TNT equivalence - Revision history

Jan: Add 5 watermarked SVG illustrations from the Expert visual plan

2026-11-02T16:48:20Z

Add 5 watermarked SVG illustrations from the Expert visual plan

← Older revision		Revision as of 17:48, 2 November 2026
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	Far from the source the blast wave has a characteristic shape. A shock raises the pressure suddenly to a peak, a rarefaction follows in which the pressure falls below atmospheric, and the pressure then recovers.<ref name="Z-418">Zalosh (2002), p. 3-418.</ref><ref name="Z-419" /> When the recovery takes the form of a second shock, the pressure history looks like a slightly deformed letter N and is called an N wave.<ref name="Z-419" /> The impulse of the wave, its overpressure integrated over time, matters for the dynamic response of structures.<ref name="Z-419" />		Far from the source the blast wave has a characteristic shape. A shock raises the pressure suddenly to a peak, a rarefaction follows in which the pressure falls below atmospheric, and the pressure then recovers.<ref name="Z-418">Zalosh (2002), p. 3-418.</ref><ref name="Z-419" /> When the recovery takes the form of a second shock, the pressure history looks like a slightly deformed letter N and is called an N wave.<ref name="Z-419" /> The impulse of the wave, its overpressure integrated over time, matters for the dynamic response of structures.<ref name="Z-419" />
			[[File:fse-tnt-equivalence-v1.svg\|thumb\|upright=1.5\|alt=Pressure against time at a point far from an explosion: a sudden jump to a peak, a fall below atmospheric pressure, then recovery.\|Pressure history of a far-field blast wave at a fixed point: a shock raises the pressure to its peak, a rarefaction takes it below atmospheric pressure, and the pressure then recovers. Based on Zalosh (2002), pp. 3-418 to 3-419.]]

	Ideal blast wave theory assumes that the energy is released instantaneously at a single point, so that the wave is described by one parameter, the blast energy.<ref name="Z-419" /> Its correlations combine theory with test data from compact condensed-phase explosives.<ref name="Z-419" /> Because the blast effects of TNT are well documented as a function of charge mass and distance, it is convenient to express other explosions as an equivalent TNT charge.<ref name="IS-15-10" /> As a unit of energy, the conversion table of the SFPE Handbook lists the ton (nuclear equivalent of TNT) as 4.20 × 10<sup>9</sup> J.<ref name="DiN-A9">DiNenno et al. (2002), p. A-9.</ref>		Ideal blast wave theory assumes that the energy is released instantaneously at a single point, so that the wave is described by one parameter, the blast energy.<ref name="Z-419" /> Its correlations combine theory with test data from compact condensed-phase explosives.<ref name="Z-419" /> Because the blast effects of TNT are well documented as a function of charge mass and distance, it is convenient to express other explosions as an equivalent TNT charge.<ref name="IS-15-10" /> As a unit of energy, the conversion table of the SFPE Handbook lists the ton (nuclear equivalent of TNT) as 4.20 × 10<sup>9</sup> J.<ref name="DiN-A9">DiNenno et al. (2002), p. A-9.</ref>
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	== Calculation method ==		== Calculation method ==
	NUREG-1805 sets out the method in three steps, based on the explosion protection chapter by Zalosh in the second edition (1995) of the SFPE Handbook.<ref name="IS-15-9" /><ref name="IS-15-10" /><ref name="IS-15-17">Iqbal and Salley (2004), p. 15-17.</ref> It applies to a flammable gas or vapour that has been released, has mixed with air within its flammable limits and has then been ignited.<ref name="IS-15-9" /><ref name="IS-15-15">Iqbal and Salley (2004), p. 15-15.</ref> The first step gives the explosive energy of a flammable vapour release from its mass, its heat of combustion and the yield:<ref name="IS-15-9" />		NUREG-1805 sets out the method in three steps, based on the explosion protection chapter by Zalosh in the second edition (1995) of the SFPE Handbook.<ref name="IS-15-9" /><ref name="IS-15-10" /><ref name="IS-15-17">Iqbal and Salley (2004), p. 15-17.</ref> It applies to a flammable gas or vapour that has been released, has mixed with air within its flammable limits and has then been ignited.<ref name="IS-15-9" /><ref name="IS-15-15">Iqbal and Salley (2004), p. 15-15.</ref> The first step gives the explosive energy of a flammable vapour release from its mass, its heat of combustion and the yield:<ref name="IS-15-9" />
			[[File:fse-tnt-equivalence-v2.svg\|thumb\|upright=1.5\|alt=Flowchart from released fuel mass to explosive energy, TNT mass, scaled distance, overpressure and damage.\|The three steps of the TNT equivalence method: explosive energy from the released fuel, equivalent TNT mass, and scaled distance, followed by reading the overpressure from an ideal blast chart. Based on Iqbal and Salley (2004), pp. 15-9 to 15-11.]]

