Aviation and Trigonometry Pre Calculus Project

Aviation is related to trigonometry in many ways. 

One way is the design of the plane itself. The tail of the plane is typically a right triangle on top of the empennage/ fuselage; however it sometimes is a right trapezoid.

Another way that trigonometry is incorporated into aviation is through the two most recognizable in-air maneuvers, pitch changes (up and down) and roll changes (bank left and bank right). The trigonometry involved in pitch is seen when the plane's nose begins to rise above or sink below the horizon.  When this occurs, the plane can be thought of as the hypotenuse of the right triangle, while the horizon is one leg of the triangle and the tangent between the horizon and the plane is the other leg. The angle that is formed between the plane and the horizon is known as angle of attack, or AOA. At a certain AOA and velocity the air flowing over the wing separates from the wing sooner than normal, causing the wing to produce less lift. When this occurs it is known as a stall.  Similarly, the trigonometry behind roll is that a triangle is created between the horizon, the plane’s wingtip to wingtip, and the tangent from the wingtip to the horizon. The angle that is formed is called bank angle and is measured in degrees of bank. Pitch and roll are important when flying because they affect the trajectory of the airplane. Additionally, you never want to exceed your maximum pitch angle, as measured by the attitude indicator because it can cause a stall.

A third way that trigonometry is incorporated into aviation is in descent planning. Descent planning uses the following formula to calculate how far away from a destination (measured in nautical miles (NM)) you need to start your descent so you reach your destination (normally an airport or waypoint) at the required altitude.

In aviation vectors are often used. For instance, ATC (Air Traffic Control) will tell a pilot “fly heading 060 vectors.” Aviation vectors are slightly different than Cartesian vectors as they are based on degrees from magnetic north. However, Cartesian vectors can be used to show the track of an object over the ground and to calculate the effect of wind.

Works Cited

"Yaw Pitch Roll." Camera. SourceForge, n.d. Web. 5 Nov. 2015. <http://sceengine.sourceforge.net/ 

         pics/ypr.gif>. 

© 2015 Adam Kass