The Pathfinder: How Gladys West shaped the Earth for modern GPS

BY STEVEN JOHNSON

As a young African American girl living on a farm during the Great Depression, Gladys West discovered she had a gift for math. Forty years later, she mapped the shape of Earth and helped invent GPS.

Illustration: Ewelina Gąska

Gladys West

The road to the one-room schoolhouse in Sutherland, Virginia, was three miles long, crossing railroad tracks and route 460, lined with honeysuckle and pines. An African American girl named Gladys Brown, the daughter of sharecroppers, walked the three miles to school each morning, often accompanied by a handful of friends. It was the late 1930s, but other than the occasional automobile passing the children on the highway, the world the girl lived in could have belonged to the 19th century. The small farmhouse where she lived had no indoor plumbing or electricity; when school was out, she would help her mother scrubbing clothes clean on a washboard, pressing them with an iron heated directly from a wood fire. “I dreamed of one day living somewhere bigger, prettier, and different,” she would later write, “but the dreams were vague because I had not been anywhere outside of Sutherland.”

Young Gladys West. Courtesy of Gladys West

Even at an early age, Gladys West (née Brown) was a promising student and a hard worker, sensing that a solid education would be crucial if she wanted to ultimately explore a wider world beyond rural Virginia. She had an aptitude for math, though the resources for actually nurturing those skills were limited, given that the one teacher at the Butterwood Road School—for “colored” students only—had to simultaneously teach a class composed of students ranging from first to seventh grades. And so Gladys West began to nurture her talents on her own. “I counted fenceposts along the road and across the fields as we walked to school, just to have something different to do,” she later recalled. “I became good at it, never realizing that I was sharpening some skills and abilities that I would one day utilize to help calculate the hypothetical shape of the Earth.”

The house where Gladys West grew up. Courtesy of Gladys West

“I dreamed of one day living somewhere bigger, prettier, and different, but the dreams were vague because I had not been anywhere outside of Sutherland.”

A small girl with big dreams. Illustration: Ewelina Gąska

You might well have benefited from those calculations several times today, while you were following the directions of your car’s navigation system, or looking for the nearest Italian restaurant on your phone—or anything else that relies on our modern-day ability to determine our exact geographic location using computers and satellites. Eight-year-old Gladys West wouldn’t have been able to even imagine such a thing, counting fenceposts on her way to the Butterwood Road school, but the path she was on would eventually lead to the creation of one of the modern world’s true miracles: the Global Positioning System, commonly known as GPS.

That map of Earth’s gravitational fields was the final missing piece that allowed the creation of the modern GPS system, with its near-instant results and remarkable accuracy.

Finding space in time

Like many of the core technologies that define the digital age, GPS was an offshoot of American Cold War competition with the Soviet Union and the threat of nuclear annihilation. After the Soviets launched Sputnik, the first man-made satellite to orbit Earth, in October of 1957, a pair of graduate students at the Applied Physics Laboratory in Maryland devised an ingenious system for tracking Sputnik’s location by analyzing slight variations in the microwave signals the satellite was transmitting, in effect using an antenna’s known location on Earth to calculate the satellite’s unknown location in orbit. Impressed with the demo, the grad students’ supervisor suggested that the approach could be reversed: if you knew the exact location of at least three satellites in orbit above you, by triangulating their various signals you could theoretically determine your location on the ground—or, if you happened to be on one of the new Polaris nuclear submarines the military was building, you could use it to determine your location in the middle of the ocean.

GRAB 1 satellite on top of the Transit 2A, April 29, 1960, NASA Hangar AA. ©US Navy

By 1964, the Navy had deployed the first satellite-based navigation system, a predecessor of GPS called Transit. The system used five satellites and could generate a location that was accurate to within about 150 meters, though it would usually take as long as an hour to obtain a result. In the 1970s, the military began plans for a more advanced system that could produce location data almost instantaneously. But a fundamental problem limited their ability to generate the kind of precise location data that we enjoy today with GPS, which is generally accurate to about one meter. The problem was fundamental in a cosmic sense: it was embedded in the very nature of Einstein’s theory of relativity.

