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Rebound Rumble ballistic trajectory with air friction drag and Magnus Effect (backspin/topspin lift/dive). For students interested in the physics, math, and computer simulation aspects of this problem. Freebody force diagram, derivation of differential equations of motion, and C pseudocode for trapezoidal numerical integration.
Rebound Rumble ballistic trajectory with air friction drag and Magnus Effect (backspin/topspin lift/dive).
For students interested in the physics, math, and computer simulation aspects of this problem.
Freebody force diagram, derivation of differential equations of motion, and C pseudocode for trapezoidal numerical integration.
Note: In this paper, I have used the sign convention that "g" (acceleration due to gravity) is negative. So if you are trying the integration algorithm, make sure to set g equal to 9.8 m/s/s (or 32 ft/s/s).
ballistic trajectory with drag & magnus.pdf
download fileAppendix A.pdf
download fileAppendix B.pdf
download file12042012 02:14 PM
Ether
Appendix A (2^{nd} order integration) added.
12102012 07:28 PM
Ether
Appendix B added. Graphs of simulation runs.
http://www.chiefdelphi.com/media/papers/2725
12102012 07:39 PM
Michael HillPretty interesting. Unfortunately it looks like just a 2D simulation. The 3rd dimension can really play into the aerodynamics, for example, the surface velocity of a spinning ball spins relatively slower the closer you get to the "poles" of the sphere. This would be valid for an infinitely long, smooth cylinder. Not to say this doesn't provide valuable insight into how the Magnus effect affects rotating bodies in air.
12102012 09:03 PM
Ether
This would be valid for an infinitely long, smooth cylinder.

Not to say this doesn't provide valuable insight into how the Magnus effect affects rotating bodies in air. 
12112012 05:27 AM
Michael HillHmm, perhaps you're right (capital D instead of lowercase D in CD). However, finding the correct constants aren't so trivial.
12112012 05:27 PM
Ether
Hmm, perhaps you're right (capital D instead of lowercase D in CD). However, finding the correct constants aren't so trivial.
