Where on Earth?

ON THE COVER:

where on earth?

It can guide emergency dispatchers or surveillance drones, and other applications are on the way; GPS has come a long way since Desert Storm.

By Frank Wicks

The Global Positioning System is a technological marvel that has found unexpected uses. It was conceived by the U.S. Department of Defense 30 years ago, with the specific objective of providing a means for ground troops to pinpoint their position. Military applications over the last decade have gone far beyond the original intentions.

However, unforeseen engineering, scientific, commercial, and hobbyist applications are surpassing military uses. The terrorist attacks of September 11 have further stimulated a rapidly growing market for GPS equipment that is forecast to reach $41 billion by 2006.

The partly operative GPS was first used for determining troop positions and for air navigation during the 1991 Gulf War, which was fought in unrelieved desert. A decade later, GPS has become a critical technology used in the United States military operation in Afghanistan.

Bombs, which since World War I have been dropped from aircraft with limited accuracy, can now be equipped with a $20,000 kit comprising a computer, a GPS receiver, and a means of steering, to be delivered with high precision.

While newspapers and television call these devices smart bombs, engineers would classify them as autonomous robots. The military name is JDAM, for "joint direct attack munitions."

Meanwhile, the GPS provides guidance for a new generation of unmanned surveillance aircraft. The Global Hawk and Predator can fly over distant parts of the world and transmit images to any other location.

The military originally set up a positioning system with two levels of accuracy. A degraded signal accurate to 300 feet was available for receivers without a military code. The end of the dual system, in May 2000, opened up opportunities for civilian use.

The view from above: Each of the two dozen GPS satellites circles the Earth every 12 hours at an altitude of more than 12,000 miles.

Traditional methods of surveying, for example, require benchmarks of known coordinates, followed by a sequential process of measuring angles and distances to calculate the coordinates of any other point. A GPS receiver uses satellites for benchmarks and rapidly processes timed signals into precise values of longitude, latitude, and elevation.

Current air traffic control coordinates the position, speed, and direction of aircraft from information obtained by radar, which has limited range and discontinuities. A GPS receiver on each aircraft could continually radio the plane's coordinates to a control center. The method could avoid airport delays and let planes fly the most direct routes.

(GPS plays a key role in a new, advanced flight navigation system described in "Tighter Air Control," also in this issue.)

Wildlife managers are installing GPS transmitters on animals, and fishermen are using GPS to mark the best spots. GPS locators on police cars and taxis continually radio positions, so dispatchers can assign the nearest available vehicle.

Car rental agencies, trucking companies, and railroads are able to monitor the location, speed, and route of any vehicle. In this case, GPS is raising legal issues related to the owner's rights over property versus a user's right to privacy.

Hobbyists have created an international GPS-based scavenger hunt called Geocaching. In May 2000, a GPS enthusiast buried a container in Oregon and posted the coordinates on the Internet. A year later, the Web site, geocaching.com, listed 4,100 caches in 60 countries. An estimated 50,000 participants are now hiking, climbing mountains, or scuba diving to locate caches.

The basic equipment is a $100 GPS receiver the size of a pack of cigarettes. A typical site is by a stream in a nature preserve posted at 42 degrees, 47.506 minutes north and 73 degrees, 51.633 minutes west. Since one minute of latitude is one nautical mile, or 6,080 feet, coordinates to the third decimal place define a location within 6.08 feet. The player may find a can tied to the trunk of an apple tree. The can contains a logbook and some token or a picture. The finder signs the log, takes the token, and replaces it with a similar item for the next finder.

An early concern was that GPS would also be available to adversaries. The suicide pilots of September 11 had trained with GPS. On a clear day, GPS was not needed to locate the 110-floor World Trade Center towers, but may have been used for finding the low-profile Pentagon building.

Finding the Way

Whether by ground, sea, or air, there are two parts to the navigation problem. The first is to determine your position, and the second is to find the destination.

A coordinate system provides a common basis for defining positions. Since the Earth is a sphere with a fixed axis of rotation, latitude has been defined as the angular distance from the equator. The reference point, or meridian, for the east and west longitude is arbitrary.