Transit

The initial need for the satellite navigation system was to provide accurate location information on Polaris ballistic missile submarines that the Navy was developing at the time. Sponsored by the Navy, Transit was developed jointly by DARPA and the Johns Hopkins Applied Physics Laboratory. The first prototype, launched in 1959, failed to reach orbit, and it was the following year that the second satellite successfully went through all the tests. Except for submarine tracking, Transit was also used as a navigation system by the surface ships, as well as for hydrographic survey and geodetic surveying, and later for civilian use as well.

When you are measuring microseconds to determine your exact location using GPS, those gravitational variations can make a massive difference—the difference between landing your plane on the runway and crashing it into the airport parking garage.

The ironic thing about GPS is that it is a technology designed to locate your position spatially that is enabled largely by an ultra-precise measurement of time. When your phone picks up signals from GPS satellites, the information it’s receiving is a time-stamp marking of the exact moment each satellite sent out its signal. (Each satellite contains a fantastically precise atomic clock.) Because radio waves take time to travel over long distances, a receiver on the ground can calculate its distance from each satellite by calculating the difference between the transmission time of the signal and its reception. (A satellite farther away from you will have an earlier transmission time, a satellite closer to you will have a later transmission time.) Because the satellites have predictable orbits, a GPS receiver can determine its location if it can get an accurate reading of its distance from four satellites. In a world of Newtonian physics, this would all work perfectly. But Einstein proved that time was distorted by gravity—the technical term for it is “time dilation”—and Earth’s gravitational fields are wildly inconsistent, depending on where you happen to be on the planet. When you are measuring microseconds to determine your exact location using GPS, those gravitational variations can make a massive difference—the difference between landing your plane on the runway and crashing it into the airport parking garage.

Time dilation

One of the main concepts of the theory of relativity by Albert Einstein, time dilation describes the difference in the elapsed time as measured by two clocks, either due to a relative velocity between them, or to a difference in gravitational potential between their locations. In simple terms, the time slows down when the object moves really fast.

All of this would be relatively easy to calculate if Earth itself happened to be a perfect sphere. But while it looks to the naked eye from space like an exact circle of Euclidean perfection, in reality our planet bulges out slightly at the equator, while the poles are flatter than they would be in a true sphere. And Earth’s gravitational fields are also distorted by many of its distinguishing features: tides, mountain ranges, and ocean trenches. To make GPS work, you didn’t just need satellites and atomic clocks. You also needed to know the true shape of Earth’s gravity.

And that is what Gladys West figured out.

Perfectly imperfect Earth. Illustration: Ewelina Gąska

“GPS Only Exists Because Of Two People:
Albert Einstein And Gladys West.”

A solitary leap into an unknown world

As a teenager, West moved from the one-room schoolhouse in Sutherland to the Dinwiddie Training School for the Colored, where a charismatic math teacher named Mr Lee had a notable skill at making geometry “enjoyable, and relating it to everyday life.” She graduated as the class valedictorian, earning herself a scholarship to the historically Black public college, Virginia State, where she majored in mathematics—and after a few years working as a schoolteacher, returned to get a master’s degree in the same field.

Gladys West and Sam Smith look over data from the Global Positioning System, 1985, Dahlgren, VA. ©US Navy

By this point, it was the mid-1950s, and a new employment position was beginning to appear in government agencies and military institutions around the country, a job that would go on to become one of the most highly-coveted careers in the 21st century: computer programmer. In the summer of 1955, IBM delivered to the Naval Proving Ground in Dahlgren, Virginia, a custom-built, room-sized, vacuum-tube-based machine that was, by many accounts, the most powerful computer the world had ever seen. The Navy dubbed it NORC, short for Naval Ordnance Research Calculator. The Navy’s primary interest in this “supercomputer” derived from its ability to do complex ballistic computations that could project the exact trajectory of missiles, factoring in numerous variables—wind, air pressure, temperature, and more. But early experiments with the machine demonstrated that it could be used for space-related projects as well. Shortly after the NORC machine had been installed at the Dahlgren location, an astronomer named Paul Herget used it to calculate the orbits of multiple planets, including the most precise measurement of Earth’s recent orbit ever recorded. "We used nine hours of running time,” Herget boasted at the time, “and completed more computations than had ever before been done at one time in the history of astronomy."

