Nuclear weapon yield

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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.

[edit] Examples of nuclear weapon yields

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

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.

[edit] 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).^[1] 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 it 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).^[2]

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.

[edit] Milestone nuclear explosions

The following list is of milestone nuclear explosions. In addition to the atomic bombings of Hiroshima and Nagasaki, the first nuclear test of a given weapon type for a country is included, and tests which were otherwise notable (such as the largest test ever). All yields (explosive power) are given in their estimated energy equivalents in kilotons of TNT (see megaton). Putative tests have not been included.

Date	Name	Yield (kT)	Country	Significance
1945-07-16	Trinity	19	USA	First fission device test, first plutonium implosion detonation
1945-08-06	Little Boy	15	USA	Bombing of Hiroshima, Japan, first detonation of an enriched uranium gun-type device
1945-08-09	Fat Man	21	USA	Bombing of Nagasaki, Japan
1949-08-29	RDS-1	22	USSR	First fission weapon test by the USSR
1952-10-03	Hurricane	25	UK	First fission weapon test by the UK, Montebello Islands, Western Australia
1952-11-01	Ivy Mike	10,400	USA	First cryogenic fusion fuel "staged" thermonuclear weapon, developed into the TX-16/EC-16
1953-08-12	Joe 4	400	USSR	First fusion weapon test by the USSR (not "staged")
1954-03-01	Castle Bravo	15,000	USA	First dry fusion fuel "staged" thermonuclear weapon; fallout accident
1955-11-22	RDS-37	1,600	USSR	First "staged" thermonuclear weapon test by the USSR (deployable)
1957-11-08	Grapple X	1,800	UK	First (successful) "staged" thermonuclear weapon test by the UK
1960-02-13	Gerboise Bleue	70	France	First fission weapon test by France
1961-10-31	Tsar Bomba	50,000	USSR	Largest thermonuclear weapon ever tested—scaled down from its initial 100 Mt design by 50%
1964-10-16	596	22	PR China	First fission weapon test by the People's Republic of China
1967-06-17	Test No. 6	3,300	PR China	First "staged" thermonuclear weapon test by the People's Republic of China
1968-08-24	Canopus	2,600	France	First "staged" thermonuclear test by France
1974-05-18	Smiling Buddha	12	India	First fission nuclear explosive test by India
1998-05-11	Shakti I	45	India	First potential fusion/boosted weapon test by India
1998-05-11	Shakti II	15	India	First deployable fission weapon test by India
1998-05-28	Chagai-I	40	Pakistan	First fission weapon test by Pakistan
2006-10-09	2006 North Korean nuclear test	<1	North Korea	First fission device tested by North Korea; resulted as a fizzle
2009-05-25	2009 North Korean nuclear test	uncertain	North Korea	First successful fission device tested by North Korea

"Staging" refers to whether it was a "true" hydrogen bomb of the so-called Teller-Ulam configuration or simply a form of a boosted fission weapon. For a more complete list of nuclear test series, see List of nuclear tests. Some exact yield estimates, such as that of the Tsar Bomba and the tests by India and Pakistan in 1998, are somewhat contested among specialists.

[edit] 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:

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.

[edit] See also

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

[edit] References

1. ^ The B-41 Bomb
2. ^ SS-18 Satan / (RS-20A/B/R-36M/15A14/15A18) | Russian Arms, Military Technology, Analysis of Russia's Military Forces

[edit] 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