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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 (Mt—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 Atomic Age, the accepted convention is that one kt of TNT is simply defined to be 10^{12} calories equivalent, this being very roughly equal to the energy yield of 1,000 tons of TNT.
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 weapons) has been estimated to 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 single-warhead use in the early 1960s.^{[1]} 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.
In order of increasing yield (most yield figures are approximate):
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 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 is about 6 megatons of TNT per metric ton (25 TJ/kg).^{[7]} 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.
Again, it is helpful for understanding to emphasize that 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 2/3 power of its yield, due to blast "wasted" over a spherical 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/weight efficiency encountered if ballistic missile warheads are individually scaled-down from the maximal size that could be carried by a single-warhead missile.
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.
"Staging" 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.
While 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]} yield.
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 deflection of the papers fall from normal 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.^{[17]}^{[18]}
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.^{[19]}^{[20]}^{[21]}
The surface area(A) and volume(V) of a sphere are: A = 4\pi r^2 \!V = \frac{4}{3}\pi r^3
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 2.5m*2*pi*(14 km)^2 Multiply by 1 Atm to get energy of 3e14 J ~ 80 kT TN.
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 number having dimensions of length that can be constructed from these quantities is:
R=S\left( {\frac^{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 (γ = C_{p}/ 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 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 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 γ below about 2 is: S = [75(γ-1)/8π]^{1/5}. .^{[22]} 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 R^{5}/t^{2} condition holds.
A derivation of the Taylor formula is also said to be capable of determining the arrival time of the blast wave as a function of yield.^{[23]}
As it relates to fundamental dimensional analysis, if one expresses all the variables in terms of mass, M, length, L, and time, T :^{[24]}
E=]
(think of the expression for kinetic energy, E=\frac{mv^2}{2}
\rho=]
t=[T]
r=[L]
and then derive an expression for, say, E, in terms of the other variables, by finding values of \alpha \beta and \gamma in the general relation
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.
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 kilotonnes 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 kilotonnes 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 megatonnes of TNT (210 PJ) or at a maximum of 57 megatonnes 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.
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