Fragment Mass Distribution of an Exploding Cylinder: Uncertainty Estimation

Arena tests are commonly used to estimate the mass and number of fragments generated by explosive cased charges. However, the very nature of such experiments makes it possible to recover only a small portion of the fragments, and their cost reduces the number of repetitions that can be carried out. These two facts entail uncertainties and potential biases that are typically not estimated, even when adjusting the parameters of statistical laws such as Mott's or Grady's. In this work, we present unpublished experimental results of small-scale steel-cased explosive cylinders and evaluate the experimental uncertainty associated with the fragment mass statistics. Furthermore, we propose an extension of Mott's law that offers an additional degree of freedom. This extension is supported by a detailed mathematical demonstration, leveraging probability theory to provide a solid theoretical framework. Finally, using Bayesian inference, we are able to calibrate posterior probability densities of the parameters based on experimental results. The proposed model demonstrates good agreement with experimental observations.