Beirut explosion: Energy yield from the fireball time evolution in the first 230 milliseconds

TL;DR

This study estimates the energy release of the Beirut explosion by analyzing fireball evolution in amateur footage, suggesting a lower energy yield than official reports and implications for the explosive material involved.

Contribution

It introduces a novel method to estimate explosion energy from fireball dynamics using amateur footage and precise calibration techniques.

Findings

Estimated energy yield of approximately 1.3 terajoules.

Lower bound of energy yield is about 9.8×10^{11} Joules.

Implication that the explosive mass may be less than official claims.

Abstract

The evolution of the fireball resulting from the August 2020 Beirut explosion is traced using amateur footage taken during the first $\sim$ 230 $ms$ after the detonation. 38 frames separated by $\sim$ 16.66 - 33.33 $ms$ are extracted from 6 different videos located precisely on the map. Measurements of the time evolution of the radius $R_{t}$ of the shock wave are traced by the fireball at consecutive time sequence $t$. Pixel scales for the videos are calibrated by de-projecting the existing grains silos building for which accurate drawings are available and by defining the line of sight incident angles. The energy available to drive the shock wave at early times can be calculated through $E = 10^{2b} K \rho_{o}$ where $b$ is a fitted parameter dependant on the relation between $R_t$ and $t$. $K$ is a constant depending on the ratio of specific heats of the atmosphere and $\rho_0$ is the undisturbed gas density. A total energy yield of $E \approx 1.3\times 10^{12}$ Joules with a lower bound of $9.8\times 10^{11}$ and an upper bound of $\sim 1.7\times 10^{12}$ or the equivalent of $\sim 310_{235}^{405}$ tons of T.N.T. is found. Our energy yields are different from other published studies using the same method. This can present an argument that if the compound that exploded is fuel rich ammonium nitrate (ANFO), then the actual mass that detonated is less than officially claimed.