Gary S Settles. American Scientist. Volume 94, Issue 1. Jan/Feb 2006.
Shock waves were recognized as a natural phenomenon more than a century ago, yet they are still not widely understood. They are responsible for the crash of thunder, as well as the bang of a gunshot, the boom of fireworks, or the blast from a chemical or nuclear explosion. But these are not just loud noises. Sound waves can be thought of as the weaker cousins of shock waves in the air: They are both pressure waves, but they are not the same.
Shock waves play important roles in modern physics and engineering, military operations, materials processing and medicine. Historically, the study of shock waves has taught us much about the properties of gases and material responses to a sudden energy input, and has contributed to the development of gas lasers and the field of plasma dynamics.
Recent attacks by terrorists using improvised explosive devices have reinforced the importance of understanding blasts, explosions and the resulting shock waves. These waves can be powerfully damaging in their own right, but in addition, studying them can help to quantify their originating explosions and can provide insight into how buildings and airplanes can be hardened to resist damage resulting from such blasts.
Their almost-total invisibility has given shock waves a mystique that has been exploited by Hollywood in countless scenes where explosions send heroes diving for cover. Like sound waves, shock waves are as transparent as the air through which they travel. Usually they can only be seen clearly by special instruments under controlled conditions in the laboratory.
Now, however, our research group has taken modern high-speed videography equipment and combined it with some classical visualization methods to image shock waves from explosions and gunshots in more realistic environments. This allows us to capture the development and progress of these wave fronts on a scale that has not been possible in the past.
Optics in the Transparent World
Even a transparent phenomenon sometimes leaves telltale signs. For shock waves these signs can include moisture condensation, dust disturbance, white-caps on water, optical distortion and shadows. Certain aquatic predators find their transparent prey by the shadows that the Sun casts on the ocean floor.
Robert Hooke discovered this effect more than three centuries ago while observing the shadow of a burning candle cast by sunlight. Above the flame he saw a plume of hot air that was not directly visible but cast a shadow because the heat changes the density of the air, which refracts light rays. What Hooke described is now called the “shadowgraph” method, and it’s a simple approach that works extremely well for visualizing shock waves.
Hooke also discovered another visible trait of transparent phenomena: They can distort the features of a background pattern that is viewed through them. In this way an antique glass windowpane warps one’s view of the world outside. But Hooke was ahead of his time, so this observation principle lay unused until the mid-19th century, when the German scientist August Toepler rediscovered it and used it to observe electric sparks. He saw spherical waves in the air from loud spark discharges and thought he was observing sound, but actually he was the first to see shock waves. Toepler named his optical method the Schlieren method (Schlieren means “streaks” in German). Although the technology has changed significantly, particularly for capturing large fields of view, that name for this method persists today.
In the 1880s, Ernst Mach and his colleagues used the Schlieren method to observe gunshots and thereby settle an argument about what actually happens when a bullet travels faster than sound. They saw shock waves trailing from a supersonic bullet like the water waves from a speedboat. Such observations became essential to the new field of ballistics. Eventually Mach’s name was linked to the non-dimensional ratio of an object’s velocity V to the speed of sound: the Mach number.
Mach’s motto was “seeing is understanding.” He, Hooke, Toepler and other, more recent investigators all understood a principle that unites the worlds of technology and art: In order to understand a new or complicated phenomenon, one needs a physical picture of it early in its study. This is especially true of flow patterns in gases and liquids, which are usually transparent. Without at least a conceptual picture, working with fluids is like working with solid objects in the dark. Getting that picture, whether by experiment or computer simulation, invokes a special branch of the field of fluid dynamics called flow visualization. The Schlieren and shadowgraph techniques used to image shock waves are vital tools for visualizing flows that have a different refractive index than the surrounding air, and therefore bend light.
Because these tools and the study of ballistics and explosions are over a century old, it may be hard to picture what could renew interest in them. In addition to the current need for counterterrorism measures mentioned earlier, investigators also now have modern electronic high-speed cameras with which to capture transient explosive events and fast-moving shock waves. Sadly for some of us, the era of photographic film is almost over. However, with its demise, the rather painful methods of high-speed cinematography are being replaced with high-speed videography, which has an ever-improving frame rate and resolution and comparatively magnificent user-friendliness, as well as compact and robust packaging. This allows the simpler optical methods, such as shadowgraphy, to break out of the laboratory and take to the field, where one can accomplish highspeed imaging of shock waves at an unprecedented scale. Coupled with the utility of small (gram-range) explosive charges, which are used for safety and convenience in research, this technology opens new vistas in the study of shock waves and explosions.
