Nuclear weapon yield

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

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 megaton yield surface burst, is 3.3 to 3.7 km (2.1 to 2.3 mi),[5][6] and not the 1.42 km displayed in the image. Similarly the maximum average fireball radius of a 21 kiloton low altitude airburst, which is the modern estimate for the fat man, is .21 to .24 km (0.13 to 0.15 mi),[6][7] and not the 0.1 km of the image.

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.

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.

Note

• "Staged" 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.

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. 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 chemical reaction products can be measured after a chemical reaction. 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[12][13] and thermonuclear Ivy Mike's[14] 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 (Bhangmeter), seismographic data (CTBTO),[15] 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 kiloton of blast energy.[19][20]

Fermi later recalled that:

I was stationed at the Base Camp at Trinity in a position about ten miles[16 km] from the site of the explosion...About 40 seconds after the explosion the air blast reached me. I tried to estimate its strength by dropping from about six feet small pieces of paper before, during, and after the passage of the blast wave. Since, at the time, there was no wind I could observe very distinctly and actually measure the displacement of the pieces of paper that were in the process of falling while the blast was passing. The shift was about 2 1/2 meters, which, at the time, I estimated to correspond to the blast that would be produced by ten thousand tons of T.N.T.[21][22][23]

The surface area (A) and volume (V) of a sphere are: ${\displaystyle A=4\pi r^{2}}$ and ${\displaystyle V={\frac {4}{3}}\pi r^{3}}$ 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(14 km)². Multiply by 1 atm to get energy of 3×10¹⁴ J ~ 80 kT TN.

Picture of the blast, captured by Berlyn Brixner were used by G.I. Taylor to estimate the yield of the device 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 equation having compatible dimensions that can be constructed from these quantities is:

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

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

${\displaystyle \gamma ={C_{P} \over C_{V}}}$

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 of 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 ${\displaystyle \gamma }$ below about 2 is:

${\displaystyle S={\Biggl (}{75(\gamma -1) \over \ 8\pi }{\Biggr )}^{\frac {1}{5}}}$

[24] 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.

As it relates to fundamental dimensional analysis, if one expresses all the variables in terms of mass, M, length, L, and time, T :[25]

${\displaystyle E=[{M}.{L^{2}}.{T^{-2}}]}$

(think of the expression for kinetic energy, ${\displaystyle E={\frac {mv^{2}}{2}}}$

${\displaystyle \rho =[{M}\cdot {L^{-3}}]}$

${\displaystyle t=[T]}$

${\displaystyle r=[L]}$

and then derive an expression for, say, E, in terms of the other variables, by finding values of ${\displaystyle \alpha }$, ${\displaystyle \beta }$, and ${\displaystyle \gamma }$ in the general relation

${\displaystyle E={\rho ^{\alpha }}\cdot {t^{\beta }}\cdot {r^{\gamma }}}$

such that the left- and right-hand sides are dimensionally balanced in terms of M, L, and T (i.e., each dimension has the same exponent on both sides).

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

Wikimedia Commons has media related to Nuclear weapon yield.

• "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