Blast wave

Last updated December 11, 2023

In fluid dynamics, a blast wave is the increased pressure and flow resulting from the deposition of a large amount of energy in a small, very localised volume. The flow field can be approximated as a lead shock wave, followed by a self-similar subsonic flow field. In simpler terms, a blast wave is an area of pressure expanding supersonically outward from an explosive core. It has a leading shock front of compressed gases. The blast wave is followed by a blast wind of negative gauge pressure, which sucks items back in towards the center. The blast wave is harmful especially when one is very close to the center or at a location of constructive interference. High explosives that detonate generate blast waves.

Sources

High-order explosives (HE) are more powerful than low-order explosives (LE). HE detonate to produce a defining supersonic over-pressurization shock wave. Several sources of HE include trinitrotoluene, C-4, Semtex, nitroglycerin, and ammonium nitrate fuel oil (ANFO). LE deflagrate to create a subsonic explosion and lack HE's over-pressurization wave. Sources of LE include pipe bombs, gunpowder, and most pure petroleum-based incendiary bombs such as Molotov cocktails or aircraft improvised as guided missiles. HE and LE induce different injury patterns. Only HE produce true blast waves.^[1]

History

The classic flow solution—the so-called Taylor–von Neumann–Sedov blast wave solution—was independently devised by John von Neumann ^[2]^[3] and British mathematician Geoffrey Ingram Taylor ^[4]^[5] during World War II. After the war, the similarity solution was published by three other authors—L. I. Sedov,^[6] R. Latter,^[7] and J. Lockwood-Taylor^[8]—who had discovered it independently.^[9]

Since the early theoretical work, both theoretical and experimental studies of blast waves have been ongoing.^[10]^[11]

Characteristics and properties

The simplest form of a blast wave has been described and termed the Friedlander waveform.^[12] It occurs when a high explosive detonates in a free field, that is, with no surfaces nearby with which it can interact. Blast waves have properties predicted by the physics of waves. For example, they can diffract through a narrow opening, and refract as they pass through materials. Like light or sound waves, when a blast wave reaches a boundary between two materials, part of it is transmitted, part of it is absorbed, and part of it is reflected. The impedances of the two materials determine how much of each occurs.

The equation for a Friedlander waveform describes the pressure of the blast wave as a function of time:

P(t)=P_{s}e^{-{\frac {t}{t^{*}}}}\left(1-{\frac {t}{t^{*}}}\right).

where P_s is the peak pressure and t* is the time at which the pressure first crosses the horizontal axis (before the negative phase).

Blast waves will wrap around objects and buildings.^[13] Therefore, persons or objects behind a large building are not necessarily protected from a blast that starts on the opposite side of the building. Scientists use sophisticated mathematical models to predict how objects will respond to a blast in order to design effective barriers and safer buildings.^[14]

Mach stem formation

Mach stem formation occurs when a blast wave reflects off the ground and the reflection catches up with the original shock front, therefore creating a high pressure zone that extends from the ground up to a certain point called the triple point at the edge of the blast wave. Anything in this area experiences peak pressures that can be several times higher than the peak pressure of the original shock front.

Constructive and destructive interference

In physics, interference is the meeting of two correlated waves and either increasing or lowering the net amplitude, depending on whether it is constructive or destructive interference. If a crest of a wave meets a crest of another wave at the same point then the crests interfere constructively and the resultant crest wave amplitude is increased; forming a much more powerful wave than either of the beginning waves. Similarly two troughs make a trough of increased amplitude. If a crest of a wave meets a trough of another wave then they interfere destructively, and the overall amplitude is decreased; thus making a wave that is much smaller than either of the parent waves.

The formation of a mach stem is one example of constructive interference. Whenever a blast wave reflects off of a surface, such as a building wall or the inside of a vehicle, different reflected waves can interact with each other to cause an increase in pressure at a certain point (constructive interference) or a decrease (destructive interference). In this way the interaction of blast waves is similar to that of sound waves or water waves.

