The yield-to-weight ratio is the amount of weapon yield compared to the mass of the weapon. The theoretical maximum yield-to-weight 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 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.
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[edit] Examples of nuclear weapon yields
In order of increasing yield (most yield figures are approximate):| Bomb | Yield | Notes | |
|---|---|---|---|
| kt TNT | TJ | ||
| Davy Crockett | 0.01 | 0.042 | Variable yield tactical nuclear weapon—mass only 23 kg (51 lb), lightest ever deployed by the United States (same warhead as Special Atomic Demolition Munition and GAR-11 Nuclear Falcon missile). |
| Hiroshima's "Little Boy" gravity bomb | 12–15 | 50–63 | Gun type uranium-235 fission bomb (the first of the two nuclear weapons that have been used in warfare). |
| Nagasaki's "Fat Man" gravity bomb | 20–22 | 84–92 | Implosion type plutonium-239 fission bomb (the second of the two nuclear weapons used in warfare). |
| W76 warhead | 100 | 420 | Twelve of these may be in a MIRVed Trident II missile; treaty limited to eight. |
| W87 warhead | 300 | 1,300 | Ten of these were in a MIRVed LGM-118A Peacekeeper. |
| W88 warhead | 475 | 1,990 | Twelve of these may be in a Trident II missile (treaty limited to eight). |
| Ivy King device | 500 | 2,100 | Most powerful pure fission bomb, 60 kg uranium, implosion type. |
| B83 nuclear bomb | variable | Up to 1.2 megatonnes of TNT (5.0 PJ); most powerful US weapon in active service. | |
| B53 nuclear bomb | 9,000 | 38,000 | Was the most powerful US bomb until 2010; it was not in active service for many years before 2010, but during that time, 50 were retained as part of the "Hedge" portion of the Enduring Stockpile until completely dismantled in 2010, a variant of the two-stage B61 is the B53 replacement in the bunker-busting role; the B53 was similar to the W-53 warhead that has been used in the Titan II Missile; decommissioned in 1987. |
| Castle Bravo device | 15,000 | 63,000 | Most powerful US test. |
| EC17/Mk-17, the EC24/Mk-24, and the B41 (Mk-41) | various | Most powerful US weapons ever: 25 megatonnes of TNT (100 PJ); the Mk-17 was also the largest by size and mass: about 20 short tons (18,000 kg); The Mk-41 or B41 had a mass of 4800 kg and yield of 25Mt, this equates to being the highest yield-to-weight weapon ever produced; all were gravity bombs carried by the B-36 bomber (retired by 1957). | |
| The entire Operation Castle nuclear test series | 48,200 | 202,000 | The highest-yielding test series conducted by the US. |
| Tsar Bomba device | 50,000 | 210,000 | USSR, most powerful nuclear weapon ever detonated, mass of 50 megatons, (50 million tons of tnt). In its "full" form (i.e. with a depleted uranium tamper instead of one made of lead) it would have been 100 megatonnes of TNT (420 PJ). |
| All nuclear testing as of 1996 | 510,300 | 2,135,000 | Total energy expended during all nuclear testing.[1] |
[edit] Yield limits
The yield-to-weight ratio is the amount of weapon yield compared to the mass of the weapon. The theoretical maximum yield-to-weight ratio for fusion weapons is 6 megatons of TNT per metric ton (25 TJ/kg).[2] 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 B-41 would give it a yield-to-weight 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 Lithium-6 enrichment in the lithium deuteride fusion fuel. This results in the B-41 still retaining the record for the highest Yield-to-weight 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 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 B-41 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 weapon.
- 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 (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 pure-fission bomb ever constructed 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.
- Because the maximum theoretical yield-to-weight 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 air-delivered 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 yield-to-weight ratio. For example, the Mk-36 bomb as built had a yield-to-weight ratio of 1.25 megatons of TNT per metric ton. If the 12,000 pound casing of the Mk-36 was reduced by 2/3s, the yield-to-weight 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/B-53 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 An-225 could be used, a 1.3 gigaton bomb could be delivered. Likewise the maximum limit of a missile-delivered weapon is determined by the missile payload capacity. The large Russian SS-18 ICBM has a payload capacity of 7,200 kg, so the calculated maximum delivered yield would be 37.4 megatons of TNT. A Saturn V-scale missile could deliver over 120 tons with a yield of about 700 megatons.