	<math display="block">E = \alpha \, \Delta H_\mathrm{c} \, m_\mathrm{F}</math>		<math display="block">E = \alpha \, \Delta H_\mathrm{c} \, m_\mathrm{F}</math>
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	Here W<sub>TNT</sub> is in kilograms and E in kilojoules, so each kilogram of TNT stands for 4,500 kJ of blast energy.<ref name="IS-15-10" /> At full yield, one kilogram of propane is therefore equivalent to about 10 kg of TNT, and one kilogram of hydrogen to about 29 kg.<ref name="IS-15-10" /> The third step divides the distance D from the explosion by the cube root of the TNT mass to give the scaled distance:<ref name="IS-15-11" />		Here W<sub>TNT</sub> is in kilograms and E in kilojoules, so each kilogram of TNT stands for 4,500 kJ of blast energy.<ref name="IS-15-10" /> At full yield, one kilogram of propane is therefore equivalent to about 10 kg of TNT, and one kilogram of hydrogen to about 29 kg.<ref name="IS-15-10" /> The third step divides the distance D from the explosion by the cube root of the TNT mass to give the scaled distance:<ref name="IS-15-11" />
			[[File:fse-tnt-equivalence-v3.svg\|thumb\|upright=1.5\|alt=Bar chart of TNT mass per kilogram of fuel at full yield for twelve gases, about 10 for hydrocarbons and 29 for hydrogen.\|Equivalent TNT mass per kilogram of fuel at 100 % yield, from the net heat of combustion divided by 4,500 kJ per kilogram of TNT. Based on Iqbal and Salley (2004), p. 15-10.]]

	<math display="block">D_\mathrm{sc} = \frac{D}{W_\mathrm{TNT}^{1/3}}</math>		<math display="block">D_\mathrm{sc} = \frac{D}{W_\mathrm{TNT}^{1/3}}</math>
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	For risk studies, Barry gives a generic breakdown of damage levels.<ref name="B-186" /> Overpressures of 2.5 to 5 psig cause heavy damage to buildings and process equipment, and about 1 % deaths from lung damage.<ref name="B-186" /> At 1 to 2.4 psig buildings suffer repairable damage, at 0.5 to 1 psig glass breaks, and at 0.15 to 0.30 psig about 10 % of window panes break.<ref name="B-186" />		For risk studies, Barry gives a generic breakdown of damage levels.<ref name="B-186" /> Overpressures of 2.5 to 5 psig cause heavy damage to buildings and process equipment, and about 1 % deaths from lung damage.<ref name="B-186" /> At 1 to 2.4 psig buildings suffer repairable damage, at 0.5 to 1 psig glass breaks, and at 0.15 to 0.30 psig about 10 % of window panes break.<ref name="B-186" />
			[[File:fse-tnt-equivalence-v4.svg\|thumb\|upright=1.5\|alt=Chart of overpressure damage and injury thresholds from two sources on a logarithmic kilopascal axis, from glass breakage at 1 kPa to 99 % mortality at 350 kPa.\|Overpressure criteria for damage and injury from NUREG-1805 and from Barry, converted to kPa. Lung-damage criteria differ markedly between the sources. Based on Iqbal and Salley (2004), pp. 15-7, 15-8 and 15-12, and Barry (2002), p. 5-186.]]

	== Worked example: a propane forklift ==		== Worked example: a propane forklift ==
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	The yield changes the result by two orders of magnitude. With the 1 % typical of an unconfined release, the same propane is equivalent to only about 2.25 kg of TNT.<ref name="IS-15-9" /> At 50 m from the release, the scaled distance is 50/225<sup>1/3</sup>, about 8.2 m/kg<sup>1/3</sup>, for full yield, and 50/2.25<sup>1/3</sup>, about 38 m/kg<sup>1/3</sup>, for 1 % yield.<ref name="IS-15-11" /> Any given overpressure therefore occurs 100<sup>1/3</sup>, or about 4.6, times further away at full yield than at 1 % yield.<ref name="IS-15-11" /> The choice of yield thus determines the size of every hazard zone derived from the chart.		The yield changes the result by two orders of magnitude. With the 1 % typical of an unconfined release, the same propane is equivalent to only about 2.25 kg of TNT.<ref name="IS-15-9" /> At 50 m from the release, the scaled distance is 50/225<sup>1/3</sup>, about 8.2 m/kg<sup>1/3</sup>, for full yield, and 50/2.25<sup>1/3</sup>, about 38 m/kg<sup>1/3</sup>, for 1 % yield.<ref name="IS-15-11" /> Any given overpressure therefore occurs 100<sup>1/3</sup>, or about 4.6, times further away at full yield than at 1 % yield.<ref name="IS-15-11" /> The choice of yield thus determines the size of every hazard zone derived from the chart.
			[[File:fse-tnt-equivalence-v5.svg\|thumb\|upright=1.5\|alt=Two rising curves against yield on a logarithmic axis: TNT mass from 2.2 to 224 kg and distance factor from 1 to 4.6.\|Equivalent TNT mass of 21.8 kg of released propane, and the factor by which every hazard distance grows, as a function of the assumed yield. Based on Iqbal and Salley (2004), pp. 15-9 to 15-11 and 15-18.]]

