The explosive yield of a nuclear weapon is the amount of
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of ...
released when that particular
nuclear weapon
A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission bomb) or a combination of fission and fusion reactions ( thermonuclear bomb), producing a nuclear explosion. Both bomb ...
is detonated, usually expressed as a
TNT equivalent (the standardized equivalent
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
of
trinitrotoluene
Trinitrotoluene (), more commonly known as TNT, more specifically 2,4,6-trinitrotoluene, and by its preferred IUPAC name 2-methyl-1,3,5-trinitrobenzene, is a chemical compound with the formula C6H2(NO2)3CH3. TNT is occasionally used as a reage ...
which, if detonated, would produce the same energy discharge), either in kilotonnes (kt—thousands of tonnes of TNT), in megatonnes (Mt—millions of tonnes of TNT), or sometimes in
terajoules (TJ). 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 10
12 calorie
The calorie is a unit of energy. For historical reasons, two main definitions of "calorie" are in wide use. The large calorie, food calorie, or kilogram calorie was originally defined as the amount of heat needed to raise the temperature of o ...
s.
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 (
thermonuclear weapon
A thermonuclear weapon, fusion weapon or hydrogen bomb (H bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a lo ...
s) has been estimated to six megatonnes of TNT per tonne of bomb mass (25 TJ/kg). 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 (bomb damage/bomb mass) 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 (most yield figures are approximate):
In comparison, the blast yield of the
GBU-43 Massive Ordnance Air Blast bomb
The GBU-43/B Massive Ordnance Air Blast (MOAB , colloquially known as the "Mother of All Bombs") is a large-yield bomb, developed for the United States military by Albert L. Weimorts, Jr. of the Air Force Research Laboratory. It was first tes ...
is 0.011 kt, and that of the
Oklahoma City bombing
The Oklahoma City bombing was a domestic terrorist truck bombing of the Alfred P. Murrah Federal Building in Oklahoma City, Oklahoma, United States, on April 19, 1995. Perpetrated by two anti-government extremists, Timothy McVeigh and T ...
, 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. According to nuclear-weapons designer
Ted Taylor, the practical maximum yield-to-mass ratio for fusion weapons is about 6 megatonnes of TNT per tonne (25 TJ/kg). The "Taylor limit" is not derived from
first principles, and weapons with yields as high as 9.5 megatonnes per tonne have been theorized.
[.] 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 (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
Naturally occurring lithium (3Li) is composed of two stable isotopes, lithium-6 and lithium-7, with the latter being far more abundant on Earth. Both of the natural isotopes have an unexpectedly low nuclear binding energy per nucleon ( for l ...
enrichment in the
lithium deuteride
Lithium hydride is an inorganic compound with the formula Li H. This alkali metal hydride is a colorless solid, although commercial samples are grey. Characteristic of a salt-like (ionic) hydride, it has a high melting point, and it is not solub ...
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
Operation Dominic was a series of 31 nuclear test explosions with a total yield conducted in 1962 by the United States in the Pacific. This test series was scheduled quickly, in order to respond in kind to the Soviet resumption of testing af ...
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. This may have been achievable by utilizing the same design as the
B41 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
A thermonuclear weapon, fusion weapon or hydrogen bomb (H bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a lowe ...
thermonuclear weapons.
* 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 (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 megatonnes per tonne yield).
* 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. (The UK's
Orange Herald was a very large boosted fission bomb, with a yield of 800 kilotonnes.) 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.
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 (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.
;Note
* "Staged" refers to whether it was a "true"
thermonuclear weapon
A thermonuclear weapon, fusion weapon or hydrogen bomb (H bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a lo ...
of the so-called
Teller–Ulam
A thermonuclear weapon, fusion weapon or hydrogen bomb (H bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a lowe ...
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 explosion
A nuclear explosion is an explosion that occurs as a result of the rapid release of energy from a high-speed nuclear reaction. The driving reaction may be nuclear fission or nuclear fusion or a multi-stage cascading combination of the two, ...
s can be very hard to calculate, even using numbers as rough as in the kilotonne or megatonne 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. 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
In chemistry, yield, also referred to as reaction yield, is a measure of the quantity of moles of a product formed in relation to the reactant consumed, obtained in a chemical reaction, usually expressed as a percentage. Yield is one of the pr ...
in chemical reaction products can be measured after a
chemical reaction
A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking ...
. The radiochemical analysis method was pioneered by
Herbert L. Anderson
Herbert Lawrence Anderson (May 24, 1914 – July 16, 1988) was an American nuclear physicist who was Professor of Physics at the University of Chicago.
He contributed to the Manhattan Project. He was also a member of the team which made the first ...
.
For nuclear explosive devices where the fallout is not attainable or would be
misleading,
neutron activation
Neutron activation is the process in which neutron radiation induces radioactivity in materials, and occurs when atomic nuclei capture free neutrons, becoming heavier and entering excited states. The excited nucleus decays immediately by emit ...
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
Ivy Mike was the codename given to the first full-scale test of a thermonuclear device, in which part of the explosive yield comes from nuclear fusion.
Ivy Mike was detonated on November 1, 1952, by the United States on the island of Elugelab ...
's respective yields.
Yields can also be inferred in a number of other
remote sensing
Remote sensing is the acquisition of information about an object or phenomenon without making physical contact with the object, in contrast to in situ or on-site observation. The term is applied especially to acquiring information about Ear ...
ways, including scaling law calculations based on blast size,
infrasound, fireball brightness (
Bhangmeter
A bhangmeter is a non-imaging radiometer installed on reconnaissance and navigation satellites to detect atmospheric nuclear detonations and determine the yield of the nuclear weapon. They are also installed on some armored fighting vehicles, in ...
),
seismographic data (
CTBTO
The Preparatory Commission for the Comprehensive Nuclear-Test-Ban Treaty Organization, or CTBTO Preparatory Commission, is an international organization based in Vienna, Austria, that is tasked with building up the verification regime of the Com ...
), 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 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
The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of ...
(A) and volume (V) 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 × 2π(16 km)
2. Multiply by 1 atm to get an energy of ~ 100 kT TNT.
A good approximation of the yield of the Trinity test device was obtained in 1950 by the British physicist Geoffrey Ingram Taylor, G. I. Taylor">-->
A good approximation of the yield of the Trinity test device was obtained in 1950 by the British physicist Geoffrey Ingram Taylor, G. I. Taylor
from simple dimensional analysis and an estimation of the heat capacity for 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 (after the USSR had exploded its own version of this bomb).
Taylor noted that the
radius
In classical geometry, a radius (plural, : radii) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''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 (which had been publicly released by the U.S. government and published in ''
Life
Life is a quality that distinguishes matter that has biological processes, such as signaling and self-sustaining processes, from that which does not, and is defined by the capacity for growth, reaction to stimuli, metabolism, energy ...
'' magazine), using successive frames of the explosion, Taylor found that ''R''
5/''t''
2 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 being 140 metres, and taking ''ρ'' to be 1 kg/m
3 (the measured value at Trinity on the day of the test, as opposed to sea-level values of approximately 1.3 kg/m
3) and solving for ''E'', Taylor obtained that the yield was about 22 kilotonnes 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 (see G. I. Taylor, ''Proc. Roy. Soc. London A'' 200, pp. 235–247 (1950)).
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 (1.2), and under conditions of an atomic fireball is (coincidentally) close to the
STP (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 ''R''
5/''t''
2 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'':
[Thayer Watkins]
''The Expansion of the Fireball of an Explosion''
San José State University.
: