It all happened so fast.

Karsten Borner was planted on the halfdeck of his sailboat in the slanting rain. A grizzled mariner who had survived many storms, he was anchored in the same cove as Mr. Lynch’s yacht, at the same time, as the squall blew in during the early hours of Aug. 19.

Luckily, he was already awake. As the wind picked up, he and his crew scurried around closing hatches, clearing the decks and firing up the engines to keep his boat steady.

He couldn’t see much, but in flashes of lightning, he kept catching glimpses of Mr. Lynch’s long, sleek sloop bobbing behind him. It was only a few hundred feet away and its super-tall aluminum mast — one of the tallest ever made — was lit up with bright white lights, swaying in the wind.

Then he lost sight of it. The rain fell like gravel, drawing a curtain around his boat. When he looked up again, he was stunned. The Bayesian was disappearing, at a very odd angle, into the sea.

In the weeks since, Mr. Borner, who has sailed for more than half a century, still can’t believe the yacht sank in front of him. There weren’t any big waves that night, he said. Both boats were close to shore. His own sailboat — a converted tugboat built in East Germany 66 years ago — weathered the same squall just fine. And that other craft was a superyacht of the superrich, gleaming blue, 184 feet long and drawing stares wherever it went.

“It’s a mystery,” Mr. Borner said.

That mystery has rippled around the globe as several investigations into the tragedy unfold. It has vexed maritime experts and compounded the grief of family and friends of the seven people who perished, including Mr. Lynch and his teenage daughter, Hannah, whose bodies were found trapped below deck.

The investigations turn on three central questions: Why did the Bayesian, which now lies 160 feet at the bottom of the Mediterranean, sink so fast? Did the yacht have any design flaws? Did the captain or crew make any fatal mistakes?

The Bayesian was a one-of-a-kind sailboat, built by Perini Navi, a famous Italian yacht maker. The company says the group of 10 superyachts that the Bayesian belonged to was “the most successful series of large sailing yachts ever conceived.”

But the Bayesian was different. Its original buyer — a Dutch businessman, not the Lynches — insisted on a single, striking mast that would be taller than just about any other mast in the world, according to the Italian yacht maker and three people with detailed knowledge of how this boat was built.

That decision resulted in major engineering consequences that ultimately left the boat significantly more vulnerable than many comparable superyachts, The Times investigation has found.

— More than a dozen naval architects, engineers and other experts consulted by The Times found glaring weaknesses in the Bayesian’s design that they said could have contributed to the disaster.

— Basic design choices, like the two tall doors on the side of the deck, increased the Bayesian’s chances of taking on dangerous amounts of water if high winds pushed the boat over toward its side, several naval architects said.

— Witness and survivor accounts revealed how this deadly sequence unfolded in real time: The yacht fell completely on its side and sank within minutes.

Seemingly small details on any boat — like how close air vents are to the waterline, or where a ship’s ballast is placed in the hull — might not sound decisive on their own. But when taken together, experts said, they appear to have compromised this vessel.

Such built-in vulnerabilities may not have been solely responsible for the yacht’s sinking, of course. The storm’s unexpected ferocity definitely played a part in the calamitous stew of events. Italian investigators are also looking hard at the actions of the Bayesian’s captain and crew.

Giovanni Costantino, the chief executive of the Italian Sea Group, the company that owns Perini Navi, said that when operated properly, the Bayesian was “unsinkable.” He maintains that the yacht was carefully engineered to survive bad storms, and he has put the blame for the tragedy squarely on the crew, accusing them of making a chain of fatal errors.

“I know, all the crew knows, that they did not do what they should have done,” he said. (Crew members have not revealed much, saying they are under a “gag order.”)

Mr. Costantino said the design was not at fault and that the towering mast, which stood 237 feet tall, had not created “any kind of problem.”

“The ship was an unsinkable ship,” he said. “I say it, I repeat it.”

The world of superyachts is incredibly opaque, the exclusive realm of some of the richest people on the planet, and exactly how these multimillion dollar boats are designed, approved and owned remain closely guarded secrets.

