Set TNT equivalent charge weight W and standoff distance R to calculate peak overpressure, shock wave velocity, positive phase duration, and specific impulse in real time. Visualize Friedlander waveform and distance dependency for blast-resistant design.
Parameters
Presets
Results
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Scaled Distance Z (m/kg^⅓)
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Peak Overpressure Pso (kPa)
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Shock Wave Velocity Us (m/s)
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Positive Phase Duration td (ms)
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Specific Impulse is (kPa·ms)
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Damage Level
Fried
Pressure-time waveform from the Friedlander approximation. Orange line = atmospheric-pressure reference (positive and negative phases).
Dist
Relationship between distance R and peak overpressure Pso for the current W. The dot marks the current setting.
Comp
Relative comparison of Pso, td, and is at different scaled distances Z (0.5, 1, 2, 3, 5 m/kg^⅓).
Theory & Key Formulas
For scaled distance \(Z = R / W^{1/3}\) [m/kg^{1/3}], the blast parameters are calculated using the following approximation (Kingery & Bulmash, 1984) for a surface burst.
Shock wave velocity: from the Rankine-Hugoniot relation, \(U_s = a_0\sqrt{1 + \frac{6P_{so}}{7P_0}}\), where \(a_0\) is the speed of sound (340 m/s) and \(P_0\) is 101.3 kPa.
Basics of Blast Load — Learn Through Conversation
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How do you calculate blast overpressure? Is it determined only by the size of the explosion and the distance?
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Basically, yes. There's a principle called the Hopkinson-Cranz scaling law, where the 'explosion strength' can be consolidated into a single parameter: scaled distance Z = R / W^(1/3). W is the TNT equivalent (kg), and R is the distance (m). If Z is the same, observing 1 kg of explosive at 10 m gives the same waveform as observing 1000 kg at 100 m.
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What is TNT equivalent? What about explosives that aren't TNT?
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TNT (trinitrotoluene) is used as a reference standard for explosives. Other explosives are converted using a TNT equivalence factor. For example, C-4 is about 1.34 times (34% stronger than TNT for the same mass), and ANFO (ammonium nitrate fuel oil) is about 0.82 times. Explosives used in car bombs are typically around 50–200 kg in TNT equivalent.
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What is the Friedlander waveform? Why does blast overpressure take that shape?
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When an explosion occurs, the shock wave expands spherically, instantly reaching peak overpressure (Pso) and then decaying exponentially. It's expressed as P(t) = Pso × (1 - t/td) × exp(-b×t/td), which is the Friedlander waveform. After the positive phase ends, a 'negative phase' appears where pressure drops below atmospheric, creating a suction load that pulls on structures.
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Which is more important for structural damage: overpressure or specific impulse?
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Both are important, and it depends on the natural period of the target. In the 'impulsive regime' where the natural period is shorter than the duration td, specific impulse (integral of pressure over time) dominates. In the 'quasi-static regime' where the natural period is longer, peak overpressure Pso dominates. For intermediate cases, design uses a P-I diagram considering both. Window glass is often in the impulsive regime, while concrete walls are closer to the quasi-static regime.
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What is the shape factor K = 1.8? Why isn't it 1.0?
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For free air (spherical explosion), K = 1.0. For a surface burst, ground reflection gives K ≈ 1.8. If the ground were a perfectly rigid reflector, K = 2.0, but since the ground deforms and absorbs energy, a practical range of 1.7–1.8 is used. For a hemispherical charge, energy is released only into the upper hemisphere, making K close to 2.0.
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What standards are used for actual blast-resistant design of buildings?
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There are standards like the U.S. UFC 3-340-02 (formerly TM5-1300), the UK's Blast Effects of Explosions, and ISO 16933. The most effective method is to maintain a large standoff distance (minimum separation) to keep Z large. At Pso < 6.9 kPa (1 psi), damage is limited to window glass; at Pso > 69 kPa (10 psi), there is a risk of structural collapse.
