Concise history of ballistic limit equations for multi-wall spacecraft shielding

All earth-orbiting spacecraft are susceptible to impacts by orbital debris 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 at a relatively small distance away from the main “inner wall” of the spacecraft. The performance of a hypervelocity impact shield is typically characterized by its ballistic limit equation, which is typically drawn as a line of demarcation between regions of rear-wall perforation and no perforation; when graphically represented, it is often referred to as a ballistic limit curve. Once developed, these equations and curves can be used to optimize the design of spacecraft wall parameters so that the resulting shields can withstand a wide variety of high-speed impacts by orbital debris. This paper presents some comments and observations on the development of the three-part ballistic limit equation used to predict the response of dual-wall structural systems under hypervelocity projectile impact. The paper concludes with some insights into the limitations of NASA’s current MMOD risk analysis code, and offers several suggestions regarding how it could be modified so that, for example, it could be used as an integral part of a probabilistic risk assessment exercise.