(For a full discussion of these updates to EM-1, see the updated earlier post linked here.)
Above: Fig. 12 from John R. Keith and Anthony F. Portare, An Analysis of Army Thermal Transmissivity Calculations, Kaman Sciences Corp., Arlington, VA., report DNA-TR-84-388, AD-A176959 (1984). According to page 39 of the report, these are the air burst thermal yields radiated up to a time of 10 times the time of the final thermal maximum (10t2nd max.) as a function of weapon yield and burst altitude: “A general downward trend is noted with increasing yield.” This reduction of thermal yield fraction with increasing total weapon yield is the opposite of Harold L. Brode’s theoretical emission equation in his 1968 Annual Review of Nuclear Science article “Review of Nuclear Weapons Effects”. Brode’s incorrect conclusion (in simple radiative cooling models that ignore convective cooling and the engulfment of cold air) that the thermal yield fraction increases with increasing total yield, seemed to be justified by the simple fact that the concentration of nitrogen dioxide in the shock front that shields thermal emission from the hot fireball is dependent on overpressure.
This suggests that the distance of any given amount of nitrogen dioxide shielding should scale as the cube-root of the total yield, whereas the fireball radius at final thermal maximum scales as the two-fifths power of the total yield.
Consequently, as the total yield increases, a there should be a reduction in the shielding by the nitrogen dioxide, which as the total yield increases, extends to an ever smaller fraction of the fireball radius at second maximum. The fireball radius at second thermal maximum increases relative to the nitrogen dioxide shielding layer radius as the total yield increases, thus increasing the thermal yield fraction emitted up to that time as a function of total yield, because of the reduced shielding by nitrogen dioxide at higher yields.
However, this argument is only applicable during the period that nitrogen dioxide shock wave shielding of fireball core emission is important, i.e. only up to the final thermal maximum power, by which time about 20-30% of the thermal radiation is emitted. Since 70-80% of the thermal radiation is emitted after the time of the final thermal maximum power, the nitrogen dioxide shielding effect is not important in the late stages. Brode’s 1960s calculations of thermal radiation emission from the fireball omitted the effect of fireball cooling by engulfing cold air (in an air burst) and soil (in a surface burst) from the environment. Due to the inertia of air, these convection cooling effects take time to come into play and so are relatively more important in the case of megaton yields (which emit significant thermal radiation over a long period of many seconds) than kiloton yields, where most of the thermal radiation is radiated within a second, before efficient convection cooling starts. Hence, for higher yield nuclear weapons, convection cooling by the entrainment of cold air and (in the case of a surface burst) soil, quickly cools the fireball after the time of thermal maximum and reduces the fraction of the total yield emitted as thermal radiation in an air burst. The 10t2nd max. thermal yield fraction for a sea-level air density free air burst falls from 35.0% at 1 kt to 34.1% at 10 kt, 33.0% at 100 kt, 29.1% at 1 Mt and to 25.4% at 10 Mt (source: DNA-TR-84-388, AD-A176959, 1984, Table 6, page 42).
In a surface burst, the thermal yield trend as a function of total yield is the opposite to that in a free air burst, because the crater ejecta throw-out shields thermal radiation emission from the fireball more effectively at low yields than at high yields. The radius for any given degree of thermal radiation shielding by crater ejecta scales as the cube-root of yield at sub-kiloton total yields and typically as the quarter-power of total yield for the megaton yield range; thus it is always scaling as a weaker function of total yield than the fireball radius at final thermal maximum, which scales as the two-fifths power of yield. Hence, more of the fireball thermal radiation gets shielded by crater ejecta throw-out in low yield surface bursts than in high yield surface bursts. This makes the thermal yield fraction in a surface burst increase from 4.5% at 1 kt to 6.6% at 10 kt, 13% at 100 kt, 16% at 1 Mt, and 17% at 10 Mt (source: DNA-TR-84-388, AD-A176959, 1984, Table 6, page 42).
Above: Fig. 13 from John R. Keith and Anthony F. Portare, An Analysis of Army Thermal Transmissivity Calculations, Kaman Sciences Corp., Arlington, VA., report DNA-TR-84-388, AD-A176959 (1984). According to page 39 of the report, these are the air burst thermal yields radiated up to a time of 10 times the time of the final thermal maximum (10t2nd max.) as a function of weapon yield and burst altitude: “A general downward trend is noted with increasing yield.”
