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.- The 25 Mt yield option reported for the B41 would give it a yield-to-weight ratio of 5.1 megatons of TNT per metric ton. 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-weight weapon ever designed.
- The W56 demonstrated a yield-to-weight ratio of 4.96 kt per kg of device mass, and very close to the predicted 5.1 kt/kg achievable in the highest yield to weight weapon ever built, the 25 megaton 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-weight 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 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.
- The largest pure-fission bomb ever constructed, Ivy King, 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.
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.
Blast | 50% |
Thermal energy | 35% |
Initial ionizing radiation | 5% |
Residual fallout radiation | 10% |
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 :
.