Making sure a superyacht is fit for the seas is a job left to a network of private companies and public agencies, and the Bayesian’s design was approved by the American Bureau of Shipping and the British Maritime and Coastguard Agency.

All the attention this tragedy has received could result in a closer look at yachting regulations. Several naval engineers in different countries who have gained access to the Bayesian’s documents say that as yachts have become more elaborate and subject to owners’ whims, others may be in danger as well.

The Bayesian’s technical documents show just how vulnerable it was. Even without major errors by the crew, the ship could have sunk in a storm that other boats survived, engineers say.

“We can look at it in hindsight and say they were in the wrong place at the wrong time. No, that’s not true,” said Tad Roberts, a Canadian naval architect who has nearly 40 years of experience designing boats, including superyachts.

“This boat had definite shortcomings that kind of uniquely made it vulnerable to what happened.”

The Victory Voyages

A cruise on the Bayesian was a voyage into luxury. The days were typically warm, sunny and calm, and finished off with plates of fresh langoustine and sumptuous chocolate. Hours would pass lounging on sun chairs, swimming in the sea or maybe taking out a kayak while the Bayesian crew, in branded polo shirts, watched vigilantly from the deck.

“It felt like a beautiful hotel that was floating on water,” remembers Abbie VanSickle, a New York Times reporter who was invited aboard in July because her husband, Jonathan Baum, was part of Mr. Lynch’s legal defense team.

Mr. Lynch had been acquitted in June in a criminal case in which he was accused of fraudulently inflating the value of his software company when he sold it to Hewlett-Packard for $11 billion. He could have been sent to prison for years. To celebrate his win — and his freedom — he asked friends and lawyers to cruise the Mediterranean with him.

Mr. Lynch seemed proud that his boat had one of the world’s tallest masts — a little booklet in her cabin even said as much, Ms. VanSickle remembered. Whenever they chugged into a harbor, she said, “people would take photos of it constantly because it was so crazy-looking in comparison to other boats.”

Most of the time, though, the Bayesian operated like a motorboat, powered by two enormous diesel engines. During her five-day voyage, Ms. VanSickle said they sailed only once, for just a few hours. But when they did, the boat moved through the water so smoothly, she said, it felt like they were “gliding.”

A few weeks after Ms. VanSickle got off and returned to her life as a reporter in Washington, Mr. Lynch welcomed aboard his next batch of guests. This was the second celebratory voyage, beginning in mid-August, and Mr. Lynch had planned to get back to London, where he lived, around Aug. 20.

Among the 12 passengers were Mr. Lynch; his wife, Angela Bacares; their 18-year-old daughter, Hannah, who was soon off to Oxford; one of his lead lawyers, Chris Morvillo, and his wife, Neda Nassiri, who designed handcrafted jewelry; Jonathan Bloomer, an international banker and trusted adviser, and his wife, Judy, a psychotherapist celebrated for her charity work.

Mr. Lynch also invited some younger colleagues, including a couple who brought a baby on board. The crew was led by James Cutfield, an experienced New Zealand sailor, backed up by a first mate, a ship engineer, several deckhands and hostesses, totaling 10 in all.

Mr. Lynch was on the rebound, fired up about the possibility of starting a nonprofit to help exonerate people wrongly accused of crimes, said Sir David Davis, a friend and prominent conservative British politician.

Mr. Lynch sent Sir David a text message offering the choice of lunch or dinner in London on Aug. 22, when he was back.

An Unanticipated Storm

The Mediterranean Sea was flat on Aug. 18. But bad weather was moving south, from Naples toward Sicily. The Italian Air Force’s Meteomar forecast warned of scattered thunderstorms, gusts of wind and a rough sea. Several yacht captains said the weather warning was far from specific or extraordinary.

Mr. Borner, the captain who for decades has been running cruises and diving excursions on his old sailboat, the Sir Robert Baden Powell, was finishing up his own trip, picking his way west along the Sicilian coast.

