Nuclear weapon yield

The explosive yield of a nuclear weapon is the amount of energy that is discharged when a nuclear weapon is detonated, expressed usually in the equivalent mass of trinitrotoluene (TNT), either in kilotons (thousands of tons of TNT) or megatons (millions of tons of TNT), but sometimes also in terajoules (1 kiloton of TNT = 4.184 TJ). Because the precise amount of energy released by TNT is and was subject to measurement uncertainties, especially at the dawn of the nuclear age, the accepted convention is that one kt of TNT is simply defined to be 10¹² calories equivalent, this being very roughly equal to the energy yield of 1,000 tons of TNT.

Examples of nuclear weapon yields

In order of increasing yield (most yield figures are approximate):

Bomb	Yield		Notes
	kt TNT	TJ
Davy Crockett	0.01–1	0.042–4.184	variable yield tactical nuclear weapon—mass only 23 kg (51 lb), lightest ever deployed by the United States (same warhead as Special Atomic Demolition Munition and GAR-11 Nuclear Falcon missile)
Hiroshima's "Little Boy" gravity bomb	12–15	50–63	gun type uranium-235 fission bomb (the first of the two nuclear weapons that have been used in warfare)
Nagasaki's "Fat Man" gravity bomb	20–22	84–92	implosion type Plutonium-239 fission bomb (the second of the two nuclear weapons used in warfare)
W76 warhead	100	420	Twelve of these may be in a MIRVed Trident II missile; treaty limited to eight
B61 nuclear bomb	various		Mod 7—up to 350 kilotonnes of TNT (1,500 TJ) Mod 10—four yield options 0.3 kilotonnes of TNT (1.3 TJ) 1.5 kilotonnes of TNT (6.3 TJ) 60 kilotonnes of TNT (250 TJ) 170 kilotonnes of TNT (710 TJ) Mod 11—undisclosed yield
W87 warhead	300	1,300	Ten of these were in a MIRVed LG-118A Peacekeeper.
W88 warhead	475	1,990	Twelve of these may be in a Trident II missile (treaty limited to eight)
Ivy King device	500	2,100	second most powerful pure fission bomb, 60 kg uranium, implosion type
Orange Herald	700	2,900	most powerful pure fission bomb, UK
B83 nuclear bomb	variable		up to 1.2 megatonnes of TNT (5.0 PJ); most powerful US weapon in active service
B53 nuclear bomb	9,000	38,000	most powerful US warhead; no longer in active service, but 50 are retained as part of the "Hedge" portion of the Enduring Stockpile; similar to the W-53 warhead that has been used in the Titan II Missile; decommissioned in 1987
Castle Bravo device	15,000	63,000	most powerful US test
EC17/Mk-17, the EC24/Mk-24, and the B41 (Mk-41)	various		most powerful US weapons ever: 25 megatonnes of TNT (100 PJ); the Mk-17 was also the largest by size and mass: about 20 short tons (18,000 kg); the Mk-41 had a mass of 4800 kg; gravity bombs carried by B-36 bomber (retired by 1957)
The entire Operation Castle nuclear test series	48,200	202,000	the highest-yielding test series conducted by the US
Tsar Bomba device	50,000	210,000	USSR, most powerful explosive device ever, mass of 27 short tons (24,000 kg), in its "full" form (i.e. with a depleted uranium tamper instead of one made of lead) it would have been 100 megatonnes of TNT (420 PJ).
All nuclear testing	510,000	2,100,000	total energy expended during all nuclear testing.[1]

Comparative fireball diameters for a selection of nuclear weapons. Note that full blast effects would extend many times beyond the fireball itself.

Logarithmic scatterplot comparing the yield (in kilotons) and weight (in kilograms) of all nuclear weapons developed by the United States.

As a comparison, the blast yield of the GBU-43 Massive Ordnance Air Blast bomb is 0.011 kt, and that of the Oklahoma City bombing, using a truck-based fertilizer bomb, was 0.002 kt. Most artificial non-nuclear explosions are considerably smaller than even what are considered to be very small nuclear weapons.

Yield limits

The yield-to-weight ratio is the amount of weapon yield compared to the mass of the weapon. The theoretical maximum yield-to-weight ratio for fusion weapons is 6 megatons of TNT per metric ton (25 TJ/kg). The practical achievable limit is somewhat lower, and tends to be lower for smaller, lighter weapons, of the sort that are emphasized in today's' arsenals, designed for efficient MIRV use, or delivery by cruise missile systems. The United States once claimed they had the capability of tipping a Titan II ICBM with a 35-megaton-of-TNT (150 PJ) fusion bomb warhead. If this were the case, the yield to weight ratio would have been about 9.5 megatons of TNT per metric ton (40 TJ/kg). For current smaller US weapons, yield is 600 to 2,200 kilotons of TNT per metric ton (2.5–9.2 TJ/kg). By comparison, for the very small tactical devices such as the Davy Crockett it was 0.4 to 40 kilotons of TNT per metric ton (0.002–0.167 TJ/kg).

For historical comparison, for Little Boy the yield was only 4 kilotons of TNT per metric ton (17 GJ/kg), and for the largest Tsar Bomba yield was 2 megatons of TNT per metric ton (8.4 TJ/kg)) (deliberately reduced from the possible maximum which was twice as much). For the Mk-41, a U.S. late-generation large airplane deliverable bomb, yield was 5.2 megatons of TNT per metric ton (22 TJ/kg). Because of MIRV and ballistic considerations mentioned previously, efficiencies this high will not likely be seen in future weapons.

