navigation, from the latin navis (a ship) and agere (to drive), the art and science of conducting a craft as it moves about its ways. See celestial navigation; coastal navigation; hyperbolic navigation; inertial navigation; satellite navigation. What follows is a short history of navigation.

Navigation Without Artefacts.

When James Cook discovered Oceania in the 18th century the cultures were still at a Neolithic stage of development. But to Captain Cook, perhaps the most illustrious of all scientific navigators, it was a matter of wonder the way the Polynesians navigated ‘from Island to Island for several hundred leagues, the sun serving them for a compass by day and the Moon and Stars by night’. Andia y Varela, leader of a Spanish expedition to Tahiti in 1744, was similarly impressed by the skill of the navigators. ‘When the night is a clear one,’ he wrote, ‘they steer by the stars; and this is the easiest navigation for them because these being many [in number], not only do they note by them the bearings on which the several islands with which they are in touch lie, but also the harbours in them, so that they make straight for the entrance by following the rhumb of the particular star that rises or sets over it.’

The traditional navigation skills of the Pacific islanders will have encompassed the skills of all Neolithic navigators, and of navigators in the China Seas, the Indian Ocean, the Mediterranean, and the seas of northern Europe down to the Vikings of the 10th century and their Norman successors in the 11th. The methods, practised well into the 20th century by indigenous Pacific navigators, have been studied over the years by many scholars. Historically their interest is that they give us an idea of how other cultures in other seas and other centuries navigated before the introduction of the magnetic compass enabled sailing directions and charts to be scientifically based, and navigation from then on founded on measurement. From the navigational point of view no work is more informative than We, the Navigators by David Lewis, which describes his valuable and remarkable fieldwork.

In 1968–9 under a research fellowship of the Australian University Lewis spent nine months in Isbjorn, a 12-metre (39-ft) ketch, investigating native navigation in the western Pacific, learning from the surviving practising navigators and getting them to navigate Isbjorn by their methods. Hippour, as an example, an initiated Micronesian navigator from Puluwat, sailed Isbjorn on a voyage of some 1,840 kilometres (1,150 mls.) entirely without charts or instruments, relying only on his cyclopedic memory of reefs and islands under the stars spanning some 2,400 kilometres (1,500 mls.). Hippour could neither read or write, nor understand the western concept of crossing position lines to fix position.

Basically, indigenous Pacific navigation is a system of dead reckoning based on observation rather than measurement. There are, classically, no artefacts. Waves, winds, clouds, stars, sun, moon, seabirds, fish, the water itself are, to quote another authority, all there is to see, feel, smell, or hear. The navigational task is to integrate information from these sources into a system accurate and reliable enough to guide the mariner to his destination. The process is one of observation, judgement, and experience rather than measurement. The overall objective will be to bring the vessel into what Lewis terms the ‘expanded target area’, where signs of land such as birds, deflected swells, cloud formations, and so on will enable the navigator to home on to his destination.

The methods vary to some extent according to local conditions. In the Carolines, for example, wave direction is used to steer a steady course, whereas in the Marshall Islands, where atolls refract the waves, interference patterns themselves are used for orientation. In the tropics, equatorial stars near the horizon change bearing very little as they rise and set, and the navigator chooses a guiding star for his destination and steers to keep it at a steady angle on the bow. Memory necessarily plays a vital part in the whole process and star courses for a large number of islands (about 60 in the Carolines) will be committed to memory by the navigator under training.

The ocean phase of the voyage may be divided, conceptually, into a number of segments (or etak) corresponding to the apparent passage of a notional reference island under successive navigational stars using a procedure analogous to the running fix. The island is conceived as moving backwards as the canoe progresses and the segments so defined give the navigator his distance travelled and distance run. The first and last segments are identified with the dipping distance of the island of departure and the expanded target area of the destination. The speed at which the reference island is taken to move backwards reflects, of course, simply the accuracy of the dead reckoning. The island is, if you like, a metaphor, a way of organizing navigation information. Like the chart it is an abstraction.

Birth of Navigation Based on Measurement.

In the West at least, navigation based on measurement was born in the Mediterranean and was developed rapidly by the Italian city states during the 13th century. By the end of it, Mediterranean seamen had the magnetic compass (the card already subdivided into 32 points), systematically compiled sailing directions based on compass directions and estimated distances, and the nautical chart drawn from the same information.

It was, above all, the discovery and development of the magnetic compass that made mathematical navigation, the chart, and reliable pilot books possible. It also altered the pattern of Mediterranean trade. Before its introduction the seas were normally closed in winter because of the weather and the difficulty of navigating with overcast skies. Once in use it enabled the number of voyages to be doubled so that the various trading fleets could make two round voyages each year without having to lay up overseas.

