Handbook of Shock Waves, Three Volume Set

CHAPTER

1

History of Shock Waves PETER KREHL Ernst-Mach-Institut, Fraunhofer-Institutfur Kurzzeitdynamik, Eckerstr. 4, D-79104 Freiburg, Germany

A shock wave is a surface of discontinuity propagating in a gas at which density and velocity experience abrupt changes. One can imagine two types of shock waves: (positive) compression shocks which propagate into the direction where the density of the gas is a minimum, and (negative) rarefaction waves which propagate into the direction of maximum density. 1 Gy6zy Zempl~n University of Budapest 1905

1.1 1.2 1.3 1.4

1.5 1.6 1.7 1.8 1.9

Introduction Shock Waves: Definition and Scope Early Percussion Research Evolution of Shock Waves 1.4.1 Natural Supersonic Phenomena and Early Speculations 1.4.2 Shock Waves in Gases 1.4.3 Shock Waves in Liquids 1.4.4 Shock Waves in Solids Evolution of Detonation Physics Milestones in Early High-Speed Diagnostics Further Reading Chronology of Milestones Notes

1This modern and concise definition of a shock wave was first given by the young Hungarian physicist Dr. G Zempl~n [C. R. Acad. Sci. Paris 141:710 (1905)]. Visiting on a fellowship G6tingen and France (1904-1906), his interest in shock waves was obviously stimulated by Felix Klein, and Pierre Duhhem and Jacques Hadamard, respectively. Handbook of Shock Waves, Volume 1 Copyright ~ 2001 by P. Krehl. All rights of reproduction in any form reserved. ISBN: 0-12-086431-2/$35.00

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1.1 I N T R O D U C T I O N This chapter illuminates the history of shock wave physics in terms of a Chronology of Milestones. To get a realistic picture of this complex evolution process--i.e., to reflect on previous states of knowledge, motivations, speculations, and achievementsmmajor results in the progress of not only shock wave research but also closely related fields such as percussion, explosion, and detonation are covered. In addition, some of the most important milestones in the advancement of high-speed diagnosticsma key technology that has heavily determined the progress of shock wave physics in the past and the p r e s e n t ~ have been included. Some general remarks on the historical background and interrelations between the different disciplines that are not obvious from the Chronology are given in this chapter.

1.2 SHOCK WAVES: DEFINITION AND SCOPE Shock waves 2 are mechanical waves of finite amplitudes and arise when matter is subjected to a rapid compression. Compared to acoustic waves, which are 2 In the 19th century the shock wave phenomenon, a puzzle for early researchers, had a different meaning than today and designated a tidal wave resulting from an earth- or seaquake. Euler (1759), without yet coining a term, addressed the "size of disturbance" of a sound wave, meaning its amplitude. Poisson (1808) described intense sound as the case "where the molecule velocities can no longer be regarded as very small." Stokes (1848) used the term surface of discontinuity, and Airy (1848-1849) described the wave as an "interruption of continuity of particles of air." Riemann (1859) already used the modern terms shock compression [Verdichtungssprung] and compression wave [Verdichtungswelle] to illustrate the jumplike steepening of the wave front. Earnshaw (1860) used the terms positive wave, to illustrate that the motion of particles are in the direction of wave transmission, and wave of condensation, to characterize the increase in density. Toepler (1864) was the first to use the term shock wave [Stoj~welle] in the present sense; he originated a shock wave from a spark discharge and first visualized it subjectively using a stroboscopic method. He also used the terms spark wave [Funkenwelle] and air percussion wave [Lufterschfitterungswelle] interchangeably, but incorrectly used the term sound wave [Schallwelle]. Rankine (1870) used the terms abrupt disturbance and wave offinite longitudinal disturbance, and Hugoniot (1885) the term discontinuity [discontinuit~ de la vitesse du gaz et de sa pression]. Mach and coworkers (1875-1885) used the terms shock wave, Riemann wave [Riemann'sche Welle], bang wave [KnaUwelle], and explosion wave [Explosionswelle]. In the specific case of a supersonic projectile, Mach and Salcher (1887) used the terms head wave or bow wave [Kopfwelle] and tail wave [Achterwelle]. Von Oettingen and yon Gernet (1888), studying oxyhydrogen explosions, called the detonation front Sto~welle. In France the term shock wave [onde de choc] was first used by Vieille and Hadamard (1898), and later by Duhem (1901) and Jouguet (1904). Duhem also used the terms partition wave [onde-cloison], true Hugoniot wave, surface slope [surface de glissement], and quasi shock wave to characterize special types. The term shock wave was not immediately taken up by encyclopedias. For example, in the German encyclopedia Meyers Konversationslexikon (1929), a shock wave was still defined as a "tidal wave originated by an earthquake", a wave type that we designate today as a tsunami. The 1962 edition of the Encyclopaedia Britannica does not even list the term shock wave.

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waves of very small, almost infinitesimal amplitudes, shock waves can be characterized by four unusual properties: (i) a pressure-dependent, supersonic velocity of propagation; (ii) the formation of a steep wave front with abrupt change of all thermodynamic quantities; (iii) for nonplanar shock waves, a strong decrease of the propagation velocity with increasing distance from the center of origin; and (iv) nonlinear superposition (reflection and interaction) properties. Shock wave effects have been observed in all four states of matter and also in media composed of multiple phases. It is now generally recognized that shock waves play a dominant role in most mechanical high-rate phenomena. Shock waves can assume manifold geometry and exist in all proportions, ranging from the microscopic regime to cosmic dimensions. This has led to an avalanche of new shock-wave-related fields in physics, chemistry, materials science, engineering, military technology, medicine, etc. Even before World War I some new disciplines were in the process of being established, such as supersonics, cavitation, detonation, blasting technique, and underwater explosions. In the period between the two world wars, these disciplines were further extended to gas dynamics, seismology, high-speed combustion, plasma p!,ysics, chemical kinetics, thermochemistry, aeroballistics, nonlinear acoustics, transonic flows, etc. The largest expansion of shock wave physics certainly occurred during and after World War II, which created such new disciplines as hypersonic aerodynamics, nuclear explosions, detonics, exploding wires, rarefied gas dynamics, superaerodynamics, aerothermodynamics, magnetofluid dynamics, cosmic gas dynamics, reentry, laser-supported detonation, implosions, impact physics, fracture mechanics, high-rate materials dynamics, shock synthesis, laser fusion, shock lithotripsy, and explosive working. Because the literature is scattered throughout many disciplines, it has become quite difficult even for the specialist to get a survey of the present state of the art. In addition, many investigations on shock waves and detonation are classified or published as company or institute reports and not listed in public library catalogues. This enormous breadth of shock-wave-related disciplines has led also to a wealth of new technical terms that make communications among shock scientists more difficult than during the pioneering "good old days" of legendary all-round knowledge. Modern aerodynamicists, for example, accustomed to working with gases and thinking in terms of mean-free path lengths, viscosity effects, boundary and shock layers, vorticity, slipstreams, Mach and Reynolds numbers, etc. can nowadays barely communicate with solid-state shock physicists who treat shock waves in terms of Huginiot elastic limit, elastic precursor, plastic wave, spallation, lattice compression, shock polymorphism, etc. However, it should be remembered that shock waves, independent of the state of matter of the applied medium, have a common root and are based on the mighty mechanical principle of collision (percussion, impact),

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which has also become the fundament of such eminent fields of science as plasma physics and particle physics. The Chronology in Section 1.8, illuminating the historical evolution of shock wave physics in terms of milestones, emphasizes the phenomenological aspects. In a tabular form it specifies the contributor's affiliation and motivation of his research, discloses preceding work and cross connections with similar studies elsewhere, and comments on the achievements under the present point of view. This rather encyclopedic approach is certainly arbitrary and was influenced by the author's years of diagnosing a diversity of shock wave phenomena in all states of matter. It is hoped that this form of presenting historic milestones may render a better survey than a lengthy narrative description to the historically interested reader. Because of space limitations, the Chronology omits the beginning of percussion research and does not start until 1759. This was apparently the year of the earliest published reference on the reflection of the possible properties of shock waves, then considered by Euler as waves with "disturbances of large size." The Chronology ends in 1945 due to the magnitude of shock-wave-related research that has taken place since then. In the following chapters of this Handbook reference is made mostly to works published after 1945, and this complements--although presented in a different style--the Chronology. Those who are interested in a more extended chronology will find it in Krehl's monograph. 3

1.3 EARLY P E R C U S S I O N

RESEARCH

Widely used by primitive man to produce tools and weapons, and practiced in an almost unchanged manner throughout a period of several 100,000 years, percussion was a fundament of civilization. However, the basic laws of percussion were not discovered until the 17th century, only recently compared to the long history of its application. Many prominent naturalists of that century contributed to the understanding of percussion, such as Galilei (1638), Marci (1639), Descartes (1644), Wallis (1668), Wren (1668), Huygens (1669), Mariotte (1671), and Newton (1687). Percussion studies started with the use of tangible bodies like billiard balls or cannonballs and were mainly based on the observation of their velocities and directions before and after collision (central and eccentric collision). Early ballistic impact studies had revealed that the observed effects strongly depend on the hardness of the collision partners (elastic and inelastic collision) and that in the case of inelastic 3p. Krehl. A historical perspective on percussion, explosion and shock wave research. (SpringerVerlag, Heidelberg, in progress).

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collision the kinetic energy is partly transformed into heat. Since the very short moment of contact and deformation during collision were not yet accessible, neither experimentally nor theoretically, Newton's and Huygens' percussion theories relinquished from the beginning the difficult task of evaluating the enormous instantaneous force. In his Principia (1687), Newton suggested the first corpuscular model of percussion on an atomic level to illustrate that the propagation of sound occurs via percussion from one particle to another. His model, in a way representing the archetype of early shock wave models, stimulated other naturalists to explain the propagation of other mechanical waves, such as seismic shocks (Desmarest 1756), in the same manner. Newton's model was also used by Bernoulli in his Hydrodynamica (1738), in which he first expressed the phenomenon of heat by the average mean square velocity of the colliding atoms, thus initiating the first thermodynamic theory of heat (KrOnig 1856; Maxwell 1860-1866). Navier (1822) used the corpuscular model to derive the laws of motion of continuous media. The multiple-percussion pendulum, today also known as Newton's cradle, soon became a spectacular apparatus for demonstrating chain percussion. The ballistic pendulum was invented by Cassini, Jr. (1707) and is based on the law of the conservation of impulse, one of the basic findings of 17th-century percussion research. Introduced into ballistics by Robins (1746), the ballistic pendulum allowed the first quantitative determination of the velocity of a projectile. Furthermore, he used this simple but most efficient apparatus to study projectile drag as a function of its velocity, thus creating aeroballistics. Robins' remarkable supersonic experiments up to a velocity of 1700ft/sec (M ~ 1.5) revealed a considerable increase of air drag when approaching the sound velocity. Those experiments were repeated and analyzed more recently with modern means by Hoerner (1958) and proved that Robins indeed must have reached supersonic velocities in his gun shots. Percussion research reached its next climax in the second half of the 19th century. Neumann (1856-1857), De Saint-Venant (1866-1867), and Hertz (1882) developed (partly contradicting) percussion theories in which they included Hooke's law of deformation. This also allowed the determination of the instantaneous stress distribution or percussion force. Hertz theoretically demonstrated that the stress distribution in a plate, impacted by a hard sphere, has a conical geometry (the Hertzian cone) that extends from the surface into the impacted plate which can result in conical cracks. This important result explained not only previous observations but also confirmed various hypotheses of prehistorians about how hand axes, arrowheads, knives, and other objects from flint stone or other very hard minerals were produced by primitive man (Kerkhof and Muller-Beck4). Contact times during percussion were first 4E Kerkhof and H. M{iller-Beck: Zur bruchmechanischen Deutung der Schlagmarken an Steingeraten. Glastech.Bet. 42:439--448 (1969).

