The sea was stormy on Sept. 26, 1918, as a convoy of merchant ships navigated the Bristol Channel in southern England. Escorting them was the Tampa, a 190-foot U.S. Coast Guard cutter with the mission of protecting the boats from German submarines.

The cutter separated from the convoy in the misty night to take on supplies and coal at a port. And then it disappeared. For more than a century, its fate has been an enduring naval mystery of World War I.

This week, British divers announced that the wreck of the Tampa had at last been found, nestled 320 feet deep in murky waters about 50 miles off the Cornish coast.

A torpedo from a German submarine killed all those aboard the cutter: 111 Coast Guardsmen, four U.S. Navy personnel and 15 British Navy personnel and civilians.

Adm. Kevin Lunday, commandant of the Coast Guard, said that the Tampa was the largest single American naval combat loss of life in World War I and that it had left “an enduring grief in our service.”

The discovery was the culmination of a three-year effort by the Gasperados Dive Team, a group of British explorers and researchers. They combed shipping logs and wartime messages, and collaborated with the Coast Guard to pinpoint the path and resting place of the vanished vessel.

Barbara Mortimer, a Gasperados researcher, collated scraps of information, sometimes single lines of text that by themselves offered little to go on. But once all the information was meticulously pieced together, she and her teammates narrowed the search to an area clustered with thousands of wrecks from warships, commercial ships and fishing vessels lost over centuries.

The timeline of the Tampa’s final moments slowly emerged.

“Urgent. Priority,” said a telegram dated Sept. 27, 1918, sent to the admiralty in London. “USS Tampa detached herself from convoy.”

The telegram provided the longitude and latitude of that last sighting. At 7 p.m., the ship was seen on the horizon, steering toward the port of Milford Haven, it said. At 8:45 p.m., a wireless operator “felt the shock of an underwater explosion,” the telegram said.

Then, in the hours that followed, Milford Haven reported that the Tampa was 12 hours overdue for its scheduled arrival.

The research team assembled a number of clues about where the Tampa ended up.

One telegram said a seaplane had spotted a “considerable wreckage” field of seven to eight square miles. Two bodies, in Tampa uniforms, eventually washed ashore and were buried in Wales, Ms. Mortimer said in an interview. She said the researchers also studied German U-boat records.

The Coast Guard provided historical records, technical data and archival images of the ship’s features so divers knew what to look for in the deep.

In April 2023, the team made its first two dives looking for the Tampa. Seven more followed, and an assortment of shipwrecks were spotted and examined.

On Sunday they zeroed in on an area where a British hydrographic survey had noted a “significant magnetic anomaly” suggesting the possible location of a steel wreck.

That information was checked against convoy records, Ms. Mortimer said. The team decided, “It’s worth a look,” she said. But she added, “I did not have high expectations.”

Dominic Robinson, one of the team’s divers, lowered himself into the cold, dark waters of the Celtic Sea in the late afternoon of April 26.

At about 311 feet down, he spotted wreckage, piled high. As he drifted slowly over the debris field, his light picked up objects from the chaotic jumble. Some stood out: There was a brass fire extinguisher, an anchor, shell casings and a high-pressure steam boiler that was used in the engines of ships like the Tampa.

Surveying the mound, Mr. Robinson said in an interview that he had a “gut feeling” that the ship had been blown apart, making the bow crumble and absorb the impact. “And the rest of the ship settled down behind it,” he said.

Then he drifted over some crockery. Another member of the team, Jacob MacKenzie, found a similar piece that was inscribed with the maker’s mark: “New Jersey.”

They had an “American connection,” Mr. Robinson said.

“That instantly connects me with the people on the ship,” he said in a video of the dive. “They would have eaten out of those bowls. All these people would have had parents, would have had nearest and dearest, and none of them knew where they are.”

The Coast Guard is gathering data from the Gasperados’ finds to confirm it as an officially designated war grave, said William H. Thiesen, the Coast Guard’s Atlantic area historian.

The Coast Guard has been contacting the families of each lost Tampa crew member over many years, awarding them a posthumous Purple Heart medal, Mr. Thiesen said.

“It provides closure to a chapter that has been open for 100 years,” he said.

Jeremy Davids, 48, of Florida said that a relative, Wesley James Nobles, died while serving aboard the Tampa at the age of 20.

“Drowned foreign waters sinking of Tampa 9-26-1918,” the official record of Mr. Nobles’ death says. Mr. Nobles had a rating of “boy,” an enlisted rank for younger crew members.

“It feels good knowing the fact that not only him but the other soldiers who lost their lives that day can finally rest in peace,” Mr. Davids said in an interview.

When the messenger Pheidippides ran from the battlefield of Marathon to Athens to announce the Greek victory over the Persians in the 5th century B.C., he did it without shoes. His time was not officially tracked.

Millenniums later, at the London Marathon on Sunday, Sabastian Sawe and Yomif Kejelcha became the first to break the two-hour barrier in an official marathon, and Tigist Assefa set a women’s world record. All three did it in featherweight footwear.

The shoe, the Adidas Adizero Adios Pro Evo 3, weighs 97 grams, or about 3.4 ounces, depending on the shoe size. It’s the lightest running sneaker approved for competition. It sold out on Monday.

The race to near-weightlessness has been a driving force of innovation in running sneakers in the 25 centuries since shoeless Pheidippides’s run.

Heavier shoes are slower, a 2016 study showed, although that analysis was only for three-kilometer time trials. The study’s authors hid lead pellets in some Nike racing shoes and didn’t tell the subjects.

“When we added 100 grams per shoe, they ran about 1 percent slower, and when we added 300 grams, they ran about 3 percent slower,” said Rodger Kram, an emeritus professor of integrative physiology at the University of Colorado, Boulder. He called the 1 percent per 100 grams “a rule of toe.”