The word ‘compass’ originally meant the nautical division of the horizon into 32 ‘points’ rather than an instrument or device of any kind, and compass directions were named after the familiar names of the winds that the seaman distinguished. Pliny, for instance, in his Natural History writes: ‘From Carpathos is fifty miles with Africus to Rhodes’, Africus being a wind; and the pilot bound for Rhodes might well wait for the wind to blow from that quarter before setting sail.

Whether charts were used in antiquity is a matter of dispute, but none seems to have survived. In the late Middle Ages the portulan chart appeared quite suddenly, the earliest surviving example in Italy, complete in all its parts and without apparent parentage. It was mathematically based and the first map of any kind to carry a scale. With the mariner's compass and the sand-glass, which enabled the distance run to be calculated, it provided a self-contained system of navigation that seemed quite adequate for all normal purposes. Indeed, until the 17th century, there was no means of fixing a ship's position offshore in the Mediterranean. However, although voyages might now end anywhere from the Black Sea to Flanders, the Mediterranean seaman would seldom be out of sight of land for long. The fact that he would have followed magnetic, rather than true, courses would have been of little consequence since both the sailing directions and the plain charts (hence the derivation of plain sailing), were based on the same data. Nor did the inadequacy of the plain chart, where the meridians were parallel to each other and did not converge towards the pole, matter much in a sea that stretches east–west over such a narrow belt of latitude. The art of dead reckoning had been perfected, and to all intents and purposes seemed to suffice.

Early Navigation in Northern Europe.

For those navigating the Atlantic coasts of Europe matters were quite different. Here a knowledge of the tides was essential, both to determine the strong tidal streams on coastal passages and to predict the depths of water in ports and harbours. The emphasis in early English sailing directions, for instance, is on soundings and the tides. ‘Upon Portland is fair white sand and 24 fathoms’ runs one passage, showing the northern practice of establishing position on the continental shelf by the depth of water and the nature of the bottom with an early form of lead line.

A later entry reads ‘A south moon maketh high water within Wight, and all the havens be full at west-south-west between Start and the Lizard’, which refers to the practice of telling the time of high water by the bearing of the moon. For it had long been known that although high water does not occur simultaneously at all places on the same longitude it does occur at any one place when the moon is at the same position in the sky. The daily retardation of the tides was well understood. However, for the unlettered seaman, accustomed to telling the time from a compass bearing of the sun—where each of the 32 points of the compass rose represented 45 minutes—one point was, for him, close enough to the true retardation of 48 minutes. The mid-16th-century English pilot's skills in the Narrow Seas, which he shared with the seamen of Normandy and Brittany, were considerable and the waters he navigated were as perilous as any, but they were not the navigational skills required in the ocean.

Early Ocean Navigation.

From the 9th century onwards Norse traders and raiders in their longships and knarrs penetrated into the Mediterranean, and to Iceland, Greenland, and Norway in the north. Little is known of their precise navigational practices beyond what can be gleaned from the sagas, but they reached America some 500 years before Columbus and for centuries conducted regular passages of some 1,400 nautical miles to and from Greenland and Norway without the use of magnetic compass or chart. There is some archaeological evidence that they used a Viking compass, but its use is unlikely to have been critical.

In the 1420s, when the caravels of Henry the Navigator began to sail down the West African coast, a better understanding of the wind and current systems of the Atlantic Ocean became necessary if regular trade routes were to be established. The practice adopted was to take a long board out into the Atlantic, keeping the north-east trade winds abeam until the variables were met with further north and an easterly course could then be laid for home. To achieve this the pilot had to know when he had reached the parallel along which he was to run to his destination. At first this was done by comparing the altitude of Polaris, as observed with the seaman's quadrant, with what its altitude had been at the port of departure (say Lisbon). The difference was of course the difference in latitude but latitude meant nothing to the mariner at that time and was not marked on the charts. The difference in degrees and minutes was thus converted into linear distance by multiplying the readings by 16⅔ (the accepted degree of the meridian) to give the difference in leagues. Later the scale of the quadrant itself would often be marked with the names of ports and landfalls whose latitudes had been established. When the sun replaced the star as the equator was approached, first the mariner's astrolabe and later the cross-staff replaced the seaman's quadrant as the favoured instrument for observation.

Polaris is not, as sailors then believed, fixed in the sky, but circles the pole of the heavens so that its altitude will only correspond to that of the pole twice a day. Astronomers devised a simple rule for using the star to find latitude. Sailors had long used, as a form of clock, the rotation around Polaris of the two so-called Guards (or Pointers) in the Lesser Bear (Ursa Minor), a line from the front Guard (Kochab) to the star representing the hour hand. To help them memorize the midnight position of the Guards at different times of the year they imagined a giant figure in the sky, the pole at his stomach, whose head, feet, and outstretched arms, with cross lines between the limbs, defined an eightfold division of the circle. How this was used for timekeeping need not bother us but the new rules for observing Polaris made use of the familiar imagery to indicate the corrections to the star's altitude for different positions of the Guards. ‘You are to know,’ reads an English manual, ‘that when the Guards are at the head of Polaris, the star is 3 degrees below the axis.’

