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TNT equivalent

From Wikipedia, the free encyclopedia
Class of units of measurement for explosive energy
"Kiloton" redirects here. For the similarly named weight measurements, seeTonne.

TNT equivalent
The explosion from a 14-kiloton nuclear test at theNevada Test Site, in 1951
General information
Unit systemNon-standard
Unit ofEnergy
Symbolt, ton of TNT
Conversions
1 tin ...... is equal to ...
   SI base units   ≈ 4.184 gigajoules
   CGS   109 calories

TNT equivalent is a convention for expressingenergy, typically used to describe the energy released in an explosion. Aton of TNT equivalent is aunit of energy defined by convention to be4.184 gigajoules (1 gigacalorie).[1] It is the approximate energy released in the detonation of ametric ton (1,000 kilograms) oftrinitrotoluene (TNT). In other words, for each gram of TNT exploded,4.184 kilojoules (or 4184joules) of energy are released.This convention intends to compare the destructiveness of an event with that of conventionalexplosive materials, of which TNT is a typical example, although other conventional explosives such asdynamite contain more energy.A related concept is thephysical quantityTNT-equivalent mass (ormass of TNT equivalent),[2][3][4][5] expressed in the ordinaryunits of mass and its multiples:kilogram (kg),megagram (Mg) or tonne (t), etc.

Kiloton and megaton

[edit]

The "kiloton (of TNT equivalent)" is a unit of energy equal to 4.184terajoules (4.184×1012 J).[6] A kiloton of TNT can be visualized as a cube of TNT 8.46 metres (27.8 ft) on a side.

The "megaton (of TNT equivalent)" is a unit of energy equal to 4.184 petajoules (4.184×1015 J).[7]

The kiloton and megaton of TNT equivalent have traditionally been used to describe the energy output, and hence the destructive power, of anuclear weapon. The TNT equivalent appears in variousnuclear weapon control treaties, and has been used to characterize the energy released inasteroid impacts.[8]

Historical derivation of the value

[edit]

Alternative values for TNT equivalency can be calculated according to which property is being compared and when in the two detonation processes the values are measured.[9][10][11][12]

Where for example the comparison is by energy yield, an explosive's energy is normally expressed for chemical purposes as thethermodynamic work produced by its detonation. For TNT this has been accurately measured as 4,686 J/g from a large sample of air blast experiments, and theoretically calculated to be 4,853 J/g.[13]

However, even on this basis, comparing the actual energy yields of a large nuclear device and an explosion of TNT can be slightly inaccurate. Small TNT explosions, especially in the open, do not tend to burn the carbon-particle and hydrocarbon products of the explosion. Gas-expansion and pressure-change effects tend to "freeze" the burn rapidly. A large, open explosion of TNT may maintain fireball temperatures high enough that some of those products do burn up with atmospheric oxygen.[14]

Such differences can be substantial. For safety purposes, a range as wide as2,673–6,702 J has been stated for a gram ofTNT upon explosion.[15] Thus one can state that a nuclear bomb has a yield of 15 kt (6.3×1013 J), but the explosion of an actual15,000-ton pile of TNT may yield (for example)8×1013 J due to additional carbon/hydrocarbon oxidation not present with small open-air charges.[14]

These complications have been sidestepped by convention. The energy released by one gram of TNT was arbitrarily defined as a matter of convention to be 4,184 J,[16] which is exactly onekilocalorie.

