🔬 applied physics

A Novel Methodology for Evaluating Positive Phase Blast Wave Loading Parameters Using High Speed Video

This paper proposes and validates a novel methodology that accurately predicts positive phase duration and impulse for spherical free-air explosions using only time-of-arrival data extracted from high-speed video, offering a cost-effective and comprehensive alternative to traditional pressure gauge measurements.

Original authors: Caio Barbosa Amorim, Clare Knock, Dain George Farrimond, Rene Francisco Boschi Gonçalves

Published 2026-06-25

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Caio Barbosa Amorim, Clare Knock, Dain George Farrimond, Rene Francisco Boschi Gonçalves

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to understand the power of a giant firework explosion, but you can't get close enough to stick a thermometer or a pressure gauge near it without destroying your equipment. Traditionally, scientists had to place these expensive, fragile sensors right in the danger zone to measure the "blast wave"—the invisible wall of air pressure that rushes out from an explosion.

This paper proposes a clever new way to do the same job using something much safer and more common: high-speed video.

Here is the breakdown of their method, explained simply:

The Problem: The "Fragile Sensor" Dilemma

Think of traditional blast measurement like trying to measure the heat of a volcano by standing next to it with a thermometer. You need special, expensive gear, it has to be calibrated perfectly, and if you get too close, the gear (and maybe you) gets destroyed. Plus, these sensors only tell you what happened at one specific spot. If you want to know what happened two feet to the left, you need another sensor.

The Solution: The "Slow-Motion Detective"

The authors suggest that we don't need to stand in the danger zone. Instead, we can watch the explosion from a safe distance using a high-speed camera (like the ones used to film hummingbirds or crashing cars).

When an explosion happens, it creates a shockwave that moves outward. If you watch the video in slow motion, you can see exactly when that shockwave hits different objects or points in the distance. This is called the "Time of Arrival."

The paper's big idea is: If you know exactly when the shockwave arrives at different distances, you can mathematically figure out everything else about the explosion without ever needing a pressure sensor.

How the Math Works (The "Recipe")

The authors created a new "recipe" (a methodology) to turn those video timestamps into a full report on the explosion's power. They used three main ingredients:

The "Yield" Calculator: First, they use the arrival times to guess how powerful the explosion was (similar to figuring out how much TNT was used). They used a known rule called the Kingery and Bulmash model as a starting point, but they tweaked it to work with video data.
The "Duration" Timer: Next, they needed to know how long the "push" of the explosion lasted. They used a theory called the Kinney and Graham Hypothesis.
- The Analogy: Imagine the shockwave is a runner. The theory says the "positive phase" (the damaging push) ends when the air behind the runner cools down enough that the sound speed drops. By calculating how fast sound travels in that hot, disturbed air, they can predict exactly when the push stops.
The "Total Punch" Calculator: Finally, they calculated the "Impulse."
- The Analogy: If the peak pressure is how hard a punch is, the Impulse is how hard the punch is combined with how long it stays connected to your face. A quick tap hurts less than a heavy shove that lasts a split second. Their math combines the pressure and the duration to tell you the total "damage potential."

The "Test Drive"

To prove their new recipe worked, they didn't just guess. They took a massive pile of old data from other scientists who did use the dangerous pressure sensors. They had data on five different types of explosives (like PE4, Composition B, and PETN).

They fed the "Time of Arrival" data from those old experiments into their new video-based math model. Then, they compared the model's predictions against the actual sensor readings.

The Results: A Home Run

The results were surprisingly accurate.

Accuracy: Their model predicted the duration and the total "punch" (impulse) with an average error of only 5.3%.
Reliability: In the worst-case scenarios, the model was off by no more than 20% for duration and 9.4% for impulse.
Consistency: When they looked at the "confidence intervals" (a statistical way of saying "how sure are we?"), their model was right within the expected range 86% of the time for duration and 83% of the time for impulse.

Why This Matters (According to the Paper)

The paper claims this is a "step-change" (a huge leap forward) because:

Safety: You don't need to put expensive sensors in the blast zone anymore.
Full Picture: Instead of getting data from just one dot (where the sensor was), high-speed video gives you data for the whole area, creating a "full-field" map of the blast.
Versatility: It works for different types of ideal explosives and doesn't require a perfectly controlled lab environment (unlike some previous video methods).

In short: The authors built a mathematical bridge that lets us turn a simple high-speed video of an explosion into a detailed engineering report, proving that we can "see" the invisible pressure waves just by watching the shockwave move.