The need for a universal standard has resulted in a north and south line passing through the Greenwich Observatory on the outskirts of London as the prime meridian, which defines zero degrees longitude. East and west meet again in the Pacific at 180 degrees.

Christopher Columbus was lacking in both references and navigational techniques in 1492. He didn't know where he was going, he didn't know where he was when he found a new land and civilization, and he didn't know where he had been when he returned to Spain.

Columbus had a magnetic compass to determine direction and he determined latitude by measuring the angle of the North Star above the horizon. He had no method for determining longitude, which requires a precise measure of time.

The circumference of the Earth is about 21,600 nautical miles. Our 24-hour day corresponds to a rotating speed of approximately 900 nautical miles per hour at the equator. Every minute of time error results in a 15-nautical-mile error on the equator.

If one travels west by 15 degrees, the sun and the stars will rise and set one hour later. Thus, the time difference of cyclic celestial activity between two locations can determine the change in longitude. However, Columbus had no chronometer. Magellan's ships would circle the world from 1519 to 1522 without being able to measure longitude.

A GPS satellite contains two sets of festive-looking antennas. The thick, outer ones talk to other satellites, while the thin ones in the inner group transmit positioning data to receivers on the ground.

The rapidly expanding fleets of ocean-going sailing ships in the 17th and 18th century compounded the need to know longitude for charting dangerous waters, coastlines, currents, and prevailing winds, as well as for safe and timely arrival at the destination.

The British government in 1714 offered a prize equivalent to $2 million in today's currency for a means of determining longitude to one-half degree accuracy, or about 30 miles, for a voyage to the West Indies.

Self-taught clockmaker John Harrison claimed the prize in 1761, but was paid only a fraction of the sum, years later, by an act of Parliament. By reducing friction and using a temperature-compensated balance wheel, Harrison attained the remarkable precision of one second of error per five days. This clock remains on display at the Greenwich Observatory.

Navigating the Skies

The advent of air travel brought new challenges for navigation. Many air tragedies resulted from navigational failures. Methods progressed slowly, from compass-aided visual methods to increasingly effective radio-based systems, and now to the Global Positioning System.

The first scheduled flights were for postal service in the 1920s. Navigation relied on magnetic compasses and visual landmarks, such as rivers and railroads. Charles Lindbergh crossed the ocean in 1927 by dead reckoning. Estimated wind speeds and directions were combined with measured air speed to calculate the continually changing compass heading for a great circle route from Newfoundland to a point on the coast of Ireland.

Radio navigation was in its infancy in 1937, when Amelia Earhart and her navigator, Frederick Noonan, disappeared on a 2,500-mile flight from New Guinea to the small target destination of Howland Island in the Pacific. Getting lost was a major cause of air casualties during World War II. As recently as 1983, the Korean airliner shot down after penetrating Soviet airspace may have been 180 miles off course because of navigational errors.

The NAVSTAR constellation puts at least four satellites in line of sight at one time; it takes three to pinpoint location and altitude.

Before 1990, experienced navigators with the best available equipment could sometimes fail to know their positions within 100 miles. Now, anyone with a $100 GPS receiver can readily determine his position within a few feet and relate it to any other points of interest.

The radio system available to Amelia Earhart and World War II navigators is called ADF, for "automatic direction finder." Any radio transmitter of known frequency and location can serve as a beacon. The direction to or from a transmitter can be determined with a direction-sensitive loop antenna.

Commercial radio broadcasts on Dec. 7, 1941, provided a homing signal for the Japanese planes that attacked Pearl Harbor.

The navigator also can calculate a position from two beacons at separate locations. The navigator measures the angle or compass heading to each beacon, and draws lines at these angles through the two beacons on a chart. The intersection is the position of the receiver. Terrain or the atmosphere reflects ADF signals and causes errors. A disoriented pilot can be going away from a beacon while intending to fly toward it.

The VOR, or very high-frequency omnidirectional
radio, of the 1950s uses frequencies of about 120 MHz as compared to one MHz for ADF. Its range, however, is limited to line of sight. Beacons are operated by the Federal Aviation Administration at major airports and across the countryside about 50 miles apart.