The wind was blowing from the northwest and Mr. Borner figured that the curvature of Sicily’s rugged coastline at Porticello, a small fishing village built around a cove, would shelter him. He arrived in the cove that afternoon, went ashore with his guests and grabbed some pizza.

“It was a nice evening,” he remembered.

While they were in town, the Bayesian chugged into the same cove. It dropped anchor at 9:35 p.m., about a third of a mile from land. As Mr. Borner went to sleep around 11, the night was clear. The lights of the Bayesian’s mast glowed behind him.

At midnight on Aug. 19, the Italian Coast Guard put out a warning for a northwesterly Gale Force 8, a serious storm in which winds could reach 46 miles per hour. But the gale was predicted to hit hundreds of miles from Sicily.

Around 3 a.m., Mr. Borner woke up to help some of his passengers catch an early flight from Palermo, Sicily’s biggest city. But as the winds picked up rapidly, whipping the cove into a frothy chop, he scratched his plan to go ashore.

He and his crew shut the portholes and skylights and started the engine, to keep the bow pointed into the wind and prevent the boat from being hit on its side.

On the Bayesian, a young deckhand, Matthew Griffiths, later told the authorities that when the wind hit 20 knots, he woke up the captain, according to a person close to the crew (who said that neither of them was allowed to speak publicly). The captain then gave the order to wake up others, the person said.

At 3:51 a.m., the Bayesian started to drift — first 80 meters one way, then 80 meters another, its data transmitter shows. Maritime experts said this meant it was being blown around and probably dragging its anchor. It’s unclear whether the engines had been started.

At 4:02 a.m., a camera mounted on a boat in Porticello’s cove shows bright blue flashes of lightning. Three minutes later, another at a Porticello cafe captures the wind tearing down deck umbrellas. So much rain hits one of the cameras, it looks as if it’s being blasted with a hose.

Mr. Borner estimated that the wind gusts reached 60 knots, or nearly 70 miles an hour — just below hurricane strength — and said they had pushed his boat onto its side about 15 degrees, a serious lean but nothing close to capsizing.

Reports immediately after the disaster raised the possibility that the Bayesian had been hit by a tornado-like disturbance called a waterspout, but the authorities don’t think that happened. Still, the wind was doing something dangerous: It was changing direction.

According to a nearby weather station, it was blowing west-southwest then southwest, then north-northwest. This increased the chances of getting ambushed by a random gust that could slam into the side of a boat, which can tilt even a big vessel.

A third video shows the Bayesian rocking back and forth and beginning to lean. Then the lights on its giant mast blink out — all but the top one, which was powered by a battery.

By 4:06 a.m., the rain has turned into a blinding cascade. That same minute, the Bayesian’s location signal cuts out. Mr. Borner’s crew squinted through the nearly impenetrable haze of sea spray and rain and spotted a large object in the water. They first thought it was a reef.

“But I knew there was no reef,” Mr. Borner said.

It was the Bayesian, they now believe, knocked onto its side.

“Two Minutes” to Tragedy

At 4:34 a.m., a red emergency flare, bright as a meteor, shot into the sky. The storm had passed, and Mr. Borner and his first mate jumped into a small boat, zooming across the black water.

First they saw cushions floating. Then a flashing light. Then a life raft built for 12 packed with 15 people, bloodied and soaked to the skin, including a baby.

One person had a cut on the head, another on his chest. Some had already been bandaged. They were cold, wet and dazed. They were too shocked, Mr. Borner said, to say what happened.

As he loaded the survivors into his boat and began to head back to the Sir Robert, one woman pleaded with him not to leave.

“Please,” she told him. “Continue searching.”

Some people were still missing.

Mr. Borner decided to unload the survivors onto the Sir Robert, then send his small boat back. His crew gave them blankets and dry clothes. Some survivors were so shaken they needed to be led below deck by hand.

Nobody said much, Mr. Borner remembered.

One man told him: “I was the captain of this.”

Another said the boat had “sunk in two minutes.”

The woman who had begged him to keep searching sat huddled on the deck.

