Magnetic declination

Last updated September 26, 2024

Magnetic declination (also called magnetic variation) is the angle between magnetic north and true north at a particular location on the Earth's surface. The angle can change over time due to polar wandering.

Somewhat more formally, Bowditch defines variation as "the angle between the magnetic and geographic meridians at any place, expressed in degrees and minutes east or west to indicate the direction of magnetic north from true north. The angle between magnetic and grid meridians is called grid magnetic angle, grid variation, or grivation."^[1]

By convention, declination is positive when magnetic north is east of true north, and negative when it is to the west. Isogonic lines are lines on the Earth's surface along which the declination has the same constant value, and lines along which the declination is zero are called agonic lines. The lowercase Greek letter δ (delta) is frequently used as the symbol for magnetic declination.

The term magnetic deviation is sometimes used loosely to mean the same as magnetic declination, but more correctly it refers to the error in a compass reading induced by nearby metallic objects, such as iron on board a ship or aircraft.

Magnetic declination should not be confused with magnetic inclination , also known as magnetic dip, which is the angle that the Earth's magnetic field lines make with the downward side of the horizontal plane.

Declination change over time and location

Magnetic declination varies both from place to place and with the passage of time. As a traveller cruises the east coast of the United States, for example, the declination varies from 16 degrees west in Maine, to 6 in Florida, to 0 degrees in Louisiana, to 4 degrees east in Texas. The declination at London, UK was one degree west (2014), reducing to zero as of early 2020.^[2]^[3] Reports of measured magnetic declination for distant locations became commonplace in the 17th century, and Edmund Halley made a map of declination for the Atlantic Ocean in 1700.^[4]

In most areas, the spatial variation reflects the irregularities of the flows deep in the Earth; in some areas, deposits of iron ore or magnetite in the Earth's crust may contribute strongly to the declination. Similarly, secular changes to these flows result in slow changes to the field strength and direction at the same point on the Earth.

NIMA Magnetic Variation Map 2000 Mv-world.jpg — NIMA Magnetic Variation Map 2000

The magnetic declination in a given area may (most likely will) change slowly over time, possibly as little as 2–2.5 degrees every hundred years or so, depending on where it is measured. For a location close to the pole like Ivujivik, the declination may change by 1 degree every three years. This may be insignificant to most travellers, but can be important if using magnetic bearings from old charts or metes (directions) in old deeds for locating places with any precision.

As an example of how variation changes over time, see the two charts of the same area (western end of Long Island Sound), below, surveyed 124 years apart. The 1884 chart shows a variation of 8 degrees, 20 minutes West. The 2008 chart shows 13 degrees, 15 minutes West.

Estimated declination contours by year, 1590 to 1990 Earth Magnetic Field Declination from 1590 to 1990.gif — Estimated declination contours by year, 1590 to 1990

Determination

Magnetic declination indicated on an Israeli map. The arrows show true north, grid north and magnetic north, and the caption explains that the average yearly change in the magnetic declination is 0deg03' eastward. IsraelCVFRmag.jpg — Magnetic declination indicated on an Israeli map. The arrows show true north, grid north and magnetic north, and the caption explains that the average yearly change in the magnetic declination is 0°03′ eastward.

Field measurement

The magnetic declination at any particular place can be measured directly by reference to the celestial poles—the points in the heavens around which the stars appear to revolve, which mark the direction of true north and true south. The instrument used to perform this measurement is known as a declinometer.

The approximate position of the north celestial pole is indicated by Polaris (the North Star). In the northern hemisphere, declination can therefore be approximately determined as the difference between the magnetic bearing and a visual bearing on Polaris. Polaris currently traces a circle 0.73° in radius around the north celestial pole, so this technique is accurate to within a degree. At high latitudes a plumb-bob is helpful to sight Polaris against a reference object close to the horizon, from which its bearing can be taken.^[5]

Determination from maps

A rough estimate of the local declination (within a few degrees) can be determined from a general isogonic chart of the world or a continent, such as those illustrated above. Isogonic lines are also shown on aeronautical and nautical charts.

