Nuclear weapon yield

Image:US nuclear weapons yield-to-weight comparison.svg|right|thumb|350px|Log–log plot comparing the yield and mass of various nuclear weapons developed by the United States.
The explosive yield of a nuclear weapon is the amount of energy released such as blast, thermal, and nuclear radiation, when that particular nuclear weapon is detonated. It is usually expressed as a TNT equivalent, the standardized equivalent mass of trinitrotoluene which would produce the same energy discharge if detonated, either in kilotonnes, in megatonnes. It is also sometimes expressed in terajoules ; an explosive yield of one terajoule is equal to. Because the accuracy of any measurement of the energy released by TNT has always been problematic, the conventional definition is that one kilotonne of TNT is held simply to be equivalent to 10¹² calories.
The yield-to-weight ratio is the amount of weapon yield compared to the mass of the weapon. The practical maximum yield-to-weight ratio for fusion weapons has been estimated to six megatonnes of TNT per tonne of bomb mass. Yields of 5.2 megatonnes/tonne and higher have been reported for large weapons constructed for single-warhead use in the early 1960s. Since then, the smaller warheads needed to achieve the increased net damage efficiency of multiple warhead systems have resulted in increases in the yield/mass ratio for single modern warheads.

Examples of nuclear weapon yields

In order of increasing yield :
Image:Comparative nuclear fireball sizes.svg|right|thumb|250px|Comparative fireball radii for a selection of nuclear weapons. Contrary to the image, which may depict the initial fireball radius, the maximum average fireball radius of Castle Bravo, a 15-megatonne yield surface burst, is, and not the 1.42 km displayed in the image. Similarly the maximum average fireball radius of a 21-kilotonne low altitude airburst, which is the modern estimate for the Fat Man, is, and not the 0.1 km of the image.
In 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. The estimated strength of the explosion at the Port of Beirut is 0.3-0.5 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-mass ratio is the amount of weapon yield compared to the mass of the weapon. The highest achieved values are somewhat lower, and the value 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 B41 would give it a yield-to-mass ratio of 5.1 megatonnes of TNT per tonne. While this would require a far greater efficiency than any other current U.S. weapon, 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 B41 still retaining the record for the highest yield-to-mass weapon ever designed.
The W56 demonstrated a yield-to-mass ratio of 4.96 kt per kilogram of device mass, and very close to the predicted 5.1 kt/kg achievable in the highest yield-to-mass weapon ever built, the 25-megatonne B41. Unlike the B41, which was never proof-tested at full yield, the W56 demonstrated its efficiency in the XW-56X2 Bluestone shot of Operation Dominic in 1962, thus, from information available in the public domain, the W56 may hold the distinction of demonstrating the highest efficiency in a nuclear weapon to date.
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-mass ratios superior to a 25 Mt Mk-41.
For current smaller US weapons, yield is 600 to 2200 kilotonnes of TNT per tonne. By comparison, for the very small tactical devices such as the Davy Crockett it was 0.4 to 40 kilotonnes of TNT per tonne. For historical comparison, for Little Boy the yield was only 4 kilotonnes of TNT per tonne, and for the largest Tsar Bomba, the yield was 2 megatonnes of TNT per tonne.
The largest pure-fission bomb ever constructed, Ivy King, had a 500 kilotonne 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.

Large single warheads are seldom a part of today's arsenals, since smaller MIRV warheads, spread out over a pancake-shaped destructive area, are far more destructive for a given total yield, or unit of payload mass. This effect results from the fact that destructive power of a single warhead on land scales approximately only as the cube root of its yield, due to blast "wasted" over a roughly hemispherical blast volume, while the strategic target is distributed over a circular land area with limited height and depth. This effect more than makes up for the lessened yield/mass efficiency encountered if ballistic missile warheads are individually scaled down from the maximal size that could be carried by a single-warhead missile.

Yield efficiency

The efficiency of an atomic bomb is the ratio of the actual yield to the theoretical maximum yield of the atomic bomb. Not all atomic bombs possess the same yield efficiency as each individual bombs design plays a large role in how efficient it can be. In order to maximize yield efficiency one must make sure to assemble the critical mass correctly, as well as implementing instruments such as tampers or initiators in the design. A tamper is typically made of uranium and it holds the core together using its inertia. It is used to prevent the core from separating too soon to generate maximum fission, so as not to cause a "fizzle". The initiator is a source of neutrons either inside of the core, or on the outside of the bomb, and in this case it shoots neutrons at the core at the moment of detonation. It is essentially kick starting the reaction so the maximum fission reactions can occur to maximize yield.

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, as well as tests that were otherwise notable. All yields are given in their estimated energy equivalents in kilotons of TNT. Putative tests have not been included.

