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 J.E. Williamsen a, * , W.P. Schonberg b , H. Evans c , S. Evans d a Institute for Defense Analyses, Alexandria, VA 22311, United States b University of Missouri-Rolla, Civil Engineering Department, Rolla, MO 65401, United States c University of Denver Research Institute, Denver, CO 80208, United States d NASA Marshall Space Flight Center, Huntsville, AL 35812, United States article info Article history: Available online 5 August 2008 Keywords: NASA DoD Hydrocode Ballistic Limit Non-Spherical Penetration Risk Dual Wall Single Wall 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 twodand for single walls by a factor of fourdby 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. Ó 2008 Published by Elsevier Ltd. 1. The three-part ballistic limit equation for Whipple shields The traditional damage mitigating shield design consists of a ‘‘bumper’’ that is placed at a relatively small distance (e.g. on the order of 5–10 cm) away from the main ‘‘inner wall’’ of a spacecraft or a spacecraft component. This concept has been studied extensively in the last four decades as a means of reducing the perforation threat of hypervelocity projectiles over an equivalent single-wall structure. The performance of a hypervelocity impact shield is typically characterized by its ballistic limit equation (BLE), which defines the threshold particle size that causes perforation of or detached spall from the inner wall of the system as a function of velocity, impact angle, particle density, shield and inner wall thicknesses and particle shape. These BLEs are typically drawn as lines of demar- cation between regions of rear-wall perforation and no perforation in two-dimensional spherical projectile diameter-impact velocity space and when graphically represented, are often referred to, in this form, as ballistic limit curves (BLCs). Once developed, BLEs and BLCs can be used to optimize the design of spacecraft wall parameters (material, thickness, etc.) so that the resulting shields can withstand a wide variety of high-speed impacts by orbital debris. By understanding the debris environment size and velocity distributions that are expected to impact a spacecraft, shield designs, and their resulting BLEs can be tailored in order to meet spacecraft risk requirements while minimizing weights. * Corresponding author. Tel.: þ1 703 578 2705; fax: þ1 703 845 6977. E-mail address: jwilliam@ida.org (J.E. Williamsen). Contents lists available at ScienceDirect International Journal of Impact Engineering journal homepage: www.elsevier.com/locate/ijimpeng 0734-743X/$ – see front matter Ó 2008 Published by Elsevier Ltd. doi:10.1016/j.ijimpeng.2008.07.076 International Journal of Impact Engineering 35 (2008) 1870–1877