Damage

Blast waves cause damage by a combination of the significant compression of the air in front of the wave (forming a shock front) and the subsequent wind that follows.^[15] A blast wave travels faster than the speed of sound and the passage of the shock wave usually lasts only a few milliseconds. Like other types of explosions, a blast wave can also cause damage to things and people by the blast wind, debris, and fires. The original explosion will send out fragments that travel very fast. Debris and sometimes even people can get swept up into a blast wave, causing more injuries such as penetrating wounds, impalement and broken bones. The blast wind is the area of low pressure that causes debris and fragments to rush back towards the original explosions. The blast wave can also cause fires or secondary explosions by a combination of the high temperatures that result from detonation and the physical destruction of fuel-containing objects.

Applications

Bombs

In response to an inquiry from the British MAUD Committee, G. I. Taylor estimated the amount of energy that would be released by the explosion of an atomic bomb in air. He postulated that for an idealized point source of energy, the spatial distributions of the flow variables would have the same form during a given time interval, the variables differing only in scale. (Thus the name of the "similarity solution.") This hypothesis allowed the partial differential equations in terms of r (the radius of the blast wave) and t (time) to be transformed into an ordinary differential equation in terms of the similarity variable ${\frac {r^{5}\rho _{o}}{t^{2}E}}$ ,

where $\rho _{o}$ is the density of the air and $E$ is the energy that's released by the explosion.^[16]^[17]^[18] This result allowed G. I. Taylor to estimate the yield of the first atomic explosion in New Mexico in 1945 using only photographs of the blast, which had been published in newspapers and magazines.^[9] The yield of the explosion was determined by using the equation: $E=\left({\frac {\rho _{o}}{t^{2}}}\right)\left({\frac {r}{C}}\right)^{5}$ ,

where $C$ is a dimensionless constant that is a function of the ratio of the specific heat of air at constant pressure to the specific heat of air at constant volume. The value of C is also affected by radiative losses, but for air, values of C of 1.00-1.10 generally give reasonable results. In 1950, G. I. Taylor published two articles in which he revealed the yield E of the first atomic explosion,^[4]^[5] which had previously been classified and whose publication was therefore a source of controversy.^{[ citation needed ]}

While nuclear explosions are among the clearest examples of the destructive power of blast waves, blast waves generated by exploding conventional bombs and other weapons made from high explosives have been used as weapons of war due to their effectiveness at creating polytraumatic injury. During World War II and the U.S.'s involvement in the Vietnam War, blast lung was a common and often deadly injury. Improvements in vehicular and personal protective equipment have helped to reduce the incidence of blast lung. However, as soldiers are better protected from penetrating injury and surviving previously lethal exposures, limb injuries, eye and ear injuries, and traumatic brain injuries have become more prevalent.

Effects of blast loads on buildings

Structural behaviour during an explosion depends entirely on the materials used in the construction of the building. Upon hitting the face of a building, the shock front from an explosion is instantly reflected. This impact with the structure imparts momentum to exterior components of the building. The associated kinetic energy of the moving components must be absorbed or dissipated in order for them to survive. Generally, this is achieved by converting the kinetic energy of the moving component to strain energy in resisting elements.^[19]

Typically the resisting elements, such as windows, building facades and support columns fail, causing partial damage through to progressive collapse of the building.

Astronomy

The so-called Sedov-Taylor solution (see § Bombs) has become useful in astrophysics. For example, it can be applied to quantify an estimate for the outcome from supernova-explosions. The Sedov-Taylor expansion is also known as the 'Blast Wave' phase, which is an adiabatic expansion phase in the life cycle of supernova. The temperature of the material in a supernova shell decreases with time, but the internal energy of the material is always 72% of E₀, the initial energy released. This is helpful for astrophysicists interested in predicting the behavior of supernova remnants.

