DALLAS — Getting people on and off an airplane quickly is so complicated that even an astrophysicist couldn’t figure it out.
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 says.
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 do not turn off their cellphones even after they have been told it is a federal law.
‘‘Well,’’ Steffen observes, ‘‘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 probable 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 elite customers, said that it takes 25 minutes to board passengers on a smaller, narrow-body plane such as a Boeing 737 and 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 do not 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. That is 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 launching them across the country for the peak summer travel season. United chief executive Jeff Smisek said his airline’s new method helped cut departure delays related to boarding by more than 60 percent.
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 have not copied Spirit for fear of angering customers.