Frequently Asked Questions
At very close range (Z < 0.3 m/kg^(1/3)), fireball and thermal radiation dominate, making the scaling law less valid. In confined spaces (inside buildings), reflected waves and residual gas pressure dominate, so the open-field model is not applicable. For extremely large events like nuclear explosions, corrections for altitude and atmospheric density are also needed.
Z < 0.5 m/kg^(1/3) indicates lethal close-range explosions (structural collapse, direct burns); Z = 0.5–2 is the critical zone for blast-resistant design (window breakage, eardrum rupture); Z = 2–5 corresponds to minor damage (e.g., window glass breakage); Z > 5 is roughly at audible distance levels. For building design, a standoff distance of at least Z > 3 is commonly required.
There are two approaches: ① Perform a fully coupled fluid-structure interaction analysis using explicit FEM (Abaqus/Explicit, LS-DYNA) including air (most accurate but computationally expensive). ② Directly apply the Friedlander waveform obtained from this tool as a pressure-time history load to the structural FEM (commonly used in engineering practice). For lightweight or thin-walled structures, the negative phase pull-back load must also be modeled.
Typical values: TNT = 1.00, C-4 (PETN-based) = 1.34, RDX = 1.60, PETN = 1.27, ANFO = 0.82, Black powder = 0.55, Gasoline vapor (confined space) ≈ 0.40. Coefficients may differ depending on whether the effect is blast (detonation speed, pressure) or explosive (mine, blasting), so refer to values appropriate for your application.
Typical window glass (6 mm thick) fails at Pso ≈ 3–7 kPa (0.5–1 psi). According to GSA (U.S. General Services Administration) standards, security glass (laminated glass + film) is required to withstand Pso = 14–28 kPa. In blast pressure design, preventing fragment scatter (hazard level) is more critical than glass damage itself.
Specific impulse is = ∫P(t)dt is the impulse obtained by integrating pressure over time. A Pressure-Impulse (P-I) diagram plots specific impulse on the x-axis and peak overpressure on the y-axis, showing iso-damage curves for a given damage level. The upper-right region of the curve is the damage zone, and the lower-left is the safe zone. Since the structural response depends on its natural period (impulse-dominated vs. quasi-static-dominated), combining both axes is important for design.
What is Explosion Blast?
Explosion Blast is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.
By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.
Physical Model & Key Equations
The simulator is based on the governing equations behind Explosion Blast Wave Calculator. Understanding these equations is key to interpreting the results correctly.
Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.
Real-World Applications
Engineering Design: The concepts behind Explosion Blast Wave Calculator are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.
Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.
CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.
Common Misconceptions and Points of Caution
Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.
Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.
Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.
Enter TNT equivalent charge weight (W) in kilograms using the slider or numerical input field (sl_w, wvNum). Range typically 0.1–10,000 kg for industrial blast scenarios.
Set standoff distance (R) in meters via slider or text input (sl_r, rvNum). This is the perpendicular distance from the charge center to the target location.
Configure the scaled distance parameter (K) if modeling confined spaces or reflective surfaces (sl_k, kvNum). Standard free-air detonation uses K=1.
Click calculate to obtain peak overpressure (kPa), shock arrival time (ms), positive phase duration, and impulse (kPa·ms).
Worked Example
For a 50 kg TNT equivalent charge at 15 m standoff distance in free air (K=1): scaled distance Z = 15/(50^0.333) ≈ 3.68 m/kg^0.333. Using the Kinney-Graham equation, peak overpressure ≈ 195 kPa. Shock velocity at this distance ≈ 380 m/s. Positive phase duration ≈ 8.5 ms. Total positive impulse ≈ 740 kPa·ms. These values are typical for blast engineering assessments near mining operations or demolition sites.
Practical Notes
Scaled distance (Z = R/W^0.333) is dimensionless and governs all blast effects; lower Z values produce higher overpressures and shorter arrival times.
In confined spaces (bunkers, tunnels), increase K above 1.0 to account for wave reflection and amplification; K=2 can increase overpressure by 40–60%.
Peak overpressure above 35 kPa causes structural damage; above 100 kPa causes building collapse. Use results for protective design thresholds.
Shock velocity decays rapidly with distance; at Z>10, velocity approaches ambient sound speed (~340 m/s in air).