Blast wave

A blast wave reflecting from a surface and forming a mach stem. The picture shows a 20 kiloton air burst at 540 meters, to optimize the area covered by at least 15 psi blast damage.

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.

An example of constructive 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.

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 ${\displaystyle {\frac {r^{5}\rho _{o}}{t^{2}E}}}$ ,

where ${\displaystyle \rho _{o}}$ is the density of the air and ${\displaystyle E}$ 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: ${\displaystyle E=\left({\frac {\rho _{o}}{t^{2}}}\right)\left({\frac {r}{C}}\right)^{5}}$,

where ${\displaystyle C}$ 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.

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.

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.

The so-called Sedov-Taylor solution 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.

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.