Larger-scale local maps may indicate current local declination, often with the aid of a schematic diagram. Unless the area depicted is very small, declination may vary measurably over the extent of the map, so the data may be referred to a specific location on the map. The current rate and direction of change may also be shown, for example in arcminutes per year. The same diagram may show the angle of grid north (the direction of the map's north–south grid lines), which may differ from true north.

On the topographic maps of the U.S. Geological Survey (USGS), for example, a diagram shows the relationship between magnetic north in the area concerned (with an arrow marked "MN") and true north (a vertical line with a five-pointed star at its top), with a label near the angle between the MN arrow and the vertical line, stating the size of the declination and of that angle, in degrees, mils, or both. However, the diagram itself is not an accurate depiction of the stated numerical declination angle, but is intentionally exaggerated by the cartographer for purposes of legibility.

Models and software

Worldwide empirical model of the deep flows described above are available for describing and predicting features of the Earth's magnetic field, including the magnetic declination for any given location at any time in a given timespan. One such model is World Magnetic Model (WMM) of the US and UK. It is built with all the information available to the map-makers at the start of the five-year period it is prepared for. It reflects a highly predictable rate of change,^{[lower-alpha 1]} and is usually more accurate than a map—which is likely months or years out of date.^{[ citation needed ]} For historical data, the IGRF and GUFM models may be used. Tools for using such models include:

Web apps hosted by the National Geophysical Data Center, a division of the National Oceanic and Atmospheric Administration of the United States.^[7]
C demo program that for WMM by the National Geospatial-Intelligence Agency, along with various other third-party implementations.^[8]

The WMM, IGRF, and GUFM models only describe the magnetic field as emitted at the core-mantle boundary. In practice, the magnetic field is also distorted by the Earth crust, the distortion being magnetic anomaly. For more precise estimates, a larger crust-aware model such as the Enhanced Magnetic Model may be used. (See cited page for a comparison of declination contours.)^[9]

Compass Declination Adjustment

Rotating dial compasses

A magnetic compass points to magnetic north, not geographic (true) north. Compasses of the style commonly used for hiking (i.e., baseplate or protractor compass) utilize a dial or bezel which rotates 360 degrees and is independent of the magnetic needle. To manually establish a declination for true north, the bezel is rotated until the desired number of degrees lie between the bezel's designation N (for North) and the direction (east or west) of magnetic north indicated by the polarized tip of the needle (usually painted red). The entire compass is then rotated until the magnetic needle lies within the outlined orienting arrow or box on the bottom of the capsule, and the course heading (in degrees) is displayed at the base of the direction-of-travel arrow on the baseplate. A compass thus adjusted provides a course bearing in relation to true north instead of magnetic north as long as it remains within an area on the same isogonic line.

In the image at the right, the bezel's N has been aligned with the direction indicated by the magnetic end of the compass needle, adjusted for local declination (10 degrees west of magnetic north). The direction-of-travel arrow on the baseplate thus reflects a true north heading.

After determining local declination, a rotating dial compass may be altered to give true north readings by taping or painting a small delta-point or arrowhead on the compass baseplate west or east of magnetic north pointing to true north on the compass bezel. Other compasses of this design utilize an adjustable declination mechanism integrated with the compass bezel, resulting in true north readings each time the needle is aligned with the orienting arrow.

Floating magnetic card compasses

Compasses that utilize a floating magnetized dial or card are commonly found in marine compasses and in certain models used for land navigation that feature a lensatic or prismatic sighting system. A floating card compass always gives bearings in relation to magnetic north and cannot be adjusted for declination. True north must be computed by adding or subtracting local magnetic declination. The example on the left demonstrates a typical conversion of a magnetic bearing from a floating card compass to a true bearing by adding the magnetic declination. The declination in the example is 14°E (+14°). If, instead, the declination was 14°W (−14°), you would still “add” it to the magnetic bearing to obtain the true bearing: 40°+ (−14°) = 26°.