Technical Summary: A Novel Methodology for Evaluating Positive Phase Blast Wave Loading Parameters Using High Speed Video

Problem Statement
Traditionally, characterizing blast wave loading conditions relies on pressure gauge measurements to determine critical parameters such as peak overpressure ( $P_{max}$ ), positive phase duration ( $t_d$ ), and positive phase impulse ( $I_+$ ). However, these instruments are costly, require rigorous calibration, provide only discrete spatial data, and must be deployed in hazardous environments, often limiting data availability for accidental explosions or complex urban scenarios. While high-speed video (HSV) recordings have emerged as a valuable alternative for post-event analysis—providing time of arrival ( $t_a$ ) versus distance data—existing methodologies capable of predicting $t_d$ and $I_+$ using video data alone remain limited. Previous optical approaches often required controlled laboratory conditions or were restricted to single case studies with limited validation.

Methodology
The authors propose a novel, hybrid optical-theoretical methodology to predict positive phase duration and impulse for spherical, non-cased, free-air bursts of ideal explosives using only time of arrival ( $t_a$ ) data derived from high-speed video. The approach integrates the following theoretical frameworks:

Peak Overpressure Estimation: The method utilizes a previously developed algorithm [17] to estimate the TNT equivalence ( $TNT_e$ ) of the explosive based on $t_a$ data. This estimated $TNT_e$ is then used with Kingery and Bulmash (KB) semi-empirical models [14] to predict the peak overpressure ( $P_{max}$ ) and its derivative.
Positive Phase Duration ( $t_d$ ): The duration is estimated using the Kinney and Graham Hypothesis (KGH) [1]. This hypothesis posits that the end of the positive phase corresponds to a boundary traveling at the local speed of sound ( $a_+$ ). The study evaluates the speed of sound at the shock front ( $a_{max}$ ) and the post-shock region ( $a_{ps}$ ) as bounds. The methodology determines that using $a_{max}$ alone provides sufficient accuracy, effectively neglecting near-field fireball thermal effects for distances beyond the near-field boundary ( $R^* > 1 \text{ m/kg}^{1/3}$ ).
Positive Phase Impulse ( $I_+$ ): Once $t_d$ is established, the impulse is calculated using the Sadek and Gottlieb Equation (SGE) [22]. This formulation combines the Rankine-Hugoniot relations, Euler flow equations, and the modified Friedlander equation to relate the pressure derivative at the shock front to flow properties, allowing the derivation of the decay constant ( $\alpha$ ) and subsequent integration for impulse.
Scaling: All parameters are scaled according to Hopkinson-Cranz scaling laws to account for variations in charge mass, ambient pressure, and sound speed, enabling comparison across different datasets.

Validation and Results
The methodology was validated against experimental datasets from the literature involving five ideal explosives: Bulk PE4, Cartridge PE4, PE7, Composition B, and PETN. The validation framework employed a robust set of metrics, including Mean Absolute Percentage Error (MAPE), Maximum Deviation (MD), absolute bias, and 95% Confidence Interval (CI95) coverage, to assess both accuracy and consistency relative to experimental variability.

Key performance results include:

Positive Phase Duration ( $t_d$ ): Achieved a MAPE of 5.3%, a maximum deviation of 20%, zero absolute bias, and an 86% CI95 coverage.
Positive Phase Impulse ( $I_+$ ): Achieved a MAPE of 5.3%, a maximum deviation of 9.4%, an absolute bias of 3.1%, and an 83% CI95 coverage.
Signal Reconstruction: Qualitative analysis of reconstructed pressure-time profiles and pressure-time integrals demonstrated significant agreement with experimental gauge recordings.

The study notes that the proposed model's error levels (MAPE and MD) are lower than those reported for recent numerical models [32]-[33] and comparable to semi-empirical models for peak overpressure [34]. Furthermore, unlike previous optical methods that required controlled conditions and reported ~15% deviation in single-case studies [21], this approach maintains similar accuracy across extensive multi-trial datasets without such constraints.

Significance and Claims
The paper claims that this work represents a "step-change" in explosive characterization. By enabling the prediction of full-field spatial blast loading parameters ( $t_d$ and $I_+$ ) using only high-speed video and time-of-arrival data, the methodology eliminates the need for pressure gauges in many scenarios. This reduces the number of trials required for blast loading assessments and removes the risk of exposing instrumentation to severe environmental conditions.

The authors assert that the study successfully validates the Kinney and Graham hypothesis for a range of explosives beyond the near-field region and demonstrates the practical applicability of the Sadek and Gottlieb equation for impulse prediction. The proposed framework offers a robust, validated alternative for engineering assessments of blast incidents, particularly where conventional instrumentation is unavailable or impractical.