# Nuclear weapon yield

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

The explosive yield of a nuclear weapon is the amount of energy 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.

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 (thermonuclear weapons) is 6 megatons of TNT per metric ton of bomb mass (25 TJ/kg). Yields of 5.2 megatons/ton and higher have been reported for large weapons constructed for single-warhead use in the early 1960s.[1] Since this time, the smaller warheads needed to achieve the increased net damage efficiency (bomb damage/bomb weight) of multiple warhead systems, has resulted in decreases in the yield/weight ratio for single modern warheads.

## 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 0.042 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 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.
W87 warhead 300 1,300 Ten of these were in a MIRVed LGM-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 Most powerful pure fission bomb, 60 kg uranium, implosion type.
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 Was the most powerful US bomb until 2010; it was not in active service for many years before 2010, but during that time, 50 were retained as part of the "Hedge" portion of the Enduring Stockpile until completely dismantled in 2011[2], a variant of the two-stage B61 is the B53 replacement in the bunker-busting role; the B53 was 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 or B41 had a mass of 4800 kg and yield of 25Mt, this equates to being the highest yield-to-weight weapon ever produced; all were gravity bombs carried by the 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 nuclear weapon ever detonated, mass of 50 megatons, (50 million tons of tnt). 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 as of 1996 510,300 2,135,000 Total energy expended during all nuclear testing.[1]
Comparative fireball radii for a selection of nuclear weapons. Note that full blast effects would extend many times beyond the fireball itself.

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).[3] 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 25 Mt yield option reported for the B-41 would give it a yield-to-weight ratio of 5.2 megatons of TNT per metric ton. While this would require a far greater efficiency than any other current U.S. weapon (at least 40% efficiency in a fusion fuel of lithium deuteride), this was apparently attainable, probably by the use of higher than normal Lithium-6 enrichment in the lithium deuteride fusion fuel. This results in the B-41 still retaining the record for the highest Yield-to-weight weapon ever made.
• In 1963 DOE declassified statements that the U.S. had the technological capability of deploying a 35 MT warhead on the Titan II, or a 50-60 MT gravity bomb on B-52s. Neither weapon was pursued, but either would require yield-to-weight ratios superior to a 25 MT Mk-41. This may have been achievable by utilizing the same design as the B-41 but with the addition of a HEU tamper, in place of the cheaper, but lower energy density U-238 tamper which is the most commonly used tamper material in Teller-Ulam thermonuclear weapons.
• For current smaller US weapons, yield is 600 to 2200 kilotons of TNT per metric ton. 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. For historical comparison, for Little Boy the yield was only 4 kilotons of TNT per metric ton, and for the largest Tsar Bomba, the yield was 2 megatons of TNT per metric ton (deliberately reduced from about twice as much yield for the same weapon, so there is little doubt that this bomb as designed was capable of 4 megatons per ton yield).
• The largest pure-fission bomb ever constructed had a 500 kiloton 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 bomb.
• Because the maximum theoretical yield-to-weight ratio is about 6 megatons of TNT per metric ton, and the maximum achieved ratio was apparently 5.2 megatons of TNT per metric ton, there is a practical limit on the total yield for air-delivered weapon. Note that most later generation weapons have eliminated the very heavy casing once thought needed for the nuclear reactions to occur efficiently - this greatly increases the achievable yield-to-weight ratio. For example, the Mk-36 bomb as built had a yield-to-weight ratio of 1.25 megatons of TNT per metric ton. If the 12,000 pound casing of the Mk-36 was reduced by 2/3s, the yield-to-weight ratio would have been 2.3 megatons of TNT per metric ton, which is about the same as the later generation, much lighter 9 megaton Mk/B-53 bomb.
• Delivery size limits can be estimated to ascertain limits to delivery of extremely high yield weapons. If the full 250 metric ton payload of the Antonov An-225 could be used, a 1.3 gigaton bomb could be delivered. 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. A Saturn V-scale missile could deliver over 120 tons with a yield of about 700 megatons.

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.