Conversely, local declination is subtracted from a true bearing to obtain a magnetic bearing. With a local declination of 14°E, a true bearing (i.e. obtained from a map) of 54° is converted to a magnetic bearing (for use in the field) by subtracting declination: 54° – 14° = 40°. If the local declination was 14°W (−14°), it is again subtracted from the true bearing to obtain a magnetic bearing: 54°- (−14°) = 68°.

On aircraft or vessels there are three types of bearing: true, magnetic, and compass bearing. Compass error is divided into two parts, namely magnetic variation and magnetic deviation, the latter originating from magnetic properties of the vessel or aircraft. Variation and deviation are signed quantities. As discussed above, positive (easterly) variation indicates that magnetic north is east of geographic north. Likewise, positive (easterly) deviation indicates that the compass needle is east of magnetic north.^[10]

Compass, magnetic and true bearings are related by:

${\begin{aligned}T&=M+V\\M&=C+D\end{aligned}}$

The general equation relating compass and true bearings is

$T=C+D+V$

Where:

$C$ is Compass bearing
$M$ is Magnetic bearing
$T$ is True bearing
$V$ is magnetic Variation
$D$ is compass Deviation
$V<0,D<0$ for westerly Variation and Deviation
$V>0,D>0$ for easterly Variation and Deviation

For example, if the compass reads 32°, the local magnetic variation is −5.5° (i.e. West) and the deviation is 0.5° (i.e. East), the true bearing will be:

$T=32^{\circ }+(-5.5^{\circ })+0.5^{\circ }=27^{\circ }$

To calculate true bearing from compass bearing (and known deviation and variation):

Compass bearing + deviation = magnetic bearing
Magnetic bearing + variation = true bearing

To calculate compass bearing from true bearing (and known deviation and variation):

True bearing - variation = Magnetic bearing
Magnetic bearing - deviation = Compass bearing

These rules are often combined with the mnemonic "West is best, East is least"; that is to say, add W declinations when going from True bearings to Magnetic bearings, and subtract E ones.

Another simple way to remember which way to apply the correction for continental USA is:

For locations east of the agonic line (zero declination), roughly east of the Mississippi: the magnetic bearing is always bigger.
For locations west of the agonic line (zero declination), roughly west of the Mississippi: the magnetic bearing is always smaller.

Common abbreviations are:

TC = true course;
V = variation (of the Earth's magnetic field);
MC = magnetic course (what the course would be in the absence of local deviation);
D = deviation caused by magnetic material (mostly iron and steel) on the vessel;
CC = compass course.

Deviation

Magnetic deviation is the angle from a given magnetic bearing to the related bearing mark of the compass. Deviation is positive if a compass bearing mark (e.g., compass north) is right of the related magnetic bearing (e.g., magnetic north) and vice versa. For example, if the boat is aligned to magnetic north and the compass' north mark points 3° more east, deviation is +3°. Deviation varies for every compass in the same location and depends on such factors as the magnetic field of the vessel, wristwatches, etc. The value also varies depending on the orientation of the boat. Magnets and/or iron masses can correct for deviation, so that a particular compass accurately displays magnetic bearings. More commonly, however, a correction card lists errors for the compass, which can then be compensated for arithmetically. Deviation must be added to compass bearing to obtain magnetic bearing.

Air navigation

Air navigation is based on magnetic directions thus it is necessary to periodically revise navigational aids to reflect the drift in magnetic declination over time. This requirement applies to VOR beacons, runway numbering, airway labeling, and aircraft vectoring directions given by air traffic control, all of which are based on magnetic direction.

Runways are designated by a number between 01 and 36, which is generally one tenth of the magnetic azimuth of the runway's heading: a runway numbered 09 points east (90°), runway 18 is south (180°), runway 27 points west (270°) and runway 36 points to the north (360° rather than 0°).^[11] However, due to magnetic declination, changes in runway designators have to occur at times to keep their designation in line with the runway's magnetic heading. An exception is made for runways within the Northern Domestic Airspace of Canada; these are numbered relative to true north because proximity to the magnetic North Pole makes the magnetic declination large and changes in it happen at a high pace.

Radionavigation aids located on the ground, such as VORs, are also checked and updated to keep them aligned with magnetic north to allow pilots to use their magnetic compasses for accurate and reliable in-plane navigation.

For simplicity aviation sectional charts are drawn using true north so the entire chart need not be rotated as magnetic declination changes. Instead individual printed elements on the chart (such as VOR compass roses) are updated with each revision of the chart to reflect changes in magnetic declination. For an example refer to the sectional chart slightly west of Winston-Salem, North Carolina in March 2021, magnetic north is 8 degrees west of true north (Note the dashed line marked 8°W).^[12]

When plotting a course, some small aircraft pilots may plot a trip using true north on a sectional chart (map), then convert the true north bearings to magnetic north for in-plane navigation using the magnetic compass. These bearings are then converted on a pre-flight plan by adding or subtracting the local variation displayed on a sectional chart.

GPS systems used for aircraft navigation also display directions in terms of magnetic north even though their intrinsic coordinate system is based on true north. This is accomplished by means of lookup tables inside the GPS which account for magnetic declination. If flying under visual flight rules it is acceptable to fly with an outdated GPS declination database however if flying IFR the database must be updated every 28 days per FAA regulation.

As a fail-safe even the most advanced airliner will still have a magnetic compass in the cockpit. When onboard electronics fail, pilots can still rely on paper charts and the ancient and highly reliable device—the magnetic compass.

Related Research Articles

A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with magnetic north. Other methods may be used, including gyroscopes, magnetometers, and GPS receivers.

An azimuth is the horizontal angle from a cardinal direction, most commonly north, in a local or observer-centric spherical coordinate system.

<span class="mw-page-title-main">Bearing (navigation)</span> Angle between two objects

In navigation, bearing or azimuth is the horizontal angle between the direction of an object and north or another object. The angle value can be specified in various angular units, such as degrees, mils, or grad. More specifically:

A non-directional beacon (NDB) or non-directional radio beacon is a radio beacon which does not include inherent directional information. Radio beacons are radio transmitters at a known location, used as an aviation or marine navigational aid. NDB are in contrast to directional radio beacons and other navigational aids, such as low-frequency radio range, VHF omnidirectional range (VOR) and tactical air navigation system (TACAN).

A compass rose, sometimes called a wind rose, rose of the winds or compass star, is a figure on a compass, map, nautical chart, or monument used to display the orientation of the cardinal directions and their intermediate points. It is also the term for the graduated markings found on the traditional magnetic compass. Today, a form of compass rose is found on, or featured in, almost all navigation systems, including nautical charts, non-directional beacons (NDB), VHF omnidirectional range (VOR) systems, global-positioning systems (GPS), and similar equipment.

An automatic direction finder (ADF) is a marine or aircraft radio-navigation instrument that automatically and continuously displays the relative bearing from the ship or aircraft to a suitable radio station. ADF receivers are normally tuned to aviation or marine NDBs operating in the LW band between 190 – 535 kHz. Like RDF units, most ADF receivers can also receive medium wave (AM) broadcast stations, though these are less reliable for navigational purposes.

<span class="mw-page-title-main">Meridian (geography)</span> Line between the poles with the same longitude

In geography and geodesy, a meridian is the locus connecting points of equal longitude, which is the angle east or west of a given prime meridian. In other words, it is a line of longitude. The position of a point along the meridian is given by that longitude and its latitude, measured in angular degrees north or south of the Equator. On a Mercator projection or on a Gall-Peters projection, each meridian is perpendicular to all circles of latitude. A meridian is half of a great circle on Earth's surface. The length of a meridian on a modern ellipsoid model of Earth has been estimated as 20,003.93 km (12,429.87 mi).

<span class="mw-page-title-main">Magnetic deviation</span>

Magnetic deviation is the error induced in a compass by local magnetic fields, which must be allowed for, along with magnetic declination, if accurate bearings are to be calculated.

