A review of Whipple shield ballistic limit equations

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.