## 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 TNT equivalent). Putative tests (like Vela Incident) 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, first use of a nuclear device in military combat.
1945-08-09 Fat Man 21 USA Bombing of Nagasaki, Japan, as of this writing the last use of a nuclear device in military combat.
1946-07-01 Test Able 23 USA Bikini Atoll; the Crossroads tests were the fourth and fifth nuclear explosions conducted by the United States. Their purpose was to investigate the effect of nuclear weapons on naval ships. They were the first of many nuclear tests held in the Marshall Islands, and the first to be publicly announced beforehand and observed by an invited audience, including a large press corps.
1946-07-25 Test Baker 23 USA
1949-08-29 RDS-1 22 USSR First fission weapon test by the USSR
1951-05-09 Test George 225 USA "George" shot was physics experiment relating to the hydrogen bomb.
1952-10-03 Hurricane 25 UK First fission weapon test by the UK
1952-11-01 Ivy Mike 10,400 USA First cryogenic fusion fuel "staged" thermonuclear weapon, primarily a test device and not weaponized
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; a serious nuclear fallout accident occurred
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 First fission weapon test by the People's Republic of China
1967-06-17 Test No. 6 3,300 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 Pokhran-II 60[4] India First potential fusion/boosted weapon test by India; first deployable fission weapon test by India
1998-05-28 Chagai-I 45[5] Pakistan First fission weapon test by Pakistan
1998-05-30 Chagai-II 12~20[6][7][8] Pakistan First fusion weapon test by Pakistan
2006-10-09 2006 North Korean nuclear test ~1 First fission plutonium-based device tested by North Korea; likely resulted as a fizzle
2009-05-25 2009 North Korean nuclear test 5–15 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.

## 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 in 1950 from simple dimensional analysis as well as an estimation of the heat capacity for very hot air, by the British physicist G. I. Taylor. Taylor had initially done this highly classified work in mid-1941, and published a paper which included an analysis of the Trinity data fireball when the Trinity photograph data was declassified in 1950 (after the USSR had exploded its own version of this bomb).

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:

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

Here S is a dimensionless constant having a value approximately equal to 1, since it is low order function of the heat capacity ratio or adiabatic index (γ = Cp/ Cv), which is approximately 1 for all conditions.

Using the picture of the Trinity test shown here (which had been publicly released by the U.S. government and published in Life magazine), using successive frames or the explosion, Taylor found that R5/t2 is a constant in a given nuclear blast (especially between 0.38 ms after the shock wave has formed, and 1.93 ms before significant energy is lost by thermal radiation). Furthermore, he estimated a value for S numerically at 1.

Thus, with t = 0.025 s and the blast radius was 140 metres, and taking ρ to be 1 kg/m³ (the measured value at Trinity on the day of the test, as opposed to sea level values of approximately 1.3 kg/m³) and solving for E, Taylor obtained that the yield was about 22 kilotons of TNT (90 TJ). This does not take into account the fact that the energy should only be about half this value for a hemispherical blast, but this very simple argument did agree to within 10% with the official value of the bomb's yield in 1950, which was 20 kilotons of TNT (84 TJ) (See G. I. Taylor, Proc. Roy. Soc. London A 200, pp. 235-247 (1950).)

A good approximation to Taylor's constant S for γ below about 2 is: S = [75(γ-1)/8π]1/5. [9]. The value of the heat capacity ratio here is between the 1.67 of fully dissociated air molecules and the lower value for very hot diatomic air (1.2), and under conditions of an atomic fireball is (coincidentally) close to the S.T.P. (standard) gamma for room temperature air, which is 1.4. This gives the value of Taylor's S constant to be 1.036 for the adiabatic hypershock region where the constant R5/t2 condition holds.

### Other methods and controversy

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.

## References

1. ^ The B-41 Bomb
2. ^ Ackerman, Spencer (October 23, 2011). "Last Nuclear ‘Monster Weapon’ Gets Dismantled". Wired. Retrieved 23 October 2011.
3. ^ The B-41 Bomb
4. ^ [2010 test] Kakodkar says Pokhran-II tests fully successful], 24 September 2009
5. ^ Pakistan Nuclear Weapons. Federation of American Scientists. December 11, 2002
6. ^ (FAS), Federation of American Scientists (December 11, 2002 8:57:58 AM). "2nd Nuclear Tests". Federation of American Scientists. Retrieved 2011.
7. ^ (Broadband Seismic Data Collection Center) (2010-11-23). "2nd Pakistan Nuclear Test's Mathematical Sequence". Broadband Seismic Data Collection Center (ANZA), Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California San Diego, Pakistan Atomic Scientists Federation (PASF), and the Institute of Space and Planetary Astrophysics. USCD. Retrieved 2011.
8. ^ (Broadband Seismic Data Collection Center) (2010-11-23). "2nd Pakistan Nuclear Test's KNET recording". Broadband Seismic Data Collection Center (ANZA), Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, University of California San Diego, Pakistan Atomic Scientists Federation (PASF), and the Institute of Space and Planetary Astrophysics. USCD. Retrieved 2011.
9. ^ http://glasstone.blogspot.com/2006/03/analytical-mathematics-for-physical.html.

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