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Photogrammetric techniques of analyzing vehicles and scenes for accident reconstruction are well documented and have appeared in various forms and levels of complexity over the years. Plane-to-plane rectification algorithms, frequently used for accident reconstruction, are subsets of a growing field of computer vision algorithms, which are rigorously developed in [1,2,3,4]. While these algorithms are well formulated, they are not well illustrated. It is often not clear how to leverage advancements in computer vision algorithms for the purposes of rectification photogrammetry in the context of accident reconstruction. Perhaps as expected, a second strategy exists in the literature, which describes the use, as opposed to the development, of commercial computer programs for rectification photogrammetry [5,6,7,8]. Commercial software applications provide a robust and wide array of photogrammetric analysis.

In 2008, Hovey et al. [1] published a mathematical analysis that, for the first time, incorporated yaw data into the trajectory analysis, yielding occupant ejection results that are three-dimensional. We extend on that work to investigate the ability of the mathematical model to predict outcomes of the Ford Expedition dolly rollover test, details of which have been published in Carter et al. [2], Exponent [3], and Luepke et al. [4]. This research validates our occupant trajectory model with the Expedition dolly rollover experimental test data. Previous research had modeled the Expedition rollover test as a two-dimensional, straight-line, roll-only configuration, assuming yaw effects were negligible [17]. We incorporated the longitudinal and lateral components of the vehicle trajectory, eliminating the straight-line limitation. Moreover, we included yaw in addition to roll. Both enhancements resulted in a higher fidelity occupant ejection description.

In the fields of accident reconstruction and injury biomechanics, it is often of interest to know details of an occupant's ejection from a vehicle during a rollover. Current occupant trajectory models do not account for vehicle yaw and yaw rate. Such considerations are compulsory if the occupant's rest point has a non-trivial deviation from the vehicle's roll path. Moreover, many existing models use a single, generic function for the roll rate for all analyses. Such approaches intrinsically model all rollovers as identical events, regardless of the underlying uniqueness a particular accident may exhibit. The objective of this work is to model the trajectory of an occupant ejected from a vehicle in a rollover event. In particular, we model the vehicle's longitude, latitude, roll, yaw, and time derivatives thereof, based on data extracted from a particular accident reconstruction. We model the occupant moving in the vehicle and possibly ejected at any time during the rollover.