“Are you OK?” Mr. Borner asked her.

“No,” she replied. “I am not OK at all.’’

Mr. Borner said he later realized it was Angela Bacares, wife of Mr. Lynch and mother of Hannah Lynch. Neither had made it onto the life raft. (Salamander Davoudi, a spokeswoman for Lynch family, told The Times that Ms. Bacares was not speaking to the media because she was grieving and wanted privacy.)

A few hours after, a string of ambulances arrived at Palermo’s main hospital. Dr. Domenico Cipolla, the head of pediatric emergency, evaluated the youngest survivor, a 1-year-old girl.

The baby was OK, Dr. Cipolla said, but she had experienced quite an ordeal. She and her mother had been sleeping on a sofa on deck because of the rough sea, Dr. Cipolla said, when the boat suddenly lurched and threw them to the deck.

A moment later the boat turned completely on its side, the baby’s father told the doctor, flipping his hand as he described it. The doctor said the mother told him that she and her baby were hurled into the water and that her baby nearly slipped away. But then she grabbed her and swam to a nearby life raft, which was designed to deploy automatically.

The parents were later identified as Charlotte Golunski, a colleague of Mr. Lynch, and James Emslie. Ms. Golunski did not respond to several messages left for her, and efforts to reach Mr. Emslie were unsuccessful.

Mistakes by the Crew?

The biggest question that investigators are focused on is how the Bayesian filled with water so fast. To many in the yachting world, it doesn’t make sense.

The boat had been built with several watertight compartments under the deck, to prevent water from spreading from one area to others. And it had been approved as safe by the Maritime and Coastguard Agency, part of Britain’s Department for Transport, and by the American Bureau of Shipping, a private company that reviews boat designs.

On top of that, one Italian official and underwater video footage broadcast on Italian television indicated that there were no holes or other structural damage visible in the hull.

Even so, the Bayesian, like many superyachts, had all kinds of openings in which water could theoretically get in: big air vents for the engines; smaller ones for the kitchen, crew quarters and guest cabins; large glass doors at the back and the sides so that people could walk onto the deck; and various hatches for crew and passenger access.

In interviews with Mr. Costantino, the chief executive of the Italian Sea Group, and his spokeswoman, the company accused the crew of leaving hatches open during the storm, including a doorway-size opening on the left rear of the hull, close to the water line. The spokeswoman claimed that hatch was the only place where so much water could have come gushing in.

The company speculated that the crew did not close a watertight door between this hatch and the engine room. A flooded engine room might explain the sudden blackout that killed the mast lights and then, a few minutes later, the location transmitter.

But witnesses, an Italian official familiar with the investigation and the underwater video challenged the company’s versions of events. The footage appeared to show the watertight door to the engine room closed, and the Italian official said the divers had not seen any open hatches on the hull.

Mr. Borner also said that after rescuing the captain, he asked him if he had shut the hatches. The captain said he had. Mr. Borner shared pictures taken by his guests a few moments before the Bayesian sank that appear to show that hull hatches were closed.

A Compromised Design?

The Bayesian’s origins go back to 2000. That year, Perini hired Ron Holland Design, a premier naval architectural firm, to design a series of 56-meter sailboats, said a person with knowledge of the timeline. As the superrich have become even richer, yachts have grown steadily bigger, and Perini was emerging as one of the world’s best-known builders of superyachts, often defined as motor yachts or sailboats longer than 24 meters, or 79 feet.

The Ron Holland firm, based in Ireland at the time, drew up plans for the hull, keel, rudder and, crucially, the placement of the masts — two masts. All other features, like the cabins, decks and vent system, were designed by Perini, according to the person, who did not want to be identified because of the possibility of legal action connected to the sinking.

In 2003, the first yacht in the series hit the water, the Burrasca (which means storm in Italian). Over the next four years, Perini built three more 56-meter superyachts from these blueprints, all with two masts. On Perini’s website, they look nearly identical.

Then came the Bayesian.