Grams TNTSymbolTons TNTSymbolEnergy [joules]Energy [Wh]Corresponding mass loss[a]
milligram of TNTmgnanoton of TNTnt4.184 J or 4.184 joules1.162 mWh46.55 fg
gram of TNTgmicroton of TNTμt4.184×103 J or 4.184 kilojoules1.162 Wh46.55 pg
kilogram of TNTkgmilliton of TNTmt4.184×106 J or 4.184 megajoules1.162 kWh46.55 ng
megagram of TNTMgton of TNTt4.184×109 J or 4.184 gigajoules1.162 MWh46.55 μg
gigagram of TNTGgkiloton of TNTkt4.184×1012 J or 4.184 terajoules1.162 GWh46.55 mg
teragram of TNTTgmegaton of TNTMt4.184×1015 J or 4.184 petajoules1.162 TWh46.55 g
petagram of TNTPggigaton of TNTGt4.184×1018 J or 4.184 exajoules1.162 PWh46.55 kg

Conversion to other units

[edit]

1 ton of TNT equivalent is approximately:

Examples

[edit]
Further information:Orders of magnitude (energy)
EnergyDescription
Megatons of TNTWatt-hours [Wh]
1×10−121.162 Wh≈ 1 foodkilocalorie (kilocalorie, kcal), which is the approximate amount of energy needed to raise the temperature of onekilogram of water by one degreeCelsius at a pressure of oneatmosphere.
1×10−91.162 kWhUnder controlled conditions one kilogram of TNT can destroy (or even obliterate) a small vehicle.
4.8×10−95.6 kWhThe energy to burn 1 kilogram of wood.[23]
1×10−811.62 kWhThe approximate radiant heat energy released during 3-phase, 600 V, 100 kAarcing fault in a 0.5 m × 0.5 m × 0.5 m (20 in × 20 in × 20 in) compartment within a 1-second period.[further explanation needed][citation needed]
1.2×10−813.94 kWhAmount of TNT used (12 kg) inCoptic church explosion inCairo,Egypt on December 11, 2016 that left 29 dead and 47 injured[24]
1.9×10−62.90 MWhThe television showMythBusters used 2.5 tons ofANFO to make "homemade" diamonds. (Episode 116.)
2.4×10−7–2.4×10−6280–2,800 kWhThe energy output released by an averagelightning discharge.[25]
(1–44)×10−61.16–51.14 MWhConventional bombs yield from less than one ton toFOAB's 44 tons. The yield of aTomahawk cruise missile is equivalent to 500 kg of TNT.[26]
4.54×10−4581 MWhA real 0.454-kiloton-of-TNT (1.90 TJ) charge atOperation Sailor Hat. If the charge were a full sphere, it would be 1 kiloton of TNT (4.2 TJ).
454 tons ofTNT (5 by 10 m (17 by 34 ft)) awaitingdetonation atOperation Sailor Hat.
1.8×10−32.088 GWhEstimated yield of theBeirut explosion of 2,750 tons of ammonium nitrate[27] that killed initially 137 at and near a Lebanese port at 6 p.m. local time Tuesday August 4, 2020.[28] An independent study by experts from the Blast and Impact Research Group at theUniversity of Sheffield predicts the best estimate of the yield of Beirut explosion to be 0.5 kilotons of TNT and the reasonable bound estimate as 1.12 kilotons of TNT.[29]
(1–2)×10−31.16–2.32 GWhEstimated yield of theOppau explosion that killed more than 500 at a German fertilizer factory in 1921.
2.3×10−32.67 GWhAmount ofsolar energy falling on 4,000 m2 (1 acre) of land in a year is 9.5 TJ (2,650 MWh) (an average over the Earth's surface).[30]
2.9×10−33.4 GWhTheHalifax Explosion in 1917 was the accidental detonation of 200 tons of TNT and 2,300 tons ofPicric acid[31]
3.2×10−33.6 GWhTheOperation Big Bang on April 18, 1947, blasted the bunkers onHeligoland. It accumulated 6700 metric tons of surplus World War II ammunition placed in various locations around the island and set off. The energy released was1.3×1013 J, or about 3.2 kilotons of TNT equivalent.[32]