Research

Blast waves are generated in research environments using explosive or compressed-gas driven shock tubes in an effort to replicate the environment of a military conflict to better understand the physics of blasts and injuries that may result, and to develop better protection against blast exposure.^[20] Blast waves are directed against structures (such as vehicles),^[21] materials, and biological specimens^[22] or surrogates. High-speed pressure sensors and/or high speed cameras are often used to quantify the response to blast exposure. Anthropomorphic test devices (ATDs or test dummies) initially developed for the automotive industry are being used, sometimes with added instrumentation, to estimate the human response to blast events. For examples, personnel in vehicles and personnel on demining teams have been simulated using these ATDs.^[23]

Combined with experiments, complex mathematical models have been made of the interaction of blast waves with inanimate and biological structures.^[24] Validated models are useful for "what if" experiments – predictions of outcomes for different scenarios. Depending on the system being modeled, it can be difficult to have accurate input parameters (for example, the material properties of a rate-sensitive material at blast rates of loading). Lack of experimental validation severely limits the usefulness of any numerical model.

Related Research Articles

In physics and chemistry, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal energy. Most modern equations of state are formulated in the Helmholtz free energy. Equations of state are useful in describing the properties of pure substances and mixtures in liquids, gases, and solid states as well as the state of matter in the interior of stars.

In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater intensity or lower amplitude if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves.

In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). The term "wavelength" is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.

In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance of one or more quantities. Periodic waves oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a traveling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero. Waves are often described by a wave equation or a one-way wave equation for single wave propagation in a defined direction.

A supernova remnant (SNR) is the structure resulting from the explosion of a star in a supernova. The supernova remnant is bounded by an expanding shock wave, and consists of ejected material expanding from the explosion, and the interstellar material it sweeps up and shocks along the way.

In physics, a shock wave, or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a medium but is characterized by an abrupt, nearly discontinuous, change in pressure, temperature, and density of the medium.

<span class="mw-page-title-main">Heat equation</span> Partial differential equation describing the evolution of temperature in a region

In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region.

<span class="mw-page-title-main">Effects of nuclear explosions</span> Type and severity of damage caused by nuclear weapons

The effects of a nuclear explosion on its immediate vicinity are typically much more destructive and multifaceted than those caused by conventional explosives. In most cases, the energy released from a nuclear weapon detonated within the lower atmosphere can be approximately divided into four basic categories:

The Rankine–Hugoniot conditions, also referred to as Rankine–Hugoniot jump conditions or Rankine–Hugoniot relations, describe the relationship between the states on both sides of a combustion wave in a one-dimensional flow in fluids. They are named in recognition of the work carried out by Scottish engineer and physicist William John Macquorn Rankine and French engineer Pierre Henri Hugoniot.

In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality.

<span class="mw-page-title-main">Rayleigh–Taylor instability</span> Unstable behavior of two contacting fluids of different densities

The Rayleigh–Taylor instability, or RT instability, is an instability of an interface between two fluids of different densities which occurs when the lighter fluid is pushing the heavier fluid. Examples include the behavior of water suspended above oil in the gravity of Earth, mushroom clouds like those from volcanic eruptions and atmospheric nuclear explosions, supernova explosions in which expanding core gas is accelerated into denser shell gas, instabilities in plasma fusion reactors and inertial confinement fusion.

The explosive yield of a nuclear weapon is the amount of energy released such as blast, thermal, and nuclear radiation, 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 kilotonnes (kt—thousands of tonnes of TNT), in megatonnes (Mt—millions of tonnes 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 kilotonne of TNT is held simply to be equivalent to 10¹² calories.

The Chapman–Jouguet condition holds approximately in detonation waves in high explosives. It states that the detonation propagates at a velocity at which the reacting gases just reach sonic velocity as the reaction ceases.

Acoustic waves are a type of energy propagation through a medium by means of adiabatic loading and unloading. Important quantities for describing acoustic waves are acoustic pressure, particle velocity, particle displacement and acoustic intensity. Acoustic waves travel with a characteristic acoustic velocity that depends on the medium they're passing through. Some examples of acoustic waves are audible sound from a speaker, seismic waves, or ultrasound used for medical imaging.

