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103-411: A magnetic field is the physical phenomenon produced by moving electric charges and exhibited by ferrous materials. Magnetic field or magnetic fields may also refer to: Magnetic field A magnetic field (sometimes called B-field ) is a physical field that describes the magnetic influence on moving electric charges , electric currents , and magnetic materials. A moving charge in

206-473: A magnetic monopole is a hypothetical particle (or class of particles) that physically has only one magnetic pole (either a north pole or a south pole). In other words, it would possess a "magnetic charge" analogous to an electric charge. Magnetic field lines would start or end on magnetic monopoles, so if they exist, they would give exceptions to the rule that magnetic field lines neither start nor end. Some theories (such as Grand Unified Theories ) have predicted

309-459: A magnetometer . Important classes of magnetometers include using induction magnetometers (or search-coil magnetometers) which measure only varying magnetic fields, rotating coil magnetometers , Hall effect magnetometers, NMR magnetometers , SQUID magnetometers , and fluxgate magnetometers . The magnetic fields of distant astronomical objects are measured through their effects on local charged particles. For instance, electrons spiraling around

412-469: A defined initial bearing. That is, upon taking an initial bearing, one proceeds along the same bearing, without changing the direction as measured relative to true or magnetic north. Most modern navigation relies primarily on positions determined electronically by receivers collecting information from satellites. Most other modern techniques rely on finding intersecting lines of position or LOP. A line of position can refer to two different things, either

515-543: A degree or so. Similar to latitude, the longitude of a place on Earth is the angular distance east or west of the prime meridian or Greenwich meridian . Longitude is usually expressed in degrees (marked with °) ranging from 0° at the Greenwich meridian to 180° east and west. Sydney , for example, has a longitude of about 151° east . New York City has a longitude of 74° west . For most of history, mariners struggled to determine longitude. Longitude can be calculated if

618-478: A distance produces a circle or arc of position. Circles, arcs, and hyperbolae of positions are often referred to as lines of position. If the navigator draws two lines of position, and they intersect he must be at that position. A fix is the intersection of two or more LOPs. If only one line of position is available, this may be evaluated against the dead reckoning position to establish an estimated position. Lines (or circles) of position can be derived from

721-587: A few meters using time signals transmitted along a line of sight by radio from satellites . Receivers on the ground with a fixed position can also be used to calculate the precise time as a reference for scientific experiments. As of October 2011, only the United States NAVSTAR Global Positioning System (GPS) and the Russian GLONASS are fully globally operational GNSSs. The European Union 's Galileo positioning system

824-419: A field line produce synchrotron radiation that is detectable in radio waves . The finest precision for a magnetic field measurement was attained by Gravity Probe B at 5 aT ( 5 × 10  T ). The field can be visualized by a set of magnetic field lines , that follow the direction of the field at each point. The lines can be constructed by measuring the strength and direction of the magnetic field at

927-407: A hundred years, from about 1767 until about 1850, mariners lacking a chronometer used the method of lunar distances to determine Greenwich time to find their longitude. A mariner with a chronometer could check its reading using a lunar determination of Greenwich time. In navigation, a rhumb line (or loxodrome) is a line crossing all meridians of longitude at the same angle, i.e. a path derived from

1030-409: A large number of points (or at every point in space). Then, mark each location with an arrow (called a vector ) pointing in the direction of the local magnetic field with its magnitude proportional to the strength of the magnetic field. Connecting these arrows then forms a set of magnetic field lines. The direction of the magnetic field at any point is parallel to the direction of nearby field lines, and

1133-402: A line on a chart or a line between the observer and an object in real life. A bearing is a measure of the direction to an object. If the navigator measures the direction in real life, the angle can then be drawn on a nautical chart and the navigator will be somewhere on that bearing line on the chart. In addition to bearings, navigators also often measure distances to objects. On the chart,

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1236-420: A magnetic H -field is produced by fictitious magnetic charges that are spread over the surface of each pole. These magnetic charges are in fact related to the magnetization field M . The H -field, therefore, is analogous to the electric field E , which starts at a positive electric charge and ends at a negative electric charge. Near the north pole, therefore, all H -field lines point away from

1339-648: A magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet 's magnetic field pulls on ferromagnetic materials such as iron , and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism , diamagnetism , and antiferromagnetism , although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of

1442-494: A magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, called a vector field (more precisely, a pseudovector field). In electromagnetics , the term magnetic field is used for two distinct but closely related vector fields denoted by the symbols B and H . In the International System of Units , the unit of B , magnetic flux density,