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measured electrically by Sabine (1876). Those measurements revealed that the contact times are indeed of very short duration--somewhere in the microsecond regime, depending on the mass of the percussion partners and their initial velocities. Tait's percussion machine (1890-1895) allowed for the first time the continuous recording of the contact time of percussion. Using a graphical method he also evaluated the duration of percussion for various examples, such as contact times between a golf ball and a club, one billiard ball with another, and a hammer and a nail.

1.4 E V O L U T I O N

OF SHOCK

WAVES

The large number of disciplines that now fall in the category of shock waves did not evolve along a straight path into the present state. Rather, they emerged from complex interactions among shock-wave-related disciplines or independently from other branches of science. One practical means of getting a useful survey on the development of shock wave physics is to classify the large number of milestones in terms of states of mattermi.e., shock waves in gases, liquids, solids, and plasmas. The following paragraphs will refer to the first three states of matter only.

1.4.1 NATURAL S U P E R S O N I C P H E N O M E N A AND EARLY SPECULATIONS Shock waves are a common phenomenon on Earth and under certain conditions are produced during volcanic eruptions and earthquakes. The most striking natural shock wave phenomena are certainly thunder and the fall of meteors. Earnshaw (1851) was probably the first who reflected on the possibility that thunder would propagate with supersonic velocity as he noticed that the time delay between lightning and thunder was less than one would expect when assuming that thunder propagates with the velocity of sound. Nine years later, Montigny, Hirn, and Raillard, independently of each other, resumed the problem, thereby partly assuming unrealistically high propagation velocities of thunder. Accounts of the famous KAigle Fall (Blot 1803), a meteorite shower that spawned a barrage of reports, and the Washington Meteor (1873) provoked disputes among contemporary scientists on the possible cause of observed shock phenomena (Abbe 1877). Ernst Mach, renowned together with Peter Salcher as the discoverer of the head wave phenomenon (1887), correctly explained this phenomenon likewise by the supersonic motion of the meteor (E. Mach and Doss 1893). Cosmic shock

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phenomena compared to terrestrial ones reach enormous dimensions, such as the solar wind (Parker 1958), which is a stream of ionized gas particles emitted from the sun's corona that is accelerated in Earth's magnetic field and produces a bow wave similar to that ahead of a supersonically moving blunt object (Axford and Kellog 1962). Much larger shock dimensions are generated during stellar explosions (supernovae). Earliest accounts of these date back to Chinese and Swiss annals (A.D. 1006). The shock wave of largest imaginable dimensions would be the "Big Bang," the "shock of all shocks," which, according to the big bang theory, resulted about 10 to 20 billion years ago from a gigantic explosion of a highly concentrated mass of gaseous matter at a single point in space. The relic radiation field resulting from the fireball of the Big Bang eventmpredicted by Alpher, Herman, and Gamow (1948-1949) to be around 5 K--was recorded by Penzias and Wilson (1965) as a residual blackbody radiation of 3 K. Until the advent of gunpowder, the only means available to man for producing shock waves was whip cracking, probably used since antiquity. However, it was scarcely used by early scientists as a subject of investigation because the mechanism of shock generation and its analysis are rather complicated. Lummer (1905) first speculated that the shock might be caused by supersonic motion of the whip tip. The solution of this puzzle required ambitious diagnostics and was not uncovered until the advent of sophisticated high-speed photographic recording techniques. 5 Black powder (gunpowder) was invented in China and first described in Europe by Roger Bacon (1267) for incendiary and explosive applications. Since it can only burn rapidly and cannot detonate, it cannot be used to generate shock waves. However, applied in fire arms, which were in use in Europe since the early 14th century, the hot gases of the reacting gunpowder are initially confined in the barrel but are suddenly released at the moment when the projectile leaves the muzzle, which generates the impressive muzzle blast, a shock wave. After the inventions of the electrostatic generator (von Guericke 1663) and the Leiden jar (von Kleist and Cuneus 1745), it became possible for the first time to store considerable electric charges and to discharge them in a very short time. The discharge is accompanied by a spectacular flash and a sharp report, an impressive demonstration that was often shown in university lectures and private circles and that stimulated discussions on the nature of lightning and thunder. The electric spark proved to be not only useful to generate shock waves at any time, in any space, and of any desired geometry, but was also precisely triggerable in time with an electric light source (Knochenhauer 1858), in most case a second spark discharge confined to a pointlike geometry to meet the requirement of illumination for the shadow or 5cf. ref. 357 in Chronology.

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schlieren method. Furthermore, the alternative method of generating shock waves by chemical explosives allowed the differentiation between electrical and chemical secondary effects of observed shock phenomena, an important advantage that facilitated the interpretation of Mach reflection (E. Mach and Wosyka 18 7 5). It is quite possible that early acousticians also reflected on unusual phenomena associated with intense sound. Prof. Sir Richard Southwell, 6 commemorating at the University of Glasgow the centennial of Rankine's appointment to the Queen Victoria Chair of Civil Engineering and Mechanics, made the interesting annotation that the voice, kept down to a mannerly noise volume, will get through a speaking-tube unaltered but becomes increasingly distorted when the volume is raised. Early experiments on the velocity of sound at very low temperatures--i.e., in air of perfect dryness--were performed in the North Pole regions by the famous Arctic explorers Parry and Ross (1821--1825). The fact that the report of a gun was heard at their further station before the command to fire was heard suggested also the idea that intense air waves travel more quickly than weaker waves. The puzzling shock wave, characterized by a stepped wave front, was difficult to accept by early naturalists because it involved the abandonment of the principle Natura non facit saltus, i.e., the denial of the continuity of dynamic effects. Surprisingly, however, the problem was successfully tackled neither by experimentalists nor philosophers, but rather by mathematical physicists. Jouguet 7 wrote: "The shock wave represents a phenomenon of rare peculiarity such that it has been uncovered by the pen of mathematicians, first by Riemann, then by Hugoniot. The experiments followed not until afterwards." Riemann and Hugoniot, however, were not the only pioneers. As shown in the Chronology, they had a surprisingly large number of predecessors who substantially contributed to this new field, thus paving the way for understanding discontinuous wave propagation.

1.4.2

S H O C K WAVES IN GASES

The impetuous development of experimental shock wave physics started with studies in gases primarily for the following reasons: (i) In the 17th century the elastic nature of air was studied experimentally and already used in practice-such as in the wind-gun and pneumatic lighter, which revealed the adiabatic properties of quickly compressed air. The first scientific milestone was the 6R. Southwell.W.J. M. Rankine: A commemorativelecture delivered on 12 December, 1955, in Glasgow. Proc. Inst. Civ. Eng. (London) 5:177 (1956). 7E. Jouguet: R~sum~des theories sur la propagation des explosions. La science agrienne 3(No. 2): 138-155 (1934).

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determination of the isothermal equation of state (Boyle and Townley 1660). (ii) The relatively low sound velocity of air in comparison to a liquid or solid-for example, smaller by a factor of about 5 and 20 in the case of water and iron, respectivelymwas advantageous for early experimentalists, when high-speed diagnostics were still in their infancy. (iii) All three optical methods (schlieren, shadowgraph, and interferometry) are light transmission techniques, i.e., require a translucent medium, and therefore are ideally suited for studies in gases. (iv) In practice, the majority of shock wave applications, then and now, take place in air. Early ballisticians already noticed the importance of air resistance and its dependency on projectile geometry and velocity. Up to the 18th century the resistance of bodies was measured by the timing of free fall, the mounting of the body on a pendulum, and suspension of the body in the flow. Systematic aeroballistic studies at substantial velocities were performed by Robins (1746) in his sensational ballistic experiments. He also devised a rotating-arm machine that allowed rotation of the test object in a reproducible manner by means of a falling weight. Von Karm~in8 (1932), who coined the term wave drag for a new type of drag at supersonic velocity, appropriately called these pioneering studies of early ballisticians "the theoretical-empirical preschool of supersonic aerodynamics." Early attempts at measuring the sound velocity, both in air (Mersenne 1636, Cassini, Jr. et al. 1738) and water (Colladon 1826), used a long baseline to compensate for the limited accuracy of available clocks. This method, however, was not directly transferable to the crucial test of whether waves of intense sound would propagate faster than sound velocity, because the pressure rapidly decreases with distance from the source; i.e., the region of supersonic velocity would be limited only to the near field of the explosion source. Regnault (1863), widely known for his careful measurements and sophisticated methods, originally had in mind to measure sound velocities in various gases and liquids. To secure a long baseline, he performed his experiments in the public sewage channels and gas pipe lines of Paris, which advantageously confined the sound within two dimensions. To secure sufficient sound intensity at the receiver station, he generated the sound at the tube entrance with small amounts of explosives, at first not being aware that he applied shock (blast) waves rather than sound waves. His remarkable results, published in various international journals but today almost forgotten, obviously proved quantitatively the existence of supersonic velocities for the first time and certainly must have encouraged contemporaries from other countries to tackle this subject further.

