Significant figures: Gladys West

Madeleine Hall looks at one of the minds behind GPS


When was the last time you used a satnav in your car? Tagged your location on a social media post? Or used maps on your phone to figure out where to go? Allow me to introduce a significant figure to you, without whom none of those things would be possible.

Gladys West was a pioneer in geodesy—the branch of mathematics that deals with the precise shape and area of the Earth. Her work was critical in the development of global positioning systems (GPS). Specifically, her work was used to put together extremely precise models of the Earth’s shape, enabling GPS technology which impacts every single one of us on the planet.

Go West

Gladys West, born 27 October 1930, grew up in rural Virginia on her family’s small farm. Her mother worked at a tobacco factory, and her father worked for the railroad while also being a farmer, growing mostly corn, cotton, and tobacco. The Great Depression in the late 1920s and early 1930s hit Virginia farmers especially hard, as smoking declined significantly during this time. When recalling her childhood, West describes waking early to perform work on the farm before going to school for the day, and upon returning from school, having to complete more farm work before doing homework and having dinner. Speaking about her childhood, she has remarked that her family were “rich when it came to having good food and good meals, but when it came to money, we were not so rich”. In her community the typical options for a young black girl’s future were continuing to farm or working at a tobacco processing plant, like her mother.

Virginia State College in the 1930s. Image: Boston Public Library, CC BY 2.0

West knew from an early age that these options were not for her, saying “I realised I had to get an education to get out”. She had an unwavering belief and determination that her life path was taking her far beyond her family’s farm. West graduated high school in 1948, first in her graduating class, which awarded her a full scholarship to Virginia State College (now University), of which there were only two available. Virginia State, founded in 1882, was a black college at the time. The institution did not become racially integrated until the American civil rights movement (1954–1968). At Virginia State College, Gladys West majored in mathematics, and was a member of the Alpha Kappa Alpha sorority, the first intercollegiate historically African American sorority.

Gladys West graduated from Virginia State in 1952 with a bachelor’s in mathematics. She began working as a maths and science teacher immediately after graduation in the small town of Waverly, Virginia. She worked there for two years, before returning to Virginia State College to undertake a master’s in mathematics, from which she graduated in 1955.

In the navy

A Fortran punch card

A pivotal moment came in 1956 when she was hired by a weapons laboratory: the US naval proving ground in Dahlgren, Virginia. During the second world war the proving ground had received groundbreaking (pun intended) early computers to help with ballistic work—the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles and ranged weapons like bullets or bombs.


West was the second black woman ever hired there, and one of only four black employees. She was a human computer, tasked with solving complex mathematical equations by hand, before transitioning to programming the computers there to solve the mathematical equations for her. This programming involved punching holes in stiff pieces of paper termed ‘punch cards’ (typically only 80 characters or 29 centitweets long). These punch cards were then stacked into decks (this was the ‘computer program’), which were then fed into the machine to tell it what calculations to do.

One of West’s first major achievements was participating in the award-winning astronomical study that proved the regularity of Pluto’s motion relative to Neptune in the early 1960s (which deserves its own whole Chalkdust article IMHO). Following this study, she became project manager for Seasat. Seasat was the first satellite designed to obtain data on a range of ocean features, including wave height, water temperature, currents, winds, icebergs, and coastal characteristics. She went on to program an IBM 7030 Stretch computer, which was significantly faster than other machines at the time, to provide increasingly precise calculations to model the Earth’s shape. Many mathematical and physical factors needed to be taken into account for her models, including gravitational forces, tidal forces, as well as the Doppler effect.

GPS is actually the name given to specifically the United States-owned global navigation satellite system (GNSS). As of September 2020, Russia’s GNSS (known as Glonass), China’s BeiDou NSS (known as BDS), and the EU’s Galileo are also fully operational GNSSs. That means there are four fully operational GNSSs in orbit, with the Indian Regional NSS (IRNSS) also planning to expand to a global version in the long term (too many satellites orbiting the Earth? technological overkill? politically necessary?).


Geoid undulation in false colour, to scale. Image: ES Ince, F Barthelmes et al, CC BY 4.0

The Doppler effect needs to be taken into account because the relative movement between a GPS receiver and a GPS satellite causes the received signal to shift in frequency—if the satellite is travelling towards the receiver when sending the signal, the received signal is ‘squished’, whereas in contrast, if the satellite is moving away from the receiver, the received signal is ‘stretched’.

Geoid heights (the shape of the ocean surface) derived from Seasat data were adjusted according to all of these factors, in order to determine a precise mean radius of the Earth. In her paper Mean Earth ellipsoid determined from Seasat 1 altimetric observations, published in 1982, she calculated the mean radius of the Earth to be precisely 6,378.1349km. In a later paper, Determination of ocean geodetic data from Geosat (1987), satellite measurements corrected for orbital and environmental effects resulted in extremely precise geoid height contours and three-dimensional projections of the Earth’s surface.

This detailed mathematical model of the shape of the Earth was a building block for what would become GPS technology. Of course, the satellites themselves fundamentally enable GPS technology to work. However, without the understanding of the Earth’s surface, it would be like building a record player without the vinyl being invented: the technology is useless without the subject of its analysis.

Part of the console for the IBM 7030 Stretch computer

During her time at the naval proving ground, Gladys West attended evening classes and gained a second master’s degree in public administration from the University of Oklahoma. West retired from the proving ground (at the time of her retirement named a naval surface warfare centre) in 1998, after 42 years of working there.

Though she was retired, she continued her education, and was awarded her PhD from Virginia Tech in public administration and policy affairs in 2000, aged 70. Her doctoral thesis, titled The effects of downsizing on survivors, analysed the effects and repercussions faced by those who remain employed, or ‘survive’ redundancy programmes in the workplace.

I wanna shake your hand

Gladys West being inducted into the the Space and Missile Pioneers Hall of Fame

West’s contributions to GPS technology went largely unremarked for many years. In the late 2010s, she sent a short autobiography to an Alpha Kappa Alpha sorority function, which was celebrating the achievements of members past and present. West’s sorority sisters were amazed by her story. “I just thought it was my work, and we’d never talk to our friends about work. I just never thought about it. I didn’t brag about what I was working on,” she has said. “But to see other people so excited about it, that was amazing.” One of her sorority sisters, determined to get West’s story told, shared the autobiography in early 2018 with the Associated Press, which kickstarted the domino effect of revealing West as among the so-called hidden figures that were computers for the US military in the 1960s.

In mid 2018, West was nominated and won the award for female alumna of the year at the annual Historically Black Colleges and Universities awards. In December 2018, she was inducted into the US air force’s hall of fame for space and missile pioneers in recognition of her work on the extremely accurate geodetic Earth model. This induction is one of the space command’s highest honours, paying tribute to the leaders of the early years of the programme, as well as the subsequent innovators. In 2020, Gladys West published her memoirs, It Began With a Dream, and in 2021, she was awarded the Prince Philip medal by the UK’s Royal Academy of Engineering, their highest individual honour. In 2021, looking back on her life, she said “I keep changing my mind about the highlight of my career. I would think first, when I got that college degree and I knew that I was ready. Nowadays, I’m just thankful for being able to see the recognition that other people are giving me and how much I have affected other people. To me, that is a big thing.”

Madeleine Hall is a mathematical consultant at the Smith Institute, based in Oxford. She likes writing, open water swimming, the Oxford comma, and tHiS mEmE. Her PhD research was on optimal swimming for microorganisms. She has found none of her results of any use in the lido.

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