1545-424: A magnetized material, the quantities on each side of this equation differ by the magnetization field of the material. Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin . Magnetic fields and electric fields are interrelated and are both components of the electromagnetic force , one of

1648-429: A magnetized object is divided in half, a new pole appears on the surface of each piece, so each has a pair of complementary poles. The magnetic pole model does not account for magnetism that is produced by electric currents, nor the inherent connection between angular momentum and magnetism. The pole model usually treats magnetic charge as a mathematical abstraction, rather than a physical property of particles. However,

1751-402: A north and a south pole. The magnetic field of permanent magnets can be quite complicated, especially near the magnet. The magnetic field of a small straight magnet is proportional to the magnet's strength (called its magnetic dipole moment m ). The equations are non-trivial and depend on the distance from the magnet and the orientation of the magnet. For simple magnets, m points in

1854-450: A number of stars in succession to give a series of overlapping lines of position. Where they intersect is the celestial fix. The Moon and Sun may also be used. The Sun can also be used by itself to shoot a succession of lines of position (best done around local noon) to determine a position. In order to accurately measure longitude, the precise time of a sextant sighting (down to the second, if possible) must be recorded. Each second of error

1957-399: A particularly good navigation system for ships and aircraft that might be flying at a distance from land. RDFs works by rotating a directional antenna and listening for the direction in which the signal from a known station comes through most strongly. This sort of system was widely used in the 1930s and 1940s. RDF antennas are easy to spot on German World War II aircraft, as loops under

2060-418: A radio time signal. Times and frequencies of radio time signals are listed in publications such as Radio Navigational Aids . The second critical component of celestial navigation is to measure the angle formed at the observer's eye between the celestial body and the sensible horizon. The sextant, an optical instrument, is used to perform this function. The sextant consists of two primary assemblies. The frame

2163-400: A single object," "two or more bearings," "tangent bearings," and "two or more ranges." Radar can also be used with ECDIS as a means of position fixing with the radar image or distance/bearing overlaid onto an Electronic nautical chart . Parallel indexing is a technique defined by William Burger in the 1957 book The Radar Observer's Handbook . This technique involves creating a line on

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2266-500: A small distance vector d , such that m = q m   d . The magnetic pole model predicts correctly the field H both inside and outside magnetic materials, in particular the fact that H is opposite to the magnetization field M inside a permanent magnet. Since it is based on the fictitious idea of a magnetic charge density , the pole model has limitations. Magnetic poles cannot exist apart from each other as electric charges can, but always come in north–south pairs. If

2369-452: A small magnet is proportional both to the applied magnetic field and to the magnetic moment m of the magnet: τ = m × B = μ 0 m × H , {\displaystyle {\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B} =\mu _{0}\mathbf {m} \times \mathbf {H} ,\,} where × represents the vector cross product . This equation includes all of

2472-404: A sufficient depth of water below the hull as well as a consideration for squat . It may also involve navigating a ship within a river, canal or channel in close proximity to land. A military navigation team will nearly always consist of several people. A military navigator might have bearing takers stationed at the gyro repeaters on the bridge wings for taking simultaneous bearings, while

2575-408: A torque proportional to the distance (perpendicular to the force) between them. With the definition of m as the pole strength times the distance between the poles, this leads to τ = μ 0 m H sin  θ , where μ 0 is a constant called the vacuum permeability , measuring 4π × 10 V · s /( A · m ) and θ is the angle between H and m . Mathematically, the torque τ on

2678-413: A variety of sources: There are some methods seldom used today such as "dipping a light" to calculate the geographic range from observer to lighthouse. Methods of navigation have changed through history. Each new method has enhanced the mariner's ability to complete his voyage. One of the most important judgments the navigator must make is the best method to use. Some types of navigation are depicted in

2781-449: Is Pulsar navigation , which compares the X-ray bursts from a collection of known pulsars in order to determine the position of a spacecraft. This method has been tested by multiple space agencies, such as NASA and ESA . A radio direction finder or RDF is a device for finding the direction to a radio source. Due to radio's ability to travel very long distances "over the horizon", it makes

2884-501: Is tesla (symbol: T). The Gaussian-cgs unit of B is the gauss (symbol: G). (The conversion is 1 T ≘ 10000 G. ) One nanotesla corresponds to 1 gamma (symbol: γ). The magnetic H field is defined: H ≡ 1 μ 0 B − M {\displaystyle \mathbf {H} \equiv {\frac {1}{\mu _{0}}}\mathbf {B} -\mathbf {M} } where μ 0 {\displaystyle \mu _{0}}