Developments of Charts and Manuals during the 15th–18th centuries.

When the Portuguese explorers crossed the equator in 1471 Polaris was no longer visible and in 1484 King John II of Portugal appointed a mathematical commission to examine the problem of using the sun to determine latitude at sea, and its conclusions are described in the oldest surviving Portuguese navigation manual, Regimento do astrolabio e do quadrante. This gives seventeen examples of determining latitude from the sun's meridian altitude with different combinations of latitude and declination, as well as rules for ‘raising the pole’ (finding how far the ship must run on a particular course to raise its latitude one degree).

In 1537 the great Portuguese mathematician Pedro Nuñes (1492–1577) published an important study on the errors of the plain chart. Navigation in the Atlantic had now become astronomical and the pilot required a meridian on his chart to identify the latitudes he was expected to attain and then ‘run down’. The problem was that since the plain chart ignored the earth's curvature, an east–west compass course would eventually carry the ship off the east–west line of latitude marked on the chart. Mercator's projection in his world map of 1569 solved this problem by introducing proportionally the same error into the spacing of the lines of latitude as there was in the lines of longitude.

While the Portuguese, and later the Spaniards, were transforming the practices of ocean navigation, the English, although they traded as far afield as Iceland and fished the Grand Banks of Newfoundland, were still following earlier navigational methods. For England at that time lacked the Continent's common mathematical culture, which had led to English ships employing Spanish, Portuguese, or French pilots and having their instruments made in Flanders and their charts in Portugal.

The answer lay in scientific education which, during the latter half of the 16th century, English navigators had just started to acquire. The first English navigation manual was a translation of the leading Spanish one of the time and appeared in 1561 as The Art of Navigation by Martin Cortes. William Bourne, an instructor in mathematics described as an innkeeper, produced a popular version of the book, A Regiment for the Sea (1574), which was perhaps more suited to seamen. Then in 1599 Edward Wright published Certaine Errors in Navigation, perhaps the most important navigational work of the 16th century. It explained Mercator's projection (which Mercator had not) and included a table of meridional parts which gave the spacing of the minutes of latitude along the meridians so that anyone competent in chartmaking could now draw a ‘true’ chart. Seventy years later, John Seller, an instrument maker, chartmaker, and instructor in navigation, published the first volume of his monumental Practical Navigation, a work that demonstrated how completely the navigational climate had changed under the influence of the talented astronomers, instrument makers, and mathematicians who so improved the practice of navigation and led ultimately to English supremacy at sea.

As navigation became increasingly based on mathematics, nautical publications assumed greater importance. For example, amplitude tables enabled the pilot to establish the magnetic variation at any place and so increase the accuracy of his compass readings. In 1686 the great scientist turned navigator Edmond Halley (1656–1742) published his study of ocean wind systems and, in the winter of 1669–1700, undertook a voyage to chart the world's isogonic lines, lines connecting points of equal magnetic variation. The British nautical almanac for 1767 became the first to publish data for the determination of longitude by lunar distance. This method prevailed well after the Board of Longitude had made its award to John Harrison (1693–1776).

Modern Navigational Aids.

Until the 20th century, the only way of establishing a ship's position offshore was still celestial navigation, although improved instruments, from the early quadrants to the modern double-reflection sextant, increased the accuracy and reliability of observation, whilst improvements in nautical tables and almanacs constantly evolved with the growth of nautical astronomy and, latterly, computers. Both the notion of the position line, stumbled across accidentally by the American Captain Sumner in 1837 (it had been missed by the astronomers), and then the idea of the intercept propounded by the French naval officer Marcq Saint-Hilaire, did much to make the principles of celestial navigation more widely understood and to ease the navigator's task.

Electronic aids to navigation, most of which were conceived either during or shortly after the Second World War (1939–45), revolutionized navigation at sea. Radar could obtain the bearing of coastal echoes in poor visibility; electronic echo sounders monitored the depth of water below a ship's keel; the electronic log accurately recorded the distance it covered; and the various hyperbolic navigation systems gave quick, simple, and accurate positions throughout much of the world, day or night. However, it is satellite navigation, with its worldwide coverage, precision, and flexibility, that is the principal aid to navigation today.