A VOR beacon transmits two signals at the same frequency. One signal is uniform in all directions. The other one is directional and phase shifted, with the angle equal to the magnetic direction. Thus, two signals in phase are transmitted north, while the direction-dependent signal lags by 90 degrees to the east, 180 degrees to the south and 270 degrees to the west. The receiver is tuned to the transmitter frequency and processes the phase difference between the signals into the direction of the beacon.

LORAN, which stands for "long-range navigation," was installed for sea and air in the 1960s, and provided a major technological step forward. LORAN was based upon the distance from the transmitter and required precise, synchronized clocks. The LORAN system calculates distance by the time it takes a radio signal to travel from transmitter to receiver.

LORAN was made possible by the atomic clock, which uses the 9,192,631,770 cycles-per-second resonant frequency of a cesium atom for a pendulum. Isidor Rabi researched the vibration of atoms in the 1930s and designed a tuned receiver that detected atomic motion. This work earned him the 1944 Nobel Prize.

The National Bureau of Standards (now the National Institute for Standards and Technology) demonstrated an atomic clock using ammonia in 1949 and an improved cesium-based clock in 1957. Atomic clocks now have an error of less than 1 millionth of a second per year.

Civilian GPS receivers have helped to route taxis and started global scavenger hunts.

Calculating the solution for time-based methods is also challenging. Finding the common intersection points of circles or spheres and time error requires a trial solution and then iterative calculations within a converging algorithm, rather than the simple mathematics of determining the intersection of lines for directional techniques.

The navigator on a ship, for instance, can draw three circles on his chart based on the measured arrival time of signals from three transmitters. If all three circles intersect at the same point, this would indicate the ship's location and that the ship's clock has no error. A ship's clock error is indicated if there is no common intersection for the three circles. The navigator would then assume a value for this time error and draw the circles again, with the actual time being the measured time plus the assumed error.

This process would be repeated until there is a common intersection of the three circles to define position. The time error would show the adjustment needed to the ship's clock to synchronize it with the precise atomic clocks on three transmitters.

Because it is a mathematical procedure, the human calculator is replaced by a microprocessor and a database. The timed signals from the beacons are processed by ingenious algorithms to rapidly and continuously calculate the ship's position and clock error.

LORAN's Limited Reach

Extending LORAN to worldwide coverage would be technically difficult, because the transmitters are of limited range and the Earth is covered by water and competing political jurisdictions.

A satellite signal can reach nearly half the world and no nation has sovereignty over space. Satellite-based beacons also allow the calculation of altitude, along with latitude and longitude.

The high-resolution version of the Global Positioning System reserved for the military became available for civilian use in May 2000.

The Global Positioning System was developed in phases by the United States and was completed in March 1994. It uses 24 satellites called NAVSTAR, for "navigation system timing and ranging." At a height of more than 12,000 miles, the satellites orbit the Earth every 12 hours in six orbital planes at 55 degrees relative to the plane of the Equator and separated by 60 degrees. This pattern means that at least four satellites will be in line of sight at all times from anyplace on Earth. Up to 12 satellites can be in sight from the Equator.

Since the satellites are always in motion, they keep track of their own positions by referring to ground transmitters distributed around the world and coordinated by the GPS Master Control Station in Colorado Springs, Colo.

A GPS receiver can accurately calculate position, velocity, and heading for a person walking at 3 mph or the Space Shuttle traveling at 17,000 mph.

Uses of GPS are growing because the system interfaces with technologies used in such entities as personal computers, Palm Pilots, the Web, and cell phones in ways that had not been envisioned. Integrating GPS receivers into cell phones, for example, can make more efficient use of cell towers and identify the locations of emergency calls.

GPS-based air traffic control is just beginning to be realized. The conversion to GPS has been slow in the United States because the large established system is difficult to change. Australia, with its much smaller system, has been able to convert rapidly to GPS-based air traffic control.

The Global Positioning System may also have profound consequences beyond those we can now identify. Humans have only recently had access to portable and affordable clocks to measure time. Originally a tool for the military, the GPS now provides us with a device to extend our measurements into the three dimensions of space. More unintended consequences for the human condition are quite possible in the future.

Frank Wicks is a professor of mechanical engineering at Union College in Schenectady, N.Y., and a frequent contributor to Mechanical Engineering. He is a GPS-using aircraft pilot and has served on Navy and Merchant Marine ships.