Nuclear Weapon Yield
The explosive yield of a nuclear weapon is the amount of energy discharged when a nuclear weapon is detonated, expressed usually in TNT equivalent "the standardized equivalent mass of trinitrotoluene which, if detonated, would produce the same energy discharge", either in kilotons "kt;" thousands of tons of TNT" or megatons "t; millions of tons of TNT", but sometimes also in terajoules "1 kiloton of TNT = 4.184 TJ". Because the precise amount of energy released by TNT is and was subject to measurement uncertainties, especially at the dawn of the nuclear age, the accepted convention is that one kt of TNT is simply defined to be 1012 calories equivalent, this being very roughly equal to the energy yield of 1,000 tons of TNT.
US Nuclear Weapons YieldtoWeight Comparison
Logarithmic scatter plot comparing the yield in "kilotons" and weight
in "kilograms" of all nuclear weapons developed by the United States
The yieldtoweight ratio is the amount of weapon yield compared to the mass of the weapon. The theoretical maximum yieldtoweight ratio for fusion weapons "thermonuclear weapons" is 6 megatons of TNT per metric ton of bomb mass "25 TJ/kg". Yields of 5.2 megatons/ton and higher have been reported for large weapons constructed for singlewarhead use in the early 1960s. Since this time, the smaller warheads needed to achieve the increased net damage efficiency "bomb damage/bomb weight" of multiple warhead systems, has resulted in decreases in the yield/weight ratio for single modern warheads.
Examples of Nuclear Weapon Yields
In order of increasing yield "most yield figures are approximate":
As a comparison, the blast yield of the GBU43 Massive Ordnance Air Blast bomb is 0.011kt, and that of the Oklahoma City bombing, using a truckbased fertilizer bomb, was 0.002kt. Most artificial nonnuclear explosions are onsiderably smaller than even what are considered to be very small nuclear weapons.
Comparative fireball radii for a selection of nuclear weapons.
Note that full blast effects would extend many times beyond the fireball itself
Yield Limits
The yieldtoweight ratio is the amount of weapon yield compared to the mass of the weapon. The theoretical maximum yieldtoweight ratio for fusion weapons is 6 megatons of TNT per metric ton "25 TJ/kg". The practical achievable limit is somewhat lower, and 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 yieldtoweight ratio of 5.2 megatons of TNT per metric ton. 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 Lithium6 enrichment in the lithium deuteride fusion fuel. This results in the B41 still retaining the record for the highest YieldtoWeight weapon ever made.
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 5060 MT gravity bomb on B52s. Neither weapon was pursued, but either would require yieldtoweight ratios superior to a 25 MT Mk41. 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 U238 tamper which is the most commonly used tamper material in TellerUlam 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, [ See Appendix VII] the yield was 2 megatons of TNT per metric ton "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 megatons per ton yield".
The largest purefission 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 fissionbased 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.
Because the maximum theoretical yieldtoweight ratio is about 6 megatons of TNT per metric ton, and the maximum achieved ratio was apparently 5.2 megatons of TNT per metric ton, there is a practical limit on the total yield for airdelivered weapon. Note that most later generation weapons have eliminated the very heavy casing once thought needed for the nuclear reactions to occur efficiently  this greatly increases the achievable yieldtoweight ratio. For example, the Mk36 bomb as built had a yieldtoweight ratio of 1.25 megatons of TNT per metric ton. If the 12,000 pound casing of the Mk36 were reduced by 2/3s, the yieldtoweight ratio would have been 2.3 megatons of TNT per metric ton, which is about the same as the later generation, much lighter 9 megaton Mk/B53 bomb.
Delivery size limits can be estimated to ascertain limits to delivery of extremely high yield weapons. If the full 250 metric ton payload of the Antonov An225 could be used, a 1.3 gigaton bomb could be delivered. Likewise the maximum limit of a missiledelivered weapon is determined by the missile payload capacity. The large Russian SS18 ICBM has a payload capacity of 7,200kg, so the calculated maximum delivered yield would be 37.4 megatons of TNT. A Saturn Vscale missile could deliver over 120 tons with a yield of about 700 megatons.
Again, it is helpful for understanding to emphasize that large single warheads are seldom a part of today's arsenals, since smaller MIRV warheads are far more destructive for a given total yield or payload capacity. This effect, which results from the fact that destructive power of a single warhead scales approximately as the 2/3 power of its yield, more than makes up for the lessened yield/weight efficiency encountered if ballistic missile warheads are scaleddown from the maximal size that could be carried by a singlewarhead 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, 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. Putative tests "like Vela Incident" have not been included.
"Staging" refers to whether it was a "true" hydrogen bomb of the socalled TellerUlam 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 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. Yields can be calculated in a number of ways, including calculations based on blast size, blast brightness, seismographic data, 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 at how far they were moved by the shock wave of the explosion.
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 mid1941, 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 number having dimensions of length 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 [γ = Cp/ Cv], 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 or 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 meters, 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".
A good approximation to Taylor's constant S for γ below about 2 is: S = [75(γ1)/8π]1/5. 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 hyper shock region where the constant R5/t2 condition holds.
Other Methods and Controversy
Where this data is 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 12 and 18 kilotons of TNT "50 and 75 TJ" "a 20% margin of error", while the Nagasaki bomb, "Fat Man", is estimated to be between 18 and 23 kilotons of TNT "75 and 96 TJ" "a 10% margin of error". 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 "for example, the Ivy Mike hydrogen bomb was
equivalent to either 867 or 578 Hiroshima weapons a rhetorically quite substantial difference depending on whether one uses the high or low figure for the calculation". Other disputed yields have included the massive Tsar Bomba,
whose yield was claimed between being "only" 50 megatons of TNT "210 PJ" or at a maximum of 57 megatons of TNT "240 PJ" by differing political figures, either as a way for hyping the power of the bomb or as an attempt to undercut it.
Revised: 02/04/2013 – 11:49:23