The contribution of my lab, the Perm State Gas Dynamics Lab, to this topic has been primarily in freeing the shadowgraph and Schlieren methods from the benchtop, applying them to large fields of view without the need for impractically large parabolic telescope mirrors, and even taking them outdoors. We have extended these methods to security applications such as aircraft hardening, where they had never been used before but were sorely needed. Currently we are exploring the broad range of scientific studies that can be done safely and inexpensively with small, gram-sized explosive charges and the quantitative optical measurement of shock-wave motion using modern high-speed videography. Such experimental data are important not only to elucidate the physics of explosions, fragmentation and blast damage, but also to guide and validate computational simulations of these events.
But first consider what a shock wave is and what it is not. What does it mean to read that some political event “sent shock waves around the world”? Such “shock waves” are obviously figurative and not real. The meteorite impact that led to the demise of the dinosaurs at the end of the Cretaceous Period and the volcanic explosion of Krakatoa in 1883 really did send shock waves around the world, but such destructive events are fortunately rare.
Hollywood clearly does not understand shock waves, resulting in some ludicrous cinematic special effects. On television, Bart Simpson sent a shock wave rippling across Springfield by yelling into a row of megaphones ganged together in series. Children who try this at home will be disappointed-it doesn’t actually work to produce shock waves. In movies, the hero might outrun the blast from an explosion on his motorcycle. Real motorcycles cannot begin to approach such speeds, and if they did they would not likely stay on the ground. But actual shock waves, in fact, are much more interesting than anything Hollywood has come up with so far to represent them.
A shock wave has no substance itself; rather it is an extremely thin wavefront that passes tsunami-like through solids, liquids and gases at high speeds, driven by molecular collisions at the nanoscale. It is defined as a compression wave-a sudden spike in pressure followed by a sudden drop in pressure-formed, for example, when the speed of an object (such as a bullet) is faster than the speed at which the surrounding medium (such as air) transmits sound.
Sound waves in the air, whether from a whisper or a yell, travel at the speed of sound, called a, for “acoustic” speed. This speed depends on air temperature, but a is typically about 340 meters per second in “standard” air. Shock waves, on the other hand, travel faster than a, being supersonic wave phenomena. They’re also stronger and more energetic than sound waves, are highly nonlinear and cause significant jumps in temperature, pressure and density of the air over their wave thickness of only nanometers. The passage of a strong shock wave through the human body, for example, causes severe damage owing to the large instantaneous pressure change.
Normal conversation, with a sound intensity in the 60- to 70-decibel (dB) range, involves minuscule air-pressure fluctuations of less than one millionth of an atmosphere. Painfully loud “noises,” such as those from a jet engine in the 110-dB range, are actually very weak shock waves. One can see them using the optical methods described here, but they travel barely faster than sound waves, with pressure peaks of only some hundred-thousandths of an atmosphere. On the other hand, a strong shock wave in air, such as one traveling at Mach 2, produces an overpressure peak of 4.5 atmospheres-more than enough to destroy the delicate human hearing mechanism and wreak other biological havoc. However, this phenomenon can be controlled for medically beneficial purposes as well: A method called shock wave lithotripsy focuses shock-wave energy at a point inside the body to break up kidney stones without significantly damaging the surrounding tissue.
Spherical shock waves from explosions decrease quickly in strength with distance from the explosion center, rapidly leveling out to Mach 1.0, or the speed of sound. This rate of speed decrease can be extracted from a high-speed shadowgraph video. As Harald Kleine of the Australian Defence Force Academy and his colleagues outlined in their 2003 paper in the journal Shock Waves, the shape of the curve produced by graphing this speed-decrease data can be used to find an explosive’s equivalent mass, as compared with the standard of trinitrotoluene (TNT).
Close to an explosion, a shock wave can travel at several times the speed of sound and reach pressures of ten or more atmospheres, producing devastating effects. Also, the “wind” that immediately follows a strong shock wave is brief but very intense. In an explosion, the fireball expands very quickly and pushes air ahead of it. As the shock wave ripples out from the explosion center, the speed of its following wind is the same as the speed of expansion of the initial fireball. A shock wave at a mere Mach 1.3 already has a stronger following wind than the fastest natural tornado-generated wind speed ever recorded. Footage of pre-1963 aboveground nuclear tests shows the shock wave smashing whole buildings, whose debris is then swept downrange by the following wind.
