Publication Date



aircraft takeoff distance, Newton's second law, ordinary differential equations


Mathematics | Ordinary Differential Equations and Applied Dynamics | Physical Sciences and Mathematics | Science and Mathematics Education


Real-world applications can demonstrate how mathematical models describe and provide insight into familiar physical systems. In this paper, we apply techniques from a first-semester differential equations course that shed light on a problem from aviation. In particular, we construct several differential equations that model the distance that an aircraft requires to become airborne. A popular thumb rule that pilots have used for decades appears to emanate from one of these models. We will see that this rule does not follow from a representative model and suggest a better method of ensuring safety during takeoff. Aircraft safety is definitely a matter of public concern, although it is the FAA (Federal Aviation Administration) that makes the regulations.



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