[edit] 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 (see TNT equivalent). Putative tests (like Vela Incident) have not been included.Date | Name | Yield (kT) | Country | Significance |
|---|---|---|---|---|
| 1945-07-16 | Trinity | 19 |  USA | First fission device test, first plutonium implosion detonation |
| 1945-08-06 | Little Boy | 15 | USA | Bombing of Hiroshima, Japan, first detonation of an enriched uranium gun-type device, first use of a nuclear device in military combat. |
| 1945-08-09 | Fat Man | 21 | USA | Bombing of Nagasaki, Japan, as of this writing the last use of a nuclear device in military combat. |
| 1946-07-01 | Test Able | 23 | USA | Bikini Atoll; the Crossroads tests were the fourth and fifth nuclear explosions conducted by the United States. Their purpose was to investigate the effect of nuclear weapons on naval ships. They were the first of many nuclear tests held in the Marshall Islands, and the first to be publicly announced beforehand and observed by an invited audience, including a large press corps. |
| 1946-07-25 | Test Baker | 23 | USA | |
| 1949-08-29 | RDS-1 | 22 |  USSR | First fission weapon test by the USSR |
| 1951-05-09 | Test George | 225 | USA | "George" shot was physics experiment relating to the hydrogen bomb. |
| 1952-10-03 | Hurricane | 25 |  UK | First fission weapon test by the UK |
| 1952-11-01 | Ivy Mike | 10,400 | USA | First cryogenic fusion fuel "staged" thermonuclear weapon, primarily a test device and not weaponized |
| 1953-08-12 | Joe 4 | 400 | USSR | First fusion weapon test by the USSR (not "staged") |
| 1954-03-01 | Castle Bravo | 15,000 | USA | First dry fusion fuel "staged" thermonuclear weapon; a serious nuclear fallout accident occurred |
| 1955-11-22 | RDS-37 | 1,600 | USSR | First "staged" thermonuclear weapon test by the USSR (deployable) |
| 1957-11-08 | Grapple X | 1,800 | UK | First (successful) "staged" thermonuclear weapon test by the UK |
| 1960-02-13 | Gerboise Bleue | 70 |  France | First fission weapon test by France |
| 1961-10-31 | Tsar Bomba | 57,000 | USSR | Largest thermonuclear weapon ever tested—scaled down from its initial 100 Mt design by 50% |
| 1964-10-16 | 596 | 22 |  PR China | First fission weapon test by the People's Republic of China |
| 1967-06-17 | Test No. 6 | 3,300 | PR China | First "staged" thermonuclear weapon test by the People's Republic of China |
| 1968-08-24 | Canopus | 2,600 | France | First "staged" thermonuclear test by France |
| 1974-05-18 | Smiling Buddha | 12 |  India | First fission nuclear explosive test by India |
| 1998-05-11 | Pokhran-II | 43 [3] | India | First potential fusion/boosted weapon test by India; first deployable fission weapon test by India |
| 1998-05-28 | Chagai-I | 45 [4] |  Pakistan | First fission weapon test by Pakistan |
| 2006-10-09 | 2006 North Korean nuclear test | ~1 |  North Korea | First fission plutonium-based device tested by North Korea; likely resulted as a fizzle |
| 2009-05-25 | 2009 North Korean nuclear test | 5–15 | North Korea | First successful fission device tested by North Korea |
[edit] 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.
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 dimentionless 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 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).)
Further physical analysis shows that Taylor's constant S can be calculated from first thermodynamic principles: S = [75(γ-1)/8π]1/5. [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 hypershock region where the constant R5/t2 condition holds.
[edit] 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 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.[edit] See also
- Effects of nuclear explosions — goes into detail about different effects at different yields
[edit] References
- ^ The B-41 Bomb
- ^ The B-41 Bomb
- ^ [2010 test] Kakodkar says Pokhran-II tests fully successful], 24 September 2009
- ^ Pakistan Nuclear Weapons. Federation of American Scientists. December 11, 2002
- ^ http://glasstone.blogspot.com/2006/03/analytical-mathematics-for-physical.html See this paper for a theoretical derivation of Taylor's dimensionless heat capacity-related factor.
