Two years ago, Brian Sheehy saw something crazy on the internet: Videos of people who looked like they were flying over water on futuristic contraptions called eFoils.

Mr. Sheehy was obsessed. He immediately bought two as soon as they were available and taught himself to use them.

He now stores the five-foot-long boards on the balcony of his apartment on the Upper East Side of Manhattan. “They drive my wife crazy, because we don’t have a place to store them, and they take up a lot of space,” he said. During his free time he lugs them into an Uber and then finds a spot on the banks of one of the city’s rivers, or the Long Island Sound.

“It’s the coolest new thing that I am aware of,” said Mr. Sheehy, 49, an investment fund manager. “This is my dream toy.”

The eFoil, short for electric hydrofoil surfboard, was brought to market by Nick Leason, an engineer and avid surfer in Puerto Rico. Technology from smartphones, electric vehicles and drones was used to create a remote-controlled board that could fly over the water without wind or waves. Now the boards are sold by two companies: Lift, owned by Mr. Leason, and Flite, owned by David Trewern, a sailer and surfer in Australia.

Roughly described as a cross between a surfboard and a Jet Ski, an eFoil can go as fast as 25 miles per hour and is powered by a battery, which lasts just 90 minutes. But that is long enough for Mr. Sheehy to use it for sightseeing. He has visited Randalls Island, where he climbed down rocks to get into the Harlem River. He also visits beaches and towns around Connecticut and Westchester.

“I am always trying to discover new places,” he said. “I haven’t gone around the Statue of Liberty, but I want to.”

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Chang W. Lee/The New York TimesCreditCredit…Chang W. Lee/The New York Times

Squint these days, and you may spot the occasional eFoil joining the ranks of the 1 percent’s Jet Skis and sailboats in the Hudson or East Rivers.

They are prohibitively expensive. Boards run $12,000 each, and private lessons cost hundreds of dollars. The sport can also be dangerous, especially in rivers with strong currents and big boats, like the Hudson and East Rivers, or if the battery runs out, stranding the user.

Still, a growing number of adventure seekers around New York City, mostly men, believe the hefty price tag and risk are worth it.

“Wherever you go, when people see you do it, they are completely stunned and amazed,” Mr. Sheehy said.

Adam Kenworthy, a former private chef who appeared on the “Real Housewives of New York City,” is an eFoil convert. Last December a video went viral of him in a Santa suit zooming atop the East River on one, he said.

Mr. Kenworthy, 35, likes to put in around the waters of Dumbo, Brooklyn, where there is a beach near Jane’s Carousel in Brooklyn Bridge Park. From there he cruises to some of the city’s most famous sights.

“I grew up surfing, and we always dreamed that there would be a wave across the Statue of Liberty or under the Brooklyn Bridge,” he said. “Now that I can actually surf it, it’s super rad.”

But the experience is not always carefree. Large boats in the East and Hudson Rivers produce strong waves, which makes it hard to stay balanced. “It feels like you are skiing across ice for 20 seconds,” Mr. Kenworthy said.

The Coast Guard has trailed him more than once. There was also that time when his battery died near the Statue of Liberty. He had been with a friend on a Jet Ski, but they got separated, and the sun had set. “I’m out in the pitch black, paddling,” he said. “I had to keep calm and analyze the situation. Which way will the current push me? Where are the boats?” His friend found him about an hour later, and took him back to land on his Jet Ski.

Mr. Sheehy faced a similar situation when his battery died in the Harlem River. A fishing boat picked him up.

“The fishermen told me how dangerous the river is,” Mr. Sheehy said. “It’s a famous dumping ground for bodies because they just disappear.”

Brad Conway, commander of the U.S. Coast Guard Station New York, said that his team had not seen many eFoils yet, but that they are basically simple boards was concerning. “Once you are in the water, off your board, your head is the only thing showing above the water, like a coconut,” he said. “You have someone going through on a speedboat or a Jet Ski, they aren’t paying attention, which is very common, you could get run over.” And as for the batteries’ short lives: “If you run out of battery and drift in front of a barge that can’t stop,” he said, “you might go under.”

Although eFoils, like most water toys (even foam noodles), are legal to use in city rivers, they are not currently regulated by state or federal law, Commander Conway said. But that could change. “It depends on how popular they become, where they start operating, and do they impact other vessels,” he explained. “Surfboards, for example, have never been regulated, but stand-up paddle boards have.” Jet Skis were around for over 20 years before they were regulated by the state in 1999, he said. “It’s the natural evolution of technology, and we have to be ready to look at it and manage it as safely as possible.”

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Richie Lambertson, an eFoil instructor who lives in Greenpoint, Brooklyn, won’t let his students ride in city rivers until they have mastered the board in calmer water, like at Navy Beach or Fort Pond, both in Montauk, on the tip of Long Island.

For 10 years Mr. Lambertson, 39, worked as a chiropractor. But in February, while on vacation in Florida, he tried eFoiling and loved it so much he opened a school in New York, Project Surf, in May, in the middle of a pandemic. He and his fiancée, Klodiana Kazazi, a dental hygienist, took a break from their jobs to teach the sport in the Hamptons full time.

They lucked out. Many wealthy New Yorkers had fled the city early because of the coronavirus, and were a little stir crazy, seeking out novel activities like eFoiling, which costs $450 for a private, half-day session. To meet the demand, the couple relocated to the Hamptons, where they live out of a trailer during the week. On the weekends, they return to Brooklyn, where they pursue eFoiling themselves in the more challenging East River.

“I really see this as an urban activity, as something people can do casually after work,” Mr. Lambertson said.

Ms. Kazazi, 35, who manages the business side of the school, is one of the few women involved in the male-dominated sport. “We think Ana was the first girl in the East River,” Mr. Lambertson said. “If there is a girl out there who’s done it, hit us up. We would love to give her credit.”

Will Skudin, who runs a surf school in the Rockaways and eFoils in his free time, says eFoiling is pricey because two companies have a monopoly on the market. “There are more companies trying to get involved, which will make this cheaper,” he said.

The sport requires different muscles and skills than surfing. But Mr. Skudin believes surfers will embrace eFoiling because it can be done in any type of water. The board’s motor can cut through still or choppy water, rivers and oceans, he said. You just have to be skilled enough to handle it.

When there are no big waves for surfing it’s another thing to do, Mr. Skudin said. “It opens up an additional day to stay in the water and foil instead of doing nothing.”

That’s exactly why Adam Kallen, a surfer and the owner of Jane Motorcycles in Williamsburg, Brooklyn, tried eFoiling, after encountering it on Instagram.

“Nothing will beat the experience of actually surfing on a wave, but this was really, really fun,” he said. “You are literally floating on the water, and it’s an amazing sensation. It’s electric and quiet, and you are kind of gliding.”