2987-436: Is a quartz crystal oscillator. The quartz crystal is temperature compensated and is hermetically sealed in an evacuated envelope. A calibrated adjustment capability is provided to adjust for the aging of the crystal. The chronometer is designed to operate for a minimum of one year on a single set of batteries. Observations may be timed and ship's clocks set with a comparing watch, which is set to chronometer time and taken to

3090-425: Is a rigid triangular structure with a pivot at the top and a graduated segment of a circle, referred to as the "arc", at the bottom. The second component is the index arm, which is attached to the pivot at the top of the frame. At the bottom is an endless vernier which clamps into teeth on the bottom of the "arc". The optical system consists of two mirrors and, generally, a low power telescope. One mirror, referred to as

3193-552: Is a specific example of a general rule that magnets are attracted (or repulsed depending on the orientation of the magnet) into regions of higher magnetic field. Any non-uniform magnetic field, whether caused by permanent magnets or electric currents, exerts a force on a small magnet in this way. The details of the Amperian loop model are different and more complicated but yield the same result: that magnetic dipoles are attracted/repelled into regions of higher magnetic field. Mathematically,

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3296-434: Is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks. All navigational techniques involve locating the navigator's position compared to known locations or patterns. Navigation, in a broader sense, can refer to any skill or study that involves the determination of position and direction . In this sense, navigation includes orienteering and pedestrian navigation. In

3399-1027: Is considered to be the V-2 guidance system deployed by the Germans in 1942. However, inertial sensors are traced to the early 19th century. The advantages INSs led their use in aircraft, missiles, surface ships and submarines. For example, the U.S. Navy developed the Ships Inertial Navigation System (SINS) during the Polaris missile program to ensure a reliable and accurate navigation system to initial its missile guidance systems. Inertial navigation systems were in wide use until satellite navigation systems (GPS) became available. INSs are still in common use on submarines (since GPS reception or other fix sources are not possible while submerged) and long-range missiles. Not to be confused with satellite navigation, which depends upon satellites to function, space navigation refers to

3502-441: Is equivalent to 15 seconds of longitude error, which at the equator is a position error of .25 of a nautical mile, about the accuracy limit of manual celestial navigation. The spring-driven marine chronometer is a precision timepiece used aboard ship to provide accurate time for celestial observations. A chronometer differs from a spring-driven watch principally in that it contains a variable lever device to maintain even pressure on

3605-491: Is in the opposite direction. If both the speed and the charge are reversed then the direction of the force remains the same. For that reason a magnetic field measurement (by itself) cannot distinguish whether there is a positive charge moving to the right or a negative charge moving to the left. (Both of these cases produce the same current.) On the other hand, a magnetic field combined with an electric field can distinguish between these, see Hall effect below. The first term in

3708-417: Is no net force on that magnet since the force is opposite for opposite poles. If, however, the magnetic field of the first magnet is nonuniform (such as the H near one of its poles), each pole of the second magnet sees a different field and is subject to a different force. This difference in the two forces moves the magnet in the direction of increasing magnetic field and may also cause a net torque. This

3811-478: Is not affected by adverse weather conditions and it cannot be detected or jammed. Its disadvantage is that since the current position is calculated solely from previous positions and motion sensors, its errors are cumulative, increasing at a rate roughly proportional to the time since the initial position was input. Inertial navigation systems must therefore be frequently corrected with a location 'fix' from some other type of navigation system. The first inertial system

3914-422: Is particularly true for magnetic fields, such as those due to electric currents, that are not generated by magnetic materials. A realistic model of magnetism is more complicated than either of these models; neither model fully explains why materials are magnetic. The monopole model has no experimental support. The Amperian loop model explains some, but not all of a material's magnetic moment. The model predicts that

4017-449: Is particularly useful due to their high power and location near major cities. Decca , OMEGA , and LORAN-C are three similar hyperbolic navigation systems. Decca was a hyperbolic low frequency radio navigation system (also known as multilateration ) that was first deployed during World War II when the Allied forces needed a system which could be used to achieve accurate landings. As

4120-455: Is reasonable for the navigator to simply monitor the progress of the ship along the chosen track, visually ensuring that the ship is proceeding as desired, checking the compass, sounder and other indicators only occasionally. If a pilot is aboard, as is often the case in the most restricted of waters, his judgement can generally be relied upon, further easing the workload. But should the ECDIS fail,

