Effects of nuclear explosions on human health

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https://en.wikipedia.org/wiki/Effects_of_nuclear_explosions_on_human_health 

 

The medical effects of the atomic bomb on Hiroshima upon humans can be put into the four categories below, with the effects of larger thermonuclear weapons producing blast and thermal effects so large that there would be a negligible number of survivors close enough to the center of the blast who would experience prompt/acute radiation effects, which were observed after the 16 kiloton yield Hiroshima bomb, due to its relatively low yield:

• Initial stage—the first 1–9 weeks, in which are the greatest number of deaths, with 90% due to thermal injury and/or blast effects and 10% due to super-lethal radiation exposure.
• Intermediate stage—from 10–12 weeks. The deaths in this period are from ionizing radiation in the median lethal range - LD50
• Late period—lasting from 13–20 weeks. This period has some improvement in survivors' condition.
• Delayed period—from 20+ weeks. Characterized by numerous complications, mostly related to healing of thermal and mechanical injuries, and if the individual was exposed to a few hundred to a thousand Millisieverts of radiation, it is coupled with infertility, sub-fertility and blood disorders. Furthermore, ionizing radiation above a dose of around 50-100 Millisievert exposure has been shown to statistically begin increasing a person's chance of dying of cancer sometime in their lifetime over the normal unexposed rate of c. 25%, in the long term, a heightened rate of cancer, proportional to the dose received, would begin to be observed after c. 5+ years, with lesser problems such as eye cataracts and other more minor effects in other organs and tissue also being observed over the long term.

Depending on whether individuals further afield shelter in place or evacuate perpendicular to the direction of the wind, and therefore avoid contact with the fallout plume, and stay there for the days and weeks after the nuclear explosion, their exposure to fallout, and therefore their total dose, will vary. With those who do shelter in place, and or evacuate, experiencing a total dose that would be negligible in comparison to someone who just went about their life as normal.

Staying indoors until after the most hazardous fallout isotope, I-131 decays away to 0.1% of its initial quantity after ten half-lives – which is represented by 80 days in the care of I-131 case, would make the difference between likely contracting thyroid cancer or escaping completely from this substance depending on the actions of the individual.

Some scientists estimate that if there were a nuclear war resulting in 100 Hiroshima-size nuclear explosions on cities, it could cause significant loss of life in the tens of millions from long term climatic effects alone. The climatology hypothesis is that if each city firestorms, a great deal of soot could be thrown up into the atmosphere which could blanket the earth, cutting out sunlight for years on end, causing the disruption of food chains, in what is termed a nuclear winter scenario.

Blast effects — the initial stage

Immediate post-attack period

Melted and fused pieces of metal (including coins that were in people's pockets) from the Atomic bombings of Japan. The melting of metal like this occurred during the ensuing fires and firestorms, long after the bombs had exploded.

 

The main causes of death and disablement in this state are thermal burns and the failure of structures resulting from the blast effect. Injury from the pressure wave is minimal in contrast because the human body can survive up to 2 bar (30 psi) while most buildings can only withstand a 0.8 bar (12 psi) blast. Therefore, the fate of humans is closely related to the survival of the buildings around them.

Fate within certain peak overpressure

• over 0.8 bar (12 psi) - 98% dead, 2% injured
• 0.3 - 0.8 bar (5-12 psi) - 50% dead, 40% injured, 10% safe
• 0.14 - 0.3 bar (2-5 psi) - 5% dead, 45% injured, 50% safe

Types of radioactive exposure after a nuclear attack

Japanese woman (one of the Hiroshima Maidens) suffering burns from thermal radiation after the United States dropped nuclear bombs on Japan.

 

In a nuclear explosion the human body can be irradiated by at least three processes. The first, and most major, cause of burns is due to thermal radiation and not caused by ionizing radiation.

