Physics:TNT equivalent

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

TNT equivalent is a convention for expressing energy, typically used to describe the energy released in an explosion. A ton of TNT equivalent is a unit of energy defined by convention to be 4.184 gigajoules (gigacalorie).[1] It is the approximate energy released in the detonation of a metric ton (megagram) of trinitrotoluene (TNT). In other words, for each gram of TNT exploded, 4.184 kilojoules (or 4184 joules) of energy are released. This convention intends to compare the destructiveness of an event with that of conventional explosive materials, of which TNT is a typical example, although other conventional explosives such as dynamite contain more energy. A related concept is the physical quantity TNT-equivalent mass (or mass of TNT equivalent),[2][3][4][5] expressed in the ordinary units of mass and its multiples: kilogram (kg), megagram (Mg) or tonne (t), etc.

The unit is routinely used to describe the yield of nuclear weapons. The 1945 atomic bombings of Hiroshima and Nagasaki used the Little Boy and Fat Man bombs, with yields of 15 and 20 kilotons respectively.[6] During the nuclear arms race, thermonuclear weapons were developed with yields in the megaton range. The largest nuclear weapon ever tested was the Tsar Bomba at 50 megatons.[7] Only a handful of nuclear tests exceeded 10 megatons. Modern strategic nuclear weapons have yields of at least 100 kilotons.[8]

Kiloton and megaton

The "kiloton (of TNT equivalent)" is a unit of energy equal to 4.184 terajoules (4.184×1012 J).[9] 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).[10]

The kiloton and megaton of TNT equivalent have traditionally been used to describe the energy output, and hence the destructive power, of a nuclear weapon. The TNT equivalent appears in various nuclear weapon control treaties, and has been used to characterize the energy released in asteroid impacts.[11]

Historical derivation of the value

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.[12][13][14][15]

Where for example the comparison is by energy yield, an explosive's energy is normally expressed for chemical purposes as the thermodynamic 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.[16]

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.[17]

Such differences can be substantial. For safety purposes, a range as wide as 2,673–6,702 J has been stated for a gram of TNT upon explosion.[18] Thus one can state that a nuclear bomb has a yield of 15 kt (6.3×1013 J), but the explosion of an actual 15,000-ton pile of TNT may yield (for example) 8×1013 J due to additional carbon/hydrocarbon oxidation not present with small open-air charges.[17]

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,[19] which is exactly one kilocalorie.

Grams TNT Symbol Tons TNT Symbol Energy Corresponding mass loss[lower-alpha 1]
milligram of TNT mg nanoton of TNT nt 4.184 J (1.162 mWh) 46.55 fg
gram of TNT g microton of TNT μt 4.184 kJ (4,184 J; 1.162 Wh) 46.55 pg
kilogram of TNT kg milliton of TNT mt 4.184 MJ (4,184,000 J; 1.162 kWh) 46.55 ng
megagram of TNT Mg ton of TNT t 4.184 GJ (4.184×109 J; 1.162 MWh) 46.55 μg
gigagram of TNT Gg kiloton of TNT kt 4.184 TJ (4.184×1012 J; 1.162 GWh) 46.55 mg
teragram of TNT Tg megaton of TNT Mt 4.184 PJ (4.184×1015 J; 1.162 TWh) 46.55 g
petagram of TNT Pg gigaton of TNT Gt 4.184 EJ (4.184×1018 J);1.162 PWh 46.55 kg

Conversion to other units

1 ton of TNT equivalent is approximately:

Examples

Relative effectiveness factor

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 on octanitrocubane'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. Using PETN, engineers would need 1.0/1.66 (or 0.60) kg to obtain the same effects as 1 kg of TNT. With ANFO or ammonium 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 where one can produce double the shockwave output (this depends on the distance of measuring instruments), the difference in direct metal cutting ability may be quadruple for one type of metal and septuple 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.

