Consortium for Mathematics and its Applications

Product ID: Geometer’s Corner
Supplementary Print
High School

Modeling the Rotations of Flight: Yaw, Pitch, and Roll

Author: Jon Choate

Manned and unmanned vehicles, be they airplanes or drones, play increasingly important roles in the technological world in which we live. This month’s Geometer’s Corner is about the mathematics used in controlling aerial vehicles. This is the first of a two‑part series and will show how 3D matrices are used. The next column will focus on the work of William Rowan Hamilton, a 19th century mathematician who in 1843 developed Quaternions, which are very useful tools for describing and combining 3D rotations.

To keep things simple, I am going to focus on winged aircraft such as commercial aircraft like the Airbus 220 or private aircraft like the Cessna 172. The mathematics that is developed here is used in gaming simulations and in the simulators used to train commercial and military pilots. My son, who flies for a commercial airline, learned how to fly a Boeing 737 in a simulator. The first time he flew a real 737 there were 120 passengers on board.

© 2023, COMAP, Inc.
Consortium 124
3 Pages

Mathematics Topics:

  • Geometry ,
  • Trigonometry, Matrices, Vectors, Complex Numbers, Rotations

Application Areas:

  • Engineering & Construction ,
  • Transportation & Travel ,
  • Aviation

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COMAP develops curriculum resources, professional development programs, and contest opportunities that are multidisciplinary, academically rigorous, and fun for educators and students. COMAP's educational philosophy is centered around mathematical modeling: using mathematical tools to explore real-world problems.

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