	A second example in NUREG-1805 compares 10 lb of acetylene with 5 lb of hydrogen.<ref name="IS-15-24">Iqbal and Salley (2004), p. 15-24.</ref> The hydrogen has half the mass, but its heat of combustion is almost three times that of acetylene.<ref name="IS-15-10" /> It is therefore equivalent to 66.0 kg of TNT against 48.7 kg for the acetylene, and NUREG-1805 concludes that the hydrogen produces the larger explosive force.<ref name="IS-15-24" />		A second example in NUREG-1805 compares 10 lb of acetylene with 5 lb of hydrogen.<ref name="IS-15-24">Iqbal and Salley (2004), p. 15-24.</ref> The hydrogen has half the mass, but its heat of combustion is almost three times that of acetylene.<ref name="IS-15-10" /> It is therefore equivalent to 66.0 kg of TNT against 48.7 kg for the acetylene, and NUREG-1805 concludes that the hydrogen produces the larger explosive force.<ref name="IS-15-24" />

Mark: FSE wiki: corrections after independent fact-check (written by Claude Opus 5.5)

2026-11-01T23:31:11Z

FSE wiki: corrections after independent fact-check (written by Claude Opus 5.5)

← Older revision		Revision as of 00:31, 2 November 2026
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	'''TNT equivalence''' is a method that expresses the blast energy of an [[explosion]] as the mass of trinitrotoluene (TNT) that would release the same energy.<ref name="IS-15-10">Iqbal and Salley (2004), p. 15-10.</ref> NUREG-1805 calls it one of the most common methods for estimating the effects of an explosion, because the blast effects of TNT have been studied extensively as a function of charge mass and distance.<ref name="IS-15-10" /> The method multiplies the mass of released fuel by its heat of combustion and by a yield, the fraction of the energy that drives the blast wave.<ref name="IS-15-9">Iqbal and Salley (2004), p. 15-9.</ref> It then divides the result by 4,500 kJ per kilogram of TNT.<ref name="IS-15-10" /> The distance to a target, divided by the cube root of the TNT mass, gives a scaled distance at which the overpressure is read from an ideal blast wave chart.<ref name="IS-15-11">Iqbal and Salley (2004), p. 15-11.</ref> The yield is ~~the largest uncertainty, ranging~~ from ~~about~~ 1 % for unconfined releases to 100 % for confined ones.<ref name="IS-15-9" />		'''TNT equivalence''' is a method that expresses the blast energy of an [[explosion]] as the mass of trinitrotoluene (TNT) that would release the same energy.<ref name="IS-15-10">Iqbal and Salley (2004), p. 15-10.</ref> NUREG-1805 calls it one of the most common methods for estimating the effects of an explosion, because the blast effects of TNT have been studied extensively as a function of charge mass and distance.<ref name="IS-15-10" /> The method multiplies the mass of released fuel by its heat of combustion and by a yield, the fraction of the energy that drives the blast wave.<ref name="IS-15-9">Iqbal and Salley (2004), p. 15-9.</ref> It then divides the result by 4,500 kJ per kilogram of TNT.<ref name="IS-15-10" /> The distance to a target, divided by the cube root of the TNT mass, gives a scaled distance at which the overpressure is read from an ideal blast wave chart.<ref name="IS-15-11">Iqbal and Salley (2004), p. 15-11.</ref> The yield is highly uncertain: it typically ranges from 1 % for unconfined releases to 100 % for confined ones.<ref name="IS-15-9" />