The Barber–Layden–Power effect is a blast wave phenomenon observed in the immediate aftermath of the successful functioning of air-delivered high-drag ordnance at the target. In common with a typical blast wave, the flow field can be approximated as a lead shock wave, followed by a 'self-similar' subsonic flow field. The phenomenon appears to adhere to the basic principles of the Sedov solution.

Astrophysical fluid dynamics is a branch of modern astronomy which deals with the motion of fluids in outer space using fluid mechanics, such as those that make up the Sun and other stars. The subject covers the fundamentals of fluid mechanics using various equations, such as continuity equations, the Navier–Stokes equations, and Euler's equations of collisional fluids. Some of the applications of astrophysical fluid dynamics include dynamics of stellar systems, accretion disks, astrophysical jets, Newtonian fluids, and the fluid dynamics of galaxies.

In the study of partial differential equations, particularly in fluid dynamics, a self-similar solution is a form of solution which is similar to itself if the independent and dependent variables are appropriately scaled. Self-similar solutions appear whenever the problem lacks a characteristic length or time scale. These include, for example, the Blasius boundary layer or the Sedov–Taylor shell.

Taylor–von Neumann–Sedov blast wave refers to a blast wave induced by a strong explosion. The blast wave was described by a self-similar solution independently by G. I. Taylor, John von Neumann and Leonid Sedov during World War II.

Zeldovich–Taylor flow is the fluid motion of gaseous detonation products behind Chapman–Jouguet detonation wave. The flow was described independently by Yakov Zeldovich in 1942 and G. I. Taylor in 1950, although G. I. Taylor carried out the work in 1941 that being circulated in the British Ministry of Home Security. Since naturally occurring detonation waves are in general a Chapman–Jouguet detonation wave, the solution becomes very useful in describing real-life detonation waves.

Guderley–Landau–Stanyukovich problem describes the time evolution of converging shock waves. The problem was discussed by G. Guderley in 1942 and independently by Lev Landau and K. P. Stanyukovich in 1944, where the later authors' analysis was published in 1955.