Construction on its hull began in 2005 at a shipyard in Tuzla, Turkey, according to the boat’s documents. But the original buyer for this yacht didn’t want the standard two-mast design. Instead, the Italian Sea Group said, he wanted the boat to be built with one large mast for better sailing performance.

That led to a radically different design, said three people with knowledge of what followed, and a cascade of modifications — some to accommodate the gigantic mast, and some apparently for stylistic or other reasons.

The most obvious departure from the previous Perini ships was the mast itself. Beyond being exceptionally tall — more than 40 feet higher than the original foremast — it was also very heavy, at least 24 tons of aluminum, possibly more. This alone would have challenged the boat’s stability, because so much weight was high above deck.

Since then, many yacht makers have switched to lighter, carbon-fiber masts.

“Technology moved on,” Mr. Costantino said.

Naval engineers pointed out that the heavier a yacht is up high, the more ballast it often needs down low — weight at the bottom of the boat to lower its center of gravity and resist its tendency to lean over.

Small notes on hull diagrams in the Bayesian’s documents show that the Turkish shipyard revised the ballast in July 2006, nearly 10 months after the keel was laid, which is one of the first steps of production.

“Values updated as from information by Yildiz,” the notes say in all caps, naming the shipyard.

But where this ballast was placed was curious, maritime experts said. Rather than spreading the ballast evenly across the bottom of the boat — which would have guaranteed the best stability — the builders stacked it toward the rear of the ship’s hull.

“When I first saw this, I couldn’t believe it,” said Mr. Roberts, the naval architect. “It made no sense to me.”

The ballast seems to have been pushed toward the rear of the boat to offset the single, heavy mast closer toward the front, Mr. Roberts concluded. He said he had never seen the main ballast used in such a design tactic before.

That was not the only change, experts said. A single mast would have plunged almost directly through the wheelhouse, an interior station where the ship can be controlled, so that was moved, too. A deck lounge was added, along with two tall doors on the sides. None of the other Perini yachts in the 56-meter series have these design elements.

The Bayesian sat lower in the water than other yachts in the same Perini series, said Stephen Edwards, the Bayesian’s captain from 2015 to 2020. Naval architects said this by itself would make it easier for water to pour through vents and other openings when the boat leans on its side.

Whenever a boat leans too far and water starts gushing in through open doors or vents, it can set off a dangerous downward spiral that is hard to stop and that can sink a boat in minutes.

Such risks are calculated and laid out in a lengthy, proprietary document — kind of a safety bible — for many vessels certified to ply the seas.

The Times has obtained that safety bible, called a stability book, for the Bayesian. Copies of the 88-page book are also sweeping through a global community of experts who are obsessively trying to solve the puzzle of how and why the boat sank. More than a dozen of those experts, including naval architects and engineers, found weaknesses in the Bayesian’s design that they said could have contributed to the disaster.

The stability book obtained by The Times was written before the Lynches bought the boat in 2014, when the yacht was called the Salute and owned by John Groenewoud, a Dutch businessman. In an email, he confirmed signing a contract for “the boat with 1 mast” in 2005, but declined to discuss any safety implications that may have had.

The Times obtained the stability book for another 56-meter Perini yacht, with two masts instead of one. A comparison of the boats showed that the Bayesian was significantly less stable.

Specifically, the data shows that the two-masted ship could lean at least 10 degrees farther onto its side before taking on dangerous amounts of water.

The documents also show that the Bayesian could begin taking on some water at angles that appeared to violate the safety threshold set by the British Maritime and Coastguard Agency.

The Italian Sea Group responded that the boat was in line with regulations and had been approved. When asked how that happened, an agency spokesman refused to clarify, citing the continuing investigations.

The other boat’s documents also showed that the sister yacht sat a little higher in the water than the Bayesian did, as Mr. Edwards emphasized. And under many circumstances, experts said, the sister ship had a better center of gravity and was more resistant to capsizing, two additional factors that would have made it safer.

“The other boat is, at least on paper, a better boat,” Mr. Roberts said.

