= Atmospheric blast-wave range
{title2=$D_s\sim[E/(\pi\Sigma c_a^2)]^{1/2}$}
For an explosion confined approximately to a thin atmospheric layer with column <mass density> $\Sigma=\int\rho\,dz$, an optimistic conserved-energy scaling is $E\sim\pi D^2\Sigma U^2$. The strong <blast wave> approximation becomes invalid near front speed $U\sim c_a$, where $c_a$ is the ambient <speed of sound>, giving the displayed distance scale. Its numerical coefficient depends on the flow profiles, geometry and <heat capacity ratio>. Vertical energy escape makes full confinement an optimistic approximation. The criterion estimates survival of a strong <shock wave>, rather than whether any later <acoustic wave> is detectable.
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