References

↑ Explosions and Blast Injuries: A Primer for Clinicians (PDF) (Report). Centers for Disease Control (CDC). Archived (PDF) from the original on 4 March 2022. Retrieved 7 March 2022.
↑ Neumann, John von, "The point source solution," John von Neumann. Collected Works, edited by A. J. Taub, Vol. 6 [Elmsford, N.Y.: Permagon Press, 1963], pages 219 – 237.
↑ Bethe,H.A., et al, BLAST WAVE, Los Alamos Report LA-2000, Ch. 2, (1947). read online
1 2 Taylor, Sir Geoffrey Ingram (1950). "The Formation of a Blast Wave by a Very Intense Explosion. I. Theoretical Discussion". Proceedings of the Royal Society A . 201 (1065): 159–174. Bibcode:1950RSPSA.201..159T. doi:10.1098/rspa.1950.0049. S2CID 54070514.
1 2 Taylor, Sir Geoffrey Ingram (1950). "The Formation of a Blast Wave by a Very Intense Explosion. II. The Atomic Explosion of 1945". Proceedings of the Royal Society A . 201 (1065): 175–186. Bibcode:1950RSPSA.201..175T. doi: 10.1098/rspa.1950.0050 .
↑ Sedov, L. I., "Propagation of strong shock waves," Journal of Applied Mathematics and Mechanics, Vol. 10, pages 241 – 250 (1946); in Russian: Седов Л. И. "Распространение сильных взрывных волн," Прикладная математика и механика, т. X, № 2, С. 241-250.
↑ Latter, R., "Similarity solution for a spherical shock wave," Journal of Applied Physics, Vol. 26, pages 954 – 960 (1955).
↑ Lockwood-Taylor, J., "An exact solution of the spherical blast wave problem," Philosophical Magazine, Vol. 46, pages 317 – 320 (1955).
1 2 Batchelor, George, The Life and Legacy of G. I. Taylor, [Cambridge, England: Cambridge University Press, 1996], pages 202 – 207.
↑ Dewey JM. 53 years of blast wave research, a personal history. 21st International Symposium on Military and Blast, Israel, 2010
↑ Rinehart EJ, et al. DTRA weapons effects testing: a thirty year perspective. 21st International Symposium on Military and Blast, Israel, 2010 read online Archived 13 March 2012 at the Wayback Machine
↑ Dewey JM. THE SHAPE OF THE BLAST WAVE: STUDIES OF THE FRIEDLANDER EQUATION. Presented at the 21st International Symposium on Military Aspects of Blast and Shock, Israel 2010 read online
↑ Remmenikov AM. Modelling blast loads on buildings in complex city geometries. Computers and Structures, 2005, 83(27), 2197-2205. read online
↑ for example,Cullis IG. Blast waves and how they interact with structures. J.R. Army Med Corps 147:16-26, 2001
↑ Neff M. A visual model for blast waves and fracture. Master's Thesis, University of Toronto, Canada, 1998
↑ Discussion of similarity solutions, including G. I. Taylor's: Buckingham Pi theorem
↑ Derivation of G. I. Taylor's similarity solution: http://www.atmosp.physics.utoronto.ca/people/codoban/PHY138/Mechanics/dimensional.pdf
↑ Discussion of G. I. Taylor's research, including his similarity solution: http://www.deas.harvard.edu/brenner/taylor/physic_today/taylor.htm Archived 4 February 2012 at the Wayback Machine
↑ Dusenberry, Donald. 'Handbook for Blast Resistant Design of Buildings', 2010, pages 8-9.
↑ Rinehart, Dr. E. J., Henny, Dr. R. W., Thomsen, J. M., Duray, J. P. DTRA Weapons Effects Testing: A Thirty Year Perspective. Applied Research and Associates, Shock Physics Division
↑ for example, Bauman, R. A., Ling, G., Tong, L., Januszkiewicz, A., Agoston, D., Delanerolle, N., Kim, Y., Ritzel, D., Bell, R., Ecklund, J., Armonda, R., Bandak, F., Parks, S. An Introductory Characterization of a Combat-Casualty-Care Relevant Swine Model of Closed Head Injury Resulting from Exposure to Explosive Blast. Journal of Neurotrauma, June 2009, Mary Ann Liebert, Inc.
↑ Cernak, I. The importance of systematic response in the pathobiology of blast-induced Neurotrauma. Frontiers in Neurology December, 2010.
↑ Makris, A. Nerenberg, J., Dionne, J. P., Bass, C. R., Chichester. Reduction of Blast Induced Head Acceleration in the Field of Anti-Personnel Mine Clearance. Med-Eng Systems Inc.
↑ for example, Stuhmiller JH. Mathematical Modeling in Support of Military Operational Medicine Final Report J3150.01-06-306 prepared for the U.S. Army Medical Research and Materiel Command Fort Detrick, Maryland 21702-5012 OMB No. 0704-0188, July, 2006.

External links

"The formation of a blast wave by a very intense explosion" Archived 9 September 2006 at the Wayback Machine G. I. Taylor's solution

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[1] Explosions and Blast Injuries: A Primer for Clinicians (PDF) (Report). Centers for Disease Control (CDC). Archived (PDF) from the original on 4 March 2022. Retrieved 7 March 2022.

[2] Neumann, John von, "The point source solution," John von Neumann. Collected Works, edited by A. J. Taub, Vol. 6 [Elmsford, N.Y.: Permagon Press, 1963], pages 219 – 237.

[3] Bethe,H.A., et al, BLAST WAVE, Los Alamos Report LA-2000, Ch. 2, (1947). read online

[taylor_1950-4] 1 2 Taylor, Sir Geoffrey Ingram (1950). "The Formation of a Blast Wave by a Very Intense Explosion. I. Theoretical Discussion". Proceedings of the Royal Society A . 201 (1065): 159–174. Bibcode:1950RSPSA.201..159T. doi:10.1098/rspa.1950.0049. S2CID 54070514.

