Blast Shock Wave Pressure Calculator
Computes peak shock wave overpressure in kPa at a distance in meters from a TNT charge in kg using Hopkinson scaling empirical relation.
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Blast overpressure — shock wave
When a high explosive detonates it throws off a shock wave, and the peak overpressure P (how far above atmospheric the pressure spikes, in kPa) falls off with distance while also tracking the TNT-equivalent mass W of the charge. The engineering correlation most people reach for feeds the scaled distance Z = R/W^(1/3) (m/kg^⅓), where R is in metres and W in kilograms of TNT, into empirical curves such as Kingery–Bulmash or Sadovsky. As a rough guide to damage: ~1 kPa is a light noise, ~7 kPa is enough to break ordinary window glass, ~35 kPa means serious structural damage, and ~70 kPa+ can be lethal. For scale, the Hiroshima Little Boy bomb came in around 15 kt TNT equivalent.
Applications
Civil defence agencies lean on it to set evacuation and exclusion radii. In controlled demolition with RDX, dynamite or emulsions, it helps size the charges and the safety distances. Forensic investigators of bomb attacks and industrial accidents work it backwards, estimating the charge mass from the damage they find on site (broken windows, collapsed walls). It also turns up in military engineering for fortification and standoff design, and in safety analysis of fuel depots and pyrotechnics warehouses.
FAQ
What is "TNT equivalent"? It's the mass of TNT that would release the same energy as the explosive you actually have. RDX runs about ~1.6× TNT, ANFO ~0.8×, gunpowder ~0.5×, so the conversion gives you a common yardstick across very different materials.
Why use scaled distance? Cube-root scaling lets one curve cover charges of wildly different sizes. Double W and you have to push the distance out by 2^(1/3) ≈ 1.26× just to hold the same overpressure.
Does this account for reflections? No, these are free-air values. A surface burst roughly doubles the effective charge, and a confined space pushes the pressure higher still.
At what overpressure do windows break? Ordinary glass starts cracking around 3–4 kPa, and most residential windows are gone by 7 kPa. Hardened or laminated glass holds out longer.
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Hemispherical Head Thickness (ASME)
Calculate the minimum thickness of a pressure-vessel hemispherical head by the ASME Section VIII formula, t = (P·r) ÷ (2·S·E − 0.2·P), from the internal pressure P (MPa), internal radius r (mm), allowable stress S (MPa) and joint efficiency E. Heads close the ends of a pressure vessel's cylindrical shell, and their shape is decisive for structural efficiency. The HEMISPHERICAL (half-sphere) head is the MOST EFFICIENT of all: since the sphere distributes pressure equally in all directions (uniform membrane stress), the hemispherical head needs only about HALF the thickness of the cylindrical shell of the same radius and pressure (compare the '2·S·E' in the denominator with the shell's 'S·E'). So it is the choice for high-pressure vessels. The drawbacks are costlier fabrication and greater height (more space). For moderate pressures and costs, elliptical (2:1) or torispherical heads, intermediate, are used. The head-type choice is a trade-off among thickness/material (cost), space and fabrication ease. This formula is fundamental in the complete vessel design, combining shell and heads. Enter the pressure, internal radius, allowable stress and joint efficiency.
Hydrostatic Test Pressure
Calculate the hydrostatic test pressure of a pressure vessel by the (simplified) ASME rule, P_test = 1.3 · MAWP, from the maximum allowable working pressure MAWP (MPa). Before entering service (and periodically, at revalidations), every pressure vessel undergoes a HYDROSTATIC TEST: it is filled with WATER (not gas!) and pressurized ABOVE the operating pressure, to verify structural integrity and tightness before entrusting it with a hazardous fluid. ASME VIII Div. 1 (rule UG-99) requires a test pressure of 1.3 times MAWP (corrected by the allowable-stress ratio at test and design temperatures, simplified here). Using WATER is a fundamental safety matter: water is practically incompressible, so it stores very little energy when pressurized — if the vessel ruptures during the test, the failure is localized and relatively safe (it leaks, not explodes); whereas a compressed gas stores enormous energy and a rupture would be EXPLOSIVE, possibly lethal. The 1.3×MAWP test subjects the vessel to higher-than-operating stresses, revealing defects (cracks, bad welds, insufficient thickness) with margin, without reaching general yielding. Passing the hydrostatic test is a condition for the vessel's certification and operation. Enter the MAWP.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.