Paul Herget

The astronomer Paul Herget, who was at the time the Director of the Cincinnati Observatory, was so impressed by NORC that he named an asteroid after the computer. Beyond Herget’s calculations, other scientists used NORC’s then-extraordinary powers to compute the wave function of helium atoms and analyze patterns in the Moon’s orbit. But Herget knew even more impressive machines were on the way: “A calculation involving a billion arithmetical operations on large numbers can be completed on the NORC in approximately one day,” he said in 1958, “yet more powerful calculators are foreseen to to meet the ever-increasing demands of science and technology where the solution of a large problem generates even larger problems."

Naval Ordnance Research Calculator

The NORC machine had originally been built at Columbia University’s Watson Scientific Computing lab in the early 1950s; according to some accounts, it remained the most powerful computer in the world for almost ten years. It cost IBM $2.5 million to build at the time—which would be roughly $25 million in today’s dollars. The computer lacked a video display; output from the machine’s calculations were generated by two printers capable of generating 150 lines per minute. Despite its immense size and fragile vacuum tubes, the machine proved to be remarkably reliable: more than 90% of its time was spent online running 15,000 operations per second. Of course, by modern standards, NORC was preposterously slow; the iPhone 13, for instance, does 15 trillion operations a second.

But getting NORC to run all those calculations required humans to input and format the data—and the instructions for how to manipulate that data—in a manner that was intelligible to the machine. In 1955, there were no computer science majors to hire, and so organizations like the Naval Proving Ground sought out potential employees with a background in mathematics, with the idea that they would be able to learn the new skill of “computer programming” on the job. At the time, Gladys West was teaching high-school math in Virginia, but still dreaming of a more adventurous life. “I was sending job applications everywhere,” she later recalled. “I just kept thinking that there was something else that I was meant to do.”

“I was sending job applications everywhere. I just kept thinking that there was something else that I was meant to do.”

One of those applications was sent to the Naval Proving Grounds, and much to her surprise, she found herself with a job offer to join the team working with the NORC supercomputer. West had no way of knowing it at the time, but she was part of a cohort of African American women who were joining branches of the military—and eventually NASA—to work as computer programmers, most famously Katherine Johnson, Mary Jackson, and Dorothy Vaughan whose work in the space program was celebrated in the film Hidden Figures. But from West’s point of view, she was making a solitary leap into an unknown world. “I would be going to a place where I knew no one, not even my supervisor, because I was never interviewed,” she thought. “Questions were swirling in my mind—How many Black employees would be there, and would I be comfortable with this new work and living environment? Lastly, would I be smart enough to do the work they hired me to perform? All these questions came to mind because I was going to be a long way from that little farm in Sutherland, where I knew those tobacco fields like the back of my hand.”

Other women in the military and NASA

Arguably the most celebrated of the African American mathematicians profiled in the book and film Hidden Figures, Katherine Johnson played a crucial role in calculating the launch trajectories and return paths for the Apollo astronauts. Much like Gladys West, Johnson was born in a poor rural community in the mid-Atlantic—in her case West Virginia—and demonstrated an early prowess at math. In addition to her role calculating the trajectory of the successful Apollo 11 flight that landed on the Moon, she also contributed to the heroic efforts to improvise a safe return for the astronauts on the failed Apollo 13 mission. Johnson was awarded the Presidential Medal of Freedom by Barack Obama in 2015.

Shape of Earth

West’s nervousness about her new role turned out to be unwarranted; programming the NORC machine came easily to her. She had a gift for quickly tracking down “bugs” in the software, as they were starting to be called, and she was brilliant at optimizing the algorithms to make them more efficient. While she was only one of four African Americans employed at the Dahlgren center, one of them turned out to be another mathematician named Ira West, then working on submarine missile programs. The two married in 1957 and would go on to have three children. She took his last name, and from that point on she was known as Gladys West.

She had a gift for quickly tracking down “bugs” in the software.

Against the odds. Illustration: Ewelina Gąska

West and her husband did battle against discrimination inside the Navy over their subsequent careers, but to their credit, military institutions like the Dahlgren center and NASA offered more opportunity to Black women to excel in intellectually challenging positions than most private sector enterprises did during that period—and West took full advantage of the opportunity. After the shocking Sputnik launch at the end of that year, the military’s computing resources were increasingly devoted to its embryonic satellite program, including TRANSIT, the predecessor of GPS. By the 1960s, West was working on experimental satellite altimeter systems that were designed to measure the exact shape of the Earth. In the following decade, she was promoted to project lead for the SEASAT program, which deployed a new kind of three-dimensional radar technology to detect oceanographic conditions, including winds, water temperature, ice formations, and other crucial data.