	The method rests on ideal blast wave theory, which treats an explosion as an instantaneous release of energy at a single point.<ref name="Z-419">Zalosh (2002), p. 3-419.</ref> That suits compact condensed-phase explosives and bursting pressure vessels.<ref name="Z-419" /> For vapour clouds, however, the SFPE Handbook reports that early assessments with such correlations were not very successful, and newer methods use the flame speed or computational fluid dynamics instead.<ref name="Z-420">Zalosh (2002), p. 3-420.</ref> In risk studies, the resulting overpressures are related to the distances at which buildings are damaged and people are injured.<ref name="B-186">Barry (2002), p. 5-186.</ref>		The method rests on ideal blast wave theory, which treats an explosion as an instantaneous release of energy at a single point.<ref name="Z-419">Zalosh (2002), p. 3-419.</ref> That suits compact condensed-phase explosives and bursting pressure vessels.<ref name="Z-419" /> For vapour clouds, however, the SFPE Handbook reports that early assessments with such correlations were not very successful, and newer methods use the flame speed or computational fluid dynamics instead.<ref name="Z-420">Zalosh (2002), p. 3-420.</ref> In risk studies, the resulting overpressures are related to the distances at which buildings are damaged and people are injured.<ref name="B-186">Barry (2002), p. 5-186.</ref>
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	Zalosh gives two reasons. Most of the interest lies in the near field, close to the cloud, and even in the far field the blast from a vapour cloud decays much less rapidly than an ideal blast wave.<ref name="Z-420" /> NUREG-1805 states a related limitation: the ideal point-source correlations cannot be valid within or near the flammable vapour cloud.<ref name="IS-15-15">Iqbal and Salley (2004), p. 15-15.</ref> Current methods instead estimate the flame speed empirically and calculate a non-ideal blast wave, or they model the flame propagation with computational fluid dynamics.<ref name="Z-420" />		Zalosh gives two reasons. Most of the interest lies in the near field, close to the cloud, and even in the far field the blast from a vapour cloud decays much less rapidly than an ideal blast wave.<ref name="Z-420" /> NUREG-1805 states a related limitation: the ideal point-source correlations cannot be valid within or near the flammable vapour cloud.<ref name="IS-15-15">Iqbal and Salley (2004), p. 15-15.</ref> Current methods instead estimate the flame speed empirically and calculate a non-ideal blast wave, or they model the flame propagation with computational fluid dynamics.<ref name="Z-420" />

	Further assumptions limit the method. The fuel must be mixed with air between its flammable limits, and real mixtures may be non-uniform or stratified.<ref name="IS-15-15" /> The yield~~, which~~ spans two orders of magnitude, ~~has~~ to ~~be chosen by judgement~~.<ref name="IS-15-9" /> NUREG-1805 adds that the pressures produced are usually difficult to predict.<ref name="IS-15-12" /> A [[detonation]] of the released gas, inside or outside a building, would give even higher pressures, although detonations are very rare.<ref name="IS-15-12" />		Further assumptions limit the method. The fuel must be mixed with air between its flammable limits, and real mixtures may be non-uniform or stratified.<ref name="IS-15-15" /> The yield typically spans two orders of magnitude, from 1 % for unconfined to 100 % for confined vapour releases.<ref name="IS-15-9" /> NUREG-1805 adds that the pressures produced are usually difficult to predict.<ref name="IS-15-12" /> A [[detonation]] of the released gas, inside or outside a building, would give even higher pressures, although detonations are very rare.<ref name="IS-15-12" />

	Damage criteria also differ between sources. Barry associates about 1 % deaths from lung damage with 2.5 to 5 psig, about 17 to 34 kPa.<ref name="B-186" /> NUREG-1805, by contrast, gives 70 kPa as the limit for lung damage and 180 kPa for 1 % mortality.<ref name="IS-15-12" /> The energy assigned to TNT is not uniform either: the method uses 4,500 kJ per kilogram, while the SFPE conversion table lists 4.20 × 10<sup>9</sup> J for the ton (nuclear equivalent of TNT).<ref name="IS-15-10" /><ref name="DiN-A9" /> A TNT equivalent and the damage it implies should therefore be read with the yield and the criteria that were used to obtain it.		Damage criteria also differ between sources. Barry associates about 1 % deaths from lung damage with 2.5 to 5 psig, about 17 to 34 kPa.<ref name="B-186" /> NUREG-1805, by contrast, gives 70 kPa as the limit for lung damage and 180 kPa for 1 % mortality.<ref name="IS-15-12" /> The energy assigned to TNT is not uniform either: the method uses 4,500 kJ per kilogram, while the SFPE conversion table lists 4.20 × 10<sup>9</sup> J for the ton (nuclear equivalent of TNT).<ref name="IS-15-10" /><ref name="DiN-A9" /> A TNT equivalent and the damage it implies should therefore be read with the yield and the criteria that were used to obtain it.

