The Math Of Boarding Airplanes

It's Tuesday, September eighth. I'm flying to a friend's wedding this Friday, and for the first time in a long time, I'm not flying Delta — I'm flying Southwest. And the thing I keep returning to is boarding. Southwest's process is famous: no assigned seats, you walk on and sit wherever's open. I always thought that was the smarter way to do it. Everyone else boards in slow, staggered zones, back to front, and it never feels faster. It just feels like standing in a longer line with extra steps.

There is real science here. Live experiments, peer-reviewed papers, an astrophysicist who ran the numbers — they all point to the same conclusion. Back-to-front boarding, the method almost every airline uses, is the slowest possible way to get people on a plane. The fastest methods have been known for almost twenty years. And airlines won't use them — not because they don't work, but because a slow line makes more money than a fast one. As of this year, Southwest made the same choice.

In 2014, the television show MythBusters built a replica airplane cabin with 173 real seats, overhead bins, and a single aisle. They brought in professional flight attendants, handed out assigned seat tickets to volunteers, and tested six different boarding methods. Five percent of the passengers were instructed to behave like actual humans: going the wrong way down the aisle, sitting in the wrong seat, boarding with small children, folding a coat while blocking everyone behind them.

When they boarded back to front — the method almost every airline uses — it took twenty-four minutes and twenty-nine seconds. That was the slowest of all six methods tested.

Random boarding with assigned seats took seventeen minutes and fifteen seconds. That is seven minutes faster. No rules, no zones, no groups. Just everyone gets on when the door opens. Seven minutes saved, just by doing nothing.

The WILMA method — window seats first, then middle, then aisle — clocked in at fourteen minutes and fifty-five seconds. Ten minutes faster than back to front, and passengers rated it the most satisfying experience. The name WILMA is an acronym: Window, Middle, Aisle. You fill the seats from the outside in so nobody has to stand up to let someone else in, nobody has to shuffle past a seated stranger, and the aisle stays clear for people walking to their row.

The reverse pyramid method, a more complex variation of WILMA that also moves back to front in blocks, came in at fifteen minutes and ten seconds with the highest satisfaction score of any method.

And the absolute fastest method? No assigned seats. Let people pick wherever they want to sit. Fourteen minutes and seven seconds. That is ten minutes faster than back to front. But it also had the lowest satisfaction score, because passengers hated the stress of finding a seat.

Nobody who has ever flown on Southwest Airlines will be surprised by this number. Southwest never assigned seats. Their open boarding, where you line up by check-in order and pick any available seat, was one of the most efficient in the industry. Not because Southwest passengers are more cooperative. Because when nobody knows where they are sitting, every passenger has a personal incentive to get on the plane and sit down as fast as possible. There is a chair problem, and everyone is trying to solve it at the same time.

Jason Steffen is an astrophysicist at the University of Nevada, Las Vegas. He studies exoplanets — planets orbiting other stars. He was part of the Kepler mission team. His research involves orbital dynamics, planetary system architecture, and the structure of the Milky Way.

In 2008, Steffen was boarding a flight to a conference. He stood in the usual jetway line, watching the usual cascade of people blocking the aisle while wrestling luggage into bins, and he thought: there has to be a mathematically optimal way to do this. So he went home and wrote a paper.

Steffen treated airplane boarding as an optimization problem. Using a Markov Chain Monte Carlo algorithm — a method astrophysicists use for everything from modeling galaxy formation to analyzing cosmic microwave background data — he simulated thousands of boarding sequences to find the arrangement that minimizes the total time. His model assumed luggage stowage is the dominant bottleneck, because that is what it is. When a passenger stops in the aisle to lift a bag, everyone behind them stops too. The goal is to maximize the number of people who can stow luggage simultaneously without blocking each other.

The optimal solution looks wrong the first time you see it. Passengers board in alternating rows — row one, then row three, then row five — working from the windows inward and from the back of the plane toward the front. The spacing means each person has several empty rows around them while they load their bag. Nobody is standing in anyone else's way. By the time two passengers end up in adjacent rows, they are both already seated.

Steffen published his paper in the Journal of Air Transport Management in 2008. The math said his method could board a plane four times faster than back to front. In 2011, he ran a live test with 72 passengers and a real aircraft mockup for a television show called This vs. That. His method took about three and a half minutes. The standard block boarding took nearly seven. For a full 173-seat plane, the gap would be even wider.

No airline has ever adopted it.

Steffen later devised a simplified version — the Steffen Modified — where passengers board in four groups: right side odd rows, left side odd rows, right side even rows, left side even rows. Still window to aisle. It is twice as slow as the full method but much easier to execute at a gate. No airline adopted this either.

The obvious question is why. If these methods are faster, and faster boarding means quicker turnarounds, and quicker turnarounds mean more flights per day with the same aircraft, why would any airline leave ten minutes of gate time on the table?

Every minute a narrow-body jet sits at the gate costs the airline money. Low-cost carriers like Ryanair and Wizz Air schedule turns as short as twenty-five minutes. Legacy carriers schedule forty-five to sixty. The reason Ryanair can do twenty-five is that they board through both the front and rear doors, which cuts the passenger flow in half, and their cabin is a single class with no premium seat selection drama. Most US airports only have one jet bridge per gate, so dual-door boarding is not even possible for most domestic flights.

But the bigger reason is that boarding inefficiency has become a product. Airlines sell priority boarding. They sell it to elite status members as a loyalty perk. They sell it to basic economy passengers as an upgrade. They bundle it with credit cards. They offer it as an add-on for twenty-five dollars at checkout. The entire economic model of boarding has been built around making the experience bad enough that you will pay to escape it.

The WILMA method, the reverse pyramid, the Steffen method — they all require one thing that airlines cannot monetize: a specific boarding order based only on where you are sitting. If everyone boards when their seat position calls them, nobody can pay to go earlier. The hierarchy dissolves.

United Airlines adopted WILMA in 2023 and reported it cuts about two minutes per flight. But United still boards premium cabins and elite status holders first, before the window-middle-aisle sequence begins, which partially undoes the optimization.

Southwest is the clearest case. For fifty years, Southwest used open seating and had some of the fastest turnarounds in the industry. In January 2026, Southwest switched to assigned seats with eight boarding groups. They added premium extra-legroom seats at the front of the cabin that people can pay extra for, and priority boarding that people can pay extra for. The new system is slower. Southwest knows it is slower. They made the trade anyway, because assigned seating and upgrade fees are projected to generate hundreds of millions of dollars in new revenue annually.

Bill Franklin, the Southwest executive who designed the airline's legendary ten-minute turn in the nineteen-seventies, would not recognize the airline today. When Southwest sold one of its four aircraft to raise cash, Franklin redesigned the entire ground operation so three planes could fly the same schedule as four. Boarding was part of that equation. Everyone moved fast because the economics demanded it.

The economics now demand the opposite. An airline makes more money selling you a way to suffer less than it loses by making you suffer in the first place.

A problem with a known mathematical solution, studied by scientists who have nothing to gain from it, published in peer-reviewed journals, demonstrated in live experiments on television, ignored by the entire industry for eighteen years because the inefficiency is worth more than the fix. That is not a failure of science. It is a business model that found a way to monetize a bottleneck instead of removing it.

Stay informed, stay curious, and we'll see you tomorrow.