8 T. von KCtrman: H6her, schneller und heisser. Interavia 11:407 (1956).

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At low speeds the air behaves like an incompressible fluid. The classical theory of hydrodynamics, which involves no viscosity and is concerned with irrotational motion, predicts that a body moving steadily will experience no resistance or lift. At higher speeds, however, energy is increasingly dissipated so that bodies moving at speeds faster than that of sound have a considerable resistance. Ernst Mach, who held the chair of experimental physics at the German Karl-Ferdinand Universitat of Prague (1867-1895), was interested in physical and physiological acoustics. He was supported by a team of coworkers, later including also his son Ludwig Mach, and had the opportunity to systematically continue his research in this particular field throughout a period of almost 28 years, certainly a peculiarity in the research scenery of the 19th century. E. Mach even began his gas dynamics studies with one of the most difficult subjects of shock wave physics, the oblique interaction of shock waves (E. Mach and Wosyka 1875)--a curiosity in the evolution of gas dynamics. Later called the Mach effect by yon Neumann (1943), this interaction is a complex nonlinear superposition phenomenon and has remained even today a challenging subject of continuous research. Subsequently, E. Mach and Sommer (1877) proved experimentally that indeed a shock wave propagates with supersonic velocity but rapidly approaches sound velocity at increasing distance from the source, thus confirming on a laboratory scale Regnault's previous result. E. Mach and Salcher (1887) first showed that a projectile flying supersonically produces a hyperbolic shock wave, the so-called head wave, which moves stationary with the projectile. These pioneering experimental investigations of Ernst Mach and his team, together with theoretical studies in England, France and Germany established the basic knowledge of supersonic flows in the late 1880s. Practical aerodynamics, however, was still in its infancy, and the first flight of man (von Lilienthal 1891) had not yet been achieved. It appears that studies on the exhaust of compressed gas from an orifice originated from malfunctions of Papin's safety valve (1679). These valves were quite frequently applied in steam engines but often had too narrow an outflow diameter and could not quickly reduce dangerous overpressures, thus causing disastrous steam boiler explosions with many casualties and great damage to neighboring equipment (Arago 1830). This problem prompted not only engineers but also scientists to studies that became substantial roots of early supersonic research (de Saint-Venant and Wantzel 1839; Napier 1866; Reynolds 1885; Emden Bros. 1899; Stodola 1903; Prandtl 1904-1907). The invention of the Laval nozzle (de Laval 1888), a nozzle of convergent-divergent geometry, first allowed supersonic exit velocities. Soon an important device in engineering, such as for increasing the efficiency of steam turbines, this nozzle had also an enormous impact on supersonic flows and the development of aerodynamics. Progress in this field was immediately fructified by progress of high-speed photography. After successful visualization and interpretation of

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the flow phenomena in front of a Laval nozzle (Salcher and Whitehead 1889; L. Mach 1897) and later also of those in its interior (Prandtl 1904; Meyer and Prandtl 1908), the nozzle was adapted in England in the world's first supersonic wind tunnel at the National Physics Laboratory, Teddington, which reached supersonic flow velocities up to M = 2 (Stanton 1920-1926). The first hypersonic velocities (Erdmann 1944) were reached at the large supersonic wind tunnel facility at Heeresversuchsstelle Peenemf~nde, the main center of German rocketry during World War II. The shock tube, invented in France by Vieille (1899) as a by-product of his detonation studies, became the most important measuring and testing device of gas dynamics. He applied the shock tube to demonstrate that shock waves generated by the detonation of explosives propagate essentially in the same manner as shock waves generated by the bursting diaphragm of the highpressure section that formed one end of his tube. The basic theory of the shock tube was laid down by Kobes (1910), Hildebrandt (1927), and Schardin (1932). Kobes and Hildebrandt had a rather curious approach to gas dynamics: they investigated whether it would be possible to improve the performance of air suction brakes on long railway trains by using shock waves. The shock tube, rediscovered during World War II by Bleakney (1949) and associates at Princeton University, soon proved its excellent applicability for quantitatively investigating propagation and interaction phenomena of shock waves within a large range of gas dynamics parameters. Furthermore, it was introduced worldwide in other laboratories for the study of shock wave interactions with scaled architectural structures such as model houses, plants, shelters, and vehicles. Then in the long period of the Cold War such interactions were of great practical concern because of the constant threat of nuclear blast to civil and military installations. That the shock tube was also useful for generating high temperatures in gases was first recognized and exploited in high-speed spectroscopic studies by Laporte (1953). The theoretical approach of treating shock waves can be traced back as far as Newton's Principia (1687). Assuming incorrectly that sound is an isothermal process, he made a crude calculation of sound velocity in air. Laplace (1816), noticing a discrepancy of almost 20% between Newton's theoretical result and already-existing measured data, improved the theory by assuming that sound is an adiabatic process. Prior to this, Poisson (1808), stimulated by Laplace in this subject, had mathematically tackled the sound velocity problem in a paper published in the Journal de l'Ecole Polytechnique. Under the heading "Onedimensional movement of air in the case that the velocities of the molecules are no longer very small" [Mouvement d'une ligne d'air dans le cas of~ les vitesses des molecules ne sont pas supposees tr~s-petites], he also touched the basic question of how to solve the wave equation in the case of noninfinitesimal amplitudes, thus laying the foundation for the first shock wave theory. Most noteworthy,

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this happened at a time when an experimental verification of such discontinuities, propagating as a wave throughout the medium, was still pending. Poisson's early approach, first resumed in England by Challis (1848), was quickly extended by Airy (1848), Stokes (1848-1849), Rankine (1858, 1870), Earnshaw (1858-1860), Riemann (1859), Christoffel (1877), Hugoniot (18851887), Tumlirz (1887), Burton (1893), Hadamard (1898-1905), H. Weber (1901), Duhem (1901-1909), Jouguet (1901-1910), Zemplen (1905), Lummer (1905), Lord Rayleigh (1910), G. I. Taylor (1910), etc. However, the transition to present-day shock wave theory, largely a result of many international contributions, was not straightforward, and their disputes and cumbersome struggles for understanding the shock wave puzzle may be dimmed in light of things we now take for granted. Details of this gradual process of understanding may be found in the Chronology. In this context, some remarks concerning their motivations seem worthwhile. Airy, Challis, and Jouguet first studied tidal waves, which, steepened in shallow water into hydraulic jumps, propagate rather slowly and are clearly observable with the naked eye. The analogy between the reflection properties of a hydraulic jump and a shock wave in a gas is indeed striking (Jouguet 1920) and was later applied in water table experiments (Preiswerk 1938; Einstein 1948; Crossley, Jr. 1949). Earnshaw treated the great solitary wave (1845) before he had his key experience with thunder (1851). Riemann's interest in "air waves of finite amplitude" [Luftwellen von endlicher Schwingungsweite] did not arise from a purely mathematical curiosity. Stimulated by von Helmholtz, he treated the problem of combination tones, a phenomenon of the nonlinearity of the ear and observable only at sufficiently high sound levels. Rankine and Hugoniot approached the shock wave phenomenon from the thermodynamic point of view, Lord Rayleigh from the acoustic. Heinrich Weber, treating shock waves also as a mathematical problem to find solutions for various types of partial differential equations, edited Riemann's lectures on mathematical physics and extended his theoretical studies on shock waves by numerous examples and comments.

1.4.3

S H O C K WAVES IN LIQUIDS

Liquids were regarded for a long time as incompressible matter, until Canton (1762) first demonstrated its very low compressibility. In shock wave physics, liquids and gases are both treated as compressible fluids. Liquids, however, are much more difficult to compress than gases and, as a consequence, typical shock wave properties such as wave-steepening effects and supersonic propagation are clearly observable only at significantly higher shock pressures. Furthermore, shock-compressed liquids may show unusual properties (high

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viscosity, phase transformations) and generate complicated side effects (cavitation). Shock waves in liquids, particularly in water, were hardly treated until the beginning of World War I. However, a few remarkable contributions, described in more detail in the Chronology, should be emphasized here. Water hammer, a steep-fronted pressure wave that is felt as a sharp hammerlike blow, is caused by the sudden retardation or acceleration of flow in a long pipe, for example when a valve is closed sufficiently rapidly. Montgolfier and Argand (1796) applied this phenomenon successfully in constructing a hydraulic pump they called a "hydraulic ram" [belier hydraulique]. Generally, however, this effect is detrimental in pipe systems because the pressure pulse can propagate to remote areas and destroy tubes, valves, and other installations. Kareljkich and Zhukovsky (1898-1900) in Moscow first scientifically treated the problem of water hammer or hydraulic shocks in water supply lines. At the turn to the 20th century, this problem also became important in other countries when large water pipe systems had to be built to satisfy the increasing water requirements of fast-growing urban communities. The water hammer can also be generated by an object impacting and penetrating a liquid and in this modification was probably the earliest observed shock wave effect in a liquid. Carr~ (1705) observed the curious phenomenon that a bullet shot into a wooden box filled with water blew up the box. The impacting bullet, transferring a large amount of momentum to the water, generates a shock wave that ruptures the walls. Since the first air battles of World War I this effect has been a constant menace to military aircraft, whose fuel tanks cannot fully be armored against gun shots. 9 Other shock wave effects in liquids were also observed in military applications. For example Abbot in the United States (1881) and Blochmann (1898) in Germany studied underwater explosion phenomena of submarine mines, a subject of increasing interest to the navy since the invention of the torpedo in the 1860s. During World War II, research on underwater explosions was pushed forward by the United States and England on a large scale. Their UNDEX Reports, published shortly after the end of war, include a wealth of data on underwater explosion phenomena and their analytical treatment, and even today are a rich source of information. I~ Water ricochets, a now well-known percussion phenomenon, was studied by Marci (1639), who threw a stone on a pond's surface at a low angle and explained the effect with the law of reflection. This phenomenon gained new

9 R. Yurkovich. "Hydraulic ram: a fuel tank vulnerability study." Rept. No. G964, McDonnell Douglas Corporation, St. Louis, MO (Sept. 1969). 10Underwater Explosion Research (UNDEX). A Compendium of British and American Reports. 3 vols., ed. by G. K. Hartmann, U.S. Naval Ordnance Laboratory, and E. G. Hill, British Admiralty. The Library of Congress, Photoduplication Service, Washington, DC (1950).

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interest with the advent of seaplanes and the need for them to land at high speed or on rough sea. Investigations performed in various countries, such as the United States (Von K~irman and Wattendorf 1929), Germany (Wagner 1932), and the former Soviet Union. (Sedov and Wladimirow 1942), revealed that this skipping effect is a complicated combination of gliding and periodic bouncing that also generates finite-amplitude waves in the water. Cavitation damage was first observed shortly after the first use of steam turbines. The central implosion of cavitation bubbles, accompanied by the emission of shock waves, results in material destruction. At the beginning of the age of steam turbines in the 1880s, erosion effects caused by cavitation were observed not only on the blade tips of turbine wheels but also on marine propellers that were initially driven at very high revolutions to avoid loss involving high gear reduction between turbine and propeller. Studies on cavitation phenomena were initiated both from the engineering (Thornycroft and Barnaby 1895; Cook 1928) and scientific point of view (Lord Rayleigh 1917; Prandtl 1925; Jouguet 1927; Ackeret 1938). Cavitation and associated shock pressure effects can now be generated in a very wide spatial/temporal range, covering meters/milliseconds down to nanometers/femtoseconds. An example for the upper limit is the gas sphere of an underwater explosion, which can be regarded as a single, huge bubble. An example for the lower limit, or micro-cavitation, is the irradiating of biological tissue with femtosecond laser pulses, which results in ultrashort shock pulses (the photodisruption effect). This procedure has been applied in femtosecond laser nanosurgery as a "nanoscalpel" to cut nanometer-sized particles, such as chromosomes in a living cell. 11 The electrohydraulic effect, first observed in England by Singer and Crosse (1815) and later rediscovered in the former Soviet Union, 12 uses a powerful electric discharge fed into a thin wire or spark gap submersed in water to generate shock waves. This effect was made famous by the Latvian urologist Goldberg, 13 who first successfully applied it to the disintegration of bladder stones in man (shock lithotripsy). Later the electrohydraulic effect was also used in production technology for forming metal sheets. 1.4.4

S H O C K WAVES IN SOLIDS

The pioneers of classical shock wave theory did not limit their analyses to fluids only, but had also reflected on the peculiarities of shock waves in solids. 11K. K6nig, I. Riemann, P. Fischer, and K. J. Halbhuber. Intracellular nanosurgerywith near infrared femtosecond laser pulses. Cell. & Mol. Biol. 45:195-201 (1999). 12L. A. Yutkin. Elektrogidravliceskij effekt. Masgiz, Moskva (1955). 13V. Goldberg. Zur Geschichte der Urologie: Eine neue Methode der Harnsteinzertn3mmerung--elektrohydraulische Lithotripsie. Urologe [B] 19:23-27 (1979).

