Abstract
We examine herein a simple model for the evolution in time of the
pressure which a suddenly vaporized, ablating layer exerts upon the
subjacent body. The model invokes a plausible construct of surface
material instantaneously thrust into a gaseous regime governed by a
Maxwell-Boltzmann phase space distribution. The surface pressure
per se is gotten by computing the time rate of change of the
momentum per unit area which the retrograde molecules, and only those,
transfer through impact/reflection to the unvaporized body below. An
explicit pressure formula, one alluding to the variable gas temperature
within the vaporized layer, is obtained as a single quadrature requiring
numerical integra- tion at finite times past the onset of impact.
Limiting, null pressure values, both close-in and in pulse aftermath,
can nevertheless be extracted in analytic terms, confirming in
particular the indispensable asymptotic evanescence. A universal formula
in dimensionless variables is given for pressure versus time, both
suitably normalized.