Effect of the Ratio of Charge Mass to Target Mass on Measured Impulse

A common way to measure the loading on a target above the explosion of a charge buried in soil is to measure the total vertical impulse applied to the target. The impulse is often calculated by multiplying the mass of the target by its maximum velocity. While this seems a reasonable approach, in actuality, the impulse so calculated, depends not only on the actual load applied to the target but also on the ratio of the mass of the target to the mass of the explosive. This paper shows that, if the other conditions of an explosive event are the same, i.e., depth of burial of the charge, height of the target, soil properties, etc., there is a consistent, power law, relationship between the charge to target mass ratio and the measured impulse. In this paper, this relationship is developed to provide a heuristic tool to estimate the impulse that would be measured if the charge or target mass is changed.