The largest pure-fission bomb ever constructed had a 500-kiloton-of-TNT (2,100 TJ) yield, which is probably in the range of the upper limit on such designs. Fusion boosting could likely raise the efficiency of such a weapon significantly, but eventually all fission-based weapons have an upper yield limit due to the difficulties of dealing with large critical masses. However there is no known upper yield limit for a fusion (e.g, hydrogen) bomb. In principle a fusion bomb could be many thousand megatons. Because the maximum theoretical yield-to-weight ratio is about 6 megatons of TNT per metric ton (25 TJ/kg), and the maximum achievable ratio about 5.2 megatons of TNT per metric ton (22 TJ/kg), there is a practical limit on air delivery of the weapon.

For example, if the full payload of 250 metric tons of the Antonov An-225 could be used, the limit would be 250 t × 5.2 Mt/t, or 1,300 megatons of TNT (5,400 PJ). Likewise the maximum limit of a missile-delivered weapon is determined by the missile payload capacity. The large Russian SS-18 ICBM has a payload capacity of 7,200 kg, so the calculated maximum delivered yield would be 37.4 megatons of TNT (156 PJ). In fact, the SS-18 mod 1 yield for a single warhead is about 24 megatons of TNT (100 PJ).

Again, it is helpful for understanding to emphasize that large single warheads are seldom a part of today's arsenals, since smaller MIRV warheads are far more destructive for a given total yield or payload capacity. This effect, which results from the fact that destructive power of a single warhead scales approximately as the 2/3 power of its yield, more than makes up for the lessened yield/weight efficiency encountered if ballistic missile warheads are scaled-down from the maximal size that could be carried by a single-warhead missile.

Calculating yields and controversy

Yields of nuclear explosions can be very hard to calculate, even using numbers as rough as in the kiloton or megaton range (much less down to the resolution of individual terajoules). Even under very controlled conditions, precise yields can be very hard to determine, and for less controlled conditions the margins of error can be quite large. Yields can be calculated in a number of ways, including calculations based on blast size, blast brightness, seismographic data, and the strength of the shock wave. Enrico Fermi famously made a (very) rough calculation of the yield of the Trinity test by dropping small pieces of paper in the air and measuring at how far they were moved by the shock wave of the explosion.

Picture of the blast used by G.I. Taylor to estimate the yield of the device detonated during the Trinity test

A good approximation of the yield of the Trinity test device was obtained from simple dimensional analysis by the British physicist G. I. Taylor. Taylor noted that the radius R of the blast should initially depend only on the energy E of the explosion, the time t after the detonation, and the density ρ of the air. The only number having dimensions of length that can be constructed from these quantities is:

$R=\left({\frac {{E{t}}^{2}}{\rho }}\right)^{\frac {1}{5}}$

Using the picture of the Trinity test shown here (which had been publicly released by the U.S. government and published in Life magazine), Taylor estimated that at t = 0.025 s the blast radius was 140 metres. Taking ρ to be 1 kg/m³ and solving for E, he obtained that the yield was about 22 kilotons of TNT (90 TJ). This very simple argument agrees within 10% with the official value of the bomb's yield, 20 kilotons of TNT (84 TJ), which at the time that Taylor published his result was considered highly-classified information. (See G. I. Taylor, Proc. Roy. Soc. London A201, pp. 159, 175 (1950).)

Where this data is not available, as in a number of cases, precise yields have been in dispute, especially when they are tied to questions of politics. The weapons used in the atomic bombings of Hiroshima and Nagasaki, for example, were highly individual and very idiosyncratic designs, and gauging their yield retrospectively has been quite difficult. The Hiroshima bomb, "Little Boy", is estimated to have been between 12 and 18 kilotonnes of TNT (50 and 75 TJ) (a 20% margin of error), while the Nagasaki bomb, "Fat Man", is estimated to be between 18 and 23 kilotonnes of TNT (75 and 96 TJ) (a 10% margin of error). Such apparently small changes in values can be important when trying to use the data from these bombings as reflective of how other bombs would behave in combat, and also result in differing assessments of how many "Hiroshima bombs" other weapons are equivalent to (for example, the Ivy Mike hydrogen bomb was equivalent to either 867 or 578 Hiroshima weapons — a rhetorically quite substantial difference — depending on whether one uses the high or low figure for the calculation). Other disputed yields have included the massive Tsar Bomba, whose yield was claimed between being "only" 50 megatonnes of TNT (210 PJ) or at a maximum of 57 megatonnes of TNT (240 PJ) by differing political figures, either as a way for hyping the power of the bomb or as an attempt to undercut it.

See also

• Effects of nuclear explosions — goes into detail about different effects at different yields

External links

• "What was the yield of the Hiroshima bomb?" (excerpt from official report)
• "General Principles of Nuclear Explosions", Chapter 1 in Samuel Glasstone and Phillip Dolan, eds., The Effects of Nuclear Weapons, 3rd edn. (Washington D.C.: U.S. Department of Defense/U.S. Energy Research and Development Administration, 1977); provides information about the relationship of nuclear yields to other effects (radiation, damage, etc.).
• "THE MAY 1998 POKHRAN TESTS: Scientific Aspects", discusses different methods used to determine the yields of the Indian 1998 tests.
• Discusses some of the controversy over the Indian test yields
• "What are the real yields of India's nuclear tests?" from Carey Sublette's NuclearWeaponArchive.org
• High-Yield Nuclear Detonation Effects Simulator