a pair of **leading lights****leading lights**
and turning her 360 degrees, a time-honoured method known as “swinging the compass”.

Conversely, a *hand bearing* compass does not have a deviation table, ideally bearings should be taken as far from metal and electrical wiring as possible.

## Correcting for both deviation and variation

Converting a **compass course into a true course**, we can still use our equation but we need to add the correction for deviation:

**cc + var + dev = tc**

**Example 1**: we sail a compass course of 330°, with a corresponding deviation of +3°, see**table**, and from the nautical chart we find that at our location the variation is +3°;

**330° cc + 3° var + 3° dev = ?° tc**

giving a true course of 336° which we can plot in the chart.**Example 2**: we change our compass course to 220°, the deviation is −4° (table) and the variation is still +3° (chart);

**220° cc + 3° var + −4° dev = ?° tc**

giving a true course of 219°.**Example 3**: after sailing extensively our compass course is still 220°, therefore the deviation is still −4° (table), but since we are at a new location the nautical chart specifies a variation of −10°;

**220° cc + −10° var + −4° dev = ?° tc**

giving a true course of 206°.

Converting a **true course into a compass course** – finding a Course to Steer (CTS) – is a little less straight forward, but it is still done with the same equation.

**Example 4**: the true course drawn in the chart is 305° and the local variation is +3° (found in the nautical chart), yet we don't know the deviation;

**?° cc + 3° var + ?° dev = 305° tc**

Luckily, we can rewrite this so this reads:

**cc + dev = 305° tc − + 3° var = 302°**

In plain English: the difference between the true course and the variation (305 − + 3) = 302 should also be the summation of the compass course and the deviation. So, we can tell our helms person to steer 300°, since with a cc of 300° we have a deviation of +2°,as can be deduced from the**deviation table**.**Example 5**: the true course from the chart is 150° and we have a western variation of 7 degrees (−7°). We will use the rewritten equation to get:

**150° tc − − 7° var = cc + dev = 157°**

From the deviation table we find a compass course of 160° with a deviation of −3°.

Voilà!

Lateron in this course we will discuss how to **compensate for leeway and find CTS****compensate for leeway and find CTS** and to **compensate for tidal streams and find CTS****compensate for tidal streams and find CTS**.

## Magnetic course

The **magnetic course** (mc) is the course after magnetic variation has been considered, but without compensation for magnetic deviation. This means that we are dealing with the rewritten equation from above:
**tc − var = cc + dev = mc**.

Magnetic courses are used for three reasons:

- To convert a true course into a compass course like we saw in the last paragraph.
- On vessels with more than one steering compass, also more deviation tables are in use; hence only a magnetic or true course is plotted in the chart.
- Bearings taken with a hand bearing compass often don't require a correction for deviation, and are therefore useful to plot in the chart as magnetic courses.

Note, that the actual course lines the navigator draws (plots) in the chart are always true courses, unless labeled as mc or cc.

In **chapter 4****chapter 4**
we will be plotting courses in the chart.

To summarise, we have three types of “north” (true, magnetic and compass north), correspondingly we have three types of courses: tc, mc and cc. All these are related by deviation and variation.

## Glossary

**Variation**: the angle between the magnetic north pole and the geographic north pole. Also called the**magnetic declination**. Note that magnetic*inclination*is the angle between the magnetic field and the horizontal plane. At the poles the field dips into the earth. Therefore, a corrected compass can only be used in one hemisphere.**Secular variation**: the change of magnetic declination in time with respect to both strength and direction of the earth's magnetic field; view these declination / variation maps with isogonic lines:**world – interactive and historical declination**and an**animated-in-time GIF**.

“Isogonic declination” is defined as lines of equal declination, and keep in mind that declination is exchangeable with variation.**West “ − ”, east “ + ”**: west variations / declinations as well as west deviations are designated with a negative sign by convention due to the compass card's clockwise ↻ direction.**Deviation**: the compass error caused by electrical currents and / or metal objects.**Deviation table**: a table containing deviations in degrees versus the ship's heading (compass course) in degrees; usually plotted in a graph / card.**True course**: the course corrected for compass errors and plotted in the chart, tc and is equal to Course over Ground (COG) or Course Made Good (CMG). Note that COG is an instantenous value, whereas CMG is the combined net course after some period of time and maybe several course changes.**Compass course**: (cc) the course which is corrected for both variation and deviation.**Magnetic course**: (mc) the course which is only corrected for variation.**cc + var + dev = tc**: this equation shows the connection between the compass course, its errors and the true course. It can also be read as: tc − var = cc + dev.

See the **next chapter… **

**Course overview: goals and introduction****Positions: latitude, longitude, nautical mile, scale, knots****Nautical chart: coordinates, positions, courses, chart symbols, projections**

**Compass: variation, deviation, true • magnetic • compass courses****Plotting and piloting: LOPs, (running) fix, dead reckoning, leeway, CTS, CTW, COG****Advanced piloting: double angle on the bow • four point • special angle fix, distance of horizon, dipping range, vertical sextant angle, radians, estimation of distances****Astronomical origin of tides: diurnal, semi-diurnal, sysygy, spring, neap, axial tilt Earth, apsidal • nodal precession, declination Moon and Sun, elliptical orbits, lunar nodes****Tides: tidal height prediction, chart datums, tidal curves, secondary ports****Tidal streams and currents: diamonds, Course to Steer, Estimated Position****Aids to navigation: buoys, leading lights, ranges, characteristics, visibility****Lights and shapes: vessels sailing, anchoring, towing, fishing, NUC, RAM, dredging**

Also you can download the **exercises + answers PDF **