Mark: New FSE wiki article: TNT equivalence (written by Claude Opus 5.5)

2026-11-01T22:25:07Z

New FSE wiki article: TNT equivalence (written by Claude Opus 5.5)

New page

'''TNT equivalence''' is a method that expresses the blast energy of an [[explosion]] as the mass of trinitrotoluene (TNT) that would release the same energy.<ref name="IS-15-10">Iqbal and Salley (2004), p. 15-10.</ref> NUREG-1805 calls it one of the most common methods for estimating the effects of an explosion, because the blast effects of TNT have been studied extensively as a function of charge mass and distance.<ref name="IS-15-10" /> The method multiplies the mass of released fuel by its heat of combustion and by a yield, the fraction of the energy that drives the blast wave.<ref name="IS-15-9">Iqbal and Salley (2004), p. 15-9.</ref> It then divides the result by 4,500 kJ per kilogram of TNT.<ref name="IS-15-10" /> The distance to a target, divided by the cube root of the TNT mass, gives a scaled distance at which the overpressure is read from an ideal blast wave chart.<ref name="IS-15-11">Iqbal and Salley (2004), p. 15-11.</ref> The yield is the largest uncertainty, ranging from about 1 % for unconfined releases to 100 % for confined ones.<ref name="IS-15-9" />

The method rests on ideal blast wave theory, which treats an explosion as an instantaneous release of energy at a single point.<ref name="Z-419">Zalosh (2002), p. 3-419.</ref> That suits compact condensed-phase explosives and bursting pressure vessels.<ref name="Z-419" /> For vapour clouds, however, the SFPE Handbook reports that early assessments with such correlations were not very successful, and newer methods use the flame speed or computational fluid dynamics instead.<ref name="Z-420">Zalosh (2002), p. 3-420.</ref> In risk studies, the resulting overpressures are related to the distances at which buildings are damaged and people are injured.<ref name="B-186">Barry (2002), p. 5-186.</ref>

== Principle ==
NUREG-1805 defines an explosion as a sudden and violent release of high-pressure gases into the environment, fast enough for the energy to dissipate in a shock wave.<ref name="IS-15-1">Iqbal and Salley (2004), p. 15-1.</ref> It distinguishes physical explosions, such as the failure of a tank heated from outside, from chemical explosions.<ref name="IS-15-2">Iqbal and Salley (2004), p. 15-2.</ref> Chemical explosions include gas and dust explosions as well as condensed-phase explosions of high explosives and propellants.<ref name="IS-15-2" /> When a firecracker or a stick of dynamite explodes, the violent reaction produces a shock or blast wave. This is a thin shell of highly compressed air and hot gases that expands rapidly in all directions.<ref name="IS-15-7">Iqbal and Salley (2004), p. 15-7.</ref> The peak overpressure in the wave is highest near the source and falls rapidly with distance.<ref name="IS-15-7" />

The energy behind an explosion can take several forms. Physical energy may be pressure energy in a gas, strain energy in a metal or electrical energy, as in the burst of a vessel under high gas pressure.<ref name="IS-15-16">Iqbal and Salley (2004), p. 15-16.</ref> Chemical energy comes from a reaction, such as the combustion of a flammable gas.<ref name="IS-15-16" /> An explosion in a vessel tends to be uniform, while an explosion in a long pipe propagates along it.<ref name="IS-15-16" /> TNT equivalence applies the same yardstick to all of these, by reducing each to the energy that drives the blast wave.<ref name="IS-15-10" />

Far from the source the blast wave has a characteristic shape. A shock raises the pressure suddenly to a peak, a rarefaction follows in which the pressure falls below atmospheric, and the pressure then recovers.<ref name="Z-418">Zalosh (2002), p. 3-418.</ref><ref name="Z-419" /> When the recovery takes the form of a second shock, the pressure history looks like a slightly deformed letter N and is called an N wave.<ref name="Z-419" /> The impulse of the wave, its overpressure integrated over time, matters for the dynamic response of structures.<ref name="Z-419" />

Ideal blast wave theory assumes that the energy is released instantaneously at a single point, so that the wave is described by one parameter, the blast energy.<ref name="Z-419" /> Its correlations combine theory with test data from compact condensed-phase explosives.<ref name="Z-419" /> Because the blast effects of TNT are well documented as a function of charge mass and distance, it is convenient to express other explosions as an equivalent TNT charge.<ref name="IS-15-10" /> As a unit of energy, the conversion table of the SFPE Handbook lists the ton (nuclear equivalent of TNT) as 4.20 × 109 J.<ref name="DiN-A9">DiNenno et al. (2002), p. A-9.</ref>

