Triple point path prediction for height of burst explosion in high-altitude environment

Accurately forecasting the triple point (TP) path is essential for analyzing blast loads and assessing the destructive effectiveness of the height of burst explosion. Empirical models that describe the TP path under normal temperature and pressure environments are commonly employed; however, in certain configurations, such as at high altitudes (HAs), the environment may involve low temperature and pressure conditions. The present study develops a theoretical prediction model for the TP path under reduced pressure and temperature conditions, utilizing the image bursts method, reflected polar analysis, and dimensional analysis. The model's accuracy is evaluated through numerical simulations and experimental data. Results indicate that the prediction model effectively evaluates the TP path under diminished temperature and pressure conditions, with most predictions falling within a ±15% deviation. It was found that the TP height increases with altitude. As the altitude rises from 0 m to 10,000 m, the average TP height increases by 61.7%, 87.9%, 109.0%, and 134.3% for the scaled height of burst of 1.5 m, 2.0 m, 2.5 m, and 3.0 m, respectively. Moreover, the variation in TP height under HA environments closely mirrors that observed under corresponding reduced pressure conditions. In HA environments, only the effect of low-pressure conditions on the TP path needs to be considered, as the environmental low-temperature has a minimal effect.