What causes such a strong shock wave? Since a stereo system makes sound waves, can one turn the volume up to maximum and make shock waves? No, stereo speakers are only designed to vibrate in order to reproduce sound. Shock waves are made by a rapid, continuous “push,” or by an object traveling at supersonic speed. Cracking a whip creates weak shock waves, because the whip tip moves faster than the speed of sound.
But the best way to generate a strong shock wave in the air is suddenly to release a lot of energy stored in a small space. Pressurized gas is an example: On release, the gas expands very quickly and pushes the atmosphere out of the way, forming a shock wave. Even popping a balloon is enough to generate a very weak shock wave from the gas released when the balloon skin ruptures. In the laboratory, shock waves are best studied in a facility known as a shock tube, where they are generated by the rupture of a thin diaphragm separating high- and low-pressure gases.
Explosives are another good way to produce shock waves. In this case, the energy is stored in an unstable chemical form-often in nitrates-and can be released in about a microsecond. Ironically, most chemical explosives contain less energy per unit mass than ordinary table butter, but fortunately the butter is too stable to explode.
The loss of life caused by an explosion is often due to fragmentation rather than the overpressure or the following wind of the shock wave itself. Shrapnel behaves like a hail of supersonic bullets, being accelerated along radial lines in all directions from the explosion center by the aerodynamic drag force exerted by the rapidly expanding gas.
But strong shock waves are also devastating to structures. In the 1995 terrorist bombing of the Murrah Federal Building in Oklahoma City, a huge truck bomb was detonated only a few meters from the building. The resulting strong shock wave and its many concomitant effects destroyed the columns supporting the north face of the building, whence it collapsed. As a result, 168 lives were lost and there were many more injuries. Both experiments and computational blast simulations now help inform building designers on how to mitigate such lethal effects and how to prevent building collapse and improve survivability.
The experiments can sometimes be dangerous and costly, however, when done at full scale. A recent trend is toward cheaper, safer, quicker simulations of blast effects using gram-range explosive charges, scale models and optical shock-wave imaging. By applying known scaling laws to small explosions in the laboratory, investigators can simulate shock-wave and fragmentation effects on planned buildings or transportation vehicles, for example, using scale models. The high-speed digital video cameras my colleagues and I use record shock position over time by Schlieren or shadowgraphy, from which we can determine all post-shock fluid properties.
Even after several costly full-scale blast experiments involving real airplanes, the gas-dynamics of explosions onboard commercial aircraft remains poorly understood. Better understanding is needed if aircraft are ever to be hardened against catastrophic inflight failure resulting from explosions, whether deliberate or accidental. Interior explosions in aircraft (as in buildings) are complicated by shock-wave reverberation from interior surfaces. In 1988, the wreckage of Pan Am Flight 103 in Lockerbie, Scotland, at first seemed to show the effects of multiple simultaneous blasts at various fuselage locations. As investigations progressed, it was realized that shock waves had traveled the length and breadth of the fuselage, sometimes reflecting and thus causing local blowouts remote from the actual terrorist bomb located in the forward cargo hold.
Optical shock-wave imaging can help explain the complicated consequences of such onboard explosions. In addition to simulations, the U.S. Transportation Security Administration recently did tests on actual air-cargo containers filled with luggage, which were blown up by planted terrorist-scale explosives. For the first time, high-speed videography captured shock-wave motion in these experiments. To do this, a retroreflective shadowgraphy method pioneered by Harold E. “Doc” Edgerton proved robust enough to function in the field despite environmental extremes and severe shock loads on the apparatus.
Retroreflective screens return to the camera lens orders of magnitude greater illumination than does the simple diffuse white screen that is often used for shadowgraphy. The screen functions like a spherical reflector, returning much of the light striking it to its point of origin. For high-speed video shadowgraphy, a retroreflective screen is a necessity for creating a bright image.
A flaw in Edgerton’s original method is that the camera axis had to be slightly offset from that of the light source. This creates a confusing double image in the resulting video. A beamsplitter could be used to correct this, but with a large loss in illumination intensity. Instead, we affixed a small mirror at a 45-degree angle to the center of a filter over the camera lens and reflected the beam off of this surface before sending it to the screen. This arrangement provides perfect alignment between light source and camera axes, and there is no noticeable loss of shadowgram quality as a result of the small area of camera lens occluded by the mirror.