== Calculation method ==
NUREG-1805 sets out the method in three steps, based on the explosion protection chapter by Zalosh in the second edition (1995) of the SFPE Handbook.<ref name="IS-15-9" /><ref name="IS-15-10" /><ref name="IS-15-17">Iqbal and Salley (2004), p. 15-17.</ref> It applies to a flammable gas or vapour that has been released, has mixed with air within its flammable limits and has then been ignited.<ref name="IS-15-9" /><ref name="IS-15-15">Iqbal and Salley (2004), p. 15-15.</ref> The first step gives the explosive energy of a flammable vapour release from its mass, its heat of combustion and the yield:<ref name="IS-15-9" />

<math display="block">E = \alpha \, \Delta H_\mathrm{c} \, m_\mathrm{F}</math>

The yield is the fraction of the available combustion energy that takes part in generating the blast wave. It is typically about 1 % for unconfined releases and up to 100 % for confined ones.<ref name="IS-15-9" /> NUREG-1805 lists net heats of combustion of, for example, 46,360 kJ/kg for propane, 50,030 kJ/kg for methane and 130,800 kJ/kg for hydrogen.<ref name="IS-15-10" /> The second step converts the energy into an equivalent TNT mass:<ref name="IS-15-10" />

<math display="block">W_\mathrm{TNT} = \frac{E}{4500}</math>

Here WTNT is in kilograms and E in kilojoules, so each kilogram of TNT stands for 4,500 kJ of blast energy.<ref name="IS-15-10" /> At full yield, one kilogram of propane is therefore equivalent to about 10 kg of TNT, and one kilogram of hydrogen to about 29 kg.<ref name="IS-15-10" /> The third step divides the distance D from the explosion by the cube root of the TNT mass to give the scaled distance:<ref name="IS-15-11" />

<math display="block">D_\mathrm{sc} = \frac{D}{W_\mathrm{TNT}^{1/3}}</math>

The overpressure is then read from a chart of ideal blast wave overpressure against scaled distance, which NUREG-1805 reproduces from Zalosh in English and metric units.<ref name="IS-15-11" /> The chart includes the reflected shock wave and marks the ranges in which building elements fail and in which eardrum rupture, lung damage and death occur.<ref name="IS-15-11" /> Because the overpressure depends only on the scaled distance, a charge eight times heavier produces the same overpressure at twice the distance.<ref name="IS-15-11" />

The 2002 edition of the SFPE Handbook skips the detour through TNT and scales the distance with the blast energy itself.<ref name="Z-419" /> In its dimensionless distance, R is the actual distance in metres, E the blast energy in joules and P0 the ambient pressure in pascals.<ref name="Z-419" /> The overpressure, divided by the ambient pressure, is then read against this distance:<ref name="Z-419" />

<math display="block">\bar{R} = R \left( \frac{P_0}{E} \right)^{1/3}</math>

Its chart gives both the incident overpressure and the overpressure reflected head-on from a rigid wall.<ref name="Z-419" /> Neither curve includes reflection from the ground, and the usual procedure is to double the blast energy to account for it.<ref name="Z-419" /> For the burst of a pressure vessel whose gas does not ignite, the blast energy is the isentropic expansion energy of the gas, E = (P1 − P0)V/(γ − 1).<ref name="Z-419" />

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>E</math> || explosive or blast energy || kJ (NUREG-1805) or J (SFPE)
|-
| <math>\alpha</math> || yield: fraction of the combustion energy that drives the blast wave || none
|-
| <math>\Delta H_\mathrm{c}</math> || theoretical net heat of combustion of the fuel || kJ/kg
|-
| <math>m_\mathrm{F}</math> || mass of flammable vapour released || kg
|-
| <math>W_\mathrm{TNT}</math> || equivalent mass of TNT || kg
|-
| <math>D</math>, <math>R</math> || distance from the explosion || m
|-
| <math>D_\mathrm{sc}</math> || scaled distance || m/kg1/3
|-
| <math>\bar{R}</math> || dimensionless scaled distance || none
|-
| <math>P_0</math> || ambient pressure || Pa
|-
| <math>P_1</math> || initial pressure in a bursting vessel || Pa
|-
| <math>V</math> || vessel volume || m³
|-
| <math>\gamma</math> || ratio of specific heats of the gas || none
|}

== Blast effects and damage criteria ==
NUREG-1805 lists the possible effects of an explosion: blast damage, thermal effects, missile damage, ground shock, cratering and personal injury.<ref name="IS-15-8">Iqbal and Salley (2004), p. 15-8.</ref> Indirect effects add to these, such as fragments and debris set in motion by the blast, and people thrown against the ground, walls or other objects.<ref name="IS-15-9" /> Much of the data on these effects comes from studies of industrial and military explosives, with a growing amount from investigations of process plant explosions.<ref name="IS-15-9" />