But it took many steps before running shoes evolved to the blistering pace they now allow.

‘The Platonic ideal’

Shoes once relied on leather, wood or metal reinforcements that were heavy and stiff. The rise of the rubber sole added flexibility and waterproofing. Better durability and grip were bonuses.

People could also run or walk in rubber soles without being heard. That’s why they’re called sneakers.

The first flat-soled rubber and canvas shoe was developed in 1868, almost 30 years after Charles Goodyear discovered the process of curing rubber called vulcanization. Converse and Keds made them popular in the 1920s.

“Converse All Stars are the Platonic ideal of the sneaker,” said Nicholas Smith, the author of “Kicks: The Great American Story of Sneakers.”

He noted they have not changed much.

“Canvas on top, rubber at the bottom.”

‘Chariots of Fire’

Competitive runners soon faced a trade-off: a heavier shoe with better traction or a lighter flat sole.

The heavier option, which transferred maximum force from the runner’s foot to the ground for acceleration, came from J.W. Foster of Bolton, England, who had the insight that led to the first metal spikes in shoes in the 1890s. Top British runners, including those competing in the 1924 Paris Olympics, wore these new spikes to notch their fastest times. Their story is told in “Chariots of Fire,” the Oscar-winning 1981 film.

It was at another Olympics, in Berlin, that Jesse Owens wore six-spiked shoes created by Adidas to become the most successful runner of the 1936 Games. His shoes, made of specially tanned calf leather and cowhide, weighed 201 grams.

A broken waffle iron

Running tracks made of urethane, a rubber compound, began to emerge in the 1960s. When one was installed in 1969 at the University of Oregon, the track coach, Bill Bowerman, found that runners’ spikes dug in too deep while flat shoes offered too little traction.

Having breakfast one morning in 1971, he noticed that the grid pattern on the waffle iron his wife was using might just be what his runners needed to get a grip on the track.

He tried pouring liquid urethane into the waffle iron, but only managed to seal it shut. He kept trying other waffle irons until he had the mold he wanted, according to Nike archivists.

But Bowerman wanted more than grippier sneakers.

“He was also devoted to making the lightest running shoe possible,” said Elizabeth Semmelhack, the author of “Out of the Box: The Rise of Sneaker Culture.”

Bowerman’s shoe, which Nike called the Waffle Trainer, “stands out because it had an extremely thin rubber sole but with a high tread, and then the upper of the shoe was made out of nylon.”

The light weight also helped bring running to the masses.

“You can bet there wouldn’t be so many people running today if they had to carry all the extra baggage we had back then,” Bowerman, a Nike co-founder, said in 1979.

The waffle-pattern nubs on the soles compressed under weight and helped bring spring to a runner’s step. But they only hinted at how sneakers could be cushioned. For many runners, it was not enough.

Then Nike introduced ethylene-vinyl acetate, better known as EVA foam, on the heel of its Cortez shoe in 1972. EVA offered a thicker, air-infused layer of separation from the road and absorbed more of the shock. The age of adding thick slabs of rubber for cushioning was over.

That led to a new quest that continues today: How much cushioning can you build into a shoe?

Lighter than foam

Sneaker makers next turned to a gas and a semisolid to help spread the energy of a foot’s impact with the ground.

In 1979, the Nike Air Tailwind began the airbag era, in which pressurized gas is stored in a flexible urethane bag within the sole.

Asics pioneered gel cushioning technology in 1986 with its silicone-based shock absorption. Nike countered in 1987 with the Air Max 1, which had a “window” in the sole designed to show off the air pocket. “At the time that was the cutting edge,” Mr. Smith said.

Though air is lighter than foam, it had to be kept in a rubber vessel, which added weight. So did adding silicone gel packets to the heel and forefoot.

While air bubbles felt more springy, and gel more dampening, they both were able to absorb shocks longer than the standard foam.

An icon of the 1990s tackled a different problem: how laces become loosened during a run. Reebok, building upon its wildly successful Pump basketball sneakers, which could be inflated with the press of a button on the tongue, introduced the Instapump Fury, a colorful, open-paneled, split-soled running sneaker.

“The Instapump used an air bladder that could fit your particular foot, the nuances of your own foot, very, very closely,” Ms. Semmelhack said. “Then you didn’t have to adjust any lacing throughout your run or at any time. So it was very innovative.”

Rise of the super shoes

But as new technologies made foam lighter, shoemakers soon couldn’t get enough of it.

One brand, Hoka, wedged so much cushy foam into its soles, beginning in 2009, that the shoes looked swollen. Runners could hardly “feel the ground anymore,” Smith said. The company’s designs helped push amateur runners to chunkier shoes.

But it was the thick-soled Nike Vaporflys that captured the most attention. They came with a carbon-fiber plate in the midsole that was very light and gave stability to all the squishy foam. The plate stores and releases energy with each stride, and is meant to spring runners forward.

The Vaporflys also use polyether block amide, or PEBA, a bouncier, lighter foam. The twin technologies led to the nickname “super shoes.”

“There was concern that this additional innovation in the running shoe was the equivalent of doping,” Semmelhack said. The shoes cushioned the feet of all three medalists in the men’s marathon at the 2016 Rio de Janeiro Olympics. The New York Times found in 2019 that the shoes gave a significant advantage, but they were never banned.

Adidas used its lightest foam in the sole of the Adizero Adios Pro Evo 3, which were worn by Sunday’s record-breaking marathoners. It also said that the shoe has carbon fiber rods to mimic the human foot’s bone structure.

In other words, closer to the bare feet in Pheidippides’s run.