Hopkinson-Cranz Scaling
Definition
The law relating peak overpressure and positive-phase duration to the ratio of range to cube-root-of-charge-mass (the scaled distance Z = R / W^(1/3)), allowing blast effects from different charge sizes at different ranges to be compared on a single curve.
- Also known as
- Cube-root scaling law
- Key variable
- Scaled distance Z = R / W^(1/3)
- Relates
- Peak overpressure and positive-phase duration
- Application
- Comparing blast effects across different charge sizes
Common questions
Why does scaling by cube-root of charge mass work for comparing blasts?+
Explosive energy release scales with charge volume, roughly the cube of a characteristic dimension, so blast wave parameters at geometrically similar scaled distances behave similarly regardless of the actual charge size, allowing small-scale test data to predict large-charge behaviour.
How is Hopkinson-Cranz scaling used in a bombing scene reconstruction?+
Investigators estimate charge mass by comparing observed damage, such as overpressure-related structural failure or fragmentation range, at the known scene distance against the standard scaled-distance curves derived from controlled test data.
Related terms
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- Deflagration-to-Detonation Transition (DDT)
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- DMDNB Taggant
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- Dynamic Pressure
- The pressure component due to mass flow of gas behind the shock front, proportional to gas velocity squared; the blast wind that...
- Friedlander Waveform
- The idealised time-pressure history at a point in air following a blast: instantaneous rise to peak overpressure at shock arrival, exponential decay...
- Mach Stem
- The reinforced shock front that forms near a reflective surface when the direct blast wave and its reflected wave merge, producing anomalously...
- Mott Formula
- An empirical relationship, derived from wartime UK research by N.F. Mott, predicting the statistical distribution of fragment masses from a metal casing...
- Peak Static Overpressure (Ps)
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