DALLAS -- Some frequent fliers say they aren't worried about safety aboard Boeing's problem-plagued 787 aircraft, while many less-seasoned travelers are often unaware of what model of plane they're flying on.

That makes it anyone's guess whether Boeing Co., or the airlines that use its planes, will pay a price for concerns surrounding the 787. The planes were grounded worldwide Thursday after a battery fire on one, and an emergency landing on another after pilots smelled something burning.

"I'm as excited today to get on a 787 as I was a year ago," says Edward Pizzarello, a travel blogger who has logged four flights on the 787, which Boeing calls the Dreamliner. "Boeing will fix this, and I'll be flying on this plane for many years."

Lee Simonetta, a research engineer at Georgia Tech, said he too would hop on the Dreamliner again. He was among the aviation fanatics aboard the plane's first trip with paying customers, an All Nippon Airways flight from Tokyo to Hong Kong in October 2011. It was a time to marvel at a jet made of composite materials that make it lighter and far more fuel-efficient, and at its use of electrical systems to do just about everything.

That was before a series of incidents including fuel leaks, cracked windshields and overheating batteries gained worldwide attention. Photos of charred battery boxes from the planes popped up all over the Internet. Safety officials around the world took a second look at the planes, and the Federal Aviation Administration grounded 787s in this country -- United Airlines is the only U.S. carrier to fly them, but several foreign airlines use them on flights to and from the U.S.

Boeing officials and some frequent fliers say there are hiccups with just about every new plane, and the 787 was a particularly bold technological leap over previous aircraft. But will those reassurances satisfy the flying public?

Mary Schiavo, a former inspector general of the U.S. Transportation Department and FAA critic who's now an aviation lawyer, said she would not fly aboard a Dreamliner.

"It's very serious. Nobody wants to get on a plane with these things happening," Schiavo said.

Schiavo said she thinks that if Boeing and the FAA believe there is something wrong with a few batteries, replacing them with other lithium-ion batteries would be a quick repair. But, she said, the FAA might force Boeing to use an entirely different type of battery, which could require redesign work and a new round of regulatory approvals that might take months.

Blake Fleetwood, president of Cook Travel in New York, said a few customers have called in the past two days to ask about the plane but none have changed their itineraries. Of course, those flights won't involve 787s if safety regulators haven't cleared the planes by takeoff time.

"A month ago we had people who were dying to get on this plane," Fleetwood said. "Now they're showing a bit more trepidation."

Many people who don't fly frequently may not even notice what type of plane they're on.

From interviews with more than a dozen travelers at Houston's Bush Intercontinental Airport, it appeared that price, schedule and nonstop service are more important to consumers than the type of plane itself. Only one knew that the government had grounded the 787.

Curtis Johnson, a retailer from San Antonio, said that he purposely booked on a 787 last month from Houston to Newark, N.J. "Very impressive," he said, describing the large windows, wide seats and other flourishes.

Johnson said he pays attention to the type of plane when he books a long flight, and he admitted that he might be "a little bit more nervous than I was three weeks ago" about the 787.

Christine Carlton, who arrived on a United flight from San Antonio, said she wouldn't seek to change planes but would instead "just be stuck and hope for the best."

Many sounded like Casey Ager, a 22-year-old from Seattle, who said he wouldn't have any misgivings about getting on a 787.

"If it's out there and they're letting us fly, I trust it's ready to go," he said.