• Thermal burns from infrared heat radiation, these would be the most common burn type experienced by personnel.
• If people come in direct contact with fallout, beta burns from shallow ionizing beta radiation will be experienced, the largest particles (visible to the naked eye) in local fallout would be likely to have very high radioactivity because they would be deposited so soon after detonation; this fraction of the total fallout is called the prompt or local fallout fraction. It is likely that one such particle upon the skin would be able to cause a localized beta burn. This local fallout, termed Bikini snow after the Pacific island weapon tests, was experienced by the crew on the deck of the Lucky Dragon fishing ship following the explosion of the 15 megaton Shrimp device in the Castle Bravo event. However, these particular decay particles (beta particles) are very weakly penetrating and have a short range, requiring almost direct contact between fallout and personnel to be harmful.
• Rarer still would be personnel who experience radiation burns from highly penetrating gamma radiation. This would likely cause deep gamma penetration within the body, which would result in uniform whole body irradiation rather than only a surface burn. In cases of whole body gamma irradiation (c. 10 Gy) due to accidents involving medical product irradiators, some of the human subjects have developed injuries to their skin between the time of irradiation and death.

In the picture above, the normal clothing (a kimono) that the woman was wearing attenuated the far reaching thermal radiation; the kimono, however, would naturally have been unable to attenuate any gamma radiation, if she were close enough to the weapon to have experienced any, and it would be likely that any such penetrating radiation effect would be evenly applied to her entire body. Beta burns would likely be all over the body if there was contact with fallout after the explosion, unlike thermal burns, which are only ever on one side of the body, as heat radiation infrared naturally does not penetrate the human body. In addition, the pattern on her clothing has been burnt into the skin by the thermal radiation. This is because white fabric reflects more visible and infrared light than dark fabric. As a result, the skin underneath dark fabric is burned more than the skin covered by white clothing. 

There is also the risk of internal radiation poisoning by ingestion of fallout particles, if one is in a fallout zone.

Radiation poisoning

Radiation poisoning, also called "radiation sickness" or a "creeping dose", is a form of damage to organ tissue due to excessive exposure to ionizing radiation. The term is generally used to refer to acute problems caused by a large dosage of radiation in a short period, though this also has occurred with long-term exposure to low-level radiation. Many of the symptoms of radiation poisoning occur as ionizing radiation interferes with cell division. There are numerous lethal radiation syndromes, including prodromal syndrome, bone marrow death, central nervous system death and gastrointestinal death.

Prodromal syndrome

The “prodromal syndrome” is not a diagnosis, but the technical term used by health professionals to describe a specific group of symptoms that may precede the onset of an illness. For example, a fever is “prodromal” to measles, which means that a fever may be a risk factor for developing this illness.

Bone marrow death

Bone marrow death is caused by a dose of radiation between 2 and 10 Gray and is characterized by the part of the bone marrow that makes the blood being broken down. Therefore, production of red and white blood cells and platelets is stopped due to loss of the blood-making stem cells (4.5 Gray kills 95% of stem cells). The loss of platelets greatly increases the chance of fatal hemorrhage, while the lack of white blood cells causes infections; the fall in red blood cells is minimal, and only causes mild anemia.

The exposure to 4.5 Gray of penetrating gamma rays has many effects that occur at different times:

In 24 hours:

• vomiting
• diarrhea

These will usually abate after 6–7 days. 

Within 3–4 weeks there is a period of extreme illness.

• severe bloody diarrhea, indicating intestinal disorders causing fluid imbalance
• extensive internal bleeding
• sepsis infections

The peak incidence of acute BM death corresponds to the 30-day nadir in blood cell numbers. The number of deaths then falls progressively until it reaches 0 at 60 days after irradiation. The amount of radiation greatly affects the probability of death. For example, over the range of 2 to 6 Gray the probability of death in untreated adults goes from about 1% to 99%, but these figures are for healthy adults. Therefore, results may differ, because of the thermal and mechanical injuries and infectious conditions.

Gastrointestinal death

Gastrointestinal death is caused by a dose of radiation between 10 and 50 Gray. Whole body doses cause damage to epithelial cells lining the gastrointestinal tract and this combined with the bone marrow damage is fatal. All symptoms become increasingly severe, causing exhaustion and emaciation in a few days and death within 7–14 days from loss of water and electrolytes.