History of Shock Waves

15

In his treatise On the thermodynamic theory of waves of finite longitudinal disturbance, Rankine (1869) clearly states that his derived relations are valid "for any substance, gaseous, liquid or solid." Christoffel (1877), Hugoniot (1889), Duhem (1903), Hadamard (1903), and Jouguet (1920) addressed the solid state in more detail. Other contributions that could not immediately be verified by contemporary experimentalists who lacked the diagnostic means, later stimulated the evolution of shock wave physics in solids. Prominent examples include: (i) various theories of percussion derived by early naturalists; (ii) Maxwell's theory of elasticity (1850); (iii) a theory on the equation of state for solid matter based on the lattice vibration theory derived by Mie (1903) and Gruneisen (1912); and (iv) theories on the dynamic plasticity of metals such as proposed by G. I. Taylor (1942), yon K~irman (1942), and Rakhmatulin (1945). Contrary to the rapid and steady progress of shock wave physics in gaseous matter since the 1870s, research in solids has evolved slowly. The main reason was certainly the very challenging high-speed diagnostics, which require submicrosecond resolution and thus were not available until after World War II. However, using simple experiments early researchers did study the dynamic properties of solids, particularly their rate-dependent strength. J. Hopkinson (1872) measured the strength of a steel wire when the wire was suddenly stretched by a falling weight, and he made the important observation that the strength is much greater under rapid loading than in the static case--a phenomenon that was later studied in more detail by his son (B. Hopkinson 1905). The latter also discovered the fracture phenomenon of back spalling from an explosive-loaded metal plate (B. Hopkinson 1912). In the 19th century, Parsons and Moisson (1892) attempted to use shock waves to induce polymorphic phase transformations in solids, particularly in carbon to produce artificial diamonds. However, their efforts did not give clear evidence and were just too ambitious for their time. An important step toward this goal were the later results of static high-pressure investigations on a large number of liquid and solid substances carried out by Bridgman (1903-1961) in a long-lasting campaign that formed the foundation for understanding matter under high pressures. Those results gave modern shock physicists their first clues to the static compressibility of solids at high pressures and to the stressdependent plasticity of metals, thus arousing their curiosity about how substances would behave under dynamic pressures. This promoted also various other spectacular investigations, for example on shock-induced polymorphic transitions in iron (Bancroft e t al.14), on possible ice modifications of

14D. Bancroft,E. L. Peterson,and S. Minshall. Polymorphismof iron at high pressures.J. Appl.

Phys. 27:291-298 (1956).

16

P. Krehl

shock-compressed water (Rice and Walsh; 15 Al'tshuler et a1.16), and on shockinduced transformation of graphite into diamond (DeCarli and Jamieson17). Early suppositions that craters might have been generated by meteorite impact in the geologic past had to battle against established cryptovolcanic hypotheses, but first systematic studies of meteorite material collected from various craters around the world (Spencer 1933) and the discovery of curious striated conical geologic structures (shatter cones, Butcher 1933, Boon and Albritton 1938) supported the impact theory. The famous Meteor Crater, Arizona was first brought to notice in 1891 by the discovery od many masses of meteoric iron scattered around the crater and the finding of diamond in this iron. Eventually, the sensational discovery of quartz high-pressure, shock-induced polymorphs in meteorite craters--beginning in Meteor Crater by Chao, Shoemaker and MadsenlS--constituted evidence for meteorite impact scars (socalled astroblemes) and significantly promoted knowledge on the geological history of Earth, Moon, and other planets. 19 Solid-state shock wave physics, partly an outgrowth of nuclear weapons research imposed by the Manhattan Project, did not start until 1945 and therefore is beyond the scope of this survey. Obviously, however, modern testing methods for studying materials response under shock loading have close roots to percussion. To a large extent they are based on the planar impact of two rodlike bodies, a basic arrangement treated previously (Euler 1745; Neumann 1857-1858; de Saint-Venant 1867; Ramsauer 1909; Donnell 1930) and used today in high-rate materials testing such as the Hopkinson pressure bar (B. Hopkinson 1914), which was further developed into the split Hopkinson pressure bar or the Kolsky bar (Kolsky 1949); the Taylor test (Taylor and Whiffin 1948); the flyer plate method (McQueen and Marsh 1960); and the planar impact by a high-velocity projectile (Hughes and Gourley 1961). Modern investigations of shock waves in solids revealed rather complex behavior in comparison to gases and liquids, and theories describing the solid state under shock loading, taking structural properties into account also, are still in development. The impressive advancement of solid-state shock wave physics

15 M. H. Rice and J. M. Walsh. Dynamic compression of liquids from measurements on strong shock waves. J. Chem. Phys. 26:815-823 (1957). 16 L. V. Al'tshuler, A. A. Bakanova and R. E Trunin. Phase transition of water compressed by strong shock waves. Sov. Phys. Dokl. 3:761-763 (1958). 17p. S. DeCarli and J. C. Jamieson. Formation of diamond by explosive shock. Science 133:1821-1822 (1961). 18 E. C. T. Chao, E. H. Shoemaker and B. M. Madsen: First natural occurence of coesite. Science 132:220-222 (1960) 19 B. M. French and N. M. Short (eds.). Proc. 1st Conference on Shock Metamorphism of Natural Materials. NASA Goddard Space Flight Center, Greenbelt, MD (1966). Mono Book Corporation, Baltimore (1968).

17

History of Shock Waves

was mainly based on (i) the generation of well-defined shock wave profiles, (ii) the advance of submicrosecond measurements and visualization techniques, and (iii) computational analysis employing refined thermodynamic equations of state and using more accurate dynamic materials parameters. Today this specific branch of high-pressure physics provides not only a rich source of equation-ofstate data for all kinds of solids but also information on most shock compression and diagnostic techniques used in such disciplines as impact physics, geology, seismology, fracture mechanics, laser fusion, and materials science.

1.5 E V O L U T I O N

OF DETONATION

PHYSICS

Historically, investigation on the nature of shock waves was closely related to the puzzle of detonation, a high-transient thermochemical wave phenomenon. The terms explosion and detonation were not always used as they are today. 2~ Today the more general term explosion can be defined as a process causing a rapid increase of pressure, which can steepen into a shock wave. An explosion does not necessarily have to be connected with the exothermic reaction of a chemical explosive; for example, in the case of a steam boiler the explosion is the sudden rupture of the boiler walls, or in the case of a shock tube it is the bursting membrane. Conversely, a detonation is a violent explosion related to high explosives in which the rate of heat release is great enough for the explosion to be propagated through the explosive as a steep shock front, the so-called detonation wave. The discovery and correct interpretation of this term was not achieved until the period from 1880 to 1905, which was almost 300 years after the invention of gold fulminate, the first high explosive, by the alchemist Croll (1608). The following short survey focuses on some of the circumstances in the step-by-step process of investigating the nature of detonation. Since Croll's discovery an impressive number of high explosives were invented, the most important being silver fulminate (Bertollet 1708), picric acid (Hausmann 1788), mercury fulminate (Howard 1799), guncotton (Sch0nbein 1846), nitroglycerine (Sobrero 1847), and dynamite (A. Nobel 1867) tetryl (Michler and Meyer 1879), TNT (Haeussermann 1891) and lead azide (Hyronimus 1907). Although by 1880 some of these substances were already being used for military and civil purposesmfor example, in 1835 France alone 2o The terms detonation and explosion are of Latin origin and had been used interchangeably since the late 17th century. However, the term detonation was apparently first used in the presentday meaning in England by Abel (1869) who studied detonation effects in guncotton. In France Berthelot (1870) first called the detonation front "shock" [choc] and in 1881 "explosive wave" [l'onde explosive], which apparently was taken up in England by Dixon (1893) and Chapman (1899). The term detonation was later adopted by Vieille (1900).

18

P. Krehl

produced 800 million percussion caps employing mercury fulminatemthe physicochemical processes of explosion/detonation were not yet uncovered. The first measurements of the detonation velocity in long, confined charges of various high explosives, carried out by Abel (1869-1874) in England, revealed unusual high velocities in the range of some 1000m/s. Abel stated that "the detonation of gun-cotton travels more rapidly than any other known medium with the exception of light and electricity." Studying the behavior of unconfined and confined charges, he speculated that detonation in a high explosive might be transmitted by means of some "synchronous vibrations" (1869). Shortly thereafter Berthelot (1870) in France was the first to correctly assume that detonation might be caused by a traveling mechanical shock, but an experimental proof had yet to come. At this point it is useful to look back on previous attempts at understanding explosion in gases. The discovery of oxyhydrogen and its violent explosive properties (Turquet de Mayerne 1620; Cavendish 1760) stimulated not only a crude theory on the origin of earthquakes (L~mery 1700; Kant 1756) but also turned the interest of naturalists to other explosive gaseous mixtures, particularly to firedamp, which had been a hazard to miners since the beginning of hard coal mining in the 12th century. Davy (1816) analyzed the explosivity of firedamp and discovered that the critical mixture for explosion is 9% methane and 91% air. The "Davy lamp," his famous invention to avoid firedamp explosions in mines, could only partly mitigate the risk of explosion accidents; there were other sources of open fire, such as explosives used for blasting purposes, one of the oldest and most important civil applications of explosives since the 16th century. When Bunsen (1867) measured the strength and rate of combustion of various explosive gaseous mixtures such as oxygen, he used an experimental setup that could not provoke explosion. Dust explosions, certainly the oldest kind of man-made explosion, frequently occurred in flour mills and bakeries and later in metal powder works. Such explosions stimulated hypotheses (Faraday and Lyell 1845; Rankine and Macadam 1872) that in an analogous manner coal-dust-laden air might cause explosions in coal mines. Eventually, a series of tragic firedamp explosions in the French coal mining industry (1876) led to the foundation of the French Fire-Damp Commission (1878) to investigate possible causes of these explosions from a scientific viewpoint and to reflect on possible countermeasures. Additional mining accidents in England, France, and the United States soon afterward---some of them probably produced by the presence of coal dust--initiated the foundations of similar national institutions. In France, Mallard and Le Ch~telier, from the Ecole des Mines, were asked to examine the best means of guarding against explosions of firedamp in mines. This led to a series of investigations on the specific heat of gases at high temperatures, the temperatures of ignition, and the velocities of propagation of flame in gaseous