Date	Name		Country	Significance
	Trinity		United States	First fission-device test, first plutonium implosion detonation.
	Little Boy		United States	Bombing of Hiroshima, Japan, first detonation of a uranium gun-type device, first use of a nuclear device in combat.
	Fat Man		United States	Bombing of Nagasaki, Japan, second detonation of a plutonium implosion device, second and last use of a nuclear device in combat.
	RDS-1	22	Soviet Union	First fission-weapon test by the Soviet Union.
	George	225	United States	First boosted nuclear weapon test, first weapon test to employ fusion in any measure.
	Hurricane	25		First fission weapon test by the United Kingdom.
	Ivy Mike	10,400	United States	First "Nuclear weapon design#Two-stage [thermonuclear weapons\|staged]" thermonuclear weapon, with cryogenic fusion fuel, primarily a test device and not weaponized.
	Ivy King	500	United States	Largest pure-fission weapon ever tested.
	RDS-6s	400	Soviet Union	First fusion-weapon test by the Soviet Union.
	Castle Bravo	15,000	United States	First "staged" thermonuclear weapon using dry fusion fuel. A serious nuclear fallout accident occurred. Largest nuclear detonation conducted by United States.
	RDS-37	1,600	Soviet Union	First "staged" thermonuclear weapon test by the Soviet Union.
	Orange Herald	720	United Kingdom	Largest boosted fission weapon ever tested. Intended as a fallback "in megaton range" in case British thermonuclear development failed.
	Grapple X	1,800	United Kingdom	First "staged" thermonuclear weapon test by the United Kingdom
		70	France	First fission weapon test by France.
	Tsar Bomba	50,000	Soviet Union	Largest thermonuclear weapon ever tested—scaled down from its initial 100 Mt design by 50%.
	596	22	China	First fission-weapon test by the People's Republic of China.
	Test No. 6	3,300	China	First "staged" thermonuclear weapon test by the People's Republic of China.
	Canopus	2,600	France	First "staged" thermonuclear weapon test by France
		12	India	First fission nuclear explosive test by India.
	Pokhran-II	45–50	India	First potential fusion-boosted weapon test by India; first deployable fission weapon test by India.
	Chagai-I	40	Pakistan	First fission weapon test by Pakistan
				First fission-weapon test by North Korea.
				First "staged" thermonuclear weapon test claimed by North Korea.

;Note

"Staged" refers to whether it was a "true" thermonuclear weapon 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

Blast	50%
Thermal energy	35%
Initial ionizing radiation	5%
Residual fallout radiation	10%

Yields of nuclear explosions can be very hard to calculate, even using numbers as rough as in the kilotonne or megatonne range. Even under very controlled conditions, precise yields can be hard to determine, and for less controlled conditions the margins of error can be quite large. For fission devices, the most precise yield value is found from radiochemical fallout analysis; that is, measuring the quantity of fission products generated, in much the same way as the chemical yield can be measured after a chemical reaction from its reaction products. The radiochemical analysis method was pioneered by Herbert L. Anderson.
For nuclear explosive devices where the fallout is not attainable or would be misleading, neutron activation analysis is often employed as the second most accurate method, with it having been used to determine the yield of both Little Boy and thermonuclear Ivy Mike's respective yields.
Yields can also be inferred in a number of other remote sensing ways, including scaling law calculations based on blast size, infrasound, fireball brightness, seismographic data, and the strength of the shock wave.

Enrico Fermi's calculation

Enrico Fermi famously made a rough calculation of the yield of the Trinity test by dropping small pieces of paper in the air and measuring how far they were moved by the blast wave of the explosion; that is, he found the blast pressure at his distance from the detonation in pounds per square inch, using the deviation of the papers' fall away from the vertical as a crude blast gauge/barograph, and then with pressure X in psi, at distance Y, in miles figures, he extrapolated backwards to estimate the yield of the Trinity device, which he found was about 10 kilotonnes of blast energy.
Fermi later recalled:
The surface area and volume of a sphere are and respectively.
The blast wave, however, was likely assumed to grow out as the surface area of the approximately hemispheric near surface burst blast wave of the Trinity gadget.
The paper is moved 2.5 meters by the wave, so the effect of the Trinity device is to displace a hemispherical shell of air of volume 2.5 m × 2π². Multiply by 1 atm to get an energy of ~ 100 kT TNT.

G. I. Taylor's calculation

Image:Trinity Test Fireball-25ms.jpg|right|thumb|250px|This photograph of the Trinity blast, captured by Berlyn Brixner, was used by G. I. Taylor to estimate its yield.
A good approximation of the yield of the Trinity test device was obtained in 1950 by the British physicist G. I. Taylor from simple dimensional analysis and an estimation of the heat capacity of very hot air. Taylor had initially done this highly classified work in mid-1941 and published an article with an analysis of the Trinity data fireball when the Trinity photograph data was declassified in 1950.
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 equation having compatible dimensions that can be constructed from these quantities is
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
which is approximately 1 for all conditions.
Using the picture of the Trinity test shown here, using successive frames of the explosion, Taylor found that R⁵/t² is a constant in a given nuclear blast. Furthermore, he estimated a value for S numerically at 1.
Thus, with t = 0.025 s and the blast radius being 140 metres, and taking ρ to be 1 kg/m³ and solving for E, Taylor obtained that the yield was about 22 kilotonnes of TNT. 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 .
A good approximation to Taylor's constant S for below about 2 is
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, and under conditions of an atomic fireball is close to the STP 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.
As it relates to fundamental dimensional analysis, if one expresses all the variables in terms of mass M, length L, and time T:
,
and then derive an expression for, say, E, in terms of the other variables, by finding values of,, and in the general relation
such that the left and right sides are dimensionally balanced in terms of M, L, and T.

Other methods and controversy

Where these data are 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, while the Nagasaki bomb, "Fat Man", is estimated to be between .
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.
Other disputed yields have included the massive Tsar Bomba, whose yield was claimed between being "only" or at a maximum of by differing political figures, either as a way for hyping the power of the bomb or as an attempt to undercut it.