After more than 15 hours, the passengers in the back of the airplane are family-road-trip restless: Are we there yet?

Three more hours to go. Riding the longest airline flight in the world is a traveling ultramarathon.

You’re chasing time and outrunning the moon at 550 miles an hour, stretching human tolerance in a high-altitude, desert-dry environment. You’re challenging eating and sleeping patterns and questioning just how many episodes of “The Big Bang Theory” you can watch in one sitting. (There are 24 available.)

Singapore Airlines reclaimed the title of longest flight in the world on Friday with its nonstop between Newark, N.J., and its home at Changi Airport. It’s a 9,534-mile trip scheduled for 18 hours, 45 minutes when heading to Singapore, almost halfway around the world. It’s made possible by the newest airplane in the sky, an ultralong-range version of the new Airbus A350-900 jet.

This is the future of air travel for many. Longer flights actually shorten trips by eliminating the need to stop for connections. Without the nonstop between New York and Singapore, the trip takes at least 22 to 24 hours connecting in Frankfurt, San Francisco, Tokyo or Hong Kong.

Airlines are beginning to pump ultralong flights into schedules—a landmark change some call as big as the introduction of the Boeing 747. “New aircraft have the range and the economics to do what was not possible before,” says Campbell Wilson, Singapore’s senior vice president for sales and marketing.

Singapore’s new plane has 67 business-class seats and 94 premium-economy seats, but mercifully no standard coach. What’s clear from riding Flight 21 on Friday in premium economy is that ultralong-range travel requires a different mind-set for even the most experienced road warriors.

Staying hydrated is a bigger challenge than on a typical flight. Planning sleep to reorient yourself to the backside of the clock makes a difference. Avoiding salt and calories—typically available in high quantities in airline food—can help you arrive feeling less tired.

And what we learn in these passenger endurance trials can help on shorter flights, too.

Ultralong-range flights challenge fatigue management for crew as well as passengers, says Indranil Ray Chaudhury, Singapore’s captain on Friday. “It’ll take some time for people to get used to this,” he says.

As captain, he flies the takeoff and first part of the trip, gets rest and then returns to the cockpit to handle the final three hours. The big challenge: At 18 hours in, he needs to be his sharpest.

“Here you have to manage your physical constitution so when you arrive, you are fresh, not only for the landing but for any eventuality,” Capt. Chaudhury says. “The weather may be bad. You need to be ready for anything when it comes to the last segment of the flight.”

The flight path has three options: Head east across the Atlantic, west across the Pacific or north to the North Pole and down the other side of the globe. Airline flight planners, working with pilots, choose the route with the most favorable winds. They also factor in available emergency-landing sites and storms.

On Friday, the northern route was best—over Danbury, Conn., Montreal, Greenland, passing just south of the North Pole, then down over Siberia, Mongolia, China, Laos and Thailand. Actual time in the air was only 17 hours, 30 minutes thanks to favorable winds. The flight covered 9,857 miles, 3% longer than the shortest possible route. Gate to gate, the trip took 18 hours.

Each of the 12 Singapore flight attendants onboard gets five hours’ rest in crew sleeping compartments. Flight attendants, too, have learned these very long flights are more than a typical milk run with a couple of extra hours tacked on.

“Passengers get more fidgety,” flight attendant Charmaine Ang says. “We look for passengers who are restless and suggest something to eat, something to watch on the entertainment system.” For others, “18 hours is a breeze if you can sleep well,” she says.

Singapore and Australia’s Qantas Airways ,another carrier stretching flight boundaries, have been studying the science of airborne wellness. Qantas is pressing Boeing and Airbus for an aircraft that can go even farther than the A350-900 ULR so it can get from Sydney to London and New York nonstop.

Singapore flew this route from 2004 to 2013 with a four-engine airplane fitted with only 100 business class seats. It couldn’t carry a full load that distance. It proved popular with corporate travelers but uneconomical when fuel prices soared.

The earlier experience convinced Singapore it had to do more about in-flight health for such a long flight. The airline worked with health-spa resort operator Canyon Ranch to create a more appropriate menu, and encourage in-seat stretches for better blood flow and ideal sleep cycles. The in-flight entertainment system got an additional 200 hours of programming beyond the standard lineup of 1,000 hours.

On this trip, Singapore suggests a pair of five-hour naps, with a single dinner meal in between. Ideally you want to eat two hours before sleeping, says Canyon Ranch chief executive Susan Docherty, so digestion is complete and you’ll fall asleep faster.

Just one hour after meal service, the cabin lights turn orange and simulate sundown, even though it’s midafternoon in New York. Then they darken for the first nap. (I’ve never been able to sleep sitting up on a plane. No difference this trip, unfortunately.) Wake-up for the lucky comes five hours later, with hot towels and blue lights turning bright white before dinner. An hour later, another faux sundown with orange lights before it’s lights out. (Still no joy for me.)

The menu, which includes a light lunch after takeoff and snacks before landing, is designed for a 2,000-calorie limit—unless passengers want to indulge by asking for more. The flight lands in late afternoon, so it’s best to arrive hungry for dinner and sleep so you’re properly oriented to Singapore time. (The hungry and tired parts aren’t too hard.)

In-flight, taste is diminished by the dry air and cabin pressure, so airlines often add salt to food to boost flavor. But that leads to water retention, bloating and fatigue. For this flight, chefs tricked up dishes with flavors heavy for sea level but tasty in the air, without added salt.

Chefs seasoned beef short ribs with lots of turmeric, giving them strong taste and anti-inflammatory benefits, says Singapore’s food and beverage director Antony McNeil. To reduce carbs, cauliflower was mashed like potatoes and served with the beef. Cauliflower helps hydrate, as it is mostly water. Lentil beans served with chicken were steeped in broth full of garlic and onion. A rich tomato jam on top of the chicken was actually a conduit for lots of red wine vinegar.

The dishes proved airline food could be tasty at 39,000 feet. Even the mashed cauliflower was creamy and flavorful.

Singapore’s premium-economy seat for the ultralong flights is 19 inches wide inside the arm rests—about one inch wider than on an A320. The row is 38 inches long, about 6 inches more than a typical coach row on long flights. Extra legroom makes a huge difference, but it’s still coach.

“About 14, 15 hours in, my legs were really uncomfortable,” says Bernard Yan, who works for a New York clothing manufacturer and was flying to Singapore for his mother’s 58th birthday.

He finds the premium economy seat tight even though it was specially designed by Singapore for long-haul sitting with extra thigh, calf and foot supports. Some of the extra support and under-seat entertainment gear robbed space for his backpack and reduced room to stretch his legs.

Mr. Yan has made the trip many times, usually stopping in Frankfurt, but he was still surprised at how much more taxing the single long flight proved to be.

“This is new territory, definitely not for everybody,” he says. Still, he enjoyed the food, cabin service and time-savings. “This is a better option. I would take it again.”

Enrico Esopa, a Jersey City, N.J., maritime-labor-union official on a business trip to Singapore, enjoyed the all-business-class nonstop when Singapore ran it before. So when the airline announced the re-inauguration, he switched his ticket from United flights through San Francisco and paid about $200 more for the nonstop.

“The premium economy had plenty of room, and this saved me six or seven hours,” Mr. Esopa says. “But after 15, 14 hours, you’re kind of like, let’s get on with it.”