As It Happens

Mathematician crunches the numbers to find most efficient way to board a plane

A new study finds that the fastest way to board an airplane is to let the slowest passengers board first.

Eitan Bachmat says it sounds 'counterintuitive and surprising' but it's best to board slower passengers first

A new study suggests that the most efficient way to board an airplane is to let the slower passengers board the plane first. (Denis Doyle/Getty Images)
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Figuring out the fastest way to board an airplane is a problem that researchers have been trying to figure out for years — using everything from Lorentzian geometry to the theory of relativity.

Eitan Bachmat is a mathematician and an associate professor in the computer science department at Ben-Gurion University. He worked on a new study that may have found an answer. 

The research was published in Physical Review EAs It Happens host Carol Off spoke to Bachmat about his findings.

Here is part of their conversation.

I'm trying to picture you in the waiting lounge of the airport — you're the guy in the corner who is feverishly scribbling math equations, right?

I'm usually more observing people so I can scribble later.

Eitan Bachmat says when you board an airplane you are doing 'quite complicated computation in relativity theory about the aging of some free falling particle and some model of the universe.' (Chip Somodevilla/Getty Images)

What is it that has caught your attention on how they board planes?

I look at how the boarding proceeds and whether I get stuck before the airplane entrance. What is the method of the airline? Do they board from the back to the front or by groups? 

So, in different areas and different places, I try to follow the procedures and just think about it a little bit.

So what have you determined is the fastest way to board an airplane?

In our latest studies, we've been looking at random boarding versus if you have two groups of people — some which are slower and some which are faster.

For example, people without luggage — they're supposed to be the fast group. And people with luggage, the slow group.

A lot of the times it happens they board first people who have children and need assistance. That would be a slow group.

So, if you have a fast and slow group, what we found is that you should board the slow passengers first, which is kind of counterintuitive and surprising, I think.

Comparison of four different plane boarding policies, as shown in the study. (Sveinung Erland, Jevgenijs Kaupužs, Vidar Frette, Rami Pugatch, and Eitan Bachmat)

Obviously people who are with children, people who are in wheelchairs, or the elderly. But beyond that, how do you decide who should board first? If you're saying people with all kinds of baggage that they probably shouldn't have with them get on first that would really get under people's skin. Would it not?

Actually, a couple of airlines tried that. But they tried fast [boarding] first, not slow first. Then they abandoned that.

In any case, it would board faster. But not by much. And in terms of groups, yeah, I think the only groups that make sense are by luggage or, like, people who need assistance.

But if you can come up with other methods, that would be great. The nice thing about working on airplane boarding is everybody has boarded an airplane. Everybody's an expert.

Bachmat says it's 'a hard sell' to convince passengers to let all the slower people weighed down with luggage to board before them but that mathematically it's the best option. (Eric Baradat/AFP/Getty Images)

Right. Everyone has an opinion, if they're not an expert. But the way you came up with this best — or among the best — way to board is through math, through calculations, which is not my strength. But do you want to explain, as simply as you can, how you figured this out using things like geometry and the theory of relativity?

OK. So I'll try my best to keep it really simple. So the same math can describe very different things. I can say three plus three equals six, and three apples plus three apples equals six apples. Or, it could be three houses plus three houses equals six houses.

Apples and houses have nothing in common. But, sort of, the math that describes the situation is the same.

And what turned out, and that was very surprising, is that when you and 200, or 300, other people board the airplane, in terms of the mathematics, you're doing a quite complicated computation in relativity theory about the aging of some free falling particle and some model of the universe.

Are you serious? 

I was surprised.

OK, yeah … 

I was very surprised.

And what happens is when the airline changes the policy, or the airplane is more or less congested, these are like different models of the universe. Like, you can be part of the universe near the Earth. You can be between galaxies, and the calculations are basically always the same kind of relativistic geometry. But the environment changes as all these parameters change.

OK, I want to see you on the airplane explaining to people on the intercom the relativistic geometry of why they were told to take their seats in this order and see how long you last.

Yeah, it's a hard sell, in that sense.


Written by Chris Harbord and John McGill. Interview produced by Chris Harbord. Q&A has been edited for length and clarity.

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