Assessing the effect of the role of detonation wave curvature on the firing times of high voltage detonators

In detonators the “lost time” or “excess transit time” is the difference between the measured and calculated time for the reactive wave to transit the explosive charge in the detonator. The calculated time is derived from the thickness of the charge and the steady state detonation velocity. For both exploding bridgewire (EBW) and exploding foil (EFI), or slapper, detonators the lost time is significant and, for detonators of comparable dimensions, greater in EBW detonators. Typically, the lost time is attributed to a finite growth to detonation time. The bridgewires and foil flyers of EBW and EFI detonators respectively establish reaction fronts over very small areas in the explosive. Even with a significant run to detonation distance, the detonation front may be expected to be highly curved and, thus, have a detonation velocity below the steady state velocity. Consequently, the time and distance required for a steady state detonation velocity to be established may also contribute to the lost time in EBW and slapper detonators. To assess the relevance of wave curvature on lost time a simple analytical model has been developed which takes into account growth to detonation and detonation wave curvature effects. The model showed that detonation wave curvature could be responsible for at least some of the lost time of EBW detonators.