Explosive, grade Density
(g/ml)
Detonation
vel. (m/s)
Relative
effectiveness
Ammonium nitrate (AN + <0.5% H2O) 0.88 2,700[73] 0.32[74][75]
Mercury(II) fulminate 4.42 4,250 0.51[76]
Black powder (75% KNO3 + 19% C + 6% S, ancient low explosive) 1.65 400 0.55[77]
Hexamine dinitrate (HDN) 1.30 5,070 0.60
Dinitrobenzene (DNB) 1.50 6,025 0.60
HMTD (hexamine peroxide) 0.88 4,520 0.74
ANFO (94% AN + 6% fuel oil) 0.92 4,200 0.74
Urea nitrate 1.67 4,700 0.77
TATP (acetone peroxide) 1.18 5,300 0.80
Tovex Extra (AN water gel) commercial product 1.33 5,690 0.80
Hydromite 600 (AN water emulsion) commercial product 1.24 5,550 0.80
ANNMAL (66% AN + 25% NM + 5% Al + 3% C + 1% TETA) 1.16 5,360 0.87
Amatol (50% TNT + 50% AN) 1.50 6,290 0.91
Nitroguanidine 1.76 6,750
  • 1.04, ballistic mortar test[78]
  • 1.01, Trauzl test[78]
  • 0.95, Plate dent test
Trinitrotoluene (TNT) 1.60 6,900 1.00
Hexanitrostilbene (HNS) 1.70 7,080 1.05
Nitrourea 1.45 6,860 1.05
Tritonal (80% TNT + 20% aluminium)[lower-alpha 6] 1.70 6,650 1.05
Nickel hydrazine nitrate (NHN) 1.70 7,000 1.05
Amatol (80% TNT + 20% AN) 1.55 6,570 1.10
Nitrocellulose (13.5% N, NC; AKA guncotton) 1.40 6,400 1.10
Nitromethane (NM) 1.13 6,360 1.10
PBXW-126 (22% NTO, 20% RDX, 20% AP, 26% Al, 12% PU's system)[lower-alpha 6] 1.80 6,450 1.10
Diethylene glycol dinitrate (DEGDN) 1.38 6,610 1.17
PBXIH-135 EB (42% HMX, 33% Al, 25% PCP-TMETN's system)[lower-alpha 6] 1.81 7,060 1.17
PBXN-109 (64% RDX, 20% Al, 16% HTPB's system)[lower-alpha 6] 1.68 7,450 1.17
Triaminotrinitrobenzene (TATB) 1.80 7,550 1.17
Picric acid (TNP) 1.71 7,350 1.17
Trinitrobenzene (TNB) 1.60 7,300 1.20
Tetrytol (70% tetryl + 30% TNT) 1.60 7,370 1.20
Dynamite, Nobel's (75% NG + 23% diatomite) 1.48 7,200 1.25
Tetryl 1.71 7,770 1.25
Torpex (aka HBX, 41% RDX + 40% TNT + 18% Al + 1% wax)[lower-alpha 6] 1.80 7,440 1.30
Composition B (63% RDX + 36% TNT + 1% wax) 1.72 7,840 1.33
Composition C-3 (78% RDX) 1.60 7,630 1.33
Composition C-4 (91% RDX) 1.59 8,040 1.34
Pentolite (56% PETN + 44% TNT) 1.66 7,520 1.33
Semtex 1A (76% PETN + 6% RDX) 1.55 7,670 1.35
Hexal (76% RDX + 20% Al + 4% wax)[lower-alpha 6] 1.79 7,640 1.35
RISAL P (50% IPN + 28% RDX + 15% Al + 4% Mg + 1% Zr + 2% NC)[lower-alpha 6] 1.39 5,980 1.40
Hydrazine nitrate 1.59 8,500 1.42
Mixture: 24% nitrobenzene + 76% TNM 1.48 8,060 1.50
Mixture: 30% nitrobenzene + 70% nitrogen tetroxide 1.39 8,290 1.50
Nitroglycerin (NG) 1.59 7,700 1.54
Methyl nitrate (MN) 1.21 7,900 1.54
Octol (80% HMX + 19% TNT + 1% DNT) 1.83 8,690 1.54
Nitrotriazolone (NTO) 1.87 8,120 1.60
DADNE (1,1-diamino-2,2-dinitroethene, FOX-7) 1.77 8,330 1.60
Gelignite (92% NG + 7% nitrocellulose) 1.60 7,970 1.60
Plastics Gel (in toothpaste tube: 45% PETN + 45% NG + 5% DEGDN + 4% NC) 1.51 7,940 1.60
Composition A-5 (98% RDX + 2% stearic acid) 1.65 8,470 1.60
Erythritol tetranitrate (ETN) 1.72 8,206 1.60
Hexogen (RDX) 1.78 8,600 1.60
PBXW-11 (96% HMX, 1% HyTemp, 3% DOA) 1.81 8,720 1.60
Penthrite (PETN) 1.77 8,400 1.66
Ethylene glycol dinitrate (EGDN) 1.49 8,300 1.66
MEDINA (Methylene dinitroamine)[79][80] 1.65 8,700 1.70
Trinitroazetidine (TNAZ) 1.86 9,597 1.70
Octogen (HMX grade B) 1.95 9,100 1.70
Hexanitrobenzene (HNB) 1.97 9,340 1.80
Hexanitrohexaazaisowurtzitane (HNIW; AKA CL-20) 1.97 9,500 1.90
AFX-757 (25% RDX, 30% ammonium perchlorate, 33% aluminium)[81][82] 1.84 6,080 1.90
DDF (4,4'-Dinitro-3,3'-diazenofuroxan) 1.98 10,000 1.95
Heptanitrocubane (HNC)[lower-alpha 7] 1.92 9,200 N/A
Octanitrocubane (ONC) 1.95 10,600 2.38
Octaazacubane (OAC)[lower-alpha 7] 2.69 15,000 >5.00