History of Shock Waves

19

mixtures (1880-1882). In addition, similar studies were carried out in Paris at the College de France by Berthelot, who worked together with Vieille at the Laboratoire Central, Service des Pouclres et 5alpetres. These investigations revealed (i) that an explosive wave, later generally termed a detonation wave, exists in explosive gaseous mixtures and propagates at a tremendous speed of up to 2500m/s, and (ii) that the propagation velocity only depends on the mixture composition not on the tube diameter as long as that diameter is not too small (1878-1883). Mallard and Le Chatelier (1883), who first recorded the propagation of the explosive wave in long tubes with a drum camera, observed that the transition from combustion into detonation occurs suddenly, and that the detonation velocity is comparable to the sound velocity of the burnt detonation products. These results promoted the Chapman-Jouguet theory, which evolved in England from independent contributions by Schuster (1893), Dixon (1893), and Chapman (1899); in Russia by Mikhel'son (1890); and in France by Berthelot (1891) and Jouguet (1904). The theory assumes that the hot products of the combustion wave act as an expanding hot-gas piston that accelerates the unburnt mixture ahead, thereby forming the explosive wave, which is a shock wave. In comparison to a normal shock wave with its discontinuous transition of uncompressed to compressed gas across the shock front, however, the detonation front also separates two chemically different states of unburnt and burnt gases. However, various experimental studies later revealed that the detonation front is not necessarily a homogeneous zone of reaction but can exhibit a periodic cell structure (Bone et al. 1936). In addition, the assumption of a sharp detonation front is an idealization, and the Chapman-Jouguet theory was later refined by introducing a three-layer model of the detonation front. This model was independently advanced by Zeldovich (1940) in the Soviet Union, von Neumann (1942) in the United States, and Doring (1943) in Germany, today known as the ZND theory. The study of the classic chlorine-hydrogen explosion--a puzzling photochemical-induced reaction discovered by Gay-Lussac and Thenard (1809) and investigated in more detail by Chapman (1909-1933), Bodenstein (1913), and Nernst (1918)mrevealed that detonation is not an instantaneous, single-stage chemical reaction but rather occurs in a chain reaction [Kettenreaktion], thereby passing through various short-lived intermediate states. 21 Their findings stimulated the evolution of chemical kinetics (Semenov and.Hinshelwood 1928; Nobel Prize of Chemistry 1956), which quickly became a new exciting branch of physical chemistry.

2~M. Bodenstein: 100Jahre Photochemie des Chlorknallgases. Bet. Dtsch. Chem. Gesellsch. 75A: 119-125 (1942).

20

v. Krehl

1.6 MILESTONES IN EARLY HIGH-SPEED DIAGNOSTICS The advancement of high-speed diagnostics--encompassing appropriate fast methods of measurement, visualization, and recordingmhas always been essential for a detailed analysis of shock and detonation effects and their proper applications. In this regard Ernst Mach's scientific way of experimenting was very successful and directive to his contemporaries. He was an eminent philosopher who also can be regarded as the first gas dynamicist and highspeed photographer of his time. He carried out his shock and explosion research according to the motto "Seeing is understanding." Within the short period of time from 1864 to 1891, the three principal optical techniques of flow visualization (i.e., the schlieren method, shadowgraphy, and Mach-Zehnder interferometry) had been invented. From the historical point of view it is remarkable that one of the first applications of the schlieren method, which was invented by A. Toepler (1864) at BonnPoppelsdorf, was the visualization of a propagating spark wave, a weak shock wave. The famous ballistic experiments by E. Mach and Salcher (1887) also used the schlieren method to visualize the head wave generated by a supersonic projectile. The shadowgraph technique was invented at the University of Agram [now Zagreb] by Dvof~ik (1880), who was one of E. Mach's assistants (1871-1875). Applied by Boys (1890) in England, this technique considerably simplified the visualization of supersonic flows in ballistic testing ranges. E. Mach and L. Mach proved the great potential of interferometry for flow visualization, for example by quantitatively analyzing the density jump at the shock front (E. Mach and Weltrubsky 1878) and the flow around a supersonic bullet (E. Mach and L. Mach 1889). The Mach-Zehnder interferometer is particularly appropriate for flow visualization studies in ballistic tunnels, shock tubes, and wind tunnels because it allows a large distance between object and reference beam. These three optical methods gave early shock researchers their first insights into an abundance of completely new supersonic flow phenomena. The challenge of recording gas dynamic events largely inspired the development of new high-speed photographic equipment, which in turn enabled the discovery of new shock phenomena. In the pioneering period, gas dynamicists were often also high-speed photographers who invented, developed, and built their own equipment. Snapshot photography of a dynamic event was first demonstrated by FoxTalbot (1851). With the advent of gelantin dry plates (Maddox 1871) which later could be improved significantly in sensitivity (1878-1880) and of electric spark light sources of high intensity and short duration, it became possible for the first time to both stop the motion of propagating shock waves with practically no motion blur and obtain a sufficient exposure density on photographic film. The first photographed shock wave was generated by the

History of Shock Waves

21

discharge of a Leiden jar, visualized with the schlieren method, and photographed on a high-sensitive gelantin dry plate (E. Mach and Wentzel 1884). The evolution from single-shot photography to high-speed cinematography is a story of its own, 22 but a few milestones can be illuminated here. The rotating mirror, a mechanical device for resolving the motion of an object in one dimension, was apparently first used by Wheatstone (1834). However, it took almost a hundred years before the mirror was modified into a practical streak camera for resolving the propagation and reflection of detonation waves (Payman 1931). High-speed cinematography reached a first climax with the invention of the Multiple Spark Camera (Cranz and Schardin 1929). Based on a principle of recording that allows one to realize any desired frame rate and to use any type of "light source" even beyond the visible spectrum, it was also modified later for flash X-ray and neutron cinematography. The ambitious U.S. program of atomic weapons development and testing during and after World War II resulted in further developments of mechanical framing cameras with ultrahigh frame rates. Simultaneously, the various requirements of dynamic plasma diagnosing in numerous fusion research programs stimulated new developments of ultrafast image tube cameras, particularly in the United States, England, France, and the Soviet Union. With the advent of the microchannel plate (MCP) in the 1980s~an American invention based on the electron multiplier (Farnsworth 1930)~a new optoelectronic device with excellent gating capability and of high light intensification became available that could be combined very successfully with the already existing charge-coupled device (CCD). These so-called ICCDs (intensified CCDs), applied in a multiple arrangement with optical image splitting, created a new generation of ultrafast multiple digital framing cameras that are well suited for recording all kinds of shock wave phenomena. Flash radiography, invented simultaneously in Germany (Steenbeck 1938) and the United States (Kingdon and Tanis 1938), immediately became an important diagnostic tool that particularly stimulated detonics. Contrary to optical methods, flash radiography is insensitive to self-luminous events that accompany all detonation processes, and smoke resulting from detonation products cannot obscure the test object. In addition, X rays promote insight into the interior of shock-loaded solids and the measurement of temporal shock front positions. These particular properties of flash X rays allowed, for the first time, the visualization of shock waves emerging from exploding wires, shaped charges, and detonation fronts in liquid and solid explosives. Furthermore, it also became possible to visualize shock wave propagation and interaction phenomena in optically opaque media, which represent the majority of solids, to quantitatively determine the density jump behind the shock front using photo densitometry, and to measure the lattice compression of shock-compressed crystals using flash X-ray diffraction. 22 S. F. Ray: High-Speed photography and photonics. Focal Press, Oxford (1997).

22

P. Krehl

FIGURE 1 Life spans of renowned percussion, explosion and shock wave researchers. The begin of the shock wave era, marked above by the broken line, can be attributed to Simeon Denis Poisson who first mathematically treated "waves of which the velocities of the molecules are not supposed to be very small" (1808).

1.7 FURTHER READING 1. L. V. Al'tshuler, and V. A. Simonenko, History and prospects of shock wave physics. High Pressure Research 5:813-815 (1990). 2. J. D. Anderson, Jr. Modern compressible flow, with historical perspective. McGraw-Hill, New York (1990).

History of Shock Waves

FIGURE 1

23

(Continued)

3. R. Assehton: History of explosives. Institute of Makers of Explosives, New York (1940). 4. P. A. Bauer, E. K. Dabora, and N. Manson, Chronology of early research on detonation wave. In Dynamics of detonations and explosions: Detonations, A. L. Kuhl, J. C. Leyer, A. A. Borisov, and W. A. Sirignano, eds. Progr. Astro- & Aeronautics (AIAA, Wash. D.C.) 133:3-18 (1991). 5. A. Busemann, Compressible flow in the thirties. Ann. Rev. Fluid Mech. 3:1-12 (1971). 6. R. Ch~ret, The life and work of Pierre-Henri Hugoniot. Shock Waves 2:1-4 (1992). 7. D. H. Clark, and E R. Stephenson, The historical supernovae. Pergamon Press, Oxford (1977). 8. H. Dryden, Supersonic travel within the last two hundred years. Scient. Monthly 78:289-295 (May 1954).