Bibliography

Marcus, G. , The Conquest of the North Atlantic (1980).
Ronan, C. , The Shorter Science & Civilisation in China, 3 (abridgment of Joseph Needham's text) (1986).
Seaver, K. , ‘Olaus Magnus and the “Compass” on Hvitsark’, Journal of Navigation, 54 (May 2001), 235.
Taylor, E. , The Haven Finding Art: A History of Navigation from Odysseus to Captain Cook (1954).
Williams, J. , From Sails to Satellites: The Origin and Development of Navigational Science (1992).

Mike Richey

Navigation

In the broadest sense, navigation is the act of moving about from place to place on land, sea, in air, or in outer space. Navigation, with its primitive beginnings, has evolved to become a sophisticated science.

Early Navigation

Prior to the fifteenth century, European mariners were reluctant to sail out of sight of land, partly because they feared getting lost and partly because they did not know what lay beyond the horizon. Thus, sailing voyages by Europeans were largely confined to the Mediterranean Sea or close to shore in the Atlantic Ocean. The high and broad continental shelf of Northern Europe, where the continent ends and the ocean begins, allowed for shallow sailing waters within sight of land from the Iberian Peninsula (Portugal and Spain) to Scandinavia (Norway, Sweden, and Denmark).

The Vikings of Scandinavia were renowned coastal navigators. Not only did the Vikings sail the coast of Europe, but they also followed the continental shelf into the Northern Atlantic to Iceland, Greenland, and ultimately to North America. Although such extended voyages were remarkable accomplishments, they involved no sophisticated navigational techniques.

In about the year 1000, the Norseman Leif Ericson made a transatlantic voyage to North America with the midnight sun lighting his way. Using the pole star as his only navigational guide, he followed the North Atlantic's generous continental shelf to the northeastern coast of mainland North America.

While ambitious open sea voyages such as Ericson's were possible in the extreme northern latitudes, the South Atlantic was not as accommodating. Africa's continental shelf was narrow, and left very little room for navigational error before a ship could be swept into the deep currents and unfamiliar winds off the African coast. These currents and winds were unpredictable and tended to flow to the north and east, exactly the opposite direction from that in which sailors wanted to go.

The Europeans, including the Vikings, remained essentially coastal navigators until the first half of the fifteenth century. The situation was the same in all parts of the world at that time. All navigation was local rather than global. Sailing on the open sea was possible only where there were predictable winds and currents or a wide continental shelf to follow.

Medieval Navigation

In the early part of the fifteenth century, Portuguese sailors began to sail farther out into the Atlantic using favorable winds, currents, and the paths of birds as guides. By the 1440s, they had reached as far as the Azores, an archipelago of small islands some 800 miles west of Portugal. To venture farther than this would require the beginnings of a more scientific and mathematical type of navigation. This more scientific approach took two forms. The first was a type of navigation known as "dead reckoning" and the second was the application of astronomy and mathematics to what is known as "celestial navigation," or navigation by the stars.

In the process of dead reckoning, a triangular wooden slab, called a chip log, attached to a rope with evenly spaced knots along its entire length, was tossed into the ocean from the stern of the ship. Sailors would then count the number of knots pulled out by the log in a given amount of time, usually measured by sand glasses calibrated for one minute or less. From this observation, an approximation of the speed of the ship could be calculated. Such measurements were taken each time the ship changed course due to a change in wind direction.

This was an early attempt to measure what we now call the longitude of the ship at a given moment. The method was not very accurate, but it was the best that could be done at the time. The captain's log of Christopher Columbus's 1492 journey to the Americas suggests that Columbus relied almost exclusively on dead reckoning to navigate to the New World. Truly accurate measures of longitude would have to wait until the invention of the chronometer in the eighteenth century.

Celestial navigation could help in estimating a ship's latitude . In the Northern Hemisphere, mariners could use the pole star as a reference point. At the north pole the star would be directly overhead at all times, but as one moves farther south it appears lower and lower in the sky until, at the equator, it dips below the horizon.

An instrument called a quadrant could be used to measure the angle of the pole star above the horizon. The quadrant was a quarter circle with degree markings from 0 to 90 along its arc. A plumb line hung from the point at the center of the circle and the observer would then line up the edge of the quadrant with the pole star. The plumb line would then cross the arc of the circle at the position that would indicate the number of degrees above the horizon at which the pole star was located. In this way latitude could be approximately determined.

Of course this method worked only at night, but an alternative method for determining latitude in the daytime made use of the astrolabe, a heavy brass disk with degrees marked around its edge. An observer would move a rotating arm attached at the center of a disk until sunlight shone through a hole at one end of the arm and fell on a hole at the other end. The arm would indicate the altitude of the Sun by the degrees marked around the edge of the disk.

