Dr Harold Leonard Brode's 1954 RAND Corporation computer study of blast wave characteristics from a free air burst, based on integrating the equations of motion with an equation of state and an artificial viscosity, is now available as a free download from the RAND Corporation here. It was openly published in 1955 in the Journal of Applied Physics, vol. 26, pages 766 et seq.
I've commented before here and here about such calculations that because it ignored thermal radiation, the results are imperfect compared to his 1967 study which includes thermal radiation and other phenomena. However, the shock wave itself only radiates a small amount of the thermal radiation. Most of the thermal radiation energy comes from the hot fireball well within the shock front, after the blast wave has broken away from the fireball surface. A bigger cause of error is ignoring the case-shock of the bomb, but that is only important for cratering and phenomena very near the explosion, not for consideration of widespread civil defence countermeasures.
Another online RAND report by Brode on blast is here. This illustration at shows the pioneering 1960 direct ground shock computer calculation by Brode and Bjork:
'Calculations on the cratering and ground motion in a rock medium due to a two-megaton surface burst. The theoretical approach assumes a two-dimensional hydrodynamic model, and it is used to determine the motions involved in the cratering from a large-yield surface burst. Thetechnique is found to work well and to check with experimental observations. It is shown that the primary cause of cratering for such an explosion is not "airslap," as previously suggested, but rather the direct action of the energetic bomb vapors. High-yield surface bursts are therefore less effective in cratering by that portion of the energy that escapes as radiation in the earliest phases of the explosion. The cratering action and ground shock from large-yield explosions is of primary importance to problems of hardening military installations as well as to the peaceful use of nuclear explosions.'
There is an online paper by Brode and J. J. O'Sullivan here expounding the results for protective construction (Brode and O'Sullivan point out in capital letters that you can survive a direct hit with a megaton range nuclear surface burst 'reasonable' earth cover because: 'The initial shock is shown to decrease in intensity very rapidly with increasing penetration to depth due to both the geometric effects of expanding ... and venting into the air above the surface and ... irreversible heating in the crushed, cracked and distorted material must continue to sap the shock strength...').
However, even Brode apparently did not consider the inclusion of the loss of energy in cratering from megaton bombs that is due to gravitational work in shifting millions of tons of soil out of the hole in the ground. This is the cause of the change in crater scaling law from cube-root (1/3 power) to fourth-root (1/4-power) of yield which occurs for non-porous soil media as yield increases from the kiloton to the megaton range. This fact only came to light in the 1980s and makes the empirical ad-hoc (fiddled to fit the facts) 'scaling law' (0.3 power of yield) used for cratering in The Effects of Nuclear Weapons totally obsolete. Another discussion of this can be found in the post: http://glasstone.blogspot.com/2008/05/philip-j-dolans-formerly-secret.html
The following biographical information was published in the book "Survival and the Bomb" (edited by Nobel Laureate Eugene P. Wigner, and published by Indiana University Press, Bloomington edition, London, 1969, page 105):
"Harold L. Brode (Staff Member, the RAND Corporation)
"Harold L. Brode, born in the state of Washington (1923), the son of a school teacher and administrator, spent his childhood years in Oregon and California. He was in military service in the Air Corps from 1943 to 1946. His Bachelor of Arts degree was conferred with honors by UCLA in 1947 (in physics) and a Ph.D. (in theoretical physics) by Cornell University under Professor H. A. Bethe in 1951. He was a President White Fellow at Cornell in 1948. Since 1951 Brode has been a member of the Physics Department at the RAND Corporation, Santa Monica, California. For fifteen years he has worked on the effects of nuclear explosions, contributing to the theory of the blast, fireball, thermal, ground shock, and cratering phenomena. He has been active in nuclear effects test and research planning as an advisor to the Defense Atomic Support Agency and to the Office of the Director of Research and Engineering in the Defense Department. He has long been an Air Force advisor on protective construction and system hardening. He is a member of the National Academy of Sciences Civil Defense Advisory Committee, and participated as a group leader in the Project Harbor summer study on civil defense. He is a member of the White House Engineering Advisory Board, and has been a lecturer in UCLA engineering extension courses since 1960. He has participated in international conferences dealing with weapons effects, protective construction, and civil defense. Brode is the author of several papers on nuclear explosion phenomena and weapons effects and a contributor to several books concerned with or using such information. He has published over fifty technical papers dealing with specific weapon effects. Dr. Brode was married in 1951, has six sons, is active in Boy Scouts, and is a member of Optimists International."