24

P. Krehl

9. G.E. Duvall, Shock wave research: yesterday, today and tomorrow. Proc. 4th Conf. on Shock Waves in Condensed Matter, Y. M. Gupta, ed. Spokane, WA (July 1985). Plenum Press, New York (1986), pp. 1-12. 10. R.J. Emrich, Early development of the shock tube and its role in current research. Proc. 5th Int. Shock Tube Symp., Z. I. Slawsky, J. F. Moulton, Jr., and W. S. Filler, eds. White Oak, Silver Spring, MA (April 1965), pp. 1-10. 11. E Fischer, Zur Geschichte der Dampfkesselexplosionen. Dingler's Polytechn. J. 213:296-308 (1874). 12. K. L. Goin, The history, evolution, and use of wind tunnels. AIAA StudentJ. (Febr. 1971): 3-13. 13. A. Hertzberg, Shock tube research, past, present and future. Proc. 7th Int. Shock Tube Symp., I. I. Glass, ed. Toronto (June 1969), Univ. of Toronto Press (1970), pp. 3-5. 14. J. N. Johnson, and R. Ch6ret, Shock waves in solids: an evolutionary perspective. Shock Waves 9:193-200 (1999). 15. T. von K~irm~in, Aerodynamics. Selected topics in the light of their historical development. Cornell University Press, Ithaca, NJ (1954). 16. T. yon K~irman and L. Edson: The wind and beyond. Theodore von Karm~in pioneer and pathfinder in space. Little, Brown & Co., Boston & Toronto (1967). 17. P. Krehl, and M. van der Geest, The discovery of the Mach reflection effect and its demonstration in an auditorium. Shock Waves 1:3-15 (1991). 18. P. Krehl, and S. Engemann, August Toepler, the first who visualized shock waves. Shock Waves 5:1-18 (1995). 19. N. Manson, Historique de la d6couverte de l'onde de d~tonation. [Colloque C4.] J. de Physique 48:7-37 (1987). 20. N. Manson, and E. K. Dabora, Chronology of research on detonation waves: 1920-1950. In Dynamic aspects of detonations, A. L. Kuhl, J.-C. Leyer, A. A. Borisov, and W. A. Sirignano, eds. Progr. Astro- & Aeronautics (AIAA, Wash. D.C.) 153:3-39 (1993). 21. L. M~dard, Histoire de la thermochimie. Publ. de l'Univ, de Provence, Aix-en-Provence (1994). 22. L. M~dard, Eoeuvre scientifique de Paul Vieille (1854-1934). Rev. Hist. Sci. 47:381--404 (1994). 23. W. E Merzkirch, Mach's contribution to the development of gas dynamics; Seeger, R. J., On Mach's curiosity about shock waves. In Ernst Mach, physicist and philosopher, R. S. Cohen and R. J. Seeger, eds. Boston Studies in the Philosophy of Science 6:42-67 (1970). 24. E. Oeser, Historical earthquake theories from Aristotle to Kant. Abhandl. Geolog. Bundesanstalt Wien 48:11-31 (1992). 25. H. Reichenbach, Contributions of Ernst Mach to fluid mechanics. Ann. Rev. Fluid Mech. 15:128 (1983). 26. E. W. E. Rogers, Aerodynamicsmretrospect and prospect. Aeronaut. J. 86:43-67 (1982). 27. I. Szab6, Geschichte der Theorie des Stot~es. Humanismus und Technik 17:14-44, 128-144 (1973). 28. I. Szab6, Geschichte der mechanischen Principien und ihre wichtigsten Anwendungen. Birkhauser, Basel etc. (1977). See also: Geschichte der Stoj~wellen, pp. 281-314; Geschichte der Stoj~theorie, pp. 425-479. 29. S. P. Timoshenko, History of strength of materials. McGraw-Hill, New York etc. (1953). 30. C. A. Truesdell, The mechanical foundations of elasticity and fluid dynamics. J. Ration. Mech. Annual 1, 125-171, 173-300 (1952). 31. C. A. Truesdell, Rational fluid mechanics. In Leonardi Euleri Opera Omnia XII [II]. Teubner, Leipzig etc. (1954). See also editor's introduction, pp. I-CXXV.

History of Shock Waves

25

1.8 CHRONOLOGY OF MILESTONES* 1759

Royal Academy of Sciences, Berlin I

1760s Private

1762

1770

laboratory, Great Marlborough Street, London Royal Society, London

University of Basel

Euler I addresses in a letter to Lagrange the possibility that the propagation of sound might depend on the "size of the disturbances," which expressed in modern terms would mean size of the displacement or intensity of sound. He writes to Lagrange, "It is very remarkable that the propagation of sound actually takes place more rapidly than the theory indicates, and at present I renounce the opinion I had formerly that the following disturbances could accelerate the propagation of the preceding ones, in such a way that the higher is the sound the greater is its speed, as possibly you have seen in our latest memoirs. It has also come into my mind that the size of the disturbances might cause some acceleration, since in the calculation they have been supposed infinitely small, and it is plain that [finite] size would change the calculation and render it intractable. But, in so far as I can discern, it seems to me that this circumstance would rather diminish the speed." m Euler's hypothesis was indeed correct insofar as the amplitude of sound (the "size of disturbance") might influence the speed of sound. However, he incorrectly assumed that the velocity would diminish with increasing amplitude. Cavendish 2 experiments with a mixture of "fixed air" and "inflammable air" and "inflammable air," i.e., oxyhydrogen, and its ignition by an electric spark. He constructs a "measurer of explosions of inflammable air" to quantify the released mechanical energy of a confined volume of that gas. Canton 3 demonstrates the small compressibility of liquids, which have hitherto been regarded as being incompressible. He places the test liquid in a thermometer-like arrangement and, compressing the bulb, obtains an observable magnification of the change of volume in the capillary. Daniel Bernoulli 4 treats the problem of collision by applying the theory of elasticity and develops the first wave theory of percussion. Assuming a freely suspended rod hit perpendicular to its axis, he calculates the loss of kinetic energy as a result of harmonic elastic vibrations.

* Covering not only shock waves but also related high-rate phenomena, such as percussion, blast, explosion, and implosion, as well as milestones in the development of basic shock diagnostic techniques. Dates years provided in the text by an arrow (for example --~ 1803) refer the reader to other milestones listed under these years and notes following the symbol 9 comment the milestone from the today's point of view.

26

V. Krehl

1770s Ecole Royale du Gdnie, Mdzidres, France

Monge 5 enters a field of study that will hold his interest for many years: Lagrange's theory of general partial differential equations and his own method of geometric construction of particular solutions, which he calls "method of characteristics." Starting from a first-order partial differential equation, he gives a geometric interpretation of the method of the variation of parameters and writes, "In the following I will use, as I have always done, different characteristics for the different ways of differentiating; this method is more practical, as it is not necessary to find a fractional form in order to present a partial differential." He concludes: "This memoir contains the constructions of integrals of partial differential equations, more generally than the ones I had constructed until now, and there I demonstrate that the geometrical places of these integrals generally satisfy their partial differential equations, which is what I had thought to myself". His geometric construction of a particular solution of the equations under consideration allows him to determine the general nature of the arbitrary function involved in the solution of a partial differential equation ~ Monge's graphical method was widely applied and further developed by subsequent mathematicians and physicists who introduced such basic notations as characteristic curve (or Monge's curve), characteristic cone (or Monge's cone), trajectory of characteristics, and characteristic variable etc. A detailed discussion of his work was given by Taton. 6 Earnshaw (1858) and Riemann (1859), independently of one another, first applied Monge's classic work of characteristics on gas dynamics, particularly on the propagation of the shock wave. Their studies were continued and greatly extended by various other prominent shock wave pioneers, such as Hugoniot (--~ 1887), Hadamard (--. 1903), and Prandtl and Busemann ( - , 1929). Reviews on the progress of further developments of this important mathematical tool and its application in gas dynamics and hydrodynamics were given, for example, by Oswatitsch, y Courant and Friedrichs, s and Abbott. 9

1774

London

Nairne, 1~ a British mechanic and experimentalist, studies the electrical explosion of thin wires. Discharging a battery of Leiden jars, initially charged up to a high voltage, through a 1-m-long iron wire 0.15 mm in diameter, he observes that "it flew about the room in innumerable red hot balls, on examining these balls, they were in general hollow, and seemed to be nothing but scoria."

1780

Diocese Chiemsee, Bavaria

Wisshofer, a German priest and naturalist, publishes in

Salzburg a pamphlet on the design of an electric gun that uses the discharge of a Leiden jar (1745) to ignite an inflammable gas for propelling the projectile. 11

History of Shock Waves

27

Royal Academy of Sciences, Berlin

Lagrange 12 publishes a treatise on the motion of fluids. In the last chapter entitled Du mouvement d'un fluide contenue dans

1781

un canal peu profond et presque horizontal, et en particulier du mouvement des ondes he considers a surface wave of infinitesimal height in shallow water in a canal of finite length and dervies the famous formula for the propagation velocity as v = (gh) ~/2 where g is the gravitational acceleration and h the water depth of the liquid at rest. Referring to the known formula describing the velocity v of a free-falling body, v=(2gh) 1/2 and drawing a comparison between sound waves in air and gravity waves, he states, "Thus, as the velocity of propagation of sound is found equal to that which a weight would require in falling from the height of the atmosphere (assumed homogeneous), the velocity of propagation of waves will be the same as what which a weight would acquire in falling from a height equal to half the depth of water in the canal." He refers to measurements previously performed by de la Hire in France who observed a velocity of 0.46 m/s [1.412 pied par seconde] in a water depth of about 2.2cm [ 8/,0 pouce], thus essentially confirming his theoretical result. 9 In the case of hydraulic jumps ("shooting" flow) the velocit~ v is calculated by the formula v [g(h 1 + h2)h2/2hl]/2, where h I is the water depth ahead of the jump and h2 is the water depth behind the jump. 13 For increasingly weaker jumps ("streaming" flow) h 2 approaches h 1, eventually converging with Lagrange's solution.

1783

Chair of Mathematics, Royal Military Academy, Woolwich

Hutton, 14 performing ballistic experiments in the years 1775 and 1783-1786 using the ballistic pendulum (Cassini, Jr. 1707, Robins 1740), measures supersonic muzzle velocities of cannon shots (charge: up to 16oz of gunpowder; projectile: iron cannon ball, 1.96 inch in diameter, weight up to 16oz, 13 dr,) up to 2030ft/s. His studies first confirm that supersonic velocities are not only obtainable for small caliber guns (Robins 1746) but also for larger ones. In another treatise HUTTON15 investigates the drag of projectiles within a wide range of velocities up to supersonic speeds (20--2000ft/sec) "to show according to what power of the velocity, at every point, the resistance increases." He observes that "commencing with the 2nd power or square of the velocity, at the very beginning or slow motion [5ft/sec], the exponent of the power gradually increases, till at the velocity of 1500 or 1600 ft/sec, it arrives at the 2.153 power of the same . . . . After the 1600 feet velocity, where the exponent (2.153) is greatest, it gradually decreases again to the end [towards 2000ft/sec]." He explains the velocity-dependent drag of a projectile by a vacuum generated at its rear, "The

28

P. Krehl circumstance of the variable and increasing exponent in the ratio of the resistance is owing chiefly to the increasing degree of vacuity left behind the ball, in its flight through the air, and to the condensation of the air before it. It is well known, that air can only rush into a vacuum with a certain degree of velocity, viz., about 1200 or 1400 feet in a second of time; therefore, as the ball moves through the air, there is always left behind a kind of vacuum, either partial or complete; that as the velocity is greater, the degree of vacuity behind goes on increasing, till at length, when the ball moves as rapidly as the air can rush in and follow it, the vacuum behind the ball is complete, and to complete ever after, as the ball continues to move with all greater degrees of velocity. Now the resistance, which the ball continues to move with all greater degrees of velocity. Now the resistance, which the ball suffers in its flight, is of a triple nature; one part of it being in consequence of the vis inertia of the particles of air, which the ball strikes in its course; another part from the accumulation of the elastic air before the ball; and the third part arises from the continued pressure of the air on the forepart of the ball, when the velocity of this is such as to leave a vacuum behind it in its flight, either wholly or in p a r t . . . A s soon as the motion of the ball becomes equal to that of the air, and always when greater [i.e., at supersonic speeds], then the ball has to sustain the whole pressure of the atmosphere on its forepart, without having any aid from a counter-pressure behind . . . . " Hutton's explanation well illustrates the attempts of early supersonic pioneers to find a plausible reason for the puzzling phenomenon of the strong increase of drag in the transonic regime.

