Date of Award

December 2020

Document Type


Degree Name

Master of Science (MS)


Civil Engineering

Committee Member

Nigel Kaye

Committee Member

Abdul Khan

Committee Member

William Bridges


The flight of compact debris has numerous uncertainties associated and can be highly stochastic in nature. Standard flight equations fail to take a lot of these aspects into account because of the assumption of the debris particle being spherical in shape. This study proposes a stochastic model in an attempt to resolve some key aspects of the said uncertainties originated due to the change in orientation of the debris particle during its flight, and as a result the alteration of the projected cross-sectional area, the lift and the drag coefficients. The model numerically solves the differential equations of motion for a large number of gravel pieces taken from five different size gradations. The amount by which the drag and lift coefficients (δC_D and δC_L), the orientation (δθ) and the projected area (δα) are varied at each time-step during the flight simulation of a single debris are the four parameters used to fit the model to the results obtained from gravel drop experiments. An optimization criterion (ε) has been introduced and the model has been optimized individually for each gradation and globally across gradations of different gravel sizes. Upon observing the spread of the landing locations and their radial distances obtained from the model under its optimized conditions, it has been found that while the variation of lift coefficient appears to have a minimal impact on the trajectory of the particle, the change in orientation, drag coefficient and projected area are important factors to be continuously perturbed to be able to correctly track the landing locations for a sufficient number of gravel pieces. The individual optimization technique has also proven to perform better than the global optimization, which is expected as the gravel gradations are geometrically dissimilar.



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