In 1473, the astronomer Abraham Zacuto created a book of tables called Rules for the Astrolabe that allowed mariners to determine the latitude for any day of the year. Use of the tables depended upon knowing in which constellation of stars the Sun rose on the day of the measurement. An observer would view the eastern horizon before sunrise and note the constellation in which the Sun rose. Later in the day, when the Sun reached its highest point in the sky, the observer would take a reading with the astrolabe. Zacuto's Rules for the Astrolabe could then be used to look up the latitude with a degree of accuracy never before possible.

Zacuto constructed this extensive set of tables using mathematics, specifically trigonometry, developed between the ninth and thirteenth centuries by Judeo-Arab mathematicians and astronomers in Portugal and Spain. To produce these tables, Zacuto needed, in addition to trigonometry, an accurate solar calendar giving the location of the Earth with respect to the Sun at any time during the year. Such a calendar had been constructed in the eleventh century by Muslim astronomers in Spain. Making use of this calendar, the Sun's position relative to the constellations, and the height of the midday Sun above the horizon, Zacuto produced the first scientifically accurate method for determining latitude. This method was used by European navigators for more than a century.

By the 1520s, the ability to determine latitude at sea with reasonable accuracy was well established, but the problem of finding longitude with an acceptable degree of precision remained intractable for another 300 years. Whereas latitude measures positions north and south of the equator, longitude uses imaginary "great circles" passing through the north and south poles to measure positions east and west of a predetermined great circle called the Prime Meridian .

The first prime meridian was established by the Portuguese map-maker Pedro Reinel in 1506. It passed through the Portuguese Madeira Islands. Reinel's prime meridian would remain the world's standard for more than 300 years, but with the decline of Portuguese sea power and the rise of England in the seventeenth century, a British prime meridian was established passing through Greenwich, England. In 1884, a conference of European nations ratified the new prime meridian as the world's standard. It remains so to this day.

The problem of determining longitude involves knowing the time at the prime meridian and the time aboard the ship on which one is traveling. Earth rotates on its axis once every 24 hours. One revolution is 360 degrees of longitude, so 360 ÷ 24 gives 15 degrees per hour. Thus if the ship has a clock which accurately gives the time at the prime meridian and the time on board the ship, then the longitude of the ship can be calculated.

This may seem a trivial matter to people of the twenty-first century who possess incredibly stable and accurate time-pieces, but such was not the case for navigators of the fifteenth, sixteenth, and early seventeenth centuries. Clocks of that time period were of the pendulum type and were useless on the deck of a rocking ship. An obscure English clockmaker, John Harrison, would finally solve the longitude problem in 1764 with the invention of a clock that could keep time to within less than a second of accuracy per day and could withstand the rocking and temperature extremes experienced aboard a ship on the open sea. Harrison's invention was the forerunner of the modern chronometer that is present on all ocean-going vessels today.

At about the same time that Harrison was creating his chronometer, a more stable and accurate version of the astrolabe, called the sextant, was invented. Together, these two inventions ushered in a new, more scientifically based era of navigation.

Modern Navigation

In the cold-war era of tension between the United States and the former Soviet Union, the U.S. Department of Defense authorized about $12 billion for research and development to devise and perfect a navigational system that could provide an almost instantaneous and accurate reading for the location of any point on the surface of the Earth. The military's purpose was to allow pinpoint accuracy in the launch of its missiles from submarines in the ocean. Yet in the mid-1990s, this Global Positioning System technology was made available to the civilian population.

GPS Technology. The Global Positioning System (GPS) utilizes satellites in orbit around Earth to send signals to Earth-based devices for the purpose of calculating the exact latitude and longitude of the Earth-based unit. The ability of computer-chip makers to pack more memory onto smaller and smaller chips has resulted in GPS devices that can be held in the palm of a hand and are reasonably priced.

The mathematics behind GPS is essentially the same as that used by Abraham Zacuto to develop his tables for use with the astrolabe except that the calculations are done by computer through the trigonometric idea of triangulation . The distances from a handheld GPS receiver to three of the orbiting satellites is determined by the time-encoded signals traveling at the speed of light from each satellite to the receiver. Then using the familiar "rate × time = distance" equation, the GPS device calculates the distance to each satellite from the device's position on the ground. With these three measurements, the GPS can calculate this position to within a few meters of accuracy. Essentially, the distances to the three satellites can be thought of as the radii of three imaginary spheres. These three spheres will intersect in two points, only one of which will be a reasonable position on Earth's surface. The GPS device will give a reading of the latitude and longitude of this position.

With the introduction of the Global Positioning System, the age-old problem of knowing where you are on Earth's surface at any given time has essentially been solved, assuming that you are carrying a GPS receiver at all times. That is now the case for most ocean vessels and airplanes, both commercial and military. Many of the latest model cars come equipped with navigation systems powered by GPS technology. This may well become standard equipment on all vehicles in the near future.