4×10−39.3 GWhMinor Scale, a 1985 United States conventional explosion, using 4,744 tons ofANFO explosive to provide a scaled equivalent airblast of an eight kiloton (33.44 TJ) nuclear device,[33] is believed to be the largest planned detonation of conventional explosives in history.
(1.5–2)×10−217.4–23.2 GWhTheLittle Boyatomic bomb dropped onHiroshima on August 6, 1945, exploded with an energy of about 15 kilotons of TNT (63 TJ) killing between 90,000 and 166,000 people,[34] and theFat Manatomic bomb dropped onNagasaki on August 9, 1945, exploded with an energy of about 20 kilotons of TNT (84 TJ) killing over 60,000.[34] The modern nuclear weapons in the United States arsenal range inyield from 0.3 kt (1.3 TJ) to 1.2 Mt (5.0 PJ) equivalent, for theB83 strategic bomb.
>2.4×10−1280 GWhThe typical energy yield of severethunderstorms.[35]
1.5×10−5 –6×10−120 MWh – 700 GWhThe estimatedkinetic energy oftornados.[36]
11.16 TWhThe energy contained in one megaton of TNT (4.2 PJ) is enough to power the average American household for 103,000 years.[37] The 30 Mt (130 PJ) estimated upper limit blast power of theTunguska event could power the same average home for more than 3,100,000 years. The energy of that blast could power the entire United States for 3.27 days.[38]
8.610 TWhThe energy output that would be released by a typicaltropical cyclone in one minute, primarily from water condensation. Winds constitute 0.25% of that energy.[39]
1618.6 TWhThe approximate radiated surface energy released in a magnitude 8earthquake.[40]
21.525 TWhThe complete conversion of 1 kg of matter into pure energy would yieldthe theoretical maximum (E =mc2) of 89.8 petajoules, which is equivalent to 21.5 megatons of TNT. No such method of total conversion as combining 500 grams of matter with 500 grams of antimatter has yet been achieved. In the event of proton–antiprotonannihilation, approximately 50% of the released energy will escape in the form ofneutrinos, which are almost undetectable.[41]Electron–positron annihilation events emit their energy entirely asgamma rays.
2428 TWhApproximate total yield of the1980 eruption of Mount St. Helens.[42]
26.330.6 TWhEnergy released by the2004 Indian Ocean earthquake.[43]
An animation of the 2004 Indian Ocean tsunami
4553 TWhThe energy released in the2011 Tōhoku earthquake and tsunami was over 200,000 times the surface energy and was calculated by the USGS at1.9×1017 joules,[44][45] slightly less than the 2004 Indian Ocean quake. It was estimated at a moment magnitude of 9.0–9.1.
The damage caused by the 2011 Tōhoku tsunami
50–5658 TWhTheSoviet Union developed a prototype thermonuclear device, nicknamed theTsar Bomba, which was tested at 50–56 Mt (210–230 PJ), but had a maximum theoretical design yield of 100 Mt (420 PJ).[46] The effective destructive potential of such a weapon varies greatly, depending on such conditions as the altitude at which it is detonated, the characteristics of the target, the terrain, and the physical landscape upon which it is detonated.
6170.9 TWhThe energy released by the2022 Hunga Tonga–Hunga Haʻapai volcanic eruption, in the southern Pacific Ocean, is estimated to have been equivalent to 61 Megatons of TNT.[47]
8497.04 TWhThe solar irradiance on Earth every second.[b]
200230 TWhThe total energy released by the1883 eruption of Krakatoa in the Dutch East Indies (present-day Indonesia).[48]
540630 TWhThetotal energy produced worldwide by all nuclear testing and combat usage combined, from the 1940s to the present, is about 540 megatons.
