Let Einstein Help You Board Your Plane

Dr. S.G.T Bhatt, Daejeon, South Korea

FROM YOUR chair in the departure lounge you can already see the plane, tanks topped up, ready to go. All that stands between you and a speedy departure are your fellow passengers. "Ladies and gentlemen, we are now ready to begin boarding..."

The surge begins, and within a few minutes you are all hopelessly backed up in the bridge onto the plane. It's enough to give you air rage. What's so hard about getting into a seat?

You may not realize it, but it's a question with cosmic significance. While shuffling on board a plane feels like a distinctly Earth-bound experience, there's more to it than that. In what appears to be the first out-of-physics application for Einstein's theory of relativity, it seems the answer to faster boarding lies in a trip through space-time.

And, you'll be glad to hear, this approach shows there really are ways to improve the experience.

A few seconds' thought will give you some of the options airlines could consider. One is random boarding: everyone for themselves. This is not as chaotic as it sounds, but nor is it edifying, and seems unlikely to be the most efficient approach. At the other extreme you could be ultra-organized and specify the exact order in which you want everyone to queue up. In such a rigidly marshaled scheme, however, you'd spend so much time ordering people about that it would be no better than a free-for-all. And any airline that tried to be that bossy would quickly find itself without any passengers to worry about. After all, one person's orderly queuing protocol is another's intolerable control-freakery.

In between lie myriad options: calling passengers by rows, half-rows, blocks of rows, back-of-plane-to-front-of queue, and "outside in" - window seats first, then middle, then aisle - and so on. They all sound reasonable enough, but there's scant evidence to prove that one is better than another. Isn't there a more scientific way to work this out? Enter Eitan Bachmat and his colleagues at Ben-Gurion University of the Negev in Israel. Bachmat wasn't initially aiming to solve the problem of "enplaning", as airlines rather grandly stone and you would see that, out of all for really high congestion, random boarding soon becomes the better option. For the moderate-squeeze conditions that are the reality for most of us, the best balance is a high level of row randomness combined with a touch of back to-front.

“For moderate-squeeze conditions the best balance is a high level of row randomness combined with a touch of back-to-front”

Unsurprisingly, you can improve things significantly if you can persuade people to arrange themselves in window middle-aisle order for each row. Teaming that with a bit of back-to-front helps, but row order makes relatively little difference compared with the order within each row. "Unless you can really force passengers [to do what you want playing with the row orders isn't going to get you very far," says Bachmat.

What also emerged is that boarding time is proportional to the square root of the number of passengers. Considering how complex things become as the numbers increase, that's actually not bad, but it still has significant implications for today's ever-bigger airplanes, like Airbus's 555-seat super jumbo, the A380. Airbus has clearly anticipated the problem - even without the aid of relativity. "You can get people in on two different levels at once," says spokesman Justin Dubon. "It's tantamount to loading two planes at once." In tests on real aircraft, all 555 passengers could be seated in just 22 minutes, compared with 21 minutes for the 471 passengers on a 747.

So are Bachmat and his colleagues sledge hammering a trivial problem by using relativity? Hendrik Van Landeghem of the University of Ghent in Belgium doesn't think so. Working with Ghent colleague Annelies Besuselinck, Van Landeghem carried out a simulation-based study in 2002 (see "All aboard"), and he is impressed by Bachmat's further step. "I actually think it was fairly original that they attempted such a thing. If you are able to validate simulations by mathematical formulation it strengthens both approaches." Maybe he is pleased because the results tally well with his own. "It has validated


call it. He was studying the performance of digital storage systems such as PC hard drives, looking at how to read and write data most efficiently. Say you send your hard drive a big bunch of read/write requests. What you want to know is the quickest way to carry out those tasks. How do you find the fewest drive rotations needed to do the job?

Boarding for bozos

One day a colleague who saw this work said, "Hey, that looks a lot like airplane boarding," and so Bachmat and his colleagues decided to explore this parallel route. "We thought we could do this and take stuff back to the hard drive problem," he says.

The first step, they realized, was to see what actually holds things up when you're waiting in the aisle of the plane. While that bozo up ahead of you is hunting for his iPod and then trying to jam that stupidly big bag into the locker before taking his seat, everyone behind is either standing waiting to get past - or, if they have already reached their row, doing pretty much the same thing as the bozo. Once those passengers have sat down, everyone moves on a bit, and the process repeats itself. At each stage, some passengers remain blocked by those in front: the blocked wait their turn, and then become blockers, and so on. What everyone wants is to find a way to minimize the time from the start of boarding until the last person sits down and buckles up. This is easy enough in simple approximations, but as soon as your model includes variables like distance between rows, width of passengers' bodies, time taken to stow luggage and so on, it quickly becomes intractable.

Fortunately, physics has something to say about problems like this. Odd as it may seem, it occurred to Bachmat and his colleagues that the way passengers fill up a plane looks like relativity's description of how things move through the four dimensions of space-time under the influence of gravity.

According to relativity, an object in "freefall" follows the trajectory that ages it the most. Throw a stone into the air: it will trace out an arc and return to the ground. Attach a stopwatch to the what we did, which means that we did a good job," he says.

Airlines themselves remain oddly uninterested in any of this work, however. Van Landeghem did manage to establish collaboration with Belgian airline Sabena, but the airline went bankrupt before they could take it forward.

There has been no further interest from any airline, Van Landeghem says. Neither has Bachmat been offered a chance to try out his new application for relativity. "I would be very happy if an airline that does unassigned boarding would work with us," he says.

Aside from honing their boarding policies, what else could airlines do? One thing stands out a mile: "Widen the aisle, to make it one-and-a-half person to allow bypassing, that would have the single greatest impact," says Van Landeghem. Bachmat agrees: "If you had several entrances and more aisles that would help."

You are unlikely to see airlines ripping out seats to make more space any time soon, but there are things passengers can do to ease things along. "Keep your distance from your peers to lower the congestion parameter,” says Bachmat. And obviously, take less carry-on luggage with you. "Be disciplined," he says. So next time you're surrounded by dithering travelers as you board your plane, take comfort from the fact that you're all acting out some very clever physics. "I think it's exciting," says Bachmat. "It's kind of nice that you can tell people that they compute a relativistic calculation with their feet."

About the Author: This article was posted by S.G.T Bhatt who is working as senior scientist at KRICT, Daejeon, South Korea and in India he worked as vice president of ONGC. This article was taken from New Scientist for which he is a member.

Email: bhatsgt@yahoo.com

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