Maps and Planning. Even without sophisticated technology, it is still possible to plan trips on land using a map of the area you are interested in navigating. Using a well-marked map, you can decide whether you want to take a scenic route or a more direct and quicker route. Using the mileage markings on the map or the legend that gives the scale of the map, you can determine how far you must travel using each route. With a little mathematics, you can determine the approximate length of time required to reach the destination.

If you know that you can average about 60 miles per hour on the direct route, which is 240 miles long, then you calculate 240 miles divided by 60 miles per hour to get 4 hours as the approximate time to make the trip. If the scenic route is 280 miles and you can only average 40 miles per hour then it will take 7 hours to travel the scenic route, by calculating 280/40.

You can also estimate the gasoline cost for each route. If your car gets about 24 miles to the gallon when traveling at 60 miles per hour on the open highway, and if gasoline is $1.50 per gallon, then you can calculate the gasoline cost for the direct route as approximately 240 miles divided by 24 miles per gallon times $1.50 per gallon = $15.00. Of course if you are coming back by the same route, you could double this to $30.00 for the round trip. Similar calculations would allow you to compare the cost of this route to that of the scenic route, taking into account that your car may get poorer gas mileage on the scenic route due to frequent starts and stops, climbing hills, and the like. Perhaps future generations of GPS devices will do these calculations as well as letting you know where you are at each second of your trip.

see also Angles of Elevation and Depression; Angles, Measurement of; Distance, Measuring; Flight, Measurements of; Geometry, Spherical; Global Positioning System; Mile, Nautical and Statute.

Stephen Robinson

Bibliography

Andrews, William, ed. The Quest for Longitude: The Proceedings of the Longitude Symposium. Harvard University, Cambridge, Massachusetts, November 4–6, 1993. Cambridge, MA: Collection of Historic Scientific Instruments, Harvard University, 1996.

Ferguson, Michael. GPS Land Navigation. Boise, ID: Glassford Publishing, 1997.

Sobel, Dava. Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time. New York: Walker and Company, 1995.

Toghill, Jeff. Celestial Navigation. New York: W. W. Norton and Company, 1998.

Internet Resources

All About GPS. Timble. <http://www.trimble.com/gps/index.htm>.

"Early Navigation Methods." The Mariner's Museum—Newport News, Virginia. August 1997. <http://www.mariner.org/age/earlynav.html>.

Latitude: The Art and Science of Fifteenth-Century Navigation. <http://www.ruf.rice.edu/~feegi>.

Navigation

Navigation is the art of finding one's way from one location to another. This appears pretty simple in the age of interstate highways and well-marked street intersections: follow the road signs or a map and the task should be easy. But imagine you are in an aircraft or a ship and all you can see is the blue sky above you and the clouds below you or nothing but waves. Now, imagine it is night and you can not see a thing! In our computer-centered society, we have the digital means to use satellite technology and other electronic tools to help us figure out where we are and how to get where we want to go. Long before these were available, however, mathematical navigational systems were devised to guide ship captains and travelers of centuries past; these time-tested tools provide the foundation upon which our sophisticated, electronic navigational tools are built.

Early Navigational Foundations

To aid in navigation and map making, a coordinate system was created using virtual lines of latitude and longitude that cross at 90 degree angles. Latitude is referenced to a circle circumscribed around the Earth called the equator, which is at what is called zero latitude. North of the equator, the latitude lines are parallel to the equator and are called "north latitude." The geographical North Pole is 90 degrees north latitude and the circle at that latitude has such a small radius it is virtually a point. The South Pole is 90 degrees south latitude. The angle of latitude is the angular difference between two lines: one drawn from the center of the Earth to the equator and one drawn from the center of the Earth to the latitude in question.

Longitude lines also run around the Earth but through the North and South Poles. The reference line, the zero meridian, runs through the Royal Observatory in Greenwich, just outside of London, England. Lines of longitude are designated east and west from the zero meridian. Time zones are also a function of longitude and the reference time zone from which all others are measured is called GMT, or Greenwich Mean Time. This brings up an important subject: the inseparable relationship between time and navigation.

Time Zones, Sundials, and Longitudinal Calculations

Nearly everyone is familiar with the sundial, which uses the shadow of its angled center piece, called the gnomon, to "tell" time. The sundial tells local time, based on its relationship to the Sun in any given place. As an example, at exactly "high noon" the gnomon produces no shadow as the Sun is precisely midway between sunrise and sunset. But high noon occurs at different times at different places on the Earth. This is why there are time zones.

There are generally 24 time zones corresponding roughly to the one-hour segments of a 24-hour Earth day. There are some odd time zones with half-hour and even smaller increments, but these are rare. The actual time of high noon does not jump in one-hour steps, of course, but changes gradually as one travels around the Earth. If the sundial is adjusted so the gnomon points to true north, the sundial will show true solar time. The difference between true solar time at some location and the true solar time at the zero meridian can be used to calculate longitude.