4223-449: Is strictly only valid for magnets of zero size, but is often a good approximation for not too large magnets. The magnetic force on larger magnets is determined by dividing them into smaller regions each having their own m then summing up the forces on each of these very small regions . If two like poles of two separate magnets are brought near each other, and one of the magnets is allowed to turn, it promptly rotates to align itself with

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4326-418: Is that of maximum increase of m · B . The dot product m · B = mB cos( θ ) , where m and B represent the magnitude of the m and B vectors and θ is the angle between them. If m is in the same direction as B then the dot product is positive and the gradient points "uphill" pulling the magnet into regions of higher B -field (more strictly larger m · B ). This equation

4429-547: Is the tesla (in SI base units: kilogram per second squared per ampere), which is equivalent to newton per meter per ampere. The unit of H , magnetic field strength, is ampere per meter (A/m). B and H differ in how they take the medium and/or magnetization into account. In vacuum , the two fields are related through the vacuum permeability , B / μ 0 = H {\displaystyle \mathbf {B} /\mu _{0}=\mathbf {H} } ; in

4532-446: Is the vacuum permeability , and M is the magnetization vector . In a vacuum, B and H are proportional to each other. Inside a material they are different (see H and B inside and outside magnetic materials ). The SI unit of the H -field is the ampere per metre (A/m), and the CGS unit is the oersted (Oe). An instrument used to measure the local magnetic field is known as

4635-471: The Barnett effect or magnetization by rotation . Rotating the loop faster (in the same direction) increases the current and therefore the magnetic moment, for example. Specifying the force between two small magnets is quite complicated because it depends on the strength and orientation of both magnets and their distance and direction relative to each other. The force is particularly sensitive to rotations of

4738-868: The Spanish monarchs funded Christopher Columbus 's expedition to sail west to reach the Indies by crossing the Atlantic, which resulted in the Discovery of the Americas . In 1498, a Portuguese expedition commanded by Vasco da Gama reached India by sailing around Africa, opening up direct trade with Asia . Soon, the Portuguese sailed further eastward, to the Spice Islands in 1512, landing in China one year later. The first circumnavigation of

4841-537: The United States in cooperation with six partner nations. OMEGA was developed by the United States Navy for military aviation users. It was approved for development in 1968 and promised a true worldwide oceanic coverage capability with only eight transmitters and the ability to achieve a four-mile (6 km) accuracy when fixing a position. Initially, the system was to be used for navigating nuclear bombers across

4944-400: The "index mirror" is fixed to the top of the index arm, over the pivot. As the index arm is moved, this mirror rotates, and the graduated scale on the arc indicates the measured angle ("altitude"). The second mirror, referred to as the "horizon glass", is fixed to the front of the frame. One half of the horizon glass is silvered and the other half is clear. Light from the celestial body strikes

5047-583: The "magnetic field" written B and H . While both the best names for these fields and exact interpretation of what these fields represent has been the subject of long running debate, there is wide agreement about how the underlying physics work. Historically, the term "magnetic field" was reserved for H while using other terms for B , but many recent textbooks use the term "magnetic field" to describe B as well as or in place of H . There are many alternative names for both (see sidebars). The magnetic field vector B at any point can be defined as

5150-600: The "number" of field lines through a surface. These concepts can be quickly "translated" to their mathematical form. For example, the number of field lines through a given surface is the surface integral of the magnetic field. Various phenomena "display" magnetic field lines as though the field lines were physical phenomena. For example, iron filings placed in a magnetic field form lines that correspond to "field lines". Magnetic field "lines" are also visually displayed in polar auroras , in which plasma particle dipole interactions create visible streaks of light that line up with

5253-451: The 1530s, from Latin navigationem (nom. navigatio ), from navigatus , pp. of navigare "to sail, sail over, go by sea, steer a ship," from navis "ship" and the root of agere "to drive". Roughly, the latitude of a place on Earth is its angular distance north or south of the equator . Latitude is usually expressed in degrees (marked with °) ranging from 0° at the Equator to 90° at

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5356-526: The European medieval period, navigation was considered part of the set of seven mechanical arts , none of which were used for long voyages across open ocean. Polynesian navigation is probably the earliest form of open-ocean navigation; it was based on memory and observation recorded on scientific instruments like the Marshall Islands Stick Charts of Ocean Swells . Early Pacific Polynesians used

