Final Project Recap

We’ve had a couple of days to sit back and reflect on Math and the Mouse 2024.  We, the professors, agree that this class was one of the best we’ve had, and we are so appreciative of the efforts of these students.  The class is designed to answer the question “When am I ever going to use this?” by helping students explore the ways mathematics is used to model and solve problems in a real-world, industrial setting.  In each of the three weeks of the course, we have a project.  The first two projects are designed with the help of Disney professionals to mimic the types of problems that are solved at Disney.  The third project is of the student’s design.  Here, we seek to foster a sense of (mathematical) wonder about their surroundings.  In each of the final projects, the students decided the focus of the project, how to collect the data for the project, and with a little help from us, how to analyze the data.  We will describe the projects below.

The first group worked on two different questions and consisted of Hayes, Ellis, Will, Katie, Riley, and Alyssa.  They analyzed six-seat rides (Test Track, Remy’s Ratatouille Adventure, Millennium Falcon: Smuggler’s Run, and Space Mountain) to determine their capacity usage and single-rider experience.  Some rides have special single rider lines where individuals pulled from the line when they are needed to make a ride launch with 100% capacity.  Of the six-seat rides, two (Test Track and Smuggler’s Run) have single-rider lines while the other two do not.  Further, Smuggler’s Run has a ride car that is configured as three rows of two seats while the other three rides have two rows of three seats.  To analyze how long a single rider is going to wait and how often a ride vehicle has the need for a single rider, the students needed to gather a party-size distribution.  They gathered data from several different types of rides and used chi-squared hypothesis tests to determine that six-seat rides have party-size distributions that are different from rides that have different seat configurations.  They further used a two-population test of means to determine that two six-seat rides with single rider lines have a higher capacity usage than the two six-seat rides without a single rider queue, indicating that the two rides without a single rider line would lower the wait times for guests by introducing a single rider line.  Finally, they used queuing theory to determine that single riders at Test Track and Smuggler’s Run should expect to wait 4.38 minutes for every five people, or 53 seconds per person in front of them in line on average.

The second project also concerned capacity usage.  The group consisting of Emily, Sam, Tyler, and Jack looked at the methods employed by Disney employees to seat parties on the ride Tower of Terror.  This
ride has cars with 21 seats in three rows of seven, where the first two rows are partitioned so that four seats are on the left and three are on the right of the car.  Just like the last group’s project, as parties of different sizes approach the loading area, a Disney cast member has to assign the party to certain seats in the ride vehicle.  Parties of size five are particularly hard for cast members to seat because they do not want to split this party so that four members go to one side of the aisle while a single person is isolated somewhere else in the car.  They prefer to split these types of parties as three-and-two so that each person has a familiar face next to them.  From the data they collected, ride cars on Tower of Terror launch with an average of 1.09 empty seats (94.8% efficiency), which adds a little over five minutes of extra wait time for park guests in the queue.  The group gathered party size distributions for Tower of Terror and came up with a strategy that maintained the strategy of a 3-2 split for parties of size five and broke parties of size six or more into sub-parties of two, three, or four.  They then simulated the assignment of patrons to seats using their empirical party-size distribution on Bouzarth.com, a seating simulator designed by Craig Bouzarth, Liz’s father.  They found that they could reduce the average number of empty seats per car to 0.39 when looking at the first three party sizes in the queue (which is consistent with what a Disney cast member can view).  They found this result to be statistically significant.  

Another group, consisting of Morgan, Hannah, Erin, and Jacob, asked whether Omnimover rides have a
more accurate posted wait time than non-Omnimover rides.  An Omnimover ride is one that has a continuously-moving track which allows for continuous loading.  Examples of such rides include Spaceship Earth and Peter Pan’s Flight.  Throughout the course, students had been collecting data on the posted versus actual time of wait when they entered lines.  We found a statistically-significant difference in the posted versus actual wait times.  We found that Disney’s posted wait times were an overestimate by an average of 7 minutes.  Because of the continuous nature of the load for an Omnimover ride, the students conjectured that it would have a posted wait time that is more accurate than other types of rides.  However, this group found that Omnimover rides have a posted wait time that is 31% above the average while non-Omnimover rides have posted wait times only 20.5% above the average.  They went beyond this to study to look at the difference of posted versus actual wait times in each park.  They found that rides in Hollywood Studios have the most inaccurate wait times, inflated by an average of over 40% while Epcot has the most accurate wait times, inflated by an average of under 20%.

The final group, consisting of Savannah, Virginia, John, and Tori, looked at trying to predict a cumulative total score of Toy Story Mania based on which of the Easter eggs that are opened on each screen.  Toy Story Mania is a ride where two-person cars are transitioned between five different screens and on each screen, players shoot at targets trying to accumulate points.  Each screen has the opportunity to hit select targets (Easter eggs) that cause higher point targets to appear on the screen, presumably leading to higher total scores for each player.  The whole class was informed as to how to open the special targets and then enjoyed gathering data for the project by riding the ride multiple times.  The group then used regression analysis to try to predict combined points (the total of the two players competing in each car) based on which screen’s Easter eggs were opened.  The group found that on average 266,000 points were accrued by teams who did not open any Easter eggs.  They also found that the final two screens (Buzz’s spaceship and Woody’s roundup) were most important in terms of accruing points, earning over 80,000 combined points per screen for opening those eggs!

We were very impressed with how each student was able to grasp mathematical concepts in a quick fashion in order to perform the analysis for these projects.  This is actually true for every project during the course.  Given that the course has material from thirteen different courses in it, there was no student who had seen every concept in the course before coming on the trip.  Some students had only had material out of only one or two of those courses.  So, the ability of our students to be able to perform these types of analyses quickly and present on it within a week speaks to their ability to be adaptive.  It is also a skill that will serve them will in the workforce.