Blast Overpressure at Range (Hopkinson-Cranz)
Peak incident overpressure from a hemispherical surface burst via Hopkinson-Cranz scaling and the Kinney-Graham correlation — a quick standoff and clearance estimate, not a substitute for UFC 3-340-02 design tables.
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The engineering
Blast waves scale by cube root: a charge of weight W at range R behaves like any other charge at the same scaled distance Z = R/W^(1/3). Enter the TNT-equivalent charge and standoff and the card returns peak side-on (incident) overpressure from the Kinney-Graham closed-form correlation, evaluated at the surface-burst effective yield (ground reflection is taken as 1.8x the charge). It is a quick estimate: for design work use the Kingery-Bulmash tabulations in UFC 3-340-02 directly, which this card does NOT reproduce.
Reach for it when sizing standoff distances, checking glass or wall response, or sanity-checking a test setup. Rule of thumb: roughly 7 kPa (~1 psi) shatters ordinary window glass, ~35 kPa (~5 psi) collapses unreinforced masonry, and the normal-reflected pressure on a flat wall facing the charge can run 2–8× the incident value — always design to the reflected number for a surface it hits head-on.
Gotcha: this assumes a hemispherical surface burst (charge on the ground) via the 1.8x yield enhancement. A free-air spherical burst gives lower pressures at the same Z — use the free-air option on the TNT-equivalent blast card for that. Real munitions rarely equal ideal TNT, so apply a TNT-equivalence factor before entering the weight, and treat everything here as order-of-magnitude for siting, not a design authority.
Where this math comes from
The cube-root scaling behind every blast chart is Hopkinson-Cranz similarity, worked out independently by Bertram Hopkinson in Britain (1915) and Carl Cranz in Germany — a wartime insight that let engineers collapse thousands of shots onto one universal curve.
Charles Kingery and Gerald Bulmash at the U.S. Army Ballistic Research Laboratory compiled decades of instrumented trials into high-order polynomial fits in their 1984 BRL report, giving overpressure, impulse, and arrival time as smooth functions of scaled distance; Michael Swisdak's 1994 NSWC work recast them into a compact log-polynomial form, and the curves are enshrined in UFC 3-340-02, the DoD structures-to-resist-blast standard. Gilbert Kinney and Kenneth Graham took the other route in Explosive Shocks in Air (1985): a single closed-form expression fitted to the same body of data, accurate enough for siting work and simple enough to audit by eye. That is the correlation this card evaluates.
- 1915Bertram HopkinsonStates cube-root blast scaling; Cranz reaches the same law independently.
- 1946G. I. TaylorPublishes the point-source blast-wave solution grounding the scaling physics.
- 1984C. N. Kingery & G. Bulmash (BRL)Polynomial fits to airblast data — the standard reference curves.
- 1994M. M. Swisdak (NSWC)Recasts the KB fits into compact log-polynomial form for calculators.
- 2008U.S. DoDIssues UFC 3-340-02, embedding the KB curves in blast-resistant design practice.
See the full timeline of the math behind every calculator →
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