To make boats safer, naval architects said they religiously ensured that vent openings are far from the water line. When showed a picture of a 56-meter Perini yacht that, like the Bayesian, had vents built into the hull, Philipp Luke, a Dutch naval architect, started violently shaking his head.

“No, no, no,” he said. “You don’t do that.”

In the end, several naval architects said, all these flaws may have come together at the worst time — in a sudden storm.

Two Spanish naval engineers, Guillermo Gefaell and Juan Manuel López, calculated that the sheer size of the Bayesian’s mast and rigging made the yacht a wind catcher, even with the sails down.

Writing for the Association of Naval and Ocean Engineers of Spain, they used a computer model to calculate what would have happened to the Bayesian if a strong gust of roughly 54 knots, around 62 mph, hit its side. Under those conditions, the Spanish engineers estimated, the Bayesian could lean dynamically and take on nearly a ton of water each second through an engine room vent.

In an interview, Mr. Gefaell noted that he, like almost everyone else, did not know everything that happened that night. But if the gusts were as strong as Mr. Borner estimated — 60 knots — the punch would have pushed the boat to an even more severe angle, his calculations showed, very quickly knocking the boat all the way over onto its side, as the witnesses recounted.

At that point, Mr. Gefaell said, “the boat was certainly lost.”

A Watery Maze

Within hours of the sinking, emergency divers plunged in. Their mission: Find survivors.

The Bayesian sat 160 feet below the surface, leaning on its right side on the seabed. The once-gleaming cabins were clogged with chairs, clothes, curtains and the enormous number of seat cushions that Ms. Bacares had brought onboard to make the boat more comfortable. The search was made even more difficult and dangerous, divers said, by the many mirrors installed below deck that now reflected back their lights in a disorienting, watery maze.

On the first day, divers found the body of the yacht’s chef, Recaldo Thomas, floating near the boat. Over the next three days, they found the bodies of Mr. Lynch and four other passengers in a small cabin near the foot of a narrow staircase leading down from the deck to the passenger’s quarters. Finally, divers discovered the body of the last missing person, Hannah Lynch, trapped behind furniture in a nearby cabin.

One Italian official said the six passengers might have been trying to climb the main guest staircase when a surge of water poured down the stairs and knocked them back into the cabins. With the boat flipped on its side, water gushing in, and total darkness, it would have been nearly impossible for anyone below deck to escape, experts said.

The Italian authorities plan to raise the wreck to inspect it more closely. That could take months. In the meantime, at least two major investigations are unfolding, one by Italian prosecutors and the other by the British Marine Accident Investigation Branch.

From the first weeks after the accident, Italian prosecutors said that Mr. Cutfield, the captain, and two of his crew were under investigation.

Mr. Cutfield hasn’t said a word publicly and did not respond to messages asking for comment. Several crew members, when approached at a hotel in Sicily in August, said they had all been put under a gag order. When asked who imposed it, they responded: “No comment.”

In the yachting world, Mr. Cutfield has some solid references. Turgay Ciner, a Turkish industrial magnate and sailing enthusiast, employed him to run his yacht for 12 years.

“He never made any mistakes,” Mr. Ciner said.

Mr. Ciner, speaking by phone from Istanbul, recounted a bad storm near Capri about 10 years ago that Mr. Cutfield handled. They were sailing on another 56-meter Perini yacht, the Melek, a two-masted boat in the same series as the Bayesian. He said that Mr. Cutfield performed very well and was “one out of a hundred.”

Why Mr. Cutfield left in a lifeboat with the other survivors when a half dozen passengers were still missing is a matter Italian prosecutors are looking into.

But several yacht captains have defended Mr. Cutfield, saying that whatever happened that night, it happened very quickly.

When a boat sinks fast, said Adam Hauck, an American yacht captain, there’s not much hope for anyone still onboard. The adage of the captain going down with the ship, he said, is antiquated and unrealistic.

“It’s not like a Titanic movie where you’re going through the water and you can just look in the rooms,” Mr. Hauck said. “At some point, you can’t go back for people.”