The symptoms of gastrointestinal death are:

• gastrointestinal pain
• anorexia
• nausea
• vomiting
• diarrhea

Central nervous system death

Central nervous system death is the main cause of death in 24–48 hours among those exposed to 50 Gray.  The symptoms are:

• vomiting
• nausea
• diarrhea
• drowsiness
• lethargy
• tremors
• delirium
• frequent seizures
• convulsions
• heat prostration
• coma
• respiratory failure
• death

Short-term effects (6–8 weeks)

Skin

The skin is susceptible to beta-emitting radioactive fallout. The principal site of damage is the germinal layer, and often the initial response is erythema (reddening) due to blood vessels congestion and edema. Erythema lasting more than 10 days occurs in 50% of people exposed to 5-6 Gray.

Other effects with exposure include:

• 2–3 Gray—temporary hair loss
• 7 Gray—permanent epilation occurs
• 10 Gray—itching and flaking occurs
• 10–20 Gray—weeping blistering and ulceration will occur

Lungs

The lungs are the most radiosensitive organ, and radiation pneumonitis can occur leading to pulmonary insufficiency and death (100% after exposure to 50 Gray of radiation), in a few months.

Radiation pneumonitis is characterized by:

• Loss of epithelial cells
• Edema
• Inflammation
• Occlusions of airways, air sacs and blood vessels
• Fibrosis

Ovaries

A single dose of 1–2 Gray will cause temporary damage and suppress menstruation for periods up to 3 years; a dose of 4 Gray will cause permanent sterility.

Testicles

A dose of 0.1 Gray will cause low sperm counts for up to a year; 2.5 Gray will cause sterility for 2 to 3 years or more. 4 Gray will cause permanent sterility.

Long-term effects

Cataract induction

The timespan for developing this symptom ranges from 6 months to 30 years to develop but the median time for developing them is 2–3 years.

• 2 Gray of gamma rays cause opacities in a few percent
• 6-7 Gray can seriously impair vision and cause cataracts

Cancer induction

Cancer induction is the most significant long-term risk of exposure to a nuclear bomb. Approximately 1 out of every 80 people exposed to 1 Gray will die from cancer, in addition to the normal rate of 20 out of 80. About 1 in 40 people will get cancer, in addition to the typical rates of 16-20 out of 40. Different types of cancer take different times for them to appear:

• 2 years for leukemia to appear
• 20 or more years for skin cancer or lung cancer

In utero effects on human development

A 1 Gy dose of radiation will cause between 0 and 20 extra cases of perinatal mortality, per 1,000 births and 0-20 cases per 1000 births of severe mental sub-normality. A 0.05 Gy dose will increase death due to cancer 10 fold, from the normal 0.5 per 1000 birth rate to a rate of 5 per 1,000. An antenatal dose of 1 Gy in the first trimester causes the lifetime risk of fatal cancer sometime in the child's life to increase from c. 25% in non-exposed humans to 100% in the first trimester after exposure.

Transgenerational genetic damage

Exposure to even relatively low doses of radiation generates genetic damage in the progeny of irradiated rodents. This damage can accumulate over several generations. No statistically demonstrable increase of congenital malformations was found among the later conceived children born to survivors of the Nuclear weapons at Hiroshima and Nagasaki. The surviving women of Hiroshima and Nagasaki, that could conceive, who were exposed to substantial amounts of radiation, went on and had children with no higher incidence of abnormalities than the Japanese average.

Infectious diseases resulting from nuclear attack

It was assumed in the 1983 book Medical Consequences of Radiation Following a Global Nuclear War that, although not caused by radiation, one of the long-term effects of a nuclear war would be a massive increase in infectious diseases caused by fecal matter contaminated water from untreated sewage, crowded living conditions, poor standard of living, and lack of vaccines in the aftermath of a nuclear war, with the following list of diseases being cited:

• Dysentery
• Typhoid
• Infectious hepatitis
• Salmonellosis
• Cholera
• Meningococcal meningitis
• Tuberculosis
• Diphtheria
• Whooping cough
• Polio
• Pneumonia

However although what the authors describe are conditions already prevalent in many of the world's city slums, it is inconceivable why people would try to remain living in crowded conditions by reverting to slum lifestyles, during or after a nuclear war. As many cities would already be destroyed, with urban life, slum or otherwise, this would serve no benefit to inhabitants.

There would be billions of disease carrying vectors, in the form of city residents, lying deceased in cities caused by the direct nuclear weapons effects alone, with the surviving few billion people spread out in rural communities living agrarian lifestyles, with the survivors therefore posing a way of living far less prone to creating the crowded slum living conditions required for infectious diseases to spread. Moreover, as reported in a paper published in the journal Public Health Reports, it is also one of a number of prevalent myths that infectious diseases always occur after a disaster in cities.

