The Mathematics of Disney Imagineering

Hey guys, I wanted to share this paper that I got a 96 on in my math class about the mathematics of Disney Imagineering.

            Mathematics is found in many professions around the world including in construction and theme park design. It is stated on Business.com’s article about education needed for theme park design that for minds that wish to enter the theme park construction, they should “foster a natural interest in and understanding of science, math, and physics”.   (Wheeler, 2017)  The leading example of mathematical minds in the theme park industry is perhaps the Walt Disney Imagineers.   Imagineers are some of the most creative minds working today.  Imagineering is a portmanteau word that as the About Imagineering page on the Disney Imagineers website states that it is a combination of imagination and engineering. (About Imagineering, n.d.)

            Jeff Kurtti in his book, Walt Disney’s Imagineering Legends and The Genesis of the Disney Theme Park elaborates on what Imagineering is by stating that it was first formed by Walt Disney in 1952 as Walt Disney Incorporated (which would later become WED) to build one of his biggest projects, Disneyland.  Kurtti goes onto explain that “Walt Disney Imagineering remains the design, development, and master planning branch of the company employing a multitude of disciplines utilized in places all around the world”.  (Kurtti, 2006)  It has been seen in many projects that the Imagineers have worked on, that the fields of science, technology, engineering, and mathematics (S.T.E.M.)  are required in many of their projects.  Whether it be something on a smaller scale such as replacing an old ride with a new one or adding a whole land to one of their many theme parks.   One of the prominent ways that math features in the Imagineering process is the usage of measurements and scales.   One of the most ambitious undertakings for the Imagineers came, when they brought Mount Everest to life in the state of Florida at Disney’s Animal Kingdom as the rollercoaster, Expedition Everest.     Expedition Everest as of this date is the largest manmade mountain that has been built.   And as stated at Disneyavenue.com, “Expedition Everest… is made from 18,000 tons of steel and painted with 2,000 gallons of paint. It is the tallest artificial mountain in Florida”.   (Mahne, 2015)

            As discussed by Disney Imagineer Senior VP, Joe Rhode in the classroom DVD, The Science of Disney Imagineering: Design and Models building Expedition Everest was no easy feat.   They needed to start with small models before attempting to build the real thing.   They needed to start with building what are known as presentation and research models to get a better understanding of how the mountain should look.   As Rhode explains to the host, Asa Kalama, “We started with these little paper models.  Which would give us the basic idea of what the mountain would look like.  We built these clay models and added one inch pieces of paper that covered 20 ft. of the model”.  (Kaplan, 2009)  Joe Rhode goes onto explain that by starting with these models and using these smaller models helped the Imagineers to figure how they needed to build Expedition Everest because as Rhode stated in a prior scene, it’s easier to make a mistake on the models than it is when they were building the real thing.   One of the most fascinating aspects that Rhode mentions is that they went through twenty-seven different models before building the real thing in Florida.  Building these twenty-seven different models helped the Imagineers to have a concept of what Everest should look  like, when the real mountain came to fruition.  This is an example of concept design, which is described as “the initial big picture or macro design.  It shows us what problems the product will solve… and how it will solve them”.   (Hedges, n.d.)     This goes a long way in explaining why the Imagineers had to build such a large number of different models as they would not be able to determine from just one model, what aspects could cause them difficulty.  

            Rhode further explains that by starting with the smaller models of Everest, they can figure out the scale and proportion for what Expedition Everest should’ve been before embarking upon building this rather mountainous rollercoaster.  Figuring out what the scale and proportion on the miniature mountain was a crucial necessity for them to understand what the relationship needed to be in relation to how they were going to build their artificial Everest.   With this build, they did have the real Mount Everest to use as a basis but their rollercoaster mountain needed to be scaled down considerably from 29,029 Ft.  that the real Everest stands at whereas the one at Disney’s Animal Kingdom only comes in at 199.5 Ft. but Rhode went ahead and rounded this up to 200 Ft.    That’s a difference of 28,829 Ft. between the real Everest and the one that was brought to life by the Imagineers.   To elaborate upon this, further, “scale refers to the size of an object (a whole) in relationship to another object (another whole)”.  (Lamp, n.d.) It is highly emphasized that the team of Imagineers that worked on Expedition Everest needed an understanding of how scale and proportion functioned in order to ensure that the manmade mountain was up to scale. 

The Imagineers needed to have a firm understanding of what the scale and proportion for Expedition Everest. And one way, they were able to figure how tall the mountain needed to be was by travelling to the real Everest and were able to transpose the information of what the scale of Everest, when they came back stateside to start working on building Expedition Everest.   This gave them the basis for what the rollercoaster’s height should be.  Once again, Expedition Everest’s height is 200 Ft. and that is relation to its length, which comes in at 4,424 Ft.   It should be noted that the 200 Ft. height primarily refers to the exterior and the length of the track focuses on the interior of the rollercoaster.   Concerning the length of the track that is found on the interior, this is where Disney Imagineer, Todd Camill steps in and explains that he designed a computer-aided-designed (CAD) model to figure out how to sufficiently place the track that would be laid on the inside of Expedition Everest.  Using the CAD model is yet another example of how Imagineers such as  Todd Camill needed to have a design of the concept before the construction crew could start laying the groundwork for the rollercoaster.   Camill explains that “this model at one point helped us (the Imagineers) discover a steel beam that would’ve ran right through ride track”.  (Kaplan, 2009)  This is another example of why it is important for the Imagineers to have a succinct understanding of what the relationship between the scale and proportion should be before they set upon building a ride of this magnitude. 

 One can imagine that this was a very laborious and daunting endeavor to bring the world’s most famous mountain to life in a state that is rather flat.  There were many things that the Imagineers needed to consider, when working on the architecture of this ride and knowing what the scale and proportion or the relationship for the ride was going to be while building it is perhaps the most important thing that they needed to understand.  For, if they had made any error while building the models, they may not have had the space to lay the 4,424 pieces of track that are needed for the cars that the guests sit in. It could have ended up being too tight. To most people visiting a theme park like Disney’s Animal Kingdom, they will most likely never notice of the hard work that the Imagineers put into a ride like Expedition Everest but were it not for them deducing what the ride’s mathematical relationship should be, the guests that ride this rollercoaster would never be able to experience the rush and adrenaline that comes from riding Expedition Everest.