Shape Factor Modeling and Simulation

Report No. ARL-TR-7707
Authors: Richard Saucier
Date/Pages: June 2016; 100 pages
Abstract: The dimensionless shape factor, which relates the projected area of a fragment to its mass per unit density, plays a fundamental role in ballistic penetration. Explicit analytical formulas are given for the shape factor distributions of some common shapes with random orientations. It is straightforward to simulate these shape factor distributions with computer code, and we verify that the simulations match the plots from the analytical formulas. However, none of the simple common shapes provides an adequate simulation model for natural fragments. We show that natural fragment data can be fit with a lognormal distribution, which then provides a simulation model for Monte Carlo sampling. Laser scans of fragments can also be used to compute the fragment shape factor from any viewpoint; various methods of achieving a uniform spherical distribution are described. Finally, we show that it is possible to realize each fragment as either a yawed cylinder or a cuboid with a pitch, yaw, and roll. Thus, we have a procedure for generating all the input variables required to run THOR or FATEPEN with natural fragments.
Distribution: Approved for public release
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Last Update / Reviewed: June 1, 2016