As I wait for my delayed flight at SeaTac Airport, I watch all the planes that land and take off in a constant stream. Do you realize that a handful of people direct these planes much like a choreographer who plans a dance?
Who monitors and directs this dance of planes. First there are the Air Traffic Controllers who monitor the landing and take off of all planes. They have to control multiple paths of approaching and departing traffic.
On the other hand, schedulers determine which plane goes to which gate and which people will work on that flight both pilots and hostesses. They also determine the routing each plane take between airports.
I wondered what math is required by Air Traffic Controllers to do their job. It is obvious they need to know the speed of the jet so they know where they are and how long they have before they land. So right there is rate x time = distance.
Is there other math? Perhaps the Pythagorean theorem, angles of decent, distance required to stop in, juggling the approach of multiple aircraft or knowing wind direction because that sometimes effects landing. In order to be an Air Traffic Controller, people are expected to have a degree and to have taken College Algebra, Trigonometry, Geometry, Calculus I and II, Statistics, which is quite a bit of math.
They have to monitor a circular radar grid to keep track of airplanes with the tower at the center of the circle. Their location is identified by distance and angles. The vertical distance of a plane is the distance between the plane and the ground which is important. They combine all of this information with weather conditions and speed to plot their path.
Each airline has schedulers who have the responsibility of determining which airplanes use which gates, create the schedule for crew, and determine the actual route the air plane takes between takeoff and landing and work in maintenance. This looks like a real life applications of combinatorics much like those questions "How many different combinations do you have if you have 4 pairs of pants, 3 shirts and 4 hats?"
Most of the sites that spoke of the math involved in scheduling turns out to be calculus, there is a nice 8 page pdf which discusses simulating the cost of moving planes around the airport from gate to maintenance, fuel and operating costs, etc. This paper provides the results of the simulation and at the same time gives out some real information on scheduling.
Although this Power Point presentation is designed for the industry, it has some wonderful slides which explain each part of the process and has a flowchart showing the overall departmental arrangement and work distribution.
I could not find any simple lesson plans for scheduling airplanes but I found enough information to create a simple combinations activity using planes, crew, towns, and flight paths. I hope to create an activity in the next month and post it here to share with people. Please keep checking my site out for this. Next week Tuesday, I'm looking at the math involved in the newest craze Pokeman Go! Stay Tuned.