[taylor_1950a-5] 1 2 Taylor, Sir Geoffrey Ingram (1950). "The Formation of a Blast Wave by a Very Intense Explosion. II. The Atomic Explosion of 1945". Proceedings of the Royal Society A . 201 (1065): 175–186. Bibcode:1950RSPSA.201..175T. doi: 10.1098/rspa.1950.0050 .

[6] Sedov, L. I., "Propagation of strong shock waves," Journal of Applied Mathematics and Mechanics, Vol. 10, pages 241 – 250 (1946); in Russian: Седов Л. И. "Распространение сильных взрывных волн," Прикладная математика и механика, т. X, № 2, С. 241-250.

[7] Latter, R., "Similarity solution for a spherical shock wave," Journal of Applied Physics, Vol. 26, pages 954 – 960 (1955).

[8] Lockwood-Taylor, J., "An exact solution of the spherical blast wave problem," Philosophical Magazine, Vol. 46, pages 317 – 320 (1955).

[Batchelor-9] 1 2 Batchelor, George, The Life and Legacy of G. I. Taylor, [Cambridge, England: Cambridge University Press, 1996], pages 202 – 207.

[10] Dewey JM. 53 years of blast wave research, a personal history. 21st International Symposium on Military and Blast, Israel, 2010

[11] Rinehart EJ, et al. DTRA weapons effects testing: a thirty year perspective. 21st International Symposium on Military and Blast, Israel, 2010 read online Archived 13 March 2012 at the Wayback Machine

[12] Dewey JM. THE SHAPE OF THE BLAST WAVE: STUDIES OF THE FRIEDLANDER EQUATION. Presented at the 21st International Symposium on Military Aspects of Blast and Shock, Israel 2010 read online

[13] Remmenikov AM. Modelling blast loads on buildings in complex city geometries. Computers and Structures, 2005, 83(27), 2197-2205. read online

[14] r example,Cullis IG. Blast waves and how they interact with structures. J.R. Army Med Corps 147:16-26, 2001

[15] Neff M. A visual model for blast waves and fracture. Master's Thesis, University of Toronto, Canada, 1998

[16] Discussion of similarity solutions, including G. I. Taylor's: Buckingham Pi theorem

[17] Derivation of G. I. Taylor's similarity solution: http://www.atmosp.physics.utoronto.ca/people/codoban/PHY138/Mechanics/dimensional.pdf

[18] Discussion of G. I. Taylor's research, including his similarity solution: http://www.deas.harvard.edu/brenner/taylor/physic_today/taylor.htm Archived 4 February 2012 at the Wayback Machine

[Dusenberry-19] Dusenberry, Donald. 'Handbook for Blast Resistant Design of Buildings', 2010, pages 8-9.

[20] Rinehart, Dr. E. J., Henny, Dr. R. W., Thomsen, J. M., Duray, J. P. DTRA Weapons Effects Testing: A Thirty Year Perspective. Applied Research and Associates, Shock Physics Division

[21] r example, Bauman, R. A., Ling, G., Tong, L., Januszkiewicz, A., Agoston, D., Delanerolle, N., Kim, Y., Ritzel, D., Bell, R., Ecklund, J., Armonda, R., Bandak, F., Parks, S. An Introductory Characterization of a Combat-Casualty-Care Relevant Swine Model of Closed Head Injury Resulting from Exposure to Explosive Blast. Journal of Neurotrauma, June 2009, Mary Ann Liebert, Inc.

[22] Cernak, I. The importance of systematic response in the pathobiology of blast-induced Neurotrauma. Frontiers in Neurology December, 2010.

[23] Makris, A. Nerenberg, J., Dionne, J. P., Bass, C. R., Chichester. Reduction of Blast Induced Head Acceleration in the Field of Anti-Personnel Mine Clearance. Med-Eng Systems Inc.

[24] r example, Stuhmiller JH. Mathematical Modeling in Support of Military Operational Medicine Final Report J3150.01-06-306 prepared for the U.S. Army Medical Research and Materiel Command Fort Detrick, Maryland 21702-5012 OMB No. 0704-0188, July, 2006.

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