Nuclear weapon yield


The explosive yield of a nuclear weapon is the amount of energy released when that particular nuclear weapon is detonated, usually expressed as a TNT equivalent, either in kilotons, in megatons, or sometimes 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 kiloton 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 megatons of TNT per metric ton of bomb mass. Yields of 5.2 megatons/ton 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 decreases in the yield/mass ratio for single modern warheads.

Examples of nuclear weapon yields

In order of increasing yield :
, is, 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, 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.

Yield limits

The yield-to-weight 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-weight ratio for fusion weapons is about 6 megatons of TNT per metric ton. The "Taylor limit" is not derived from first principles, and weapons with yields as high as 9.5 megatons per metric ton 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.
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.

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. 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 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.
Blast50%
Thermal energy35%
Initial ionizing radiation5%
Residual fallout radiation10%

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 kiloton of blast energy.
Fermi later recalled that:
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 energy of ~ 80 kT TN.
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.
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 was 140 metres, and taking ρ to be 1 kg/m3 and solving for E, Taylor obtained that the yield was about 22 kilotons 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 S.T.P. 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 :
.

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.