ERIC Number: EJ1410981
Record Type: Journal
Publication Date: 2024
Pages: 36
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0020-739X
EISSN: EISSN-1464-5211
Model, Analyse and Prevent Fatal Aircraft Manoeuvres
Yves Nievergelt
International Journal of Mathematical Education in Science and Technology, v55 n2 p352-387 2024
On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near Earth's surface, the distance fallen is proportional to time squared. Calculus then gives an ordinary differential equation to model free fall near Earth's surface. Second, with calculus, historical data lead to various models of drag on objects moving through air. Third, combining models of drag and gravity with Newton's Laws of Motion leads to ordinary differential equations that model free fall in air. Fourth, predictions from such models with ordinary differential equations are consistent with the aircraft crash. Further models examine the possibility of increasing engine thrust to regain the vertical component of lift. All models fit in a first course in differential equations, without requiring any computational machinery. However, numerical experiments show how uninformed use of professional software can produce rounding errors to cause the modelled aircraft to plunge to the bottom of the deepest oceans and shoot up into space.
Descriptors: Air Transportation, Mathematical Models, Prevention, Calculus, Algebra, Motion, Physics, Prediction, Equations (Mathematics)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A