Damage thresholds are expressed as peak overpressure. In a table compiled by Clancey, typical glass failure occurs at 0.15 psig, about 1 kPa, and houses become uninhabitable through partial demolition at 1.0 psig, about 7 kPa.<ref name="IS-15-7" /><ref name="IS-15-8" /> The walls and roofs of houses partly collapse at 2.0 psig, the lower limit of serious structural damage lies at 2.3 psig, and a building is probably destroyed completely at 10.0 psig.<ref name="IS-15-8" /> The extent of damage also depends strongly on nearby reflecting surfaces.<ref name="IS-15-7" />

People withstand relatively high pressures. NUREG-1805 gives 35 kPa as the limit for eardrum rupture and 70 kPa as the limit for lung damage.<ref name="IS-15-12">Iqbal and Salley (2004), p. 15-12.</ref> Mortality reaches 1 % at 180 kPa, 50 % at 260 kPa and 99 % at 350 kPa.<ref name="IS-15-12" /> When blast waves kill, it is usually through falling objects rather than through the pressure itself.<ref name="IS-15-12" /> Building elements fail at far lower pressures: glass windows at 2 to 7 kPa and unrestrained brick walls at 7 to 15 kPa.<ref name="IS-15-13">Iqbal and Salley (2004), p. 15-13.</ref>

For risk studies, Barry gives a generic breakdown of damage levels.<ref name="B-186" /> Overpressures of 2.5 to 5 psig cause heavy damage to buildings and process equipment, and about 1 % deaths from lung damage.<ref name="B-186" /> At 1 to 2.4 psig buildings suffer repairable damage, at 0.5 to 1 psig glass breaks, and at 0.15 to 0.30 psig about 10 % of window panes break.<ref name="B-186" />

== Worked example: a propane forklift ==
The examples in NUREG-1805 show how the steps work in practice. The first considers a forklift powered by liquefied petroleum gas in a nuclear power plant, whose fuel system could release 48 lb, about 21.8 kg, of propane vapour.<ref name="IS-15-18">Iqbal and Salley (2004), p. 15-18.</ref> With a yield of 100 % and the heat of combustion of propane, the first two steps give:<ref name="IS-15-10" /><ref name="IS-15-18" />

<math display="block">E = 1.0 \times 46\,360 \times 21.8 \approx 1.01 \times 10^{6}\ \mathrm{kJ}, \qquad W_\mathrm{TNT} = \frac{1.01 \times 10^{6}}{4500} \approx 225\ \mathrm{kg}</math>

The spreadsheet in NUREG-1805 reports 1,011,491 kJ and 225 kg of TNT.<ref name="IS-15-18" /> A recalculation with 21.77 kg gives 224 kg, so the difference is only rounding, and the higher value is kept because it is the more severe. A smaller case is a leaking acetylene cylinder that held 40 ft³ of gas, about 2.7 lb: at full yield NUREG-1805 finds 59,179 kJ, or 13.2 kg of TNT.<ref name="IS-15-21">Iqbal and Salley (2004), p. 15-21.</ref>

The yield changes the result by two orders of magnitude. With the 1 % typical of an unconfined release, the same propane is equivalent to only about 2.25 kg of TNT.<ref name="IS-15-9" /> At 50 m from the release, the scaled distance is 50/2251/3, about 8.2 m/kg1/3, for full yield, and 50/2.251/3, about 38 m/kg1/3, for 1 % yield.<ref name="IS-15-11" /> Any given overpressure therefore occurs 1001/3, or about 4.6, times further away at full yield than at 1 % yield.<ref name="IS-15-11" /> The choice of yield thus determines the size of every hazard zone derived from the chart.

A second example in NUREG-1805 compares 10 lb of acetylene with 5 lb of hydrogen.<ref name="IS-15-24">Iqbal and Salley (2004), p. 15-24.</ref> The hydrogen has half the mass, but its heat of combustion is almost three times that of acetylene.<ref name="IS-15-10" /> It is therefore equivalent to 66.0 kg of TNT against 48.7 kg for the acetylene, and NUREG-1805 concludes that the hydrogen produces the larger explosive force.<ref name="IS-15-24" />

== Use in quantitative risk assessment ==
In [[quantitative risk assessment]] of chemical process plants, Barry describes a sequence of steps. The analyst defines the objectives, identifies the hazards, assesses the loss event scenarios, assesses the consequences and assesses the probabilities.<ref name="B-177">Barry (2002), p. 5-177.</ref> Consequence assessment estimates the undesirable result of an accidental fire or explosion for a target, in terms of health and safety, property loss or business interruption.<ref name="B-182">Barry (2002), p. 5-182.</ref>