Above: Table 6 from John R. Keith and Anthony F. Portare, An Analysis of Army Thermal Transmissivity Calculations, Kaman Sciences Corp., Arlington, VA., report DNA-TR-84-388, AD-A176959 (1984). According to page 39 of the report, these are the thermal yields radiated up to a time of 10 times the time of the final thermal maximum (10t2nd max.). Notice that, as we have explained physically, the sea-level air burst thermal yield fraction decreases with increasing total yield because more and more of the cooling is done by convection mixing processes rather than by radiation in the longer thermal pulse of higher yields, while in a surface burst the thermal yield fraction increases with increasing total yield, because the crater ejecta throw-out radii which absorb much thermal radiation in a surface burst scale less rapidly (i.e., as the cube or fourth root) with total yield than does the fireball radius at final thermal peak power (i.e., the two-fifths power of yield).
Above: Fig. 14 from John R. Keith and Anthony F. Portare, An Analysis of Army Thermal Transmissivity Calculations, Kaman Sciences Corp., Arlington, VA., report DNA-TR-84-388, AD-A176959 (1984). This diagram shows the effect of burst altitude from sea level to 30 km upon the thermal pulse curve shape for a 100 kt air burst. The report notes that a surface burst thermal power curve is not identical to a sea level air burst, but on account of the extra opacity of the fireball due to the earth incorporated from the crater process, the surface burst thermal curve has a much smaller final thermal maximum radiating power. The surface burst fireball also takes a slightly longer time to reach the final peak thermal emission, than an equivalent yield sea level air density air burst.
Above: Fig. 15 from John R. Keith and Anthony F. Portare, An Analysis of Army Thermal Transmissivity Calculations, Kaman Sciences Corp., Arlington, VA., report DNA-TR-84-388, AD-A176959 (1984). This diagram is a linear version of the logarithmic plots in Fig. 14, showing how the shape of the standard thermal pulse curve depends on burst altitude for air bursts of 100 kt total yield.
Above: Fig. 21 from John R. Keith and Anthony F. Portare, An Analysis of Army Thermal Transmissivity Calculations, Kaman Sciences Corp., Arlington, VA., report DNA-TR-84-388, AD-A176959 (1984). This diagram shows how the different wavelengths in the thermal radiation spectrum, from 0.32 micron ultraviolet to 1.87 micron infrared, are transmitted through a standard Nevada desert atmosphere for an air burst 1 km above ground (or a megaton range surface burst fireball with a radius of over 2 km, so that the mean height of the radiating surface is 1 km above ground) with ground level taken to 1.28 km above sea level. The data come from Kaman Science Corporation’s TRAX Monte Carlo simulation code for atmospheric transmission. Notice that the 0.32 micron curve for ultraviolet shows rapid attenuation due to absorption by natural ozone in the atmosphere, and the 1.87 micron infrared curve shows absorption by water vapour and carbon dioxide; but the shape of the transmission curves for ultraviolet and infrared are totally different (each departs from a straight line exponential attenuation law by curving in a different direction from a straight line, so that the average would be close to a straight line and thus a simple exponential attenuation law). Because the transmission fraction is a logarithmic plot while distance is linear plot, a straight-line transmission on this graph represents exponential attenuation and a curve represents a departure from exponential attenuation. The data for the wavelengths between the extremes, i.e. 0.55, 0.94, and 1.23 microns, all show much less attenuation as they are closer to (or within) the visible radiation band. The 0.55-micron curve shows a transmission of 70% to a horizontal range of 30 km. If this is treated as an exponential absorption with the typical Nevada desert visibility range of 80 km, then the Nevada nuclear test data thermal radiation transmission, T = e-R/V = e-30/80 = 0.69, is similar to the 0.55-micron wavelength transmission predictions. However, this simplified approach (used in the 1960s by Gibbons) would not be justified because it would properly take account of the effect of atmospheric water vapour of air near sea level on the infrared radiation transmission.
Above: Fig. 39 from John R. Keith and Anthony F. Portare, An Analysis of Army Thermal Transmissivity Calculations, Kaman Sciences Corp., Arlington, VA., report DNA-TR-84-388, AD-A176959 (1984). Transmission for a surface burst and a 1 km altitude air burst (or a high yield surface burst where the mean height of the hemispherical fireball radiating surface is 1 km high) for sandy soil ground, 300 m base altitude cloud cover, and 25 km atmospheric visibility (1.5 g/m3 of sea level water vapour concentration). This report proves that the effect of the fireball radiating temperature on changing the source spectra of the thermal radiation as a function of weapon yield and for ground interaction is negligible in comparison to the effect of the height of the fireball. The thermal transmission as a function of distance is similar for different yields if the effective fireball height above the ground is the same. It is also similar for a surface burst and a sea level air burst (although obviously the thermal yield will be different in each case) if the mean height of the fireball is the same. However, varying the height of the centre of the radiating surface of the fireball causes a large change in the thermal transmission curve, mainly as a result of the variation in the water vapour content of the air as a function of height. The cooler air at higher altitudes contains less water vapour and therefore allows more transmission of infrared radiation than sea level air.
