How can I calculate the trajectory of a payload fairing assuming that I have several data points of height or speed of rocket?
I'd like to know which topics are necessary to study this.
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$\begingroup$ I've made some small edits. Although it's okay to use "orbit" for something falling back to Earth in space, once it starts interacting with the atmosphere the aerodynamics becomes dominant and then "trajectory" might be a better term. $\endgroup$ – uhoh Feb 20 at 1:50
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1$\begingroup$ I'm afraid modeling of the trajectory in atmosphere would be rather complex. Maybe CFD (computational fluid dynamics) would be reqired for adequate modeling. Python and Matlab have CFD modules, but I can't say are they enough. Problems are: 1. complex shape of the fairing 2. the fairing is deformable, so the shape can change depending on aerodynamic loads, and also it can vibrate 3. there are several different aerodynamical regimes before the landing: 3a) near-vacuum high altitude 3b) supersonic reentry 3c) near-sonic transitional 3d) subsonic until landing $\endgroup$ – Heopps Feb 20 at 12:54
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$\begingroup$ Yes, the model can be simplified, for example to model only subsonic regime of non-deformable fairing shell. But will the result be close enough to the trajectory of real fairing?.. DISCLAIMER: I never conducted aerodynamical simulations myself. :) $\endgroup$ – Heopps Feb 20 at 13:03
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A "classical" fairing is a ballistic object, meaning it has no active controls. You'll find that trying to model its tumbling path through a highly variable atmosphere exceeds our current computational capacity.
If you're thinking about the SpaceX fairing recovery techniques, be aware that there are some active controls, as explained in this space.SE question/answer.
