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📏 TNT-Equivalent Scaling — Safe Standoff Distance

Interactive Hopkinson-Cranz cube-root blast-scaling calculator. Set an energy yield and an overpressure hazard threshold to read the scaled distance and minimum safe standoff distance used in blast-safety engineering.

Explosions & Blast Physics2DAdvanced60 FPS🔥 Fire

About this simulation

This tool visualises the Hopkinson-Cranz cube-root scaling law — the standard method blast-safety engineers use to compare hazard distances across very different energy yields without re-deriving the physics each time. Because geometrically similar blast waves occur at the same scaled distance Z = R/W^(1/3) regardless of yield, a single reference curve p(Z) lets you read off a minimum safe standoff distance for any chosen energy and any chosen overpressure hazard threshold — exactly the calculation behind published minimum-distance tables in quarrying and structural-safety standards.

🔬 What it shows

Concentric hazard-zone rings around a source point at four standard overpressure thresholds, plus a log-log overpressure-vs-distance chart with the chosen safe-distance threshold marked.

🎮 How to use

Set the Energy Yield (a log-scale TNT-equivalent mass, purely a unit of energy) and pick a Hazard Overpressure Threshold from the dropdown. Read the scaled distance, minimum safe standoff distance and overpressure at a fixed 50 m reference point.

💡 Did you know?

Because safe distance scales with the cube root of energy, a 1,000× larger yield only requires about 10× more standoff distance for the same hazard threshold — which is why blast-safety planning focuses so heavily on standoff distance rather than trying to limit energy release itself.

Frequently asked questions

What is the Hopkinson-Cranz scaling law?

It states that two explosions of different energy yield W1 and W2 produce geometrically similar blast waves at the same scaled distance Z = R/W^(1/3). This lets a single empirical overpressure-vs-Z curve, measured once, be reused to predict hazard distances for any yield — the foundation of most published blast-safety distance tables.

What do the overpressure thresholds mean?

They are standard reference levels used in structural blast-safety assessment: roughly 1 kPa risks window glass breakage, 3.5 kPa risks minor structural damage, 7 kPa risks serious structural damage, and 20 kPa risks structural failure near the source — used for planning minimum safe distances, not for characterising any specific explosive.

Why does safe distance scale with the cube root of energy, not linearly?

Because the same total energy spreads over an ever-larger spherical shock front as it expands, overpressure at a fixed physical distance falls off much faster than energy grows — the cube-root relationship is the geometric consequence of that 3-dimensional spreading.

Does this tool model explosive composition or construction?

No — it only relates an abstract TNT-equivalent energy yield to a scaled distance and a safe-distance recommendation, the same comparative-safety calculation taught in quarrying and structural-engineering safety courses, with no chemistry, formulation or construction content.

⚙ Under the hood

Explore the Hopkinson-Cranz cube-root scaling law used in blast-safety engineering: convert an abstract energy yield into a TNT-equivalent mass, then read the scaled distance and minimum safe standoff distance for a chosen overpressure hazard threshold, exactly as used in quarry and structural blast-safety planning.

Canvas 2DHopkinson-Cranz scalingcube-root scaling lawblast safety distancescaled distance

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install