Computer Graphics Based Optical Tracking for Hypersonic Free-Flight Experiments

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Starshak, William
Laurence, Stuart
Aerodynamic measurement in hypersonic short-duration facilities – facilities with test times shorter than 10 milliseconds – is a topic of ongoing research. Standard force-balance approaches cannot handle the short test-time or the flow-initiating shock wave. Experimentalists have developed alternative techniques; but these techniques deliver merely adequate results at the cost of significant operational and – especially – calibration complexity. Recently, Laurence, et al. proposed using high-speed shadowgraph imaging and edge fitting (matching the visualized edge to an analytic equation for that edge) to make high-precision free-flight measurements of capsules. This new technique promised equivalent accuracy to existing techniques with far less pre-test calibration. The technique as developed, however, was limited to simple shapes in 2D motion. This thesis presents a generalization of the edge-fitting concept. Using the correspondence between a model's orientation and its silhouette, the trajectory of a model may be tracked to $1 \, \rm \mu m$ positional and $0.01^{\circ}$ angular accuracy. The silhouette is generated using computer-graphics techniques based upon a 3D mesh of the model's surface geometry. Consequently, the proposed technique is general to the model shape, the number of models, the properties of the camera imaging the experiment, and the number of cameras. Using the technique, we measured the hypersonic aerodynamics of a sphere, a blunt sphere-cone capsule, a lifting-body spacecraft, and the University of Maryland Testudo. In addition, multiple-camera and multiple-body tracking capability is demonstrated with an experiment investigating the dynamics of a breaking-up satellite. Results show that the method achieves accuracy comparable to or better than existing techniques with a simpler experimental procedure.