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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.

A blast wave is the expanding disturbance produced by localized rapid release of energy, initially led by a strong shock wave. An energy-conserving self-similar blast wave ties front speed to the mass swept up. Once the front is only weakly supersonic, a strong-shock approximation ceases to apply; a subsequent acoustic wave is not excluded by that transition.

Interpret “reach” first as remaining an energetic, supersonic blast wave, rather than as the arrival of any acoustic wave. An atmospheric blast-wave range estimate must account for the thin atmosphere: the distance $D=8.5\times 10^6\mathrm{m}$ is much greater than its height $H=10^4\mathrm{m}$.

For an optimistic estimate, suppose the deposited energy $E$ remains in a horizontally expanding atmospheric layer. If its representative mass density is ${\rho }_a$, the swept mass is of order $\pi D^{2}H{\rho }_a$. Conservation of energy gives the self-similar blast wave scalingUsing ordinary atmospheric estimates ${\rho }_a\sim 1\mathrm{kg}{\mathrm{m}}^{-3}$ and speed of sound $c_a\sim 300\mathrm{m}{\mathrm{s}}^{-1}$, this givesThese are scaling estimates, not an exact shock wave solution. The strong shock wave approximation would already have failed atEquivalently, keeping the disturbance strongly supersonic out to $D$ would require substantially more than the sonic-transition energy scalewhich exceeds $10^{22}\mathrm{J}$ by about a factor of twenty. Reasonable atmospheric averages and order-unity geometrical coefficients do not reverse the comparison. Escape of energy through the top of the atmosphere makes the fully confined estimate optimistic; Earth's curvature changes its area estimate by an order-unity factor.

The strong atmospheric blast will not survive to Lansing in this model. A weakened acoustic wave can nevertheless travel there. The supplied energy and atmospheric height do not determine its detectable amplitude, detailed attenuation or damage: those require an atmospheric propagation model. Thus “no disturbance of any kind reaches Lansing” would be an unjustified stronger conclusion.