1,4601.69 PWhThe total global nuclear arsenal is about 15,000 nuclear warheads[49][50][51] with a destructive capacity of around 1460 megatons[52][53][54][55] or 1.46 gigatons (1,460 million tons) of TNT. This is the equivalent of6.11×1018 joules of energy
2,680[dubious –discuss]3 PWhThe energy yield of the1960 Valdivia earthquake, was estimated at a moment magnitude of 9.4–9.6. This is the most powerful earthquake recorded in history.[56][57]
The aftermath of the 1960 Valdivia earthquake.
2,8703.34 PWhThe energy released by a hurricane per day during condensation.[58]
33,00038.53 PWhThe total energy released by the1815 eruption of Mount Tambora in the island of Sumbawa in Indonesia. Yielded the equivalent of 2.2 millionLittle Boys (the first atomic bomb to drop onJapan) or one-quarter of the entire world's annual energy consumption.[59] This eruption was 4-10 times more destructive than the1883 Krakatoa eruption.[60]
240,000280 PWhThe approximate total yield of the super-eruption of theLa Garita Caldera is 10,000 times more powerful than the1980 Mount St. Helens eruption.[61] It was the second most energetic event to have occurred on Earth since theCretaceous–Paleogene extinction event 66 million years ago.
A photo of the La Garita Caldera
301,000350 PWhThe total solar irradiance energy received by Earth in the upper atmosphere per hour.[c][d]
875,0001.02 EWhApproximate yield of the last eruption of theYellowstone supervolcano.[62]
Image of the Yellowstone supervolcano.
3.61×1064.2 EWhThe solar irradiance of the Sun every 12 hours.[c][e]
6×1067 EWhThe estimated energy at impact when the largest fragment ofComet Shoemaker–Levy 9 struckJupiter is equivalent to 6 million megatons (6 trillion tons) of TNT.[63]
The impact site of the Comet Shoemaker-Levy 9
7.2×107116 EWhEstimates in 2010 show that the kinetic energy of theChicxulub impact event yielded 72 teratons of TNT equivalent (1 teraton of TNT equals 106 megatons of TNT) which caused theK-Pg extinction event, wiping out 75% of all species on Earth.[64][65] This is far more destructive than any natural disaster recorded in history. Such an event would have caused globalvolcanism, earthquakes,megatsunamis, and globalclimate change.[64][66][67][68][69]
The animation of the Chicxulub impact.
>2.4×1010>28 ZWhThe impact energy of Archean asteroids.[70]
9.1×1010106 ZWhThe total energy output of the Sun per second.[71]
2.4×1011280 ZWhThe kinetic energy of theCaloris Planitia impactor.[72]
The photo of the Caloris Planitia on Mercury. Taken by theMESSENGER orbiter.
5.972×10156.94 RWhThe explosive energy of a quantity of TNT of themass of Earth.[73]
7.89×10159.17 RWhTotal solar output in all directions per day.[74]
1.98×10212.3×1033 WhThe explosive energy of a quantity of TNT of themass of the Sun.[75]
(2.4–4.8)×1028(2.8–5.6)×1040 WhAtype Ia supernova explosion gives off 1–2×1044 joules of energy, which is about 2.4–4.8 hundred billion yottatons (24–48 octillion (2.4–4.8×1028) megatons) of TNT, equivalent to the explosive force of a quantity of TNT over a trillion (1012) times the mass of the planet Earth. This is the astrophysicalstandard candle used to determine galactic distances.[76]
(2.4–4.8)×1030(2.8–5.6)×1042 WhThe largest type of supernova observed,gamma-ray bursts (GRBs) release more than 1046 joules of energy.[77]
1.3×10321.5×1044 WhA merger of two black holes, resulting in thefirst observation of gravitational waves, released5.3×1047 joules[78]
9.6×10531.12×1066 WhEstimated mass-energy of the observable universe.[79]