5459-586: The Lorentz equation is from the theory of electrostatics , and says that a particle of charge q in an electric field E experiences an electric force: F electric = q E . {\displaystyle \mathbf {F} _{\text{electric}}=q\mathbf {E} .} The second term is the magnetic force: F magnetic = q ( v × B ) . {\displaystyle \mathbf {F} _{\text{magnetic}}=q(\mathbf {v} \times \mathbf {B} ).} Using

5562-536: The North Pole to Russia. Later, it was found useful for submarines. Due to the success of the Global Positioning System the use of Omega declined during the 1990s, to a point where the cost of operating Omega could no longer be justified. Omega was terminated on September 30, 1997, and all stations ceased operation. LORAN is a terrestrial navigation system using low frequency radio transmitters that use

5665-626: The North and South poles. The latitude of the North Pole is 90° N, and the latitude of the South Pole is 90° S. Mariners calculated latitude in the Northern Hemisphere by sighting the pole star ( Polaris ) with a sextant and using sight reduction tables to correct for height of eye and atmospheric refraction. The height of Polaris in degrees above the horizon is the latitude of the observer, within

5768-669: The Philippines, trying to find a maritime path back to the Americas , but was unsuccessful. The eastward route across the Pacific, also known as the tornaviaje (return trip) was only discovered forty years later, when Spanish cosmographer Andrés de Urdaneta sailed from the Philippines, north to parallel 39°, and hit the eastward Kuroshio Current which took its galleon across the Pacific. He arrived in Acapulco on October 8, 1565. The term stems from

5871-522: The area of the loop and depends on the direction of the current using the right-hand rule. An ideal magnetic dipole is modeled as a real magnetic dipole whose area a has been reduced to zero and its current I increased to infinity such that the product m = Ia is finite. This model clarifies the connection between angular momentum and magnetic moment, which is the basis of the Einstein–de Haas effect rotation by magnetization and its inverse,

5974-492: The bridge wing for recording sight times. In practice, a wrist watch coordinated to the nearest second with the chronometer will be adequate. A stop watch, either spring wound or digital, may also be used for celestial observations. In this case, the watch is started at a known GMT by chronometer, and the elapsed time of each sight added to this to obtain GMT of the sight. All chronometers and watches should be checked regularly with

6077-496: The charge carriers in a material through the Hall effect . The Earth produces its own magnetic field , which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass . The force on an electric charge depends on its location, speed, and direction; two vector fields are used to describe this force. The first is the electric field , which describes

6180-421: The civilian navigator on a merchant ship or leisure craft must often take and plot their position themselves, typically with the aid of electronic position fixing. While the military navigator will have a bearing book and someone to record entries for each fix, the civilian navigator will simply pilot the bearings on the chart as they are taken and not record them at all. If the ship is equipped with an ECDIS , it

6283-403: The definition of the cross product, the magnetic force can also be written as a scalar equation: F magnetic = q v B sin ⁡ ( θ ) {\displaystyle F_{\text{magnetic}}=qvB\sin(\theta )} where F magnetic , v , and B are the scalar magnitude of their respective vectors, and θ is the angle between the velocity of

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6386-428: The direction of a line drawn from the south to the north pole of the magnet. Flipping a bar magnet is equivalent to rotating its m by 180 degrees. The magnetic field of larger magnets can be obtained by modeling them as a collection of a large number of small magnets called dipoles each having their own m . The magnetic field produced by the magnet then is the net magnetic field of these dipoles; any net force on

6489-639: The earth was completed in 1522 with the Magellan-Elcano expedition , a Spanish voyage of discovery led by Portuguese explorer Ferdinand Magellan and completed by Spanish navigator Juan Sebastián Elcano after the former's death in the Philippines in 1521. The fleet of seven ships sailed from Sanlúcar de Barrameda in Southern Spain in 1519, crossed the Atlantic Ocean and after several stopovers rounded

6592-408: The existence of magnetic monopoles, but so far, none have been observed. In the model developed by Ampere , the elementary magnetic dipole that makes up all magnets is a sufficiently small Amperian loop with current I and loop area A . The dipole moment of this loop is m = IA . These magnetic dipoles produce a magnetic B -field. The magnetic field of a magnetic dipole is depicted in

6695-411: The figure. From outside, the ideal magnetic dipole is identical to that of an ideal electric dipole of the same strength. Unlike the electric dipole, a magnetic dipole is properly modeled as a current loop having a current I and an area a . Such a current loop has a magnetic moment of m = I a , {\displaystyle m=Ia,} where the direction of m is perpendicular to