Longitude by chronometer is a method, in navigation, of determining longitude using a marine chronometer, which was developed by John Harrison during the first half of the eighteenth century. It is an astronomical method of calculating the longitude at which a position line, drawn from a sight by sextant of any celestial body, crosses the observer's assumed latitude. In order to calculate the position line, the time of the sight must be known so that the celestial position i.e. the Greenwich Hour Angle and Declination, of the observed celestial body is known. All that can be derived from a single sight is a single position line, which can be achieved at any time during daylight when both the sea horizon and the sun are visible. To achieve a fix, more than one celestial body and the sea horizon must be visible. This is usually only possible at dawn and dusk.

Diver navigation, termed "underwater navigation" by scuba divers, is a set of techniques—including observing natural features, the use of a compass, and surface observations—that divers use to navigate underwater. Free-divers do not spend enough time underwater for navigation to be important, and surface supplied divers are limited in the distance they can travel by the length of their umbilicals and are usually directed from the surface control point. On those occasions when they need to navigate they can use the same methods used by scuba divers.

Magnetic dip, dip angle, or magnetic inclination is the angle made with the horizontal by Earth's magnetic field lines. This angle varies at different points on Earth's surface. Positive values of inclination indicate that the magnetic field of Earth is pointing downward, into Earth, at the point of measurement, and negative values indicate that it is pointing upward. The dip angle is in principle the angle made by the needle of a vertically held compass, though in practice ordinary compass needles may be weighted against dip or may be unable to move freely in the correct plane. The value can be measured more reliably with a special instrument typically known as a dip circle.

<span class="mw-page-title-main">Brunton, Inc.</span>

Brunton Inc. is now Brunton International LLC after its recent acquisition in late 2021. They are a manufacturer of navigation tools including recreational compasses, navigational equipment, and geology and survey instruments. They are located in Riverton, Wyoming.

<span class="mw-page-title-main">World Magnetic Model</span> Large spatial-scale model of the Earths magnetic field

The World Magnetic Model (WMM) is a large spatial-scale representation of the Earth's magnetic field. It was developed jointly by the US National Geophysical Data Center and the British Geological Survey. The data and updates are issued by the US National Geospatial-Intelligence Agency and the UK Defence Geographic Centre.

Position resection and intersection are methods for determining an unknown geographic position by measuring angles with respect to known positions. In resection, the one point with unknown coordinates is occupied and sightings are taken to the known points; in intersection, the two points with known coordinates are occupied and sightings are taken to the unknown point.

The north magnetic pole, also known as the magnetic north pole, is a point on the surface of Earth's Northern Hemisphere at which the planet's magnetic field points vertically downward. There is only one location where this occurs, near the geographic north pole. The geomagnetic north pole is the northern antipodal pole of an ideal dipole model of the Earth's magnetic field, which is the most closely fitting model of Earth's actual magnetic field.

The history of geomagnetism is concerned with the history of the study of Earth's magnetic field. It encompasses the history of navigation using compasses, studies of the prehistoric magnetic field, and applications to plate tectonics.

In navigation, the heading of a vessel or aircraft is the compass direction in which the craft's bow or nose is pointed. Note that the heading may not necessarily be the direction that the vehicle actually travels, which is known as its course or track. Any difference between the heading and course is due to the motion of the underlying medium, the air or water, or other effects like skidding or slipping. The difference is known as the drift, and can be determined by the wind triangle. At least seven ways to measure the heading of a vehicle have been described.

An azimuth compass is a nautical instrument used to measure the magnetic azimuth, the angle of the arc on the horizon between the direction of the Sun or some other celestial object and the magnetic north. This can be compared to the true azimuth obtained by astronomical observation to determine the magnetic declination, the amount by which the reading of a ship's compass must be adjusted to obtain an accurate reading. Azimuth compasses were important in the period before development of the reliable chronometers needed to determine a vessel's exact position from astronomical observations.

The compass is a magnetometer used for navigation and orientation that shows direction in regards to the geographic cardinal points. The structure of a compass consists of the compass rose, which displays the four main directions on it: East (E), South (S), West (W) and North (N). The angle increases in the clockwise position. North corresponds to 0°, so east is 90°, south is 180° and west is 270°.