Gladys West with her husband Ira West at their wedding. Courtesy of Gladys West

“Many hotels in the south still prohibited Blacks from staying at their properties. After all I had done for my country, there was still discrimination that I was being subjected to.”

All of that work culminated in a period in the late 1970s and early 1980s, when West led a five-person team programming an IBM Stretch 7073 computer to calculate what is technically known as the “geoid”—a description of the Earth’s true gravitational shape. Imagine a hypothetical planet entirely covered by ocean water, with no land masses—but still influenced by the same gravitational forces of the real Earth, the ones created by mountain ranges or deep sea trenches. Instead of an even sea level distribution across its surface, there would be subtle undulations in the height of the oceans: sea levels would be slightly higher in places experiencing lower gravitational forces and vice versa. The geoid is a mathematical description of that shape. Not only did Gladys West create the first accurate account of the geoid, but she even wrote a handbook for future technicians describing the best techniques for creating even more accurate models of the geoid. That map of Earth’s gravitational fields was the final missing piece that allowed the creation of the modern GPS system, with its near-instant results and remarkable accuracy.

“It was exciting that it was new and there was so much data,” West recalls now. “But it was also challenging to use a new computer language. We had to learn to divide the huge data sets into smaller segments to efficiently use the computer.”

Courtesy of Gladys West

Not only did Gladys West create the first accurate account of the geoid, but she even wrote a handbook for future technicians describing the best techniques for creating even more accurate models of the geoid.

Crafting the geoid. Illustration: Ewelina Gąska

To an outside observer, West’s work during this period might reasonably have seemed esoteric—perhaps useful for oceanographers or nuclear submarine navigators, but irrelevant to the rest of us. West later claimed that she herself was not fully aware of the impact her work would ultimately have on our everyday routines in the 21st century. (“When you’re working every day, you’re not thinking, 'What impact is this going to have on the world?’,” she told a newspaper reporter. “You're thinking, 'I've got to get this right.’”) Her calculations of the geoid had been classified information, and the GPS platform itself was exclusively used by the United States military. By definition, it was difficult for the significance of the work to reach a wider audience. “I had no idea that the result would be GPS as it is today,” she says now. “I didn’t actually know everyone who was using the data because it was classified at the time.”

But all that began to change on September 1, 1983, when a Korean Airlines 747 en route to Seoul from New York City was shot down by Russian fighter planes after a navigation error using land-based beacons caused the plane to drift into Russian airspace. Shortly afterwards, President Ronald Reagan declared that satellite navigation should be a “common good” and allowed the private sector access to the technology. First adopted commercially in the form of automobile navigation systems in the 1990s, GPS hit true ubiquity when Apple added a GPS receiver to the iPhone3G in 2008, allowing everything from geo-tagged photos to augmented reality games to tracking apps for parents who want to keep an eye on their children’s locations. Modern devices using GPS can determine your exact location within a few meters—a level of accuracy that would have been unthinkable without Gladys West and her geoid.

Commercialization of GPS technology

The downing of Korean Air flight 007 was one of the most tense moments of the final decade of the Cold War. After the commercial aircraft had drifted into prohibited Soviet air space, Russian interceptors, who believed the 747 was an American spy plane, fired several warning missiles to deter the plane. When they were ignored, the Soviets destroyed the Korean plane with K-8 missiles. All 269 passengers and crew on board the plane were killed. Then-President Ronald Reagan denounced the shooting as “a crime against humanity that must never be forgotten.” Shortly thereafter, the White House announced that the GPS system would be made available for civilian use to avoid such tragedies in the future.

Not only were West’s contributions unrecognized at the time, but in the middle of her groundbreaking work calculating the geoid, West found herself still discriminated against because of the color of her skin. “We worked with research teams from other facilities such as the Naval Research Laboratory in Washington, DC, and all over the country,” she later recalled. “I traveled to the Wallops Island Station on Virginia’s Eastern Shore to observe tests and Doppler satellite launchings a few times, but in some other places there were still barriers to business travel for me. Many hotels in the south still prohibited Blacks from staying at their properties. After all I had done for my country, there was still discrimination that I was being subjected to.”