6798-522: The first. In this example, the magnetic field of the stationary magnet creates a magnetic torque on the magnet that is free to rotate. This magnetic torque τ tends to align a magnet's poles with the magnetic field lines. A compass, therefore, turns to align itself with Earth's magnetic field. In terms of the pole model, two equal and opposite magnetic charges experiencing the same H also experience equal and opposite forces. Since these equal and opposite forces are in different locations, this produces

6901-546: The force acting on a stationary charge and gives the component of the force that is independent of motion. The magnetic field, in contrast, describes the component of the force that is proportional to both the speed and direction of charged particles. The field is defined by the Lorentz force law and is, at each instant, perpendicular to both the motion of the charge and the force it experiences. There are two different, but closely related vector fields which are both sometimes called

7004-515: The force and torques between two magnets as due to magnetic poles repelling or attracting each other in the same manner as the Coulomb force between electric charges. At the microscopic level, this model contradicts the experimental evidence, and the pole model of magnetism is no longer the typical way to introduce the concept. However, it is still sometimes used as a macroscopic model for ferromagnetism due to its mathematical simplicity. In this model,

7107-408: The force on a small magnet having a magnetic moment m due to a magnetic field B is: F = ∇ ( m ⋅ B ) , {\displaystyle \mathbf {F} ={\boldsymbol {\nabla }}\left(\mathbf {m} \cdot \mathbf {B} \right),} where the gradient ∇ is the change of the quantity m · B per unit distance and the direction

7210-474: The force on the particle when its velocity is v ; repeat with v in some other direction. Now find a B that makes the Lorentz force law fit all these results—that is the magnetic field at the place in question. The B field can also be defined by the torque on a magnetic dipole, m . τ = m × B {\displaystyle {\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B} } The SI unit of B

7313-414: The four fundamental forces of nature. Magnetic fields are used throughout modern technology, particularly in electrical engineering and electromechanics . Rotating magnetic fields are used in both electric motors and generators . The interaction of magnetic fields in electric devices such as transformers is conceptualized and investigated as magnetic circuits . Magnetic forces give information about

7416-426: The horizon or more preferably a star, each time the sextant is used. The practice of taking celestial observations from the deck of a rolling ship, often through cloud cover and with a hazy horizon, is by far the most challenging part of celestial navigation. Inertial navigation system (INS) is a dead reckoning type of navigation system that computes its position based on motion sensors. Before actually navigating,

7519-480: The index mirror and is reflected to the silvered portion of the horizon glass, then back to the observer's eye through the telescope. The observer manipulates the index arm so the reflected image of the body in the horizon glass is just resting on the visual horizon, seen through the clear side of the horizon glass. Adjustment of the sextant consists of checking and aligning all the optical elements to eliminate "index correction". Index correction should be checked, using

7622-614: The initial latitude and longitude and the INS's physical orientation relative to the Earth (e.g., north and level) are established. After alignment, an INS receives impulses from motion detectors that measure (a) the acceleration along three axes (accelerometers), and (b) rate of rotation about three orthogonal axes (gyroscopes). These enable an INS to continually and accurately calculate its current latitude and longitude (and often velocity). Advantages over other navigation systems are that, once aligned, an INS does not require outside information. An INS

7725-432: The local density of field lines can be made proportional to its strength. Magnetic field lines are like streamlines in fluid flow , in that they represent a continuous distribution, and a different resolution would show more or fewer lines. An advantage of using magnetic field lines as a representation is that many laws of magnetism (and electromagnetism) can be stated completely and concisely using simple concepts such as

7828-763: The local direction of Earth's magnetic field. Field lines can be used as a qualitative tool to visualize magnetic forces. In ferromagnetic substances like iron and in plasmas, magnetic forces can be understood by imagining that the field lines exert a tension , (like a rubber band) along their length, and a pressure perpendicular to their length on neighboring field lines. "Unlike" poles of magnets attract because they are linked by many field lines; "like" poles repel because their field lines do not meet, but run parallel, pushing on each other. Permanent magnets are objects that produce their own persistent magnetic fields. They are made of ferromagnetic materials, such as iron and nickel , that have been magnetized, and they have both

7931-460: The magnet is a result of adding up the forces on the individual dipoles. There are two simplified models for the nature of these dipoles: the magnetic pole model and the Amperian loop model . These two models produce two different magnetic fields, H and B . Outside a material, though, the two are identical (to a multiplicative constant) so that in many cases the distinction can be ignored. This

