The Science of Navigation

ANCIENT NAVIGATION Mankind’s earliest navigational experiences are lost in the shadows of the past. But history does record a number of instances in which ancient mariners observed the locations of the sun, the moon, and the stars to help direct their vessels across vast, uncharted seas. Bronze age Minoan seamen, for instance, followed torturous trade […]
ANCIENT NAVIGATION Mankind’s earliest navigational experiences are lost in the shadows of the past. But history does record a number of instances in which ancient mariners observed the locations of the sun, the moon, and the stars to help direct their vessels across vast, uncharted seas. Bronze age Minoan seamen, for instance, followed torturous trade routes to Egypt and Crete, and even before the birth of Christ, the Phoenicians brought many shiploads of tin from Cornwall. Twelve hundred years later, the Vikings were probably making infrequent journeys across the Atlantic to settlements in Greenland and North America. How did these courageous navigators find their way across such enormous distances in an era when integrating accelerometers and handheld receivers were not yet available in the commercial marketplace? Herodotus tells us that the Phoenicians used the Pole Star to guide their ships along dangerous journeys, and Homer explains how the wise goddess instructed Odysseus to “keep the Great Bear on his left hand” during his return from Calypso’s Island. CELESTIAL NAVIGATION Eventually, the magnetic compass reduced mankind’s reliance on celestial navigation. One of the earliest references to compass navigation was made in 1188, when Englishmen Alexander Neckam published a colorful description of an early version consisting of “a needle placed upon a dart which sailors used to steer when the Bear is hidden by clouds.” Eighty years later the Dominican friar Vincent of Beauvais explained how daring seamen, whose boats were deeply shrouded in fog, would “magnetize the needle with a lodestone and place it through a straw floating in water.” He then went on to note that “when the needle comes to rest it is pointing at the Pole Star.” The sextant, which was developed and refined over several centuries, made Polaris and its celestial neighbors considerably more useful to navigators on the high seas. When the sky was clear, this simple device–which employs adjustable mirrors to measure the elevation angles of stellar objects with great precision– could be used to nail down the latitude of the ship so that ancient navigators could maintain an accurate east-west heading. However, early sextants were largely useless for determining longitude because reliable methods for measuring time aboard ship were not yet available. The latitude of a ship equals the elevation of the Pole Star above the local horizon, but its longitude depends on angular measurements and the precise time. The earth spins on its axis 15 degrees every hour, consequently, a one second timing error translates into a longitudinal error of 0.004 degrees–about 0.25 nautical miles at the equator. The best 17th-century clocks were capable of keeping time to an accuracy of one or two seconds over an interval of several days, when they were sitting on dry land. But, when they were placed aboard ship and subjected to wave pounding, salt spray, and unpredictable variations in temperature, pressure, and humidity, they either stopped running entirely or else were too unreliable to permit accurate navigation. To the maritime nations of 17th century Europe, the determination of longitude was no mere theoretical curiosity. Sailing ships by the dozens were sent to the bottom by serious navigational errors. As a result of these devastating disasters caused by inaccurate navigation, a special act of Parliament established the British Board of Longitude, a study group composed of the finest scientists living in the British Isles. They were ordered to devise a practical scheme for determining both latitude and longitude of English ships sailing on long journeys. After heated debate, the Board offered a prize of 20,000 British pounds to anyone who could devise a method for fixing a ship’s longitude within 30 nautical miles after a transoceanic voyage lasting six weeks. One proposal advanced by contemporary astronomers would have required that navigators take precise sightings of the moons of Jupiter as they were eclipsed by the planet. If practical trials had demonstrated the workability of this novel approach, ephemeras tables would have been furnished to the captain of every flagship or perhaps every ship in the British fleet. The basic theory was entirely sound, but, unfortunately, no one was able to devise a workable means for making the necessary observations under the rugged conditions existing at sea. THE MARINE CHRONOMETER However, in 1761, after 47 years of painstaking labor, a barely educated British cabinet maker named John Harrison successfully claimed the 20,000 British pound prize, which in today’s purchasing power would amount to about $1 million. Harrison solution centered around his development of a new shipboard timepiece, the marine chronometer, which was amazingly accurate for its day. On a rocking, rolling ship in nearly any kind of weather, it gained or lost, on average, only about one second per day. Thus, under just about the worst conditions imaginable, Harrison’s device was nearly twice as accurate as the finest landbased clocks developed up to that time. During World War II, ground-based radionavigation systems came into widespread use when military commanders in the European theater needed to vector their bombers toward specific targets deep in enemy territory. Both Allied and Axis