The above (extremely detailed) biography is dated 1969, when Dr Brode was 46, but a briefer, more recent, biography of him in a National Academy of Sciences published book called "The Medical Implications of Nuclear War", dated 1986, is available.
Harold L. Brode is a nuclear weapons effects physicist who pioneered computer simulations of nuclear explosions at the RAND Corporation in the 1950s. In 1951 he received his PhD from Cornell University where his supervisor was Hans A. Bethe. He is co-founder of R&D Associates, Vice-President of Strategic Systems at Pacific-Sierra Research Corporation and Chairman of the U.S. Defense Nuclear Agency's Scientific Advisory Group for Effects (SAGE).
One of his critics commented in Physics Today, vol. 58: "Harold Brode probably knows more about nuclear weapons effects than any other person alive."
I should also add that Wigner's book "Survival and the Bomb" (1969, cited in my previous update comment, above), contains excellent effects information.
It is written entirely by the leading experts, which in itself means absolutely nothing in science [‘Science is the organized skepticism in the reliability of expert opinion.’ - R. P. Feynman as quoted by Dr Lee Smolin, "The Trouble with Physics", 2006, p. 307], but the information is condensed from experimental and observational research and is not merely a consensus of opinion.
The article by Drs. Brode and Newman in the book is as great as the others. It is called "Offensive Weapons and Their Effectiveness" and explains not just the effects of nuclear weapons quantitatively, but also shows the lifespans of major biological war agents (spores and active cells) in darkness (hours for active cells, days for spores), overcast daytime and on a clear day (a few minutes for active cells, and a few hours for spores) - since ultraviolet radiation in sunlight quickly kills most biological agents.
More valuable still are the graphs they calculated showing the ranges for ignition of kindling from nuclear explosions of various yields as a function of atmospheric visibility. These are far more detailed and more helpful than those in any edition of "The Effects of Nuclear Weapons".
For example, Brode's graphs in that article show that a 1 megaton low air burst (detonated at the altitude required to maximise the range of 3 psi peak overpressure over a near ideal surface) would ignite fine kindling material (such as dry litter or dry leaves on a forest floor) out to distances of:
9 miles on an average clear day such as you get at Bikini Atoll (12 miles visibility)
7 miles in medium haze such as hangs over a typical city due to traffic pollution (2.5 miles visibility)
3 miles in heavy cloud, such as occurs if the air burst is within or over clouds or if there is light fog at ground level (1.2 miles visibility)
The above figures are vital for understanding how dramatically ignition ranges depend on the weather: you cannot rely on nuclear weapons to start a lot of outdoor fires if it happens to be cloudy raining. Like fallout, the effects depend as much or more on the burst altitude and the weather which happens to occur at the time of the attack, than on simply the yield.
For instance, Brode shows that a surface burst 1 Mt ignites fine kindling material out to 6 miles on an average fine day, compared to about 9 miles for an air burst.
The role of the weather and the burst altitude on ignition ranges is not clearly illustrated in "The Effects of Nuclear Weapons".
The chapter referred to above, Offensive Weapons and Their Effectiveness, by Harold L. Brode and John S. Newman (then Associate Professor of Chemical Engineering, University of California at Berkeley), in Wigner's 1969 book Survival and the Bomb, makes other interesting remarks on pp. 120-124 about cratering, ground shock and earth-penetrating nuclear weapons:
"The air pressure resulting from nuclear bursts in the air (above the ground) creates some motion in the ground, but at almost all levels the air-induced ground motions are of less consequence than the direct air blast effects. Injuries can be sustained from sudden motions of the walls and floors of buried shelters at high overpressure levels, and such structures can be collapsed by the same pressures. But the danger from shock transmitted to occupants of surviving shelters is almost never severe in areas where the overpressure does not exceed 100 psi. For shelters intended to survive above 200 psi, some special consideration should be given to protecting occupants (with padding, with straps or bunks and hammocks) and to insuring that shelter appurtenances are secured or isolated so that they do not become dangerous missiles within the shelter. Shelters in hard rock suffer less motions but higher accelerations, and are generally less likely to lead to ground shock casualties than shelters located in soil. ...
"Crushing stresses beneath a crater do not extend much more than one and one-third of the crater radii (five to seven times the depth), so that very deeply buried shelters should be immune to any but the largest imaginable weapons burst after considerable earth penetration, and even shallow buried structures may survive only a little beyond the crater's edge ...