Burt's solar compass or astronomical compass/sun compass is a surveying instrument that makes use of the Sun's direction instead of magnetism. William Austin Burt invented his solar compass in 1835. The solar compass works on the principle that the direction to the Sun at a specified time can be calculated if the position of the observer on the surface of the Earth is known, to a similar precision. The direction can be described in terms of the angle of the Sun relative to the axis of rotation of the planet.

References

↑ This rate of change is known as the geomagnetic secular variation, and current models using a constant variation over five-year periods are on average (root mean square) off by 15 arcminutes at the end of each forecast.^[6]

↑ Bowditch, Nathaniel (2002). American Practical Navigator. Paradise Cay Publications. p. 849. ISBN 9780939837540.
↑ "Find the magnetic declination at your location". Magnetic-Declination.com. Retrieved 6 December 2013.
↑ "World Magnetic Model - Epoch 2020 -Declination" (PDF).
↑ Government of Canada, Natural Resources Canada. "Magnetic declination". www.geomag.nrcan.gc.ca. Retrieved 2021-09-30.
↑ Magnetic declination, what it is, how to compensate., archived from the original on 2010-01-07, retrieved 2010-03-03
↑ Fournier, Alexandre; Aubert, Julien; Lesur, Vincent; Thébault, Erwan (December 2021). "Physics-based secular variation candidate models for the IGRF". Earth, Planets and Space. 73 (1): 190. Bibcode:2021EP&S...73..190F. doi: 10.1186/s40623-021-01507-z . S2CID 239022300.
↑ "Estimated Value of Magnetic Declination". Geomagnetism. NOAA National Geophysical Data Center. Retrieved 6 December 2013.
↑ Meyer, Brian (8 February 2022). "World Magnetic Model - Software Download". www.ngdc.noaa.gov.
↑ National Centers for Environmental Information (NCEI) (10 March 2022). "Enhanced Magnetic Model (EMM)". www.ngdc.noaa.gov.
↑ Willemsen, Diederik. "Compass navigation". SailingIssues. Retrieved 4 January 2020.
↑ Federal Aviation Administration Aeronautical Information Manual, Chapter 2, Section 3 Airport Marking Aids and Signs part 3b Archived 2012-01-18 at the Wayback Machine
↑ See also CUNY

External links

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[7] This rate of change is known as the geomagnetic secular variation, and current models using a constant variation over five-year periods are on average (root mean square) off by 15 arcminutes at the end of each forecast.^[6]

[1] Bowditch, Nathaniel (2002). American Practical Navigator. Paradise Cay Publications. p. 849. ISBN 9780939837540.

[2] "Find the magnetic declination at your location". Magnetic-Declination.com. Retrieved 6 December 2013.

[3] "World Magnetic Model - Epoch 2020 -Declination" (PDF).

[4] Government of Canada, Natural Resources Canada. "Magnetic declination". www.geomag.nrcan.gc.ca. Retrieved 2021-09-30.

[5] Magnetic declination, what it is, how to compensate., archived from the original on 2010-01-07, retrieved 2010-03-03

[6] Fournier, Alexandre; Aubert, Julien; Lesur, Vincent; Thébault, Erwan (December 2021). "Physics-based secular variation candidate models for the IGRF". Earth, Planets and Space. 73 (1): 190. Bibcode:2021EP&S...73..190F. doi: 10.1186/s40623-021-01507-z . S2CID 239022300.

[8] "Estimated Value of Magnetic Declination". Geomagnetism. NOAA National Geophysical Data Center. Retrieved 6 December 2013.

[9] Meyer, Brian (8 February 2022). "World Magnetic Model - Software Download". www.ngdc.noaa.gov.

[10] National Centers for Environmental Information (NCEI) (10 March 2022). "Enhanced Magnetic Model (EMM)". www.ngdc.noaa.gov.

[11] Willemsen, Diederik. "Compass navigation". SailingIssues. Retrieved 4 January 2020.

[12] Federal Aviation Administration Aeronautical Information Manual, Chapter 2, Section 3 Airport Marking Aids and Signs part 3b Archived 2012-01-18 at the Wayback Machine

[13] See also CUNY

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