The assessment weighs the vulnerability of the target against the intensity, distance and time of the hazardous event.<ref name="B-182" /> Barry distinguishes two levels of vulnerability assessment.<ref name="B-186" /> Generic tables of damage criteria, such as overpressure thresholds, give a good first-order review but are weak in terms of time relationships.<ref name="B-186" /> Detailed heat transfer or structural impact models form a second-order assessment, used where time or the specific design, layout or emergency response warrant it.<ref name="B-186" />

Among the outcomes of a flammable release, Barry lists the unconfined vapour cloud explosion. A large release, usually of more than 1 ton, forms a cloud that explodes on delayed ignition and exposes the surroundings to overpressure.<ref name="B-184">Barry (2002), p. 5-184.</ref> The exposures from such explosions can be correlated with the energy of the explosion to relate distances to levels of damage and of exposure of people.<ref name="B-186" /> Plotted as effect zones around the point of release, the results show a fatality zone, an injury zone and a zone of partial building damage between 2 and 0.5 psig.<ref name="B-187">Barry (2002), p. 5-187.</ref> TNT equivalence is one way to make such a correlation, because it turns the energy of a release into the distances at which chosen overpressures occur.<ref name="IS-15-10" /><ref name="IS-15-11" />

== Vapour clouds and limitations ==
The weakest point of TNT equivalence is the [[vapour cloud explosion]]. Such explosions occur when a large cloud of flammable gas or vapour is ignited in a highly obstructed area, such as a chemical plant with closely spaced process equipment and storage vessels.<ref name="Z-420" /> The strength of the blast depends on the flame speed that develops and on the degree of confinement in and around the cloud.<ref name="Z-420" /> Early assessments used ideal blast wave correlations with a rough guess at the energy yield, and they were not very successful.<ref name="Z-420" />

Zalosh gives two reasons. Most of the interest lies in the near field, close to the cloud, and even in the far field the blast from a vapour cloud decays much less rapidly than an ideal blast wave.<ref name="Z-420" /> NUREG-1805 states a related limitation: the ideal point-source correlations cannot be valid within or near the flammable vapour cloud.<ref name="IS-15-15">Iqbal and Salley (2004), p. 15-15.</ref> Current methods instead estimate the flame speed empirically and calculate a non-ideal blast wave, or they model the flame propagation with computational fluid dynamics.<ref name="Z-420" />

Further assumptions limit the method. The fuel must be mixed with air between its flammable limits, and real mixtures may be non-uniform or stratified.<ref name="IS-15-15" /> The yield, which spans two orders of magnitude, has to be chosen by judgement.<ref name="IS-15-9" /> NUREG-1805 adds that the pressures produced are usually difficult to predict.<ref name="IS-15-12" /> A [[detonation]] of the released gas, inside or outside a building, would give even higher pressures, although detonations are very rare.<ref name="IS-15-12" />

Damage criteria also differ between sources. Barry associates about 1 % deaths from lung damage with 2.5 to 5 psig, about 17 to 34 kPa.<ref name="B-186" /> NUREG-1805, by contrast, gives 70 kPa as the limit for lung damage and 180 kPa for 1 % mortality.<ref name="IS-15-12" /> The energy assigned to TNT is not uniform either: the method uses 4,500 kJ per kilogram, while the SFPE conversion table lists 4.20 × 109 J for the ton (nuclear equivalent of TNT).<ref name="IS-15-10" /><ref name="DiN-A9" /> A TNT equivalent and the damage it implies should therefore be read with the yield and the criteria that were used to obtain it.

== See also ==
* [[Deflagration]]
* [[Deflagration-to-detonation transition]]
* [[Explosion venting]]
* [[BLEVE]]
* [[Hydrogen safety]]

== Notes ==
<references />

== References ==
* Barry, T. F. (2002). Quantitative risk assessment in chemical process industries. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 5-176–5-213). National Fire Protection Association; Society of Fire Protection Engineers.
* DiNenno, P. J., Drysdale, D., Beyler, C. L., Walton, W. D., Custer, R. L. P., Hall, J. R., Jr., & Watts, J. M., Jr. (Eds.). (2002). ''SFPE handbook of fire protection engineering'' (3rd ed.). National Fire Protection Association; Society of Fire Protection Engineers.
* Iqbal, N., & Salley, M. H. (2004). ''Fire Dynamics Tools (FDTs): Quantitative fire hazard analysis methods for the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program'' (NUREG-1805). U.S. Nuclear Regulatory Commission, Office of Nuclear Reactor Regulation.
* Zalosh, R. (2002). Explosion protection. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 3-402–3-421). National Fire Protection Association; Society of Fire Protection Engineers.

[[Category:Explosions & Industrial Fires]]