Jason Steffen, a research fellow at Northwestern University, normally contemplates things such as axion-like particles. But after waiting in one boarding line too many, he turned to the mysteries of airline seating.
"I thought there had to be a better way," he said.
So, after a series of calculations, he deduced that the best system would be a combination of filling all the window seats first, then all the middle ones and then the aisle ones, while also having the passengers board every other row.
There was just one problem -- passengers would have to board in precise order. Good luck with that. These are the same passengers who don't turn off their phones even after they're told it's a federal law.
"Well," Steffen said, "I understand why airline people aren't calling me."
But the search for the perfect boarding process goes on.
Most airlines allow first-class and other elite customers to board first. After that, some fill the rear rows first and work toward the front.
Others fill window seats and work in toward the aisle. Some used to employ a hybrid called the reverse-pyramid. Southwest Airlines has random seating: There are no assigned seats -- passengers sort things out themselves. They can pay extra to be near the front of the boarding line.
All of this matters more than you might think.
Passengers want to board early to find space in the overhead bins for their rolling carry-on bags. For airlines, every minute that a plane sits at the gate makes it more likely that the flight will be late, hurting the carrier's on-time rating and causing passengers to miss connecting flights.
There's an economic cost to running late, too. Researchers from Northern Illinois University say that at one major airline, which they didn't identify, every extra minute at the gate added $30 in costs.
American Airlines, which uses a back-to-front system for boarding coach passengers after it takes care of elite customers, says that it takes about 25 minutes to board passengers on a smaller, narrow-body plane such as a Boeing 737 and about 35 minutes on a bigger plane such as a Boeing 777.
In recent weeks, United and American -- the nation's biggest and third-biggest carriers -- have rolled out new strategies for faster boarding.
American is letting passengers board sooner if they don't put anything in the overhead bins. The idea is to get more people seated quickly before passengers with rolling bags clog the aisle.
United reduced the number of boarding groups from seven to five while adding lanes in gate areas -- from two to five at big airports. That's designed to eliminate "gate lice" -- the name road warriors use for those anxious passengers with big carry-ons who cause a traffic jam by creeping forward long before their group is called.
American and United tested their new procedures in a handful of airports before rolling them out across the country in time for the peak summer travel season. United CEO Jeff Smisek said his airline's new method has helped cut departure delays related to boarding by more than 60 percent.
Boarding methods go back to the dawn of commercial flight, but they've gotten more complicated as the airlines have created different classes of passengers and sold the right to board early.
Since 2008, most large airlines have imposed fees for checking a bag, which encourages passengers to carry more on board. At the same time, airlines have reduced flights to control costs, making planes more crowded. The result: Space in the overhead bins has never been more valuable.
Recognizing the potential value in that coveted real estate, Spirit Airlines began charging for stowing a bag in the overhead three years ago -- the fee now runs up to $100.
Spirit says the fee speeds up boarding by cutting down the number of carry-on bags. The big airlines haven't copied Spirit for fear of angering customers. They've looked for other ways to improve boarding.
In May, American began offering early boarding to passengers with just a personal item that fits under the seat. In a test at several airports, it cut boarding by two minutes per flight, according to Kevin Doeksen, the airline's director of customer planning. With about 1,900 flights per day on American, that adds up.
What's to stop a passenger from moving up in line by promising to put a personal item under the seat, then stuffing it in the overhead bin anyway?
"It would be a lie to say that never happens," said Tessa Letren, an American gate agent at Baltimore-Washington International Airport.
Still, Letren supports the new policy, which she says cuts the amount of time that planes spend on the ground between flights.
Before the 2010 merger of United and Continental airlines, United used the inside-out method of boarding -- window seats first, then middle, then aisle -- while Continental used the back-to-front method, loading passengers a few rows at a time starting at the rear of the plane. After much testing, the combined airline kept the United approach. Earlier this year, United set up additional boarding lines in the terminals to attack congestion in the gate area.
The back-to-front system, still used by many airlines, seems logical. But some studies have shown that it's slower than windows-middle-aisle.
"If you're on the aisle and somebody sitting next to you in the middle seat shows up, you need to unbuckle and maybe get up," said Ken Bostock, United's managing director of customer experience. "That can take 20, 25 seconds, and that happens a lot during the boarding process."
Lou Agudo, a United gate agent who worked at Continental before the merger, says boarding by groups of rows practically invited confusion. Just when he thought everyone in Group 2 -- the rear of the plane -- had gone through, and he called Group 3 to start, "Twenty people would walk up and say they didn't hear the announcement." Some had missed the call for their group, while others decided to get in line no matter what, he says. The extra lanes have made his job easier.
Anything to tidy up the gate area will help, in the view of Yosief Ghirmai, an auditor for defense contractor Raytheon Co. in Frisco, Texas, who said foreign airlines make boarding much easier for elite-level frequent fliers like himself.
"The international airlines respect the priority boarding system," Ghirmai said, citing Hong Kong's Cathay Pacific as an example. "Here, you have to fight to get to the priority boarding line -- all the bags, all the kids. The concept (in the U.S.) is the same, but the execution is much better over there."
Selita Garcia of Chicago wondered why anybody in the front of the plane would want to board first.
"We're always bumping into all those business-class people -- if it's not my purse, then I'm hitting them with my bag," said Garcia, who manages a doctor's office and was taking her grandson to vacation Mexico, recently. "Why let them on first? The plane is not taking off until everybody is on the plane."