Epidemics seldom occur after a disaster, and dead bodies do not lead to catastrophic outbreaks of infectious diseases. Intuitively, epidemic diseases, illnesses, and injuries might be expected following major disasters. However, as noted by de Goyet, epidemics seldom occur after disasters, and unless deaths are caused by one of a small number of infectious diseases such as smallpox, typhus, or plague, exposure to dead bodies does not cause disease ... Cholera and typhoid seldom pose a major health threat after disasters unless they are already endemic.

Nuclear weapon yield

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Nuclear_weapon_yield 

 

Log–log plot comparing the yield (in kilotons) and mass (in kilograms) of various nuclear weapons developed by the United States.

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 (the standardized equivalent mass of trinitrotoluene which, if detonated, would produce the same energy discharge), either in kilotons (kt—thousands of tons of TNT), in megatons (Mt—millions of tons of TNT), or sometimes in terajoules (TJ). An explosive yield of one terajoule is equal to 0.239 kilotonnes of TNT. 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 (thermonuclear weapons) has been estimated to six 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. Since then, the smaller warheads needed to achieve the increased net damage efficiency (bomb damage/bomb mass) 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 (most yield figures are approximate):

Bomb	Yield		Notes
	kt TNT	TJ
Davy Crockett	0.02	0.084	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).
AIR-2 Genie	1.5	6.3	An unguided air-to-air rocket armed with a W25 nuclear warhead developed to intercept bomber squadrons.
Hiroshima's "Little Boy" gravity bomb	13–18	54–75	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	19–23	79–96	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 US pure fission bomb, 60 kg uranium, implosion type. Never deployed.
Orange Herald Small	720	3,000	Most powerful tested UK boosted fission missile warhead.
B83 nuclear bomb	1,200	5,000	Variable yield weapon, most powerful US weapon in active service.
B53 nuclear bomb	9,000	38,000	Was the most powerful US bomb in active service until 1997. 50 were retained as part of the "Hedge" portion of the Enduring Stockpile until completely dismantled in 2011. The Mod 11 variant of the B61 replaced the B53 in the bunker busting role. The W53 warhead from the weapon was used on the Titan II Missile until the system was decommissioned in 1987.
Castle Bravo device	15,000	63,000	Most powerful US test. Never deployed.
EC17/Mk-17, the EC24/Mk-24, and the B41 (Mk-41)	25,000	100,000	Most powerful US weapons ever: 25 megatonnes of TNT (100 PJ); the Mk-17 was also the largest by area square footage and mass cubic footage: about 20 short tons (18,000 kg). The Mk-41 or B41 had a mass of 4800 kg and yield of 25 Mt; 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, yield of 50 megatons, (50 million tons of TNT). In its "final" form (i.e. with a depleted uranium tamper instead of one made of lead) it would have been 100 megatons.
All nuclear testing as of 1996	510,300	2,135,000	Total energy expended during all nuclear testing.

Comparative fireball radii for a selection of nuclear weapons. Contrary to the image, which may depict the initial fireball radius, the maximum average fireball radius of Castle Bravo, a 15 megaton yield surface burst, is 3.3 to 3.7 km (2.1 to 2.3 mi), 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 .21 to .24 km (0.13 to 0.15 mi), 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 (25 TJ/kg). 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 (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 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 (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, 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. (The UK's Orange Herald was a very large boosted fission bomb, with a yield of 750 kilotons.) However, there is no known upper yield limit for a fusion bomb.

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.