All this leads inexorably to the topic of firearms, which, after centuries of refinement, now hurl bullets with high speed and deadly accuracy. Ernst Mach was cynical about his original supersonic-bullet research, and expected to be criticized for its lack of utility because “one cannot wage war with mere photographed projectiles.”
Controversial as the topic is, we can nevertheless learn from high-speed gunshot images and perhaps use that knowledge to save lives and prevent crime. Forensic investigation of gunpowder residues, point-blank gunshot wounds, shooter hearing protection and sniper location are a few topics that can benefit from observing and understanding shock waves and related phenomena.
The gunshot images my colleagues and I have produced were taken with a massive bullet stop, permission from the Penn State campus police and all appropriate safety precautions. Previous high-speed shadow and Schlieren images of gunshots were limited to small fields of view, typically a few centimeters, and could thus visualize only part of the discharge. My colleagues and I developed a set-up with a field of view of up to several square meters, which is able to reveal most or all of the process.
The evolving flowfield of a gunshot is rather complicated over a period of several milliseconds. The interior ballistics of firearms cannot be observed by the methods described here, so the first visible phenomenon at the muzzle is the emergence of the bullet-driven shock wave, followed immediately by the bullet itself. Then the propellant gases, the products of gunpowder combustion, exit and expand tremendously as they transfer from high pressure inside the barrel to one atmosphere outside. This rapid expansion behaves like an explosion in pushing the air out of the way and thus generating a strong spherical shock wave, or muzzle blast. The “bang” of a gunshot is almost always caused by this muzzle blast.
If you are unlucky enough to be shot at but lucky enough to be missed, sometimes you hear instead the sound of the bullet itself. Inertia keeps supersonic bullets moving at high speed, while the muzzle blast rapidly decays in strength like the spherical shock wave from an explosion. So the bullet inexorably pulls ahead of the decaying muzzle blast, trailing oblique shock waves. These shock waves produce the sensation of a sharp “crack” as the bullet passes, followed later by the “bang” of the muzzle blast. This sequence varies with timing and the hearer’s position with respect to the bullet’s path, making it very difficult to determine the direction of gunfire from its perceived sounds.
The Penn State Full-Scale Schlieren System is the largest indoor schlieren system in the world, with a field of view that is two meters by three meters. Photographs made in this system show these gunshot phenomena on a grander scale than was previously possible. Not only are the exterior ballistics of the bullet revealed, but also the interaction of the muzzle blast with the shooter. Proper ear protection is essential to prevent hearing loss. Propellant-gas interactions with the hands of the shooter, the gas-dynamic behavior of various firearms and many other related phenomena of interest to ballistics can be studied in this experimental imaging facility.
One such topic, imaged for the first time using retroreflective shadowgraphy and high-speed videography, is the effect of a suppressor or silencer in reducing the strength of a gun’s muzzle blast. Suppressors are illegal in many states but can be important assets to police special forces. Their effect is believed to involve slowing and cooling the propellant gases as they leave the muzzle. However, high-speed shadowgraphy reveals another effect: The lateral expansion of the propellant gas is channeled forward into a supersonic turbulent jet, reducing the strength of the muzzle blast but also generating jet noise. In other words, some of the “bang” is converted to a “hiss,” which can reduce the sound level by 10 to 20 dB or more. With high-speed flow imaging and the application of gas-dynamic principles, advances in suppressor design are possible.
Finally, direct illumination of bullet impacts with a microsecond flashlamp also produces revealing images, even though the shock waves and other gas-dynamic phenomena are not visible this way. The ballistic impact of a high-speed bullet does not usually just punch a clean hole in a target, but rather shatters brittle material and disrupts soft tissue. The images we have taken were triggered electronically by a microphone, located outside the field of view, which picked up the passage of the bullet’s oblique shock wave.
Ballistics, shock waves and high-speed imaging have been and continue to be crucial to many fields. Medical and materials processing applications of shock waves are similarly fascinating to observe at high speed. Faster electronic cameras with better resolution are on the horizon, potentially yielding a million frames per second and beyond. The opportunity for ingenuity in devising and applying high-speed optical imaging systems is likewise not nearly exhausted yet, and the future holds many novel applications for such experiments.