Relative effectiveness factor

[edit]

The relative effectiveness factor (RE factor) relates an explosive's demolition power to that of TNT, in units of the TNT equivalent/kg (TNTe/kg). The RE factor is the relative mass of TNT to which an explosive is equivalent: The greater the RE, the more powerful the explosive.

This enables engineers to determine the proper masses of different explosives when applying blasting formulas developed specifically for TNT. For example, if a timber-cutting formula calls for a charge of 1 kg of TNT, then based onoctanitrocubane's RE factor of 2.38, it would take only 1.0/2.38 (or 0.42) kg of it to do the same job. UsingPETN, engineers would need 1.0/1.66 (or 0.60) kg to obtain the same effects as 1 kg of TNT. WithANFO orammonium nitrate, they would require 1.0/0.74 (or 1.35) kg or 1.0/0.32 (or 3.125) kg, respectively.

Calculating a single RE factor for an explosive is, however, impossible. It depends on the specific case or use. Given a pair of explosives, one can produce 2× the shockwave output (this depends on the distance of measuring instruments) but the difference in direct metal cutting ability may be 4× higher for one type of metal and 7× higher for another type of metal. The relative differences between two explosives with shaped charges will be even greater. The table below should be taken as an example and not as a precise source of data.

Some relative effectiveness factor examples[citation needed]
Explosive, gradeDensity
(g/ml)		Detonation
vel. (m/s)		Relative
effectiveness
Ammonium nitrate (AN + <0.5% H2O)0.882,700[80]0.32[81][82]
Mercury(II) fulminate4.424,2500.51[83]
Black powder (75% KNO3 + 19% C + 6% S, ancientlow explosive)1.654000.55[84]
Hexamine dinitrate (HDN)1.305,0700.60
Dinitrobenzene (DNB)1.506,0250.60
HMTD (hexamine peroxide)0.884,5200.74
ANFO (94% AN + 6% fuel oil)0.924,2000.74
Urea nitrate1.674,7000.77
TATP (acetone peroxide)1.185,3000.80
Tovex Extra (AN water gel) commercial product1.335,6900.80
Hydromite 600 (AN wateremulsion) commercial product1.245,5500.80
ANNMAL (66% AN + 25% NM + 5% Al + 3% C + 1%TETA)1.165,3600.87
Amatol (50% TNT + 50% AN)1.506,2900.91
Nitroguanidine1.326,7500.95
Trinitrotoluene (TNT)1.606,9001.00
Hexanitrostilbene (HNS)1.707,0801.05
Nitrourea1.456,8601.05
Tritonal (80% TNT + 20% aluminium)[f]1.706,6501.05
Nickel hydrazine nitrate (NHN)1.707,0001.05
Amatol (80% TNT + 20% AN)1.556,5701.10
Nitrocellulose (13.5% N, NC; AKA guncotton)1.406,4001.10
Nitromethane (NM)1.136,3601.10
PBXW-126 (22% NTO, 20%RDX, 20%AP, 26%Al, 12%PU's system)[f]1.806,4501.10
Diethylene glycol dinitrate (DEGDN)1.386,6101.17
PBXIH-135 EB (42%HMX, 33%Al, 25%PCP-TMETN's system)[f]1.817,0601.17
PBXN-109 (64%RDX, 20%Al, 16%HTPB's system)[f]1.687,4501.17
Triaminotrinitrobenzene (TATB)1.807,5501.17
Picric acid (TNP)1.717,3501.17
Trinitrobenzene (TNB)1.607,3001.20
Tetrytol (70% tetryl + 30% TNT)1.607,3701.20
Dynamite, Nobel's (75%NG + 23%diatomite)1.487,2001.25
Tetryl1.717,7701.25
Torpex (aka HBX, 41% RDX + 40% TNT + 18%Al + 1%wax)[f]1.807,4401.30
Composition B (63% RDX + 36% TNT + 1% wax)1.727,8401.33
Composition C-3 (78% RDX)1.607,6301.33
Composition C-4 (91% RDX)1.598,0401.34
Pentolite (56%PETN + 44% TNT)1.667,5201.33
Semtex 1A (76% PETN + 6% RDX)1.557,6701.35
Hexal (76%RDX + 20%Al + 4%wax)[f]1.797,6401.35
RISAL P (50% IPN + 28% RDX + 15% Al + 4% Mg + 1% Zr + 2% NC)[f]1.395,9801.40
Hydrazine nitrate1.598,5001.42
Mixture: 24%nitrobenzene + 76%TNM1.488,0601.50
Mixture: 30%nitrobenzene + 70%nitrogen tetroxide1.398,2901.50
Nitroglycerin (NG)1.597,7001.54
Methyl nitrate (MN)1.217,9001.54
Octol (80%HMX + 19%TNT + 1%DNT)1.838,6901.54
Nitrotriazolone (NTO)1.878,1201.60
DADNE (1,1-diamino-2,2-dinitroethene, FOX-7)1.778,3301.60
Gelignite (92%NG + 7%nitrocellulose)1.607,9701.60
Plastics Gel (in toothpaste tube: 45%PETN + 45%NG + 5%DEGDN + 4%NC)1.517,9401.60
Composition A-5 (98%RDX + 2%stearic acid)1.658,4701.60
Erythritol tetranitrate (ETN)1.728,2061.60
Hexogen (RDX)1.788,6001.60
PBXW-11 (96%HMX, 1%HyTemp, 3%DOA)1.818,7201.60
Penthrite (PETN)1.778,4001.66
Ethylene glycol dinitrate (EGDN)1.498,3001.66
MEDINA (Methylene dinitroamine)[85][86]1.658,7001.70
Trinitroazetidine (TNAZ)1.859,5971.70
Octogen (HMX grade B)1.869,1001.70
Hexanitrobenzene (HNB)1.979,3401.80
Hexanitrohexaazaisowurtzitane (HNIW; AKA CL-20)1.979,5001.90
AFX-757 (25% RDX, 30%ammonium perchlorate, 33%aluminium)[87][88]1.846,0801.90
DDF (4,4'-Dinitro-3,3'-diazenofuroxan)1.9810,0001.95
Heptanitrocubane (HNC)[g]1.929,200N/A
Octanitrocubane (ONC)1.9510,6002.38
Octaazacubane (OAC)[g]2.6915,000>5.00

