Simple fragment size and shape distribution formulae for explosively fragmenting munitions

Explosively fragmenting munitions produce complex loads on nearby targets. To characterize these loads, one needs a description of the fragment size, shape, and velocity distributions. This paper reviews current predictive theories and models for these distributions, and derives simpler but equally valid formulae for them. Correlations of the simpler formulae with fragment aspect ratio data from 1/50th and 1/6th scale BLU-109 experiments, and 1/5th scale AN-Mk 1 AP 1600 bomb experiments, show promising agreement between the data and predictions. The above formulae predict approximate replica scaling behavior for the fragment size, shape, and velocity distributions, and therefore imply that a few small scale fragmentation tests would be sufficient to characterize a munition's fragmentation behavior at full scale. It is recommended that the above formulae be further tested against additional arena test data for a range of scales and steel properties.