1784

Private laboratory, Great Marlborough Street, London

Cavendish, 16 hearing about recent experiments on oxyhydrogen explosions performed by Warhire (1776) and Priestley (1781), resumes his own investigations on this subject (Cavendish -+1760s), resulting in his famous paper on the synthesis of water. He observes that mixtures of "common air" and "inflammable air," enclosed in a vessel and electrically fired, are converted into a deposit inside the vessel of dew that is pure water, whereby all of the inflammable air but only about four-fifths of the common air is converted. - Lavoisier who repeated the experiment, later termed "inflammable air" hydrogen [from the Greek hydrogenium, meaning water-former].

1785

Turin, Italy

Count Morozzo 17 reports on a flour-dust explosion in a Turin flour warehouse, probably the earliest account of such a phenomenon. He describes the circumstances as follows: "On the 14th of December, 1785, about six o'clock in the evening, there took place in the house of Mr. Giacomelli,

History of Shock Waves

29 baker in this city, an explosion which threw down the windows and window-frames of his shop, which looked into the street; the noise was as loud as that of a large cracker, and was heard at a considerable distance. At the moment of the explosion, a very bright flame, which lasted only a few seconds, was seen in the shop; and it was immediately observed, that the inflammation proceeded from the flourwarehouse, which was situated over the back shop, and where a boy was employed in stirring some flour by the light of a lamp. The boy had his face and arms scorched by the explosion; his hair was burnt, and it was more than a fortnight before his burns were healed . . . . " Count Morozzo speculated that the flour might have produced "inflammable air" by fermentation (such as observed on dampened hay) which, mixed with air and dispersed flour dust, was ignited by the light of the lamp, thus leading to this violent inflammation. However, he critically remarked that model experiments did not prove this hypothesis and that the flour, upon examination, was extraordinarily dry and originated from the Piedmont area, which had had no rain for five or six months.

Academy of Sciences, Turin

Lagrange 18 studies the percussion force of a water jet impinging perpendicularly or obliquely on a plane. This basic problem of hydrodynamics--a term coined by D. Bernoulli ~9 to analytically cover hydrostatic as well as hydraulic (i.e., dynamic) phenomena by a single method---anticipates the difficult task of evaluating the flow of water impacting the blade of a water turbine. Measurements of the percussion force performed by Krafft (1973) gave a much smaller value than predicted theoretically by D. Bernoulli (1736), D'Alembert (1769), and Bossut (1772). Assuming a simple model of fluid flow with a central core of stagnated liquid surrounded by a shell of streaming and laterally deviated liquid, Lagrange derived a simple formula for the percussion force that better matched experimental results.

1786

York, England

Goodricke 2~ publishes a report on observations in which he discloses that a star, positioned near the head of Cepheus, changes its brightness periodically. A few years before, he had observed similar phenomena in the head of Medusa (so-called Algol) and of/~ Lyrae. 9 Variable stars, also called cepheids, are found in various regions of our galaxy and in other galaxies. The change in the brightness is caused by the change in the temperature and radius of the photosphere, which also creates shock waves. 21

1792

Munich

Von Baader, 22 a German mining engineer [Bergrat] interested in the application of explosives in the mining industry, observes that the energy of a blast can be focused on a

30

P. Krehl small area by forming a hollow in the charge that increases the explosive effect and saves powder (the "cavity effect"). 9 Seven years later he makes the observation that the surface relief of an explosive is reproduced on a closely facing steel plate by the focusing of explosion products ("explosive engraving"). Von Baader's publication was aFparently read and put into practice in Norway and for a short time also in the Harz Mines. 23 However, since he used black powder, which is not capable of detonation, his arrangement was not a shaped charge device in the modem sense.

1794

Ecole Polytechnique, Paris

Originally established as Ecole Centrale des Travaux Publics by order of Napoleon under the direction of Gaspard Monge (1746-1818), the school is renamed Ecole Polytechnique the following year. 24 9 Many prominent French pioneers of fluid mechanics, percussion, explosion, and shock physics studied and/or taught here, e.g., Jean B. C. Bdanger (1790-1874), Dominique E Arago (1776--1853), Jean B. Blot (1774-1862), Jacques S. Hadamard (1865-1963), Henri-Pierre Hugoniot (1851-1887),Joseph L. Lagrange (1736-1813), Pierre-Simon Laplace (1749-1827), Henry Le Chatelier (1850-1936), Louis Navier (1785-1836), Simeon D. Poisson (1781-1840), Adhemar de Saint-Venant (1797-1886), Victor Regnault (18101878), Emile Sarrau (1837-1904), Paul Vieille (1854-1934), and Pierre L. Wantzel (1814-1848).

Wittenberg, Germany

Chladni, 25 more known to later generations of physicists by his contributions to acoustics, starts his 30-year campaign on researching meteorites ("fire balls") and first proposes their extraterrestrial origin. 9 His result was not widely accepted until the EAigle Fall of stony meteorites (--+ 1803).

Brussels, Belgium

Mons 26 reports in a letter to Prof. Gren, editor of the Journal der Physik, on experiments by Parcieux, who observed in a dark room in the moment of explosion or implosion of thinwalled glass spheres "a vivid flame similar to an electric spark"

["eine lebhafte Flamme gleich einem electrischen Funken"]. Parcieux produced (i) an explosion by using a sealed glass sphere filled with air of atmospheric pressures that, positioned in a recipient, exploded after evacuation, and (ii) an implosion by evacuating a glass recipient that, not capable of withstanding the atmospheric pressure, imploded during evacuation. 9 Similar experiments on imploding and exploding glass spheres were performed more recently by Glass 27 and associates. Using high-speed schlieren visualization, the latter researchers also noticed that in the case of implosion the glass fragments form a jet, like in a shaped charge.

History of Shock Waves

31

1796

Paris

Montgolfier, 28 13 years after his sensational hot-air balloon ascents, invents with the assistance of Argand the hydraulic ram [bdier hydraulique], a water pump that uses the kinetic energy from a copious flow of running water under a small head to force a small portion of that water to a higher level.. Hydraulic shocks are detrimental in common water pipelines (Karelijkich and Zhukovsky--~ 1898), however, when used in this type of pump they should be as strong as possible to provoke efficient pumping. Since the hydraulic ram does not require any additional source of energy and is very simple in construction, it is still in current use in the mountains. For example, modern ram pumps 29 can deliver 700 L / m i n up to a height of 300 m.

1802

Coll~gede France, Paris

Biot, 3~ mathematician and physicist, publishes the first "theory of sound" and acknowledges the assistance of Laplace. He advances physical arguments in favor of p - Kp:', which results in a sound velocity a - - ( ~ p o / P o ) 1/2, where Po and Po are the pressure and density at rest, respectively, and 7 = %/6, is the ratio of specific heats at constant pressure and constant volume.

1803

KAigle, Normandy, France

Biot 31 gives his famous account on the "EAigle fall of stony meteorites": "On Tuesday, April 26, 1802, about one in the afternoon, the weather being serene, there was observed from Caen, Pont-Audenen and the environs of Alenqon, Falaise and Verneuil, a fiery globe of a very brilliant splendor, which moved in the atmosphere with great rapidity. Some moments after there was heard at EAigle, and in the environs of that city to the extent of more than thirty leagues in every direction, a violent explosion, which lasted five or six minutes. At first there were three or four reports like those of a cannon, followed by a kind of discharge which resembled a firing of musketry; after which there was heard a dreadful rumbling like the beating of a drum, a multitude of mineral masses were seen to fall .... " 9 From the number of shock waves or explosions felt by the observer, it was concluded that the meteorite must have broken into a large number of pieces on striking the dense atmosphere at low levels. Later about 3000 meteor fragments were collected, ranging in mass from 9 g to 8 kg. 32

1807

Paris

The Niepce Brothers obtain from Napoleon a patent for their piston engine that, supposed to be driven by spark-ignited lycopodium dust explosions, was to be used as a drive motor for ships. 33 9 W h e n experiments with lycopodium dust failed, they

Pyr~olophore, an explosion-driven

32

R Krehl successfully used petroleum. With their engine, a forerunner of the Diesel engine, it became possible in 1816 to power barges on the Seine. Turning in 1813 to the problem of photography, they succeeded in 1826 to make the first photograph [h(.liographie].

1808

Ecole Polytechnique, Paris

Poisson 34 presents his "theory of sound," and at the end of his treatise he extends his theory to the special case that "the velocities of the molecules in an air column are not supposed to be very small." He assumes that disturbances with finite amplitudes propagate in an ideal gas in one (positive) direction x and applies the law a 2 = dpo/dpo, with a being the sound velocity, i.e., the limit to which the velocity of propagation of the wave approximates when the particle velocity becomes indefinitely small. He arrives at the following general equation: dtp/dt 4- a dq~/dx 4- ~1. dq~2/dx 2 = 0. Here q~ is the velocity function and dq~/dx the velocity of disturbance (or particle velocity) at time t of a particle whose distance from the origin is x. His exact solution for a wave traveling in one (positive) direction reveals that the particle velocity dq~/dx behind a pressure disturbance can be expressed as dq~/dx = F { x - a - d q ~ / d x t}, where F denotes an arbitrary function. His solution differs from the equation given previously by D'Alembert (1747) only in that dq~/dx also appears in the argument of the function E Poisson notes that Lagrange 35 had already obtained a very similar result given by dq~/dx = f { x - a t - t . f ( x - at)}. ,, Poisson's mathematical result obviously indicates the quicker propagation of the parts of the wave where the disturbance is forward (that is, the compressed parts) and the slower propagation of the parts where the disturbance is backward (that is, the dilated parts). This leads to a change of the wave profile during wave propagation, an important feature that will be first recognized by Challis (--+ 1848), and qualitatively worked out and illustrated by Stokes (-+ 1848). Retrospectively, Poisson's treatise can be regarded as the root of shock wave theory and theoretical nonlinear acoustics as well. He also coined the symbol 7 for the ratio of the specific heats, which, later resumed by Rankine (--~ 1869), is used even to this day.

1809

Ecole Polytechnique, Paris

Gay-Lussac and ThCnard 36 expose a 1:1 mixture of hydrogen and chlorine to diffuse daylight and gradually obtain hydrogen chloride [acide muriatique]. On the other hand, when being exposed to direct sunlight this gaseous mixture ("chlorine detonating gas") explodes violently and destroys the glass balloon. 9 Compared to an oxyhydrogen explosion (Turquet de Mayerne (1620; Cavendish--, 1760s-+ 1784), the

History of Shock Waves

33 released heat of a chlorine-hydrogen explosion amounts to only about 2/3. The chlorine-hydrogen reaction, today a classic example of a photochemical reaction, long remained a puzzle to chemists and physicists. Work on his puzzle eventually led to the discovery of chain reaction (Bodenstein--+ 1913).

