Ballistic limit equations (BLEs) are semi-analytical expressions used to predict the risk posed by micrometeoroid and orbital debris (MMOD) impacts on a spacecraft. A foundational BLE, known as the new non-optimum (NNO) equation was published by Eric Christiansen of NASA Johnson Space Center in 1990 for application on Whipple shields – two-plate configurations consisting of a thin sacrificial plate located at some standoff in front of the spacecraft pressure hull or structural wall. Today, BLEs for almost all multi-plate spacecraft structures, e.g., honeycomb sandwich panels, monolithic structures with thermal insulation blankets, etc., are based on the NNO Whipple BLE. We review the development of the NNO BLE as well as some prominent modifications and evaluate their performance against collated databases of hypervelocity impact experiments. Finally, a further modification to the NNO BLE is proposed that allows for extension to Whipple shields with under-sized bumper plates without the computational inconsistencies of the current state-of-the-art methodology.

中文翻译：

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惠普尔防护罩弹道极限方程综述

弹道极限方程 (BLE) 是半解析表达式，用于预测微流星体和轨道碎片 (MMOD) 撞击航天器所带来的风险。NASA 约翰逊航天中心的 Eric Christiansen 于 1990 年发表了一个基础 BLE，称为新的非最优 (NNO) 方程，用于 Whipple 护罩上的应用 - 两板配置，由位于护罩前面的某个对峙处的薄牺牲板组成。航天器耐压外壳或结构壁。如今，几乎所有多板航天器结构（例如蜂窝夹层板、带隔热层的整体结构等）的 BLE 均基于 NNO Whipple BLE。我们回顾了 NNO BLE 的发展以及一些重要的修改，并根据超高速撞击实验的整理数据库评估其性能。最后，提出了对 NNO BLE 的进一步修改，允许扩展到具有尺寸较小的缓冲板的 Whipple 屏蔽，而不会出现当前最先进方法的计算不一致问题。