A comparison of NASA, DoD, and hydrocode ballistic limit predictions for spherical and non-spherical shapes versus dual- and single-wall targets, and their effects on orbital debris penetration risk

Abstract All earth-orbiting spacecraft are susceptible to impacts by these particles, which can occur at extremely high speeds and can damage flight- and mission-critical systems. The traditional damage mitigating shield design for this threat consists of a “bumper” that is placed several cm away from the main “inner wall” of the spacecraft. Typical orbital debris risk analyses that include ballistic limit equations (BLEs) and curves (BLCs) assume that orbital debris particles are spherical in shape. However, spheres are not a common shape for orbital debris; rather, debris fragments might be better represented by other regular or irregular solids. This paper presents the results of a study comparing BLCs developed by NASA and the DoD for velocities up to 4 km/s considering spheres, cubes, and a “flake” shape that was proposed within NASA's Standard Breakup Model to represent orbital debris. It also compares performance of these shapes using hydrocodes at higher velocities (7–12 km/s), and generates a combined BLC for these shapes for the entire orbital debris velocity regime. In addition to shape, a multi-view method is used to examine the effects of a variety of cube and flake impact orientations on BLC, as well as a “characteristic length” parameter developed by NASA to compare the particle shapes on the basis of their radar cross section. The developed non-spherical BLCs are then evaluated for overall penetration risk considering the orbital debris environment. Their predictions of risk are compared to that predicted using sphere-based BLCs. This methodology is then extended to a single-wall shield design for velocities up to 15 km/sec, and the results of DoD predictions for a sphere and cube are compared with NASA predictions for a sphere having the same characteristic length. The results indicate that we may be over-predicting orbital debris risk for dual-wall shields by a factor of two—and for single walls by a factor of four—by limiting our analyses to spheres instead of using more representative debris shapes, such as cubes and flakes, and its characteristic length as the primary particle parameter.