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