Above: Fig. 40 from John R. Keith and Anthony F. Portare, An Analysis of Army Thermal Transmissivity Calculations, Kaman Sciences Corp., Arlington, VA., report DNA-TR-84-388, AD-A176959 (1984). Thermal transmission from a 100 kt surface burst with the fireball at ground level for a hypothetical dark, zero albedo ground, i.e. a totally radiation absorbing, non-reflective ground which does not reflect any of the thermal radiation, for no cloud cover (curve 1) and cloud cover with its base at altitudes of 300 m (curve 2), 1,500 m (curve 3) and 3,000 m (curve 4), with in each case 25 km atmospheric visibility (1.5 g/m3 of sea level water vapour concentration). Curve 1 therefore presents the case where the transmission is purely a function of the air characteristics, without any ground or cloud reflection effects.
Above: Fig. 41 from John R. Keith and Anthony F. Portare, An Analysis of Army Thermal Transmissivity Calculations, Kaman Sciences Corp., Arlington, VA., report DNA-TR-84-388, AD-A176959 (1984). Thermal transmission from a 100 kt surface burst with the fireball at ground level for a sandy soil, for no cloud cover (curve 1) and cloud cover with its base at altitudes of 300 m (curve 2), 1,500 m (curve 3) and 3,000 m (curve 4), with in each case 25 km atmospheric visibility (1.5 g/m3 of sea level water vapour concentration). Curve 1 therefore presents the case where the transmission is purely a function of the air characteristics and ground reflection, with no cloud reflection effects. We have added curve 5 (which is curve 1 from Fig. 40 already given, for a non-reflecting ground and no cloud cover) to show the small effect of the ground reflection on transmission. It is clear that when both ground reflection and cloud reflection occur, the surfaces act like a waveguide for thermal radiation energy, whose transmission is enhanced by “channelling” of thermal energy.
Above: Fig. 43 from John R. Keith and Anthony F. Portare, An Analysis of Army Thermal Transmissivity Calculations, Kaman Sciences Corp., Arlington, VA., report DNA-TR-84-388, AD-A176959 (1984). Thermal transmission for a sandy soil, for no cloud cover (curve 1) and cloud cover with its base at altitudes of 1,500 m (curves 2), 1,500 m (curves 3) and 3,000 m (curves 3), with in each case 25 km atmospheric visibility (1.5 g/m3 of sea level water vapour concentration). High level clouds above the nuclear explosion can enhance thermal transmission, by reflecting back to the ground some of the thermal radiation that would otherwise be lost to space. But when a nuclear explosion occurs in or above a cloud layer, or above a smoke screen, the opposite effect occurs and the thermal radiation is shielded and attenuated to a considerable extent prior to reaching a target. During Pacific nuclear tests of air and high altitude bursts in 1958 and 1962, cloud cover over ground zero was either required as a condition for firing, or alternatively was provided artificially by smoke screen generators in order to prevent any risk of injury to the dark coloured terns. Similarly, for the very high altitude tests in 1962 where the fireballs would be above the horizon as viewed from the Hawaiian islands 1,300 km always, firing was only authorized when there was low-level local cloud cover over the Hawaiian islands to protect the public from any risk of retinal injury. Nevada tests in 1955 over smoke screens demonstrated the value of smoke clouds in attenuating thermal radiation from nuclear weapons. The 110 kt 1954 CASTLE-KOON test at Bikini Atoll was detonated in a rainstorm with very low visibility, and thermal radiation effects were undetectable at the measuring stations.
Above: Fig. 44 from John R. Keith and Anthony F. Portare, An Analysis of Army Thermal Transmissivity Calculations, Kaman Sciences Corp., Arlington, VA., report DNA-TR-84-388, AD-A176959 (1984). Thermal transmission in 6.5 km atmospheric visibility (10 g/m3 of sea level water vapour concentration) for a 10 kt surface burst with 300 m base cloud cover and three different ground surface reflections: zero reflection, dirt (sandy soil), and snow. Comparisons of these curves to those of the previous figure prove that the ground reflection characteristics are much less important in determining thermal radiation transmission than the atmospheric visibility, the fireball altitude, and the cloud cover situation. The curve for dirt (sandy soil) with 6.5 km visibility due to 10 g/m3 of sea level water vapour concentration in the air and cloud cover with its base at 300 m represents the mean transmission to be expected for thermal radiation in the U.K. and other areas of Northwest Europe, as shown by statistical data in DNA-TR-84-388, AD-A176959 (1984).