In order to use the sundial to determine longitude in relationship to the zero meridian, however, a traveler must have an accurate mechanical clock set to precise GMT before traveling. The English government offered a substantial reward in 1761 for the invention of an accurate clock that would operate on a ship for precisely this reason. While the latitude of a ship could be determined by measuring the position of the Sun at its highest point, without a point of reference to time, determining longitude without an accurate GMT reading required lunar observations and time-consuming, difficult mathematical computations. Trade and exploratory ships could travel more safely, accurately, and economically with the use of reliable time-keeping technology.

The requirements for navigation became much more stringent when humans began to travel by air. A ship traveling on open water is relatively slow, so finding a "fix" or position every few hours was sufficient. Even if fog or other bad weather prohibited taking fixes, the ship could slow down or stop until conditions improved. This is not possible with aircraft! Accurate position fixes must be available continuously. Clock and sundial technology could not perform this complex task!

From Radio Beacons to On-Board Computers

One of the first aircraft navigation systems, invented in the 1920s, used radio beacons. The aircraft could hop from one beacon to another on what were called airways. Position could be determined from these airways but this involved tedious procedures that were not only difficult but time-consuming, as well. The beacons were strategically located so that the airways passed directly over airports to simplify the navigation. Similar homing beacons were used for ships but only near shore due to the limited range of the beacon's radio signal.

Later, more sophisticated radio navigation systems for both air and sea actually measured the vessel's latitude and longitude, which was plotted on a navigation chart. This was acceptable for ships at sea but unfolding a large navigation chart and plotting a course in an aircraft cockpit was not particularly convenient. However, because it was the best option at the time, it was done.

What would have been ideal would be a computer that took the latitude and longitude information and automatically calculated steering information. Some ship navigators had access to such a computer, which worked with the first long-range radio navigation systems during World War II. These computers were huge mechanical monsters that were acceptable for a battleship but not suited for aircraft.

It was not until small digital computers became available that long-range navigation became commonplace in aircraft. The aircrew could enter the desired final or intermediate destinations, called "waypoints," into the computer, and the computer would calculate the steering information, which was displayed with an indicator. It was even possible to use the steering information in the form of electrical signals to control a ship or aircraft with an autopilot.

Long-Distance Navigation Systems

Since World War II, several improved long distance radio navigation systems have been developed. The first was LORAN, which stands for "long range navigation." Shortly after LORAN was Omega, which was followed by a much-improved LORAN called LORAN-C. Finally, in the late 1970s, the ultimate system was developed, the satellite-based Global Positioning System or GPS. GPS can provide navigation anywhere on Earth within less than one meter (about 3 feet) of error, which is superior to any previous navigation system.

The GPS navigation system consists of a "constellation" of 24 satellites in well-known orbits. A network of ground stations controls the orbits and functions of the satellites. Satellites transmit radio signals that are used to measure the distance from the user to each satellite. A computer solves the geometry problem and determines the user's position.

GPS depends on the very accurate atomic clocks located in the satellites and ground control stations. It is fascinating to realize that the secret to accurate navigation in 1761 was precise clocks, and the same remains true today.

In addition to a radio receiver, the GPS user equipment has a rather extensive computer. It is necessary to separate the signals from the satellites, which are all transmitted on the same frequency and sorted out by the computer. The computer knows which satellites are present and where they are in their orbits. It inserts a number of calibration factors and calculates the position of the user equipment in latitude, longitude, altitude, and precise time. Most GPS receivers used for aircraft have large databases, which include the locations of airports, radio navigation aids, airways, and so on.

GPS products for consumer use have become increasingly popular since the late 1990s. In addition to providing convenience and security to people driving in unfamiliar areas, GPS technology such as the General Motors "OnStar" navigational system, which connects drivers to assistance operators via GPS satellites, can help save lives by directing drivers to hospitals or police stations near where they are, should an emergency arise.

see also Aircraft Traffic Management; Geographical Information Systems; Global Positioning Systems; Satellite Technology.

Albert D. Helfrick

Bibliography

Clausing, Donald J. Aviator's Guide to Navigation. Blue Ridge Summit, PA: TAB Books, 1992.

Hotchkiss, Noel J. A Comprehensive Guide to Land Navigation with GPS. Herndon,

VA: Alexis, 1995.

Lewis, Ralph. By Dead Reckoning: Recollections of a Master Navigator. McLean, VA: Paladwr Press, 1994.

Sonnenberg, G. J. Radar and Electronic Navigation. Boston: Butterworths, 1988.

Navigation

In order for a spacecraft to close in on a destination such as the International Space Station or to enable the space shuttle to retrieve the Hubble Space Telescope, scientists must do most of the groundwork prior to the launch phase. Scientists need to know the workings of the solar system well enough to predict a spacecraft's destination, when to launch, and how fast it must travel to meet the target in space.

