Blast Radius - Hopkinson-Cranz and Sadovsky
Blast radius scales with the cube root of explosive energy (Hopkinson-Cranz scaling). Overpressure decreases rapidly with distance. The Sadovsky formula relates scaled distance to peak overpressure for damage zone analysis.
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Cube-root scaling: tripling charge weight increases blast radius by ~44% Halifax Explosion (1917): 2,900 tonnes produced ~2 km blast radius Reflected waves from surfaces can amplify overpressure 2-8× Always use 2× safety factor for standoff distances
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Why: Blast radius calculations are essential for explosives safety, emergency planning, facility design, and mining operations. UFC 3-340-02 and FEMA guidelines use these empirical models for standoff distance and evacuation planning.
How: Hopkinson-Cranz scaling (Z = R/W^(1/3)) normalizes blast effects. Sadovsky formula gives overpressure from scaled distance. Damage zones use empirical thresholds: 15 psi lethal, 5 psi severe injury, 1 psi light injury.
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For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
Halifax Explosion of 1917 (2,900 tonnes) produced blast radius over 2 km—one of largest non-nuclear explosions
— Canadian Encyclopedia
Geoffrey Taylor estimated Trinity nuclear yield from declassified photos using dimensional analysis
— Proceedings of the Royal Society
Blast-resistant buildings use progressive collapse prevention—removing one element does not cause cascading failure
— FEMA 427
TNT energy density ~4.68 kJ/g; C-4 has 1.34× TNT equivalence
— Engineering Toolbox
📋 Key Takeaways
- • Blast radius scales with the cube root of explosive energy (Hopkinson-Cranz scaling law)
- • Overpressure decreases rapidly with distance - doubling distance reduces pressure by roughly 75%
- • Building damage zones are classified by overpressure levels: severe (>10 psi), moderate (3-10 psi), light (1-3 psi)
- • TNT equivalence is the standard measure for comparing different explosive materials
- • Reflected blast waves from surfaces can amplify overpressure by 2-8 times the incident pressure
🤔 Did You Know?
The Halifax Explosion of 1917 (2,900 tonnes of explosives) produced a blast radius of over 2 km and remains one of the largest non-nuclear explosions in history.
Source: Canadian Encyclopedia
Geoffrey Ingram Taylor famously estimated the yield of the Trinity nuclear test from declassified photographs using dimensional analysis and the Sedov-Taylor solution.
Source: Proceedings of the Royal Society
Modern blast-resistant buildings use progressive collapse prevention design, where removing any single structural element doesn't cause cascading failure.
Source: FEMA 427
💡 Expert Tips
- • Always use appropriate safety factors (minimum 2x) when determining safe standoff distances
- • Consider terrain, structures, and atmospheric conditions that affect blast wave propagation
- • Fragment hazard zones often extend well beyond the blast overpressure damage zone
- • For vehicle-borne threats, use UFC 4-010-01 minimum standoff distances as baseline
📊 Overpressure Damage Comparison
| Overpressure (psi) | Effect | Building Damage |
|---|---|---|
| 0.5-1 | Window breakage | Minor glass damage |
| 1-3 | Structural cracking | Moderate damage |
| 3-10 | Wall collapse | Severe damage |
| 10+ | Complete destruction | Total demolition |
❓ Frequently Asked Questions
Q: What is Hopkinson-Cranz scaling?
Also called cube-root scaling, it states that blast parameters scale with the cube root of the explosive charge weight. This means tripling the charge weight only increases the blast radius by about 44%.
Q: What is TNT equivalence?
TNT equivalence converts any explosive material to an equivalent mass of TNT based on relative energy output. For example, C-4 has a TNT equivalence of about 1.34.
Q: How does overpressure relate to damage?
Overpressure is the pressure above atmospheric pressure caused by the blast wave. Even 1 psi overpressure can shatter windows, while 5+ psi causes structural damage to buildings.
Q: Does the calculator account for reflected waves?
This calculator uses ideal free-field blast models. Reflected waves from ground, buildings, or confined spaces can significantly amplify pressures and should be considered separately.
Q: What is the difference between positive and negative phase?
The positive phase is the initial overpressure wave. The negative phase follows as a partial vacuum (suction), which can cause additional structural damage and pull debris inward.
Q: How accurate are blast radius estimates?
Empirical models like Kingery-Bulmash are accurate to within 10-20% for free-field conditions. Real-world factors (terrain, buildings, weather) introduce significant variability.
📚 Official Data Sources
⚠️ Disclaimer: This calculator provides theoretical estimates for educational purposes only. Actual blast effects depend on many factors including explosive type, confinement, terrain, and atmospheric conditions. Always consult qualified explosives engineers and follow all applicable safety regulations.
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