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
July 16, 1945	Trinity	18–20	United States	First fission device test, first plutonium implosion detonation
August 6, 1945	Little Boy	12–18	United States	Bombing of Hiroshima, Japan, first detonation of a uranium gun-type device, first use of a nuclear device in combat.
August 9, 1945	Fat Man	18–23	United States	Bombing of Nagasaki, Japan, second detonation of a plutonium implosion device (the first being the Trinity Test), second and last use of a nuclear device in combat.
August 29, 1949	RDS-1	22	Soviet Union	First fission weapon test by the Soviet Union
October 3, 1952	Hurricane	25	United Kingdom	First fission weapon test by the United Kingdom
November 1, 1952	Ivy Mike	10,400	United States	First cryogenic fusion fuel "staged" thermonuclear weapon, primarily a test device and not weaponized
November 16, 1952	Ivy King	500	United States	Largest pure-fission weapon ever tested
August 12, 1953	Joe 4	400	Soviet Union	First fusion weapon test by the Soviet Union (not "staged")
March 1, 1954	Castle Bravo	15,000	United States	First dry fusion fuel "staged" thermonuclear weapon; a serious nuclear fallout accident occurred; largest nuclear detonation conducted by United States
November 22, 1955	RDS-37	1,600	Soviet Union	First "staged" thermonuclear weapon test by the Soviet Union (deployable)
May 31, 1957	Orange Herald	720	United Kingdom	Largest boosted fission weapon ever tested. Intended as a fallback "in megaton range" in case British thermonuclear development failed.
November 8, 1957	Grapple X	1,800	United Kingdom	First (successful) "staged" thermonuclear weapon test by the United Kingdom
February 13, 1960	Gerboise Bleue	70	France	First fission weapon test by France
October 31, 1961	Tsar Bomba	50,000	Soviet Union	Largest thermonuclear weapon ever tested—scaled down from its initial 100 Mt design by 50%
October 16, 1964	596	22	China	First fission weapon test by the People's Republic of China
June 17, 1967	Test No. 6	3,300	China	First "staged" thermonuclear weapon test by the People's Republic of China
August 24, 1968	Canopus	2,600	France	First "staged" thermonuclear weapon test by France
May 18, 1974	Smiling Buddha	12	India	First fission nuclear explosive test by India
May 11, 1998	Pokhran-II	45–50	India	First potential fusion-boosted weapon test by India; first deployable fission weapon test by India
May 28, 1998	Chagai-I	40	Pakistan	First fission weapon (boosted) test by Pakistan
October 9, 2006	2006 nuclear test	under 1	North Korea	First fission weapon test by North Korea (plutonium-based)
September 3, 2017	2017 nuclear test	200–300	North Korea	First "staged" thermonuclear weapon test claimed by North Korea

Note

• "Staged" 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.

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. 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 (Bhangmeter), seismographic data (CTBTO), and the strength of the shock wave.

Alongside contemporary fundamental physics, data from nuclear testing resulted in the following total blast and thermal energy fractionation being observed for fission detonations near sea level

Blast	50%
Thermal energy	35%
Initial ionizing radiation	5%
Residual fallout radiation	10%

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 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:

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.

The surface area (A) and volume (V) of a sphere are: ${\displaystyle A=4\pi r^{2}}$ and ${\displaystyle V={\frac {4}{3}}\pi r^{3}}$ 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 × 2π(14 km)². Multiply by 1 atm to get energy of 3×10¹⁴ J ~ 80 kT TN.

Picture of the blast, captured by Berlyn Brixner 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 (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 equation having compatible dimensions that can be constructed from these quantities is: 

${\displaystyle R=S\left({\frac {{E{t}}^{2}}{\rho }}\right)^{\frac {1}{5}}}$

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 

${\displaystyle \gamma ={C_{P} \over C_{V}}}$

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 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).) 

A good approximation to Taylor's constant S for ${\displaystyle \gamma }$ below about 2 is:

${\displaystyle S={\Biggl (}{75(\gamma -1) \over \ 8\pi }{\Biggr )}^{\frac {1}{5}}}$

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 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 :

${\displaystyle E=[{M}.{L^{2}}.{T^{-2}}]}$

(think of the expression for kinetic energy, ${\displaystyle E={\frac {mv^{2}}{2}}}$

${\displaystyle \rho =[{M}\cdot {L^{-3}}]}$

${\displaystyle t=[T]}$

${\displaystyle r=[L]}$

and then derive an expression for, say, E, in terms of the other variables, by finding values of ${\displaystyle \alpha }$, ${\displaystyle \beta }$, and ${\displaystyle \gamma }$ in the general relation 

${\displaystyle E={\rho ^{\alpha }}\cdot {t^{\beta }}\cdot {r^{\gamma }}}$

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).

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 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.