Nuclear examples

[edit]
Nuclear weapons and the most powerful non-nuclear weapon examples
WeaponTotal yield
(kilotons of TNT)		Mass
(kg)		Relative
effectiveness
GBU-57 bomb (Massive Ordnance Penetrator, MOP)0.003513,6000.26
Grand Slam (Earthquake bomb, M110)0.00659,9000.66
Bomb used in Oklahoma City (ANFO based onracing fuel)0.00182,3000.78
BLU-82 (Daisy Cutter)0.00756,8001.10
MOAB (non-nuclear bomb, GBU-43)0.0119,8001.13
FOAB (advancedthermobaric bomb, ATBIP)0.0449,1004.83
W54, Mk-54 (Davy Crockett)0.022231,000
Little Boy (dropped onHiroshima)A-bomb154,4004,000
Fat Man (dropped onNagasaki)A-bomb204,6004,500
W54, B54 (SADM)1.02343,500
Classic (one-stage) fissionA-bomb2242050,000
Hypotheticalsuitcase nuke2.53180,000
Typical (two-stage)nuclear bomb500–1000650–1,120900,000
W88 modern thermonuclear warhead (MIRV)4703551,300,000
Tsar nuclear bomb (three-stage)50,000–56,00026,5002,100,000
B53 nuclear bomb (two-stage)9,0004,0502,200,000
Operation DominicHousatonic (two-stage)9,9603,2393,042,400
W56 thermonuclear warhead1,200272–3084,960,000
B41 nuclear bomb (three-stage)25,0004,8505,100,000

See also

[edit]

Footnotes

[edit]
  1. ^Mass–energy equivalence.
  2. ^The solar constant of the sun is 1370 watts per square meter and Earth has across-sectionalsurface area of2.6×1014 square meters.
  3. ^abThe solar constant of the sun is 1370 watts per square meter and Earth has a cross-sectional surface area of2.6×1014 square meters.
  4. ^1 hour is equivalent to 3600 seconds.
  5. ^1 day is equivalent to 86400 seconds.
  6. ^abcdefgTBX (thermobaric explosives) or EBX (enhanced blast explosives), in a small, confined space, may have over twice the power of destruction. The total power of aluminized mixtures strictly depends on the condition of explosions.
  7. ^abPredicted values

References

[edit]
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