Helping the world navigate through life. Illustration: Ewelina Gąska

West and Einstein: Parents of GPS

West continued to work at the Dahlgren facility—later renamed the Naval Surface Warfare Center—for the rest of her career, ultimately retiring in 1998 at the age of 68. But the ambition that she had first experienced as a child at the Butterwood Road School led her to enroll in graduate school with the idea of finally earning a PhD post-retirement. Though she suffered a stroke in the middle of the process, West ultimately received a doctorate in public administration from Virginia Tech. And yet, despite the long career and the pivotal role she played in creating GPS, West’s achievements were still almost entirely unacknowledged. In the 2010s, a few conversations with her former sorority sisters, who were shocked to hear that their unassuming friend had been on the cutting edge of a technological revolution, prompted West to write her autobiography, It Began With A Dream. The combination of West’s book, and the focus on the Black NASA mathematicians profiled in the movie Hidden Figures, finally cast a spotlight on West’s contributions, more than 50 years after she had first started analyzing satellite data and exploring the true contours of the planet Earth.

Gladys West was inducted into the Air Force Space and Missile Pioneers Hall of Fame during a ceremony in her honor at the Pentagon in Washington, ©US Air Force

Inspiration for Hidden Heroes

Hidden Figures is a 2016 American biographical drama loosely based on the 2016 non-fiction book by Margot Lee Shetterly about African American female mathematicians who worked at NASA during the Space Race. As we’re exploring the potential scope of the Hidden Heroes initiative, Hidden Figures served us as one of the benchmarks. Similarly, as the film aimed to uncover the hidden history behind unknown heroes who contributed to conquering space, we wanted to shed light on the heroes behind the software we take for granted today. It happened that Gladys West made significant contributions in both areas.

In 2018, she was the recipient of the Air Force Space and Missile Pioneers Award, which honors the “innovators whose vision and perseverance overcame the obstacles of the unknown, those who transformed the cutting edge of technology into operational systems, and those who dedicated their lives to exploring space in support of our national security concerns.” Several years later, the Royal Academy of Engineering awarded her the Prince Philip Medal. During the 25th annual Webby Awards that same year, she received the Lifetime Achievement Award for her contributions to GPS. After decades of obscurity, the pendulum of celebrity finally swung in the other direction. A profile in Forbes Magazine announced in its headline—only slightly hyperbolically—“GPS Only Exists Because Of Two People: Albert Einstein And Gladys West.”

Air Force Space Command Vice Commander Lt Gen DT Thompson and Gladys West with as she is inducted into the Air Force Space and Missile Pioneers Hall of Fame during a ceremony in her honor at the Pentagon in Washington, DC, December 6, 2018. US Navy. Adrian Cadiz, ©US Air Force

Awards and recognitions Gladys West received for her contributions to the development of GPS. Courtesy of Gladys West

“It is unbelievable how far I have traveled,” West says now. “I didn’t know how far I was until I took a step back and looked at the whole picture.”

It was all an extraordinary journey for a sharecropper’s daughter, who had dreamed of a wider life beyond the one-room schoolhouse on Butterwood Road. Today, Route 460—the road young Gladys West used to cross on her way to school as a child—is a major artery in Virginia, four-lane highway connecting Lynchburg to Roanoke. The drivers speeding along it are traveling too fast to count the fenceposts or smell the honeysuckle the way she did as a little girl. But the GPS system that guides them on their way relies on a model of the Earth that Gladys West first created a half century ago.

Eight-year-old Gladys West wouldn’t have been able to even imagine such a thing, counting fenceposts on her way to the Butterwood Road school, but the path she was on would eventually lead to the creation of one of the modern world’s true miracles: the Global Positioning System, commonly known as GPS.

Steven Johnson is the bestselling author of 13 books, including Where Ideas Come From. He’s the host of the PBS/BBC series Extra Life and How We Got to Now. He regularly contributes to The New York Times Magazine and has written for Wired, The Guardian, and The Wall Street Journal. His TED Talks on the history of innovation have been viewed more than ten million times.