Initial expansion to ambient pressure of chemical explosive releases in the upper atmosphere

The equilibrium radius after expansion to ambient pressure of a chemical cloud originating from an explosive release is derived by calculating the work done against the atmosphere during the expansion on the basis of a simplified theory which divides the expansion into three main phases. For a given explosive composition, the expanded radius, expressed in units of (E00/pa)1/3, where E00 is explosive energy and pa is ambient pressure, is found to be constant and independent of charge dimensions over a wide range of altitude; and good agreement is found with the observed radii of several high-altitude releases. The temperature of the expanded cloud should also be constant with respect to release height in this altitude range, and a value of 680°K is calculated for Project Firefly releases. At greater heights, the scaled radius should increase with altitude until the assumption of continuum flow breaks down. Calculations are carried out of the temperatures and radii on expansion to ambient pressure of gas clouds produced by energy releases of 1012 to 1016 ergs at heights between 60 and 160 km and for the Project Firefly releases. The time constants of thermal conduction are examined with regard to temperature equalization within the cloud and equalization with the ambient which proceeds less rapidly. For 80- to 85-km releases, conduction may be so slow that convection processes are effective.