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Nuclear weapon yield

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Nuclear weapons

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Contents
The explosive yield of a nuclear weapon is the amount of energy discharged when the 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 [10^] calories equivalent, this being very roughly equal to the energy yield of one thousand tons of TNT.

Examples of nuclear weapon yields

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

As a comparison, the Oklahoma City bombing, using a truck-based fertilizer bomb, was a mere 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 per metric ton (6 Mt/t). [link]  The practical achievable limit is somewhat lower. For current US weapons 600 kt/t (2.5 TJ/kg) to 2.2 Mt/t (9.2 TJ/kg). By comparison, for the Davy Crockett it was 0.4 - 40 kt/t (0.002 - 0.167 TJ/kg), for Little Boy 4 kt/t, and for the Tsar Bomba 2 Mt/t (8 TJ/kg) (deliberately reduced from the possible maximum which was twice as much), and for the Mk-41 5.2 Mt/t. 


Fission bombs have a maximum yield limit of roughly one megaton: [link]. 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 of the maximum theoretical yield-to-weight ratio is about 6Mt/t, and the maximum achievable ratio about 5.2 MT/t, there is a practical limit on air delivery of the weapon. 


For example, if the full payload of 250 t of the Antonov An-225 could be used, the limit would be 250 t * 5.2 Mt/t, or 1300 Mt. 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 Mt. In fact the SS-18 mod 1 yield for a single warhead is about 24 Mt. [link] In more recent practice, large single warheads are seldom used, since smaller MIRV warheads are more destructive for a given payload capacity.



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).





























































 Date
 Name
Yield (kt)
 Country
 Significance

Jul 16 1945



Trinity test>Trinity
19



USA



First fission weapon test

Aug 6 1945



Little Boy
15



USA



Bombing of Hiroshima, Japan

Aug 9 1945



Fat Man
21



USA



Bombing of Nagasaki, Japan

Aug 29 1949



Joe 1
22



USSR



First fission weapon test by the USSR

Oct 3 1952



Operation Hurricane>Hurricane
25



UK



First fission weapon test by the UK

Nov 1 1952



Ivy Mike
10,200



USA



First "staged" thermonuclear weapon test (not deployable)

Aug 12 1953



Joe 4
400



USSR



First fusion weapon test by the USSR (not "staged", but deployable)

Mar 1 1954



Castle Bravo
15,000



USA



fallout accident

Nov 22 1955



RDS-37
1,600



USSR



First "staged" thermonuclear weapon test by the USSR (deployable)

Nov 8 1957



Operation Grapple>Grapple X
1,800



UK



First (successful) "staged" thermonuclear weapon test by the UK

Feb 13 1960



France and weapons of mass destruction>Gerboise Bleue
60



France



First fission weapon test by France

Oct 31 1961



Tsar Bomba
50,000



USSR



Largest thermonuclear weapon ever tested

Oct 16 1964



596 (nuclear test)>596
22



China



First fission weapon test by China

Jun 17 1967



China and weapons of mass destruction>Test No. 6
3,300



China



First "staged" thermonuclear weapon test by China

Aug 24 1968



Canopus (nuclear test)>Canopus
2,600



France



First "staged" thermonuclear test by France

May 18 1974



Smiling Buddha
12



India



First fission nuclear explosive test by India

May 11 1998



Operation Shakti>Shakti I
43



India



First potential fusion/boosted weapon test by India
(exact yields disputed, between 25kt and 45kt)

May 13 1998



Operation Shakti>Shakti II
12



India



First fission "weapon" test by India

May 28 1998



Pakistan and weapons of mass destruction>Chagai-I
9



Pakistan



First fission weapon test by Pakistan



"Deployable" refers to whether the device tested could be hypothetically used in actual combat (in contrast with a proof-of-concept device). "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.



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. Excellent approximations of yields can be approximated by the dimensionless number developed by G. I. Taylor.  G. I. Taylor, Proc. Roy. Soc. London A201, 175 (1950) and G. I. Taylor, Proc. Roy. Soc. London A201, 159 (1950):

[c=^}^}}]


Here, [E] is the energy (in joules for SI), [t] is the time (in seconds for SI), ρ is the density of air (kg/m³ for SI) and [R] is the blast radius (in m for SI).  With [c] as a constant (for air ~1.033), all that is needed is a picture that shows the radius of the blast, a reference length scale, and the time since the blast to determine the energy.  Using the picture of the Trinity test as an example, take the density of air to be 1 kg/m³, the radius as approximately 140 m, solving for [E]:


[E=^}}]


and substituting in, [E]=8.889e13 J.  With 1 kiloton of TNT= 4.184e12 J the result is  21.24 kilotons of TNT, which agrees nicely with commonly stated value of 20 KT.


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 kt (a 20% margin of error), while the Nagasaki bomb, "Fat Man", is estimated to be between 18 and 23 kt (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 Mt or at a maximum of 57 Mt by differing political figures, either as a way for hyping the power of the bomb or as an attempt to undercut it. 


Nuclear testing yields, as in the Tsar Bomba example, can also be used as a way of reflecting upon technical expertise, and claiming higher yields or accusations of lower yields can be used as a way of promoting or disparaging the technical abilities of a nuclear program. When India claimed to have successfully detonated a hydrogen bomb in their 1998 Operation Shakti tests, many Western observers relied on analysis of seismographic data to determine whether the Indian tests reflected a successful hydrogen bomb detonation. Some have alleged that India's reported yields have been higher than their actual test yields, a move which would apparently be for political purposes (to claim more nuclear ability than their rival Pakistan, for example, or to demonstrate their military might to other potential rivals such as nearby China) if true.



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