Above: Ernest Bauer's August 1990 Institute for Defense Analyses report, Physics of High-Temperature Air. Part. 2. Applications, ADA229778, contains a useful section summarising a little of the available nuclear testing data on the mass of fallout as a function of burst altitude for surface bursts, free air bursts, and tower burst nuclear weapons tests, as well as the family of computed curves above showing the transition from a single thermal pulse for a 1 Mt air burst at 50 km altitude to a double-pulse for a 1 Mt sea level air burst. The main reason for the transition is the weakening of the shock wave due to the lower air density at higher altitudes: the lower air density at high altitudes simply allows the X-rays (which comprise 75% of the primary energy emission from a typical 1 ton mass, 1 megaton yield detonation) to travel much larger distances before being absorbed by the air.
This means that same amount of energy is spread over a larger volume of air in a high altitude burst, so the energy density (energy per unit volume) in the fireball is lower than it is for the tiny initial X-ray fireball at sea level, and this lower energy density produces a smaller temperature rise, and thus a weaker blast wave. This weaker blast wave at high altitudes is unable to compress air to a high enough density to form the concentrations of nitrogen dioxide that shield thermal radiation after shock formation in a sea level detonation. The nitrogen dioxide formed in the shock wave from compressed hot air absorbs the thermal radiation from the fireball core in a sea level detonation, causing the minimum and thus the two pulses, but nitrogen dioxide is not formed in a high altitude burst because the shock wave is not strong enough to produce it, hence the thermal minimum gradually disappears as the burst height is increased, merging the two pulses together into a single pulse for a 1 Mt detonation at 50 km altitude.
Another interesting report now online (23 MB PDF) is Dan H. Holland, et al., Physics of High-Altitude Nuclear Burst Effects, Mission Research Corp., Santa Barbara, CA., ADA068541, December 1977:
'This compendium presents a reasonably thorough summary of the physics and chemistry that is particularly relevant to the prediction of effects of high-altitude nuclear bursts on radar, optical, infrared, and communication systems. The various chapters have been written by experts on the particular subjects. Most of the presentations are on a fairly advanced level, but a serious attempt has been made to keep in mind the special needs of new workers in this field. It is assumed that the reader has a thorough general background in physics.'
A 57 MB March 2008 report by V. A. Logachev and L. A. Mikhalikhina, Animal Effects from Soviet Atmospheric Nuclear Tests, ITT Corp., Alexandria, VA., report ADA485845, is available online in PDF download format. There is another version available in more compressed PDF format here. The Soviet Union exposed 8,000 animals (sheep, horses, cattle, camels, etc.) in various structures, vehicles, and in the open and shadowed positions, to nuclear explosions in order to assess the effects in different situations, and to different combinations of the various effects of nuclear detonations. Instead of simply giving the straightforward data on effects from specific nuclear tests, the data is presented only as processed output having been combined into three categories of yield range. However, it is still an important report. Table 11 on page 27 gives the following burns energies comparison for bare skin, light summer clothing and heavy winter clothing (as with most Russian nuclear weapons research, they seem to make every effort to cause confusion and ambiguity in the simplest presentations; here it is not stated for which yields the data for burns under clothing apply to):
Above: American data for thermal energy needed for burns under clothing, from page 6.2b of the 1960 (change 2 pages revision) Capabilities of Atomic Weapons, TM 23-200, Confidential. It is interesting to compare this data to the Russian test results.
Update: some new thermal data from nuclear weapons tests is available:
Dr Abraham Broido, et al., “Operation Tumbler-Snapper, Project 8.3, Thermal Radiation from a Nuclear Detonation”, USNRDL, weapon test report WT-543, Secret – Security Information, March 1953, p. 3: “The data reported here indicate a decrease in thermal efficiency with increasing weapon yield, ranging from about 44 per cent at 1 kt to about 34 per cent at 30 kt.”
Teapot basic thermal measurements report (linked here).
Upshot Knothole report on smoke screen protection against thermal radiation (linked here).
Operation Redwing vital basic thermal measurements (report linked here).
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