ASE 167M - Lecture 9 - Equations of Motion for Gliding...

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Unformatted text preview: Equations of Motion for Gliding Flight Maximum Range Conditions Integration of the Glide EOM Numerical Integration Program #2 Equations of Motion for Gliding Flight Maximum Range Conditions Integration of the Glide EOM Numerical Integration What is Numerical Integration? Euler Integration Midpoint Integration Runge-Kutta Integration Program #2 The University of Texas at Austin Equations of Motion for Gliding Flight Maximum Range Conditions Integration of the Glide EOM Numerical Integration Program #2 Gliding Flight I From ASE 367K, we have the following equations of motion for unsteady flight in the vertical plane: x = V cos h = V sin V = g W [ T cos- D- W sin ] = g WV [ T sin + L- W cos ] W =- CT The University of Texas at Austin Equations of Motion for Gliding Flight Maximum Range Conditions Integration of the Glide EOM Numerical Integration Program #2 Gliding Flight The University of Texas at Austin Equations of Motion for Gliding Flight Maximum Range Conditions Integration of the Glide EOM Numerical Integration Program #2 Gliding Flight I We can enforce the glide condition, T = 0 , to get unsteady gliding flight equations of motion x = V cos h = V sin V =- g W [ D + W sin ] = g WV [ L- W cos ] W = 0 The University of Texas at Austin Equations of Motion for Gliding Flight Maximum Range Conditions Integration of the Glide EOM Numerical Integration Program #2 Gliding Flight I Enforcing steady conditions, V = 0 and = 0 , and assuming flat glide path, 1 , yields x = V h = V 0 = D + W 0 = L- W The University of Texas at Austin Equations of Motion for Gliding Flight Maximum Range Conditions Integration of the Glide EOM Numerical Integration Program #2 Gliding Flight I The goal of gliding flight is to I remain in the air for the maximum possible time, which means that we want the minimum possible rate of descent, h min I travel as far as possible during the glide, which implies that we want the minimum glide angle, min The University of Texas at Austin Equations of Motion for Gliding Flight Maximum Range Conditions Integration of the Glide EOM Numerical Integration Program #2 Maximum Range I We wish to integrate the glide equations of motion along the maximum range path since it is typically desirable to maximize ground distance when in gliding situations I How can we achieve maximum range? The University of Texas at Austin Equations of Motion for Gliding Flight Maximum Range Conditions Integration of the Glide EOM Numerical Integration Program #2 Maximum Range I Maximum range is achieved by I maximizing E = L/D or minimizing I max { L/D } max { C L /C D } I max { C L /C D } min { } flattest glide angle I E max = constant I How do we find E max ?...
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ASE 167M - Lecture 9 - Equations of Motion for Gliding...

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