Nuclear examples

Nuclear weapons and the most powerful non-nuclear weapon examples
Weapon Total yield
(kilotons of TNT)
Mass
(kg)
Relative
effectiveness
GBU-57 bomb (Massive Ordnance Penetrator, MOP) 0.0035 13,600 0.26
Grand Slam (Earthquake bomb, M110) 0.0065 9,900 0.66
Bomb used in Oklahoma City (ANFO based on racing fuel) 0.0018 2,300 0.78
BLU-82 (Daisy Cutter) 0.0075 6,800 1.10
MOAB (non-nuclear bomb, GBU-43) 0.011 9,800 1.13
FOAB (advanced thermobaric bomb, ATBIP) 0.044 7,100 6.20
W54, Mk-54 (Davy Crockett) 0.022 23 1,000
Little Boy (dropped on Hiroshima) A-bomb 15 4,400 4,000
Fat Man (dropped on Nagasaki) A-bomb 20 4,600 4,500
W54, B54 (SADM) 1.0 23 43,500
Classic (one-stage) fission A-bomb 22 420 50,000
Hypothetical suitcase nuke 2.5 31 80,000
Typical (two-stage) nuclear bomb 500–1,000 650–1,120 900,000
W88 modern thermonuclear warhead (MIRV) 470 355 1,300,000
Tsar nuclear bomb (three-stage) 50,000–56,000 26,500 2,100,000
B53 nuclear bomb (two-stage) 9,000 4,050 2,200,000
Operation Dominic Housatonic (two-stage) 9,960 3,239 3,042,400
W56 thermonuclear warhead 1,200 272–308 4,960,000
B41 nuclear bomb (three-stage) 25,000 4,850 5,100,000

See also

Footnotes

  1. Mass–energy equivalence.
  2. The solar constant of the sun is 1370 watts per square meter and Earth has a cross-sectional surface area of 2.6×1014 square meters.
  3. 3.0 3.1 The solar constant of the sun is 1370 watts per square meter and Earth has a cross-sectional surface area of 2.6×1014 square meters.
  4. 1 hour is equivalent to 3600 seconds.
  5. 1 day is equivalent to 86400 seconds.
  6. 6.0 6.1 6.2 6.3 6.4 6.5 6.6 TBX (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. 7.0 7.1 Predicted values

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