researchers soon learned that ground-based transmitters could provide reasonably accurate navigation within a limited coverage regime. In the intervening years America and various other countries have operated a number of ground-based radionavigation systems. Many of them – Decca, Omega, Loran – have been extremely successful. But in recent years, American and former Soviet scientists have been moving their navigation transmitters upward from the surface of the earth into outer space. There must be some compelling reason for installing navigation transmitters aboard orbiting satellites. After all, it costs something like $100 million to construct a navigation satellite and another $100 million to launch it into space. Moreover, at least a half-dozen orbiting satellites are needed for a practical spaceborne radionavigation system. WHAT IS NAVIGATION? Navigation can be defined as the means by which a craft is given guidance to travel from one known location to another. Thus, when we navigate, we not only determine where we are, we also determine how to go from where we are to where we want to be. 1. Piloting 2. Dead reckoning 3. Celestial navigation 4. Inertial navigation 5. Electronic or radionavigation Piloting, which consists of fixing the craft’s position with respect to familiar landmarks, is the simplest and most ancient method of navigation. In the 1920s bush pilots often employed piloting to navigate from one small town to another. Such a pilot would fly along the railroad tracks out across the prairie, swooping over isolated farmhouses along the way. Upon arrival at a village or town, the pilot would search for a water tower with the town’s name printed in bold letters to make sure the intended destination have not been overshot. Dead reckoning is a method for determining position by extrapolating a series of velocity increments. In 1927 Charles Lindbergh used dead reckoning when he flew his beloved Spirit Of St. Louis on a 33-hour journey from Long Island to Le Bourget Field outside Paris. Incidentally, Lindberg hated the name. The original name was “dead reckoning” (deduced reckoning), but newspapers of the day could never resist calling it “dead reckoning” to remind their readers of the many pilots who had lost their lives attempting to find their way across the North Atlantic. Celestial navigation is a method of computing position from precisely timed sightings of the celestial bodies, including the stars and the planets. Primitive celestial navigation techniques date back thousands of years, but celestial navigation flourished anew when cabinetmaker John Harrison constructed surprisingly accurate clocks for use in conjunction with sextant sightings aboard British ships sailing on the high seas. The uncertainty in a celestial navigation measurement builds up at a rate of a quarter of a nautical mile for every second timing error. This cumulative error arises from the fact that the earth rotates to displace the stars along the celestial sphere. Inertial navigation is a method of determining a craft’s position by using integrating accelerometers mounted on gyroscopically stabilized platforms. Years ago navigators aboard the Polaris submarine employed inertial navigation systems when they successfully sailed under the polar ice caps. Electronic or radionavigation is a method of determining craft’s position by measuring the travel time of an electromagnetic wave as it moves from transmitter to receiver. The position uncertainty in a radionavigation system amounts to at least one foot for every billionth of a second timing error. This error arises from the fact that an electromagnetic wave travels at a rate of 186,000 miles per second or one foot in one billionth of a second ACTIVE AND PASSIVE RADIONAVIGATION According to the Federal Radionavigation Plan published by the United States government, approximately 100 different types of domestic radionavigation systems are currently being used. All of them broadcast electromagnetic waves, but the techniques they employ to fix the user’s position are many and varied. Yet, despite its apparent complexity, radionavigation can be broken into two major classifications: 1. Active radio navigation 2. Passive radio navigation. A typical active radionavigation system is sketched in Figure 1. Notice that the navigation receiver fixes its position by transmitting a series of precisely timed pulses to a distant transmitter, which immediately rebroadcast them on a different frequency. The slant range from the craft to the distant transmitter is established by multiplying half of the two-way signal travel time by the speed of light. In a passive radionavigation system (see Figure 1), a distant transmitter sends out a series of precisely timed pulses. The navigation receiver picks up the pulses, measures their signal travel time, and then multiplies by the speed of light to get the slant range to that transmitter. A third navigational approach is called bent pipe navigation. In a bent-pipe navigation system a transmitter attached to a buoy or a drifting balloon broadcasts a series of timed pulses up to an orbiting satellite. When the satellite picks up each timed pulse, it immediately rebroadcasts it on a different frequency. A distant processing station picks up the timed pulses and then uses computerprocessing techniques to determine the approximate location of the buoy or balloon.
Most radionavigation systems determine the user’s position by measuring the signal travel time of an electromagnetic wave as it travels from one location to another. In active radionavigation the timed signal originates on the craft doing the navigating. In passive radionavigation it originates on a distant transmitter.