St Andrew’s College students win international maths prize with best way to board planes

Four Year 13 students from St Andrew’s College, Christchurch have won the Outstanding Team award at the International Mathematical Modeling Challenge, the competition’s highest honor.

They were one of three teams in the world to receive the outstanding award, the others came from Thailand and the United States.

The teams had to find the fastest way for passengers to board and disembark from a narrow-body and wide-body aircraft.

They were one of two New Zealand schools to face 56 other teams in the international judging round.

Team members Toby Harvie, Luke Zhu, Corin Simcock and Tom Edwards spent five days simulating different boarding and disembarking methods, generating a random queue of passengers to determine the most optimal method.

Phil Adams, professor at St Andrews’s College in charge of digital technologies and mathematics, said students should do extensive research and learn about aircraft boarding algorithms, before identifying any complicated variables like baggage and groups of passengers.

“They took the approach of mathematically modeling the variables and the onboarding process, then wrote a complex computer program in Python to run simulations of the onboarding process over and over again.”

“It allowed them to try out different boarding strategies and see how they reacted to changing variables like disobedience coefficient, passengers with carry-on bags, or groups,” Adams said.

After performing thousands of trials and analyzing the results, the students were able to agree on a strategy.

“It took them five full days, including the time to produce a professional and polished report summarizing their process and findings.

“They did an amazing job.”

Getting on a plane – the tests

The students found that three factors contribute to the time it takes to board a plane, including the speed passengers walk, the time it takes to stow luggage high up, passengers blocking the aisle while doing so, and the passengers who stood up to allow other passengers to enter. the same row.

After performing 10,000 trials, they found that the most optimal boarding order was rear, middle, and front. Using this method, the average time to fill a narrow-body aircraft was 12 minutes and 48 seconds.

By comparison, it took an average of 14 minutes and 30 seconds to board using the forward, middle, and reverse method.

They also tested boarding by seat type, seating all passengers with a window seat first, middle next, and aisle seats last. The average boarding time was 9 minutes and 49 seconds. However, this proved impractical in practice due to the separation of groups, especially in the case of children and the elderly.

The random boarding method, while seemingly crude and inefficient, proved to be reasonably effective. It took an average of 11 minutes and 30 seconds for passengers to finish boarding the plane.

Landing the plane

When it came to getting out of the plane, the optimal method for a narrow-body aircraft turned out to be to disembark from the back to the front in rows. It turned out to be the fastest due to the greater aisle throughput.

This is the opposite of the “front-to-back” boarding method that is used by most airlines and has proven to be the slowest method of disembarkation.

The best methods

The best method of choice to immediately expedite the boarding and deplaning of passengers in a standard narrow-body aircraft was to board passengers using the WMA method – window seats board first, followed by cockpit seats. middle, then aisle seats, but which include boarding. , minimizing aisle blockages and allowing for optimal aisle flow, and should disembark giving passengers coming from behind the right of way. Both methods minimize aisle blockages and allow for optimal aisle flow.

In a jumbo jet, they found that the optimal method of boarding was by section – from back to front, while disembarking using the “across” method, similar to the method for a narrow plane, where passengers furthest from the gate get the right of way.

Team teacher and advisor Phil Adams said: “The team’s creativity, teamwork and math skills make them a standout and it will be exciting to see where they go from here. here”.

The results of the study were compiled into a twenty-page report and made available to airline executives.

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