TNT-Equivalent Blast Range
Peak overpressure vs. standoff distance for a surface or free-air TNT charge using scaled distance.
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The engineering
Blast scaling collapses charge size and distance into one variable: the Hopkinson-Cranz scaled distance Z = R/W^⅓. Two detonations with the same Z produce the same peak overpressure, so a single curve covers every yield. This card uses the Kinney-Graham fit for the peak incident overpressure and applies a 1.8× yield multiplier for surface bursts, where ground reflection nearly doubles the effective energy.
Rule of thumb: window glass breaks around 1 kPa, eardrums rupture near 35 kPa, and lung damage begins around 100 kPa. If your standoff feels safe, run the numbers — overpressure falls steeply with distance but the near-field is unforgiving. The fit is valid for roughly Z = 0.05 to 40 m/kg^⅓; outside that, reach for Kingery-Bulmash tables directly.
Where this math comes from
Bertram Hopkinson (1915) and independently Carl Cranz established cube-root scaling: the blast wave from a large charge at a proportionally larger distance looks identical to a small one nearby. That single insight turned blast prediction from case-by-case testing into a universal curve, and it underpins every field manual since.
The modern coefficients come from decades of instrumented trials — Kingery and Bulmash compiled the definitive high-explosive airblast curves for the U.S. Army in 1984, and Wilfred Baker's 1983 text "Explosion Hazards and Evaluation" made the scaling methodology accessible to working engineers. Kinney and Graham's analytic fit gives the closed form this card evaluates.
- 1915Bertram HopkinsonStates cube-root blast scaling law from wartime charge tests.
- 1926Carl CranzIndependently derives the same scaling — hence Hopkinson-Cranz.
- 1983Wilfred E. BakerPublishes Explosion Hazards and Evaluation, codifying TNT-equivalent methods.
- 1984Kingery & BulmashRelease the standard U.S. Army airblast parameter curves.
- 1985Kinney & GrahamGive the analytic overpressure fit used in this card.
See the full timeline of the math behind every calculator →
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