Blast Wave Simulator

The core model for a strong, point-source explosion in a gas is described by the Sedov-Taylor similarity solution. It gives the position of the shock front over time.

$R(t)$: Shock front radius at time $t$.
$S$: A dimensionless constant (≈1) depending on the specific heat ratio of the gas.
$E$: Total energy released by the explosion.
$\rho_0$: Ambient density of the surrounding medium before the blast.
$t$: Time since the energy release.
The $t^{2/5}$ power shows the deceleration of the shock front.

To compare blasts of different sizes, we use scaled distance. This collapses overpressure data from various explosive weights onto a single curve, known as the Hopkinson-Cranz scaling law.

$Z$: Scaled distance (e.g., m/kg$^{1/3}$).
$R$: Actual distance from the explosion.
$W$: Equivalent explosive mass (e.g., TNT equivalent).
This scaling means a small explosion up close can produce the same overpressure as a large explosion farther away, if their scaled distance $Z$ is the same.

Structural Safety & Blast-Resistant Design: Engineers use these scaling laws to design buildings near hazardous sites or for embassies and government facilities. By simulating overpressure vs. scaled distance, they can specify window strengths, wall reinforcements, and safe standoff distances for a given threat level.

Military & Demolition: Predicting the effective range of munitions and planning controlled demolitions relies on accurate blast wave models. For instance, calculating the safe distance for personnel during a building implosion requires knowing how the shock overpressure decays with distance according to the Hopkinson-Cranz curves.

Accident Investigation & Hazard Analysis: After an industrial accident like a gas plant explosion, investigators use Sedov-Taylor scaling backwards. By measuring the radius of damaged structures, they can estimate the energy released to understand the severity of the incident and improve safety protocols.

Aerospace & Planetary Science: This physics applies to hypervelocity impacts and supernovae! The Sedov-Taylor solution is used to model the expansion of a supernova remnant into the interstellar medium, where $E$ is the stellar explosion energy and $\rho_0$ is the density of space.

There are a few key points you should be aware of when starting to use this simulator. First, understand that the "TNT equivalent" can vary dramatically depending on the type of explosive. The simulator uses TNT as a baseline, but real explosives differ in their energy release rate and detonation velocity based on the composition. For instance, 1 kg of the high-performance explosive C4 holds about 1.3 times the energy of 1 kg of TNT. Therefore, in practical applications, the first step is always to accurately estimate: "What is the TNT equivalent of the material in question?"

Next, it's crucial to understand the limitation that the scaling laws assume an "ideal point explosion". Real explosions occur on the ground, inside buildings, and so on. For a ground-level explosion, the shockwave propagates in a hemispherical shape, which concentrates the energy, effectively doubling it compared to a free-air burst. Since this simulator assumes a free space, you need to apply corrections, like doubling the energy, when evaluating explosions near the ground.

Finally, do not judge damage based on overpressure alone. While it's true that window glass breakage has a guideline threshold of around 3 kPa, for the same overpressure, a longer duration of the shock (higher impulse) leads to greater damage. There's a tendency for brittle structures to be vulnerable to overpressure, while tough structures are more susceptible to impulse. Get into the habit of looking at both values to make a comprehensive assessment.