8034-413: The magnets due to magnetic torque. The force on each magnet depends on its magnetic moment and the magnetic field of the other. To understand the force between magnets, it is useful to examine the magnetic pole model given above. In this model, the H -field of one magnet pushes and pulls on both poles of a second magnet. If this H -field is the same at both poles of the second magnet then there

8137-448: The mainspring, and a special balance designed to compensate for temperature variations. A spring-driven chronometer is set approximately to Greenwich mean time (GMT) and is not reset until the instrument is overhauled and cleaned, usually at three-year intervals. The difference between GMT and chronometer time is carefully determined and applied as a correction to all chronometer readings. Spring-driven chronometers must be wound at about

8240-449: The motion of electrons within an atom are connected to those electrons' orbital magnetic dipole moment , and these orbital moments do contribute to the magnetism seen at the macroscopic level. However, the motion of electrons is not classical, and the spin magnetic moment of electrons (which is not explained by either model) is also a significant contribution to the total moment of magnets. Historically, early physics textbooks would model

8343-640: The motion of stars, weather, the position of certain wildlife species, or the size of waves to find the path from one island to another. Maritime navigation using scientific instruments such as the mariner's astrolabe first occurred in the Mediterranean during the Middle Ages. Although land astrolabes were invented in the Hellenistic period and existed in classical antiquity and the Islamic Golden Age ,

8446-540: The navigation of spacecraft themselves. This has historically been achieved (during the Apollo program ) via a navigational computer , an Inertial navigation system, and via celestial inputs entered by astronauts which were recorded by sextant and telescope. Space rated navigational computers, like those found on Apollo and later missions, are designed to be hardened against possible data corruption from radiation. Another possibility that has been explored for deep space navigation

8549-459: The navigator will have to rely on his skill in the manual and time-tested procedures. Celestial navigation systems are based on observation of the positions of the Sun , Moon , planets and navigational stars . Such systems are in use as well for terrestrial navigating as for interstellar navigating. By knowing which point on the rotating Earth a celestial object is above and measuring its height above

8652-444: The north pole (whether inside the magnet or out) while near the south pole all H -field lines point toward the south pole (whether inside the magnet or out). Too, a north pole feels a force in the direction of the H -field while the force on the south pole is opposite to the H -field. In the magnetic pole model, the elementary magnetic dipole m is formed by two opposite magnetic poles of pole strength q m separated by

8755-405: The observer's horizon, the navigator can determine his distance from that subpoint. A nautical almanac and a marine chronometer are used to compute the subpoint on Earth a celestial body is over, and a sextant is used to measure the body's angular height above the horizon. That height can then be used to compute distance from the subpoint to create a circular line of position. A navigator shoots

8858-503: The oldest record of a sea astrolabe is that of Spanish astronomer Ramon Llull dating from 1295. The perfecting of this navigation instrument is attributed to Portuguese navigators during early Portuguese discoveries in the Age of Discovery . The earliest known description of how to make and use a sea astrolabe comes from Spanish cosmographer Martín Cortés de Albacar 's Arte de Navegar ( The Art of Navigation ) published in 1551, based on

8961-442: The particle and the magnetic field. The vector B is defined as the vector field necessary to make the Lorentz force law correctly describe the motion of a charged particle. In other words, [T]he command, "Measure the direction and magnitude of the vector B at such and such a place," calls for the following operations: Take a particle of known charge q . Measure the force on q at rest, to determine E . Then measure

9064-420: The particle's velocity , and × denotes the cross product . The direction of force on the charge can be determined by a mnemonic known as the right-hand rule (see the figure). Using the right hand, pointing the thumb in the direction of the current, and the fingers in the direction of the magnetic field, the resulting force on the charge points outwards from the palm. The force on a negatively charged particle

9167-476: The path a radar object should follow on the radar display if the ship stays on its planned course. During the transit, the navigator can check that the ship is on track by checking that the pip lies on the drawn line. Global Navigation Satellite System or GNSS is the term for satellite navigation systems that provide positioning with global coverage. A GNSS allow small electronic receivers to determine their location ( longitude , latitude , and altitude ) within

9270-412: The precise time of a sighting is known. Lacking that, one can use a sextant to take a lunar distance (also called the lunar observation , or "lunar" for short) that, with a nautical almanac , can be used to calculate the time at zero longitude (see Greenwich Mean Time ). Reliable marine chronometers were unavailable until the late 18th century and not affordable until the 19th century. For about

