Simulating plane designs for faster boarding

In the process of boarding a plane, you find yourself standing behind a man so unwashed that you imagine seeing a cartoonish, green stink cloud emanating from his trenchcoat. In front of him, a crouched old woman struggles futilely to lift her humongous suitcases, each of which is large enough to fit her inside them, into the luggage rack. Behind you is a red-eyed, defeated mother, who clutches a baby that screeches like an untuned violin. You think to yourself: "there has to be a faster way to get through this hell". Then the baby vomits into your backpack.

A faster way

Consider a typical plane in Europe, such as Ryanair's Boeing 737-800. Two entrances for passengers, one at each end of the plane. About 32 rows of seats give a total of approximately 200 seats, and they're split by a single aisle.

During boarding, passengers are divided into 2 groups*: those whose seats are closer to the rear entrance, who board through the rear entrance; and another group whose seats are closer to the front entrance. This makes boarding more efficient because the groups don't have to climb over each other to get to their places.

(*Discounting priority boarding for simplification).

Here's an idea: what if we moved the entrances to 1/4 and 3/4 of the way through the plane, respectively, rather than placing them at the ends. Pre-boarding, passengers would still be sorted into 2 groups based on how close their seats were to the entrances. During boarding, however, they would effectively be split into 4 groups: those who turned left at the 1st entrance, those who turned right at the 1st entrance, those who turned left at the 2nd entrance, and those who turned right at the 2nd entrance.

diagram demonstrating passenger grouping

This would further reduce the interference between passengers, and, in theory, further reduce boarding times. We're going to run an extremely simple simulation in Python to test this theory.

Simulating it

Here's an animated representation of the simulation, created using the pygame library. The simulation runs in a series of "time steps". It takes 1 time step for a passenger to move between rows, and 5 time steps for a passenger to put their luggage into the rack and take their seat. These numbers were chosen pretty much arbitrarily. Reality would be more chaotic and teeth-grindingly frustrating. First we run a simulation with entrances at the ends of the plane. Then we run a version with centered entrances.

In this case the entrances-at-ends design takes 239 time steps before everyone is seated, while the centered-entrances design takes 209 time steps, which is 12% less.

Further testing and results

Just to be scientific about it, we can run both versions of the simulation 10,000 times and see what the average number of time steps is for each. Here are the results in graph form:

results graph

The centered-entrances design is, on average, ~15% faster in this run of the simulation.

Of course, there may be engineering or safety issues that prevent plane manufacturers from playing around with their plane designs like this. Perhaps placing the entrances at the ends gives space for more seats. Perhaps the wings and emergency exits get in the way of centered entrances. Etcetera.

Whatever the case, it's a nice distraction to think about as the trenchcoat stink cloud wafts its way towards you and the baby in your vicinity makes threatening heaving motions.

Discussion

Appendix A: follow-up reading

Further thoughts on the efficiency of plane boarding can be enjoyed in this fun, informative little video by CPG Gray, which doesn't mention plane design but discusses a number of algorithms for faster boarding.

Appendix B: the code

For the curious, here's the script used to run the simulation and animate it.


Post Date: 2019-09-07

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