"So-called radiological weapons disseminate large amounts of radioactive materials. They can be nuclear bombs modified so that they produce special radioactive material in addition to the usual fission products (for example, cobalt bombs), or they can disseminate already radioactive materials in the form of a powder. The inclusion of such inert materials usually does not compensate for the consequent reduction in explosive yield. Furthermore, blast effects are so much more predictable than fallout effects that targetting calculations are usually based on the former. ...
"Penetrating weapons offer the possibility of accentuating blast damage while suppressing thermal and nuclear radiation. The depth of penetration is generally limited to depths of, at most, around 100 feet in soil - and under most cities bedrock is much nearer the surface than this. For large yields, the cratering is increased without seriously degrading the blast or thermal effects, as compared with those of surface bursts. Fallout would be very much intensified very close by. The total explosive power of an earth-penetrating weapon would be smaller than that of a standard weapon of the same weight ...
"The effects of a single nuclear explosion are reasonably well understood; the assessment of the damage from an attack is made uncertain, however, by lack of knowledge of the number of weapons, the yields employed, and the intended targets of the weapons delivered. These, of course, are factors which change with time."
RAND Corp. has now made more of Brode's crucial weapons effects papers available free of charge on line: list of RAND Corp. reports by Brode
H. L. Brode, A Review of Nuclear Explosion Phenomena Pertinent to Protective Construction, the RAND Corporation, Santa Monica, California, Report R-425-PR, May 1964, available free as a PDF download:
Also of interest:
Thermal Radiation from Nuclear Explosions, RAND Corp. paper P-2745, 1963, by Harold L. Brode
and see Fireball Phenomenology, RAND Corp. paper P-3026, 1964, by Harold L. Brode
Brode's 1968 paper in the Annual Review of Nuclear Science is mainly a summary of the papers above, with some extra clarifications and physical insights into the mechanisms at play.and for the early origins of Brode's application of computer codes to evaluating the Lagrangian equations of shock motion, see:
Numerical Solutions of Spherical Blast Waves RM-1363-AEC, 1954. In 1955 this report mentioned was published in the Journal of Applied Physics, vol. 26, pp. 766-775 (but beware that these 1954 calculations are only approximate at high peak overpressures, since the code is purely hydrodynamic; i.e., it neglects the loss of energy in the blast wave at very high overpressures which is due to the emission of thermal radiation by the very hot, compressed shock front; Brode's later works from the late 1950s onwards includes thermal radiation in blast calculations, which required a lot more computer power than the 1954 calculations)
Other interesting reports:
H. L. Brode, Analytical Approximations to the Nuclear Blast Wave, Pacific-Sierra Research Corporation, DNA-TR-82-179, June 1983.
H. L. Brode, Review of Nuclear Weapons Effects, in the Annual Review of Nuclear Science, v18, 1968, pp. 153-202.
S. J. Speicher and H. L. Brode, An Analytic Approximation for Peak Overpressure versus Burst height and Ground Range over an Ideal Surface, Pacific-Sierra Research Corporation, Note 336, September 1980.
S. J. Speicher and H. L. Brode, Airblast Overpressure Analytic Expression for Burst Height, Range, and Time - over an Ideal Surface, Pacific-Sierra Research Corporation, DNA-TR-81-218, December 1981.
Most of the interesting mathematical expressions in the above papers are quoted and compiled in the comprehensive handbook: Design of Structures to Resist Nuclear Weapons Effects, American Society of Civil Engineers, New York, 1985. (The British Library has a copy.)
Brode's very interesting early analysis of height-of-burst curves based on nuclear test data available in 1954 and used as part of the analysis for the November 1957 secret manual Capabilities of Atomic Weapons (TM 23-200), is now declassified:
Harold L. Brode, Height of Burst for Atomic Bombs (after Upshot Knothole), RAND Corp., California, report AD0354295, June 1954, PDF: http://stinet.dtic.mil/cgi-bin/GetTRDoc?AD=0354295&Location=U2&doc=GetTRDoc.pdf
(See also F. B. Porzel's May 1954 Los Alamos report LA-1664, Height of Burst for Atomic Bombs, 1954.)