Gravity also must be taken into account. Gravity exerted by large bodies like planets and the Sun will alter the trajectory of a spacecraft. Difficulties arise when a spacecraft is allowed to deviate too far off the intended course. If the error is realized late in the flight, the target may have moved a long distance from where the ship was originally supposed to meet it. The mistake often cannot be remedied because spacecraft do not carry enough fuel to make large course corrections. The launch vehicle pushes the spacecraft onto a heading that pushes it in the direction of a final destination. Sometimes mission planners use the gravity of a planet by swinging by that object to change the path of a spacecraft.

Spacecraft Position

Spacecraft navigation is comprised of two aspects: knowledge and prediction of spacecraft position and velocity; and firing the rocket motors to alter the spacecraft's velocity.

To determine a spacecraft's position in space, NASA generally uses a downlink, or radio signal from the spacecraft to a radio dish in the Deep Space Network (DSN) of ground receivers. The distance between Earth and the spacecraft is measured by sending a radio signal up from Earth with a time code on it. The spacecraft then sends back the signal. Because all radio waves travel at the speed of light, scientists can determine how long it took for the signal to travel and calculate the exact distance it traveled.

A more precise way of measuring distance uses two radio telescopes. Spacecraft send a signal back to Earth. Three times a day, this signal can be received by two different DSN radio telescopes at once. Researchers are able to compare how far the spacecraft is from each signal. Mission trackers can then calculate the distance to a known object in space whose location never changes, like a pulsar (pulsing star). From the three locations (two telescopes and a pulsar), scientists can use a technique called triangulation to get the ship's location.

By using a different process called Optical Navigation, some spacecraft can use imaging instruments to take pictures of a target planet or other body against a known background of stars. These pictures provide precise data needed for correcting any discrepancy in a spacecraft's path as it approaches its destination.

The exact location of the spacecraft must be determined before any course correction is made. The spacecraft will first fire small rockets to change the direction it is pointing. After that, the main thruster will give the spacecraft a push in the new direction.

During rendezvous and proximity operations, taking the space shuttle as an example, the onboard navigation system maintains the state vectors of both the orbiter and target vehicle. During close operations where separation is less than 15 miles, these two state vectors must be very accurate in order to maintain an accurate relative state vector. Rendezvous radar measurements are used for a separation of about 15 miles to 100 feet to provide the necessary relative state vector accuracy. When two vehicles are separated by less than 100 feet, the flight crew relies primarily on visual monitoring through overhead windows and closed-circuit television.

see also Gyroscopes (volume 3); Mission Control (volume 3); Navigation from Space (volume 1); Tracking of Spacecraft (volume 3).

Lisa Klink

Bibliography

Stott, Carole. Space Exploration. New York: Dorling Kindersley Publishing, 1997.

Internet Resources

"Spacecraft Navigation." Basics of Space Flight. Jet Propulsion Laboratory, California Institute of Technology. <http://jpl.nasa.gov/basics/bsf13-1.html>.

navigation The complex process that enables animals to travel along a particular course in order to reach a specific destination. Navigation is an important aspect of behaviour in many animals, particularly those, such as birds, fish, and some insects, that undergo migrations. Landmarks, such as coastlines and mountain ranges, are important reference points for navigation but many animals can navigate successfully without the aid of these, by using the sun, stars, magnetic fields, odours, and polarized light. For example, birds use the sun and stars as landmarks and are sensitive to the earth's magnetic fields, while salmon can identify the unique odour of their home river.

navigation Determining the position of a vehicle and its course. Five main techniques are used: dead reckoning, piloting, celestial navigation, inertial guidance, and radio navigation. The last includes the use of radio beacons, loran, radar navigation, and satellite navigation systems. Instruments and charts enable the navigator to determine position, expressed in terms of latitude and longitude, direction in degrees of arc from true north, speed, and distance travelled. See also compass; gyrocompass; sextant

nav·i·ga·tion / ˌnaviˈgāshən/ • n. 1. the process or activity of accurately ascertaining one's position and planning and following a route. 2. the passage of ships: bridges to span rivers without hindering navigation. DERIVATIVES: nav·i·ga·tion·al / -nəl/ adj.

navigation The orientation of itself by an animal towards a destination, regardless of its direction, by means other than the recognition of landmarks. Compare compass orientation and pilotage.

navigation The orientation of itself by an animal towards a destination, regardless of its direction, by means other than the recognition of landmarks. Compare COMPASS ORIENTATION; PILOTAGE.

navigation n.
1. the process or activity of accurately ascertaining one's position and planning and following a route.

2. the passage of ships.
navigational adj.