9373-607: The principle of the archipendulum used in constructing the Egyptian pyramids . Open-seas navigation using the astrolabe and the compass started during the Age of Discovery in the 15th century. The Portuguese began systematically exploring the Atlantic coast of Africa from 1418, under the sponsorship of Prince Henry . In 1488 Bartolomeu Dias reached the Indian Ocean by this route. In 1492

9476-444: The qualitative information included above. There is no torque on a magnet if m is in the same direction as the magnetic field, since the cross product is zero for two vectors that are in the same direction. Further, all other orientations feel a torque that twists them toward the direction of magnetic field. Currents of electric charges both generate a magnetic field and feel a force due to magnetic B-fields. Navigation It

9579-429: The radar scanner. When a vessel (ship or boat) is within radar range of land or fixed objects (such as special radar aids to navigation and navigation marks) the navigator can take distances and angular bearings to charted objects and use these to establish arcs of position and lines of position on a chart. A fix consisting of only radar information is called a radar fix. Types of radar fixes include "range and bearing to

9682-514: The rear section of the fuselage, whereas most US aircraft enclosed the antenna in a small teardrop-shaped fairing. In navigational applications, RDF signals are provided in the form of radio beacons , the radio version of a lighthouse . The signal is typically a simple AM broadcast of a morse code series of letters, which the RDF can tune in to see if the beacon is "on the air". Most modern detectors can also tune in any commercial radio stations, which

9785-409: The same frequency range, called CHAYKA . LORAN use is in steep decline, with GPS being the primary replacement. However, there are attempts to enhance and re-popularize LORAN. LORAN signals are less susceptible to interference and can penetrate better into foliage and buildings than GPS signals. Radar is an effective aid to navigation because it provides ranges and bearings to objects within range of

9888-412: The same time each day. Quartz crystal marine chronometers have replaced spring-driven chronometers aboard many ships because of their greater accuracy. They are maintained on GMT directly from radio time signals. This eliminates chronometer error and watch error corrections. Should the second hand be in error by a readable amount, it can be reset electrically. The basic element for time generation

9991-400: The screen that is parallel to the ship's course, but offset to the left or right by some distance. This parallel line allows the navigator to maintain a given distance away from hazards . The line on the radar screen is set to a specific distance and angle, then the ship's position relative to the parallel line is observed. This can provide an immediate reference to the navigator as to whether

10094-495: The ship is on or off its intended course for navigation. Other techniques that are less used in general navigation have been developed for special situations. One, known as the "contour method," involves marking a transparent plastic template on the radar screen and moving it to the chart to fix a position. Another special technique, known as the Franklin Continuous Radar Plot Technique, involves drawing

10197-594: The southern tip of South America . Some ships were lost, but the remaining fleet continued across the Pacific making a number of discoveries including Guam and the Philippines. By then, only two galleons were left from the original seven. The Victoria led by Elcano sailed across the Indian Ocean and north along the coast of Africa, to finally arrive in Spain in 1522, three years after its departure. The Trinidad sailed east from

10300-809: The table. The practice of navigation usually involves a combination of these different methods. By mental navigation checks, a pilot or a navigator estimates tracks, distances, and altitudes which will then help the pilot avoid gross navigation errors. Piloting (also called pilotage) involves navigating an aircraft by visual reference to landmarks, or a water vessel in restricted waters and fixing its position as precisely as possible at frequent intervals. More so than in other phases of navigation, proper preparation and attention to detail are important. Procedures vary from vessel to vessel, and between military, commercial, and private vessels. As pilotage takes place in shallow waters , it typically involves following courses to ensure sufficient under keel clearance , ensuring

10403-459: The time interval between radio signals received from three or more stations to determine the position of a ship or aircraft. The current version of LORAN in common use is LORAN-C, which operates in the low frequency portion of the EM spectrum from 90 to 110 kHz . Many nations are users of the system, including the United States , Japan , and several European countries. Russia uses a nearly exact system in

10506-401: The vector that, when used in the Lorentz force law , correctly predicts the force on a charged particle at that point: F = q E + q ( v × B ) {\displaystyle \mathbf {F} =q\mathbf {E} +q(\mathbf {v} \times \mathbf {B} )} Here F is the force on the particle, q is the particle's electric charge , v , is

10609-490: Was the case with Loran C , its primary use was for ship navigation in coastal waters. Fishing vessels were major post-war users, but it was also used on aircraft, including a very early (1949) application of moving-map displays. The system was deployed in the North Sea and was used by helicopters operating to oil platforms . The OMEGA Navigation System was the first truly global radio navigation system for aircraft, operated by

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