There is further biographical information on Dr Brode in Lynn Eden's book Whole World on Fire: organizations, Knowledge, & Nuclear Weapons Devastation, Cornell University Press, Ithaca and London, 2004, pages 27 and 227:
"Brode's five decade career has been devoted to the study of nuclear weapons effects. He received his Ph.D. in theoretical nuclear physics from Cornell University in 1951 and gained prominence at RAND (a prototypical defense consulting firm known as a think tank) in the 1950s working on blast effects. In this period, he first described the nuclear blast wave environment (later known as 'Brode-fits'), a critical component for predicting blast damage. For most of 1961 to 1993, Brode served on the Scientific Advisory Group of the Defense Nuclear Agency (DNA), the government agency responsible for studying nuclear weapons effects; he was chair from 1980 to 1991. In February 1997, the Defense Special Weapons Agency, the successor to DNA, presented Brode with its Lifetime Achievement Award, the agency's 'highest award for public service'. It said that Brode 'achieved near legendary status as an expert in nuclear weapons effects."
Also of interest on page 227 is the fact that Brode edited a major revision of Dolan's two-volume original version of DNA-EM-1, Capabilities of Nuclear Weapons:
"Brode worked at RAND for twenty years, and left in 1971 to join the newly formed Los Angeles think tank R&D Associates (RDA), founded by two former RAND scientists, brothers Albert and Richard Latter. Brode headed the physics department at RDA. In 1979 he became vice president of another Southern California research firm, Pacific-Sierra Research. During his career, Brode served on more than twenty-five governmental advisory panels, groups, and committees; perhaps most important, he was a member of the Scientific Advisory Group (SAGE) to DASA/DNA, serving almost the entire period from 1961 to 1992, and chairing it from 1980 to 1992. As chair, Brode edited a major revision of DNA's Effects Manual-1, Capabilities of Nuclear Weapons, the authoritative multivolume source on nuclear weapons for those in the government, generally referred to as EM-1. ... In 1961 he published with Robert Bjork the results of the first calculation of cratering action by a nuclear weapon burst on the surface of the earth."
[She also mentions on page 228 that Brode together with Charles McDonald at RDA also established for the U.S. Army that a neutron bomb radiation dose of 20,000 rads was required to 'immediately' incapacitate an enemy tank crew to prevent them continuing to fight.]
As indicated in my post http://glasstone.blogspot.com/2006/03/fires-from-nuclear-explosions.html, and George Stanbury's article The Fire Hazard from Nuclear Weapons in the 'Restricted' classified U.K. Home Office Scientific Adviser's Branch journal Fission Fragments (W. F. Greenhalgh, Editor), London, Issue Number 3, August 1962, pages 22-26, quoted in the blog post http://glasstone.blogspot.com/2006/08/nuclear-weapons-1st-edition-1956-by.html, plus the discussion of thermal transmittivity which follows it, there is a severe misunderstanding of thermal ignition from nuclear weapons.
Modern cities don't have the fuel density of the wooden frame houses of 1945 Japan and the medieval wooden multistorey buildings in the old city of Hamburg which was burned down in a firestorm. However, although the main thrust of Lynn Eden's book is essentially irrelevant tail-end laggard propaganda from the Cold War 'nuclear winter' era which has no relevance whatsoever to the real terrorist nuclear threat and limited warfare threats now existing, and although it gets many points wrong on thermal ignition and firestorms by ignoring the data (e.g. George Stanbury's analysis of Hamburg's firestorm, quoted on this blog) about how much fuel is needed for a firestorm and how modern (non-wooden) blasted cities would swamp any fuel with rubble of unburnable concrete, brick, mortar, metal and dust, so firestorms would not occur, there are some interesting discussions in her book concerning the history of blast wave damage modelling behind the "Physical Vulnerability Handbook" and the Teapot-Met test and Redwing-Cherokee test on steel framed sheds to establish the effects of the duration of air blast on damage caused at a fixed overpressure.
The book is not completely biased throughout, many chapters do contain quite objective and well researched sections, although the beginning and ending are loaded with propaganda type bias about brick and concrete buildings being liable to burn. It's tempting to suggest that if she had dropped a match on a brick she'd have seen the problem of firestorms in modern cities, as opposed to the wooden cities of Germany's medieval areas and of Japan in the 1940s. However, I'll resist the temptation to be sarcastic. It's a serious matter because by exaggerating nuclear effects, civil defence is effectively discredited in all situations, and the imaginary firestorms in concrete cities - while good for impressing the gullible with the politics of mainstream Cold War pontification by "nuclear winter" and firestorm disarmament arguments - have nothing whatsoever to do with terrorist nuclear threats today.