1815

Meeting of the Royal Society, London

Singer and Crosse 3r report on the effects of wire explosions carried out by De Nelis, who used an exploding lead wire placed in axial direction of a thin-walled metallic cylinder filled with water and pulsed from a large battery of Leiden jars. The cylinder itself is expanded more or less in proportion to its power of resistance, usually becoming undulated on the surface or burst open. Generating more violent wire explosions by using a larger battery, they observe that even iron cylinders with a thickness greater than that of the strongest muskets are heavily damaged by cracks. They state that "the expansive power of electricity acting in this way is therefore vastly superior to the most potent g u n p o w d e r . " . Their remarkable results anticipated the electrohydraulic effect that Yutkin (1950) rediscovered in the Soviet Union.

1816

EAcademie des Sciences, Paris

Laplace 38 publishes his previous hypothesis (Biot-+1802) that a sound wave is an adiabatic process and states, without demonstration, a correction of Newton's formula that was published in his Principia (1687).

Grand Duke's Laboratory, Florence, Italy

Davy 39 investigates the nature of firedamp. Studying test samples of firedamp collected together with Faraday on a journey in the Apennines, he observes that "1 part of gas inflamed with 6 parts of air in a similar bottle, produced a slight whistling sound: 1 part of gas with 8 parts of air, rather a louder sound; 1 part with 10, 11, 12, 13 and 14 parts, still inflamed, but the violence of combustion diminished. In 1 part of gas and 15 parts of air, the candle burnt without explosion with a greatly enlarged flame .... " He correctly states that firedamp (methane) consists of "4 proportions of hydrogen in weight 4, and 1 proportion of charcoal in weight 11.5." Using gas from the distillation of coal mixed with eight times its volume of air, he also determines the rate at which an explosion of gases propagates in a tube and makes the first rough experiment on the temperature reached in an explosion. The flame, fired in a 1-foot-long tube 1 inch in diameter, takes more than a second to traverse the tube. He also observes that the same mixture that burns in a wide tube may not support flame propagation in a narrow tube with a diameter less than a certain "critical diameter." This phenomenon will eventually lead to his construction of a safe mining

34

P. Krehl lamp (the Davy lamp) in which a copper mesh with small openings prevents flame propagation from the inside of the lamp to the atmosphere of the mine. 9 Archduke John of Austria, who visited Davy in 1815, was one of the first promoters of the Davy lamp, which shortly after was introduced in the Styrian mining industry. 4~

1822

Ecole des Ponts et Chauss4es, Paris

Navier 41 presents a paper on the law of motion of continuous media. He considers fluids and solids to be made up of particles that are close to each other and act upon each other by attraction or repulsion, resulting from the caloric heat. He derives partial differential equations to which he applies Fourier's method to find particular solutions. 9 His result, later refined by Poisson 42 (1829), de Saint-Venant 43 (1845), and Stokes 44 (1845) was called the "Navier-Stokes equations." Maxwell, 45 supplementing his dynamical theory of gases, derived the Navier-Stokes equations by assuming his distribution function of gas molecules. A first attempt to solve the Navier-Stokes equations for shock waves was first successfully achieved by Becker (-~ 1921).

1823

Ecole Polytechnique, Paris

Poisson 46 reviews the present state of treating the problem of calculating the velocity of sound. He writes, "The sound velocity in air, derived from a formula given by Newton [Principia, Book II, Scholium (after Proposition)I, differs from the observed velocity and surpasses the calculated velocity by a fifth [20%]. When Lagrange [Misc. Taur. 1, I-X, 1-112 (1759)] in his first studies on the theory of sound arrived at the same formula; he tried of course to explain this discrepancy between calculation and observation. His analysis was based on two suppositions: the minuteness of the air vibrations, and the proportionality of the elastic force with density. He proved first, against Euler's opinion [M~'m. Acad. Sci. Berlin 15 (1759)], that the amplitude of vibration does not influence the magnitude of the sound velocity; in addition he mentioned that one could coincide this velocity with the result of observation by supposing that the elastic force increases to a larger extent than the density; but he could not give any particular reason for this increase of elasticity which cannot be described by the general law of compression for air. It is not less true that this increase is really due to the air motion: It is Mr. Laplace [Ann. Chim. & Phys. 3,238-241 (1816)] who pointed out the true reason who fully explained and eliminated the difference between Newton's formula and the measurement. This cause is the release of heat which always occurs during the compression of air or the production of coldness which goes along with dilatation, likewise . . . . " Poisson, 47 stimulated by Laplace's approach, derives

History of Shock Waves

35 in the same year the two gas laws for adiabatic compression. A gas with a ratio of specific heats k, initially at pressure p, density p, and temperature O and then adiabatically compressed, reaches a new state (p', p', O') which is given by p' - p(p,/p)K and O' = (266.67 + O)(p'/p) k-1. He writes, "These equations contain the elasticity and temperature laws of gases, which are compressed or expanded without a variation in their heat quantity; which will happen when the gases are in the heat-proof glass container, or when the compression, as with the sound phenomenon, will be so fast that one can assume that the heat loss is negligible . . . . " . Poisson assumed an absolute zero at -266.67~ which we have to replace today by-273.15~ His equation of state for adiabatic compression, applicable only for sound waves of infinitesimal amplitudes and later be called the Poisson isentrope or static adiabate, was a major achievement toward the dynamic adiabate of a shockcompressed gas by Hugoniot ( - , 1887).

1824-1825

Port Bowen, Prince Regent's Inlet, Canada

Capt. Parry 48 of the Royal Navy, famous polar explorer who searches for a Northwest Passage, spends the winter in Port Bowen studying the Eskimos and, while waiting for the ice to break through, gathers scientific data. Together with Lieut. Foster, participating in the expedition as an assistant surveyor, he performs experiments on the velocity of sound "to determine the rate at which sound travels at various temperatures and pressures of the atmosphere." The measurements at very low temperatures, i.e., in air of perfect dryness, are considered to be of particular interest because they avoid any corrections of sound velocity data caused by the humidity of the atmosphere. Using a six-pounder brass gun placed on the beach at the head of Port Bowen and fired on signal from the "Hecla", Parry and Foster, carefully noting the interval elapsed between the flash and report at a distance of about 3.9 km by the beats of a pocket-chronometer held at the ear of each observer, notice an anomalous high velocity of sound. 9 Parry 49 had already made similar observations during his second polar voyage. In the appendix of his report, obviously written by Foster, it reads: "The experiments on the 9th February 1822, were attended with a singular circumstance, which was--the officers' word of command "Fire", was several times distinctly heard both by Captain Parry and myself [Foster], about one beat of the chronometer after the report of the gun; from which it would appear, that the velocity of sound depended in some measure upon its intensity . . . . " Contemporary naturalists attributed their unusual findings to possible influences of humidity and wind that they had not

36

P. Krehl precisely recorded, but Parry and Foster 5~ replied, "it was certainly far from our intention to oppose our opinions on these points to those of Newton and Laplace. We considered our remark at the time, as a fair deduction from our own experiments, without at all considering with what theory it might be at variance: our only wish being, to furnish data for philosophers to arrive at such laws as will make the computed and observed velocities of sound agree more exactly with each other, than appears to be the case, in the present state of our information of all the modifying circumstances to which the motion of sound is subjected." Parry's unusual observations, supported also by those of Ross who participated in the expeditions, were later cited by Earnshaw (--+1858) as an experimental proof of his mathematical theory of sound that intense air waves travel more quickly than weaker waves.

1826

Lake of Geneva, Switzerland

Colladon, a Swiss apothecary, measures quite accurately the sound velocity in water. As a strong source of sound he uses a bell placed under water and triggered simultaneously with a cannon, and for sound detection a long ear-trumpet submerged 5 m under the surface. To get a high accuracy he chooses the broadest part of the Lake of Geneva (about 8 km), and to better visualize the cannon fire he performs the measurements at night.

1828

Geneva

Colladon and Sturm, 51 the latter being a Swiss private tutor, publish data on the compressibility of various substances and on the measurements of the sound velocity in the Lake of Geneva. They show that putting the measured data of compressibility of water into Poisson's formula for the speed of sound yields a value of 1437.8m/s, which is in close agreement with the measured value of 1435 m / s in the Lake of Geneva. They also report on the measurement of heat emitted by liquids following the application of strong and sudden pressures. Their results earn them the prize set by the Paris Academy.

Compagnie du canal des Ardennes, France

Bdanger 52 investigates in a pioneering study the behavior of water flow in an open channel and high-speed shooting with sudden changes in depth, known as a hydraulic jump, the oldest known type of discontinuous wave motion and well resolvable with the naked eye. He derives a formula for the height Ah = h 2 - h 1 of a hydraulic jump in terms of the initial water depth h 1 and the velocity v of the jump, given by Ah = 0.Se - hi 4- (0.25g 2 q- hi) 1/2, with g = v2/2 g. 9 His remarkable study is an early attempt to characterize the propagation speed of a discontinuous wave front by its

History of Shock Waves

37 strength,--in his case of a hydraulic jump propagating in (incompressible) shallow water--by its step height. Analogically, in the case of a shock wave advancing in a (compressible) fluid in a layer of invariant thickness this would correspond to a step increase in density at the shock front. Jouguet 53 showed that, using his classic theory, the loss of internal energy [perte de charge] of a hydraulic jump can be described in terms of the difference in water heights, which is only a particular case of Hugoniot's law of the dynamic adiabate (---~1887) when the water is considered as an adiabatically moving "hydraulic gas" with 7 = 2. The analogy between a hydraulic jump and a shock wave has fascinated shock wave researchers from the early times to now (Preiswerk --~ 1938).

1830

Ecole Polytechnique, Paris

Arago 54 discusses in detail the possible causes of frequent boiler explosions of steam engines, which typically result in many casualties and heavy damage to adjacent facilities. Particularly addressing the dangers emanating from the use of Papin's safety valve (1679), he points out that many valve constructions are too narrow to allow a quick release when the internal boiler pressure suddenly increases (Airy--~1863)--a dangerous phenomenon for which he mentions various causes. 9 The limitation of the outflow of fluid through small openings became a much-discussed subject among engineers as well as scientists (Bernoulli 1738; De Saint-Venant and Wantzel--~ 1839; Napier--~ 1866; Reynolds--~1885; De Laval--~1888; Salcher and Whitehead--~ 1889; L. Mach-~ 1897; the Emden Brothers---~ 1899; Stodola--~ 1903; Prandtl---~ 1904; etc.). The topic stimulated the evolution of supersonic flows and promoted the effective operation of steam turbines.

1834

Chair of Physics, Kings College, London

Wheatstone 55 first uses a rotating mirror as a diagnostic tool to resolve high-speed phenomena. 9 34 years later Sabine, 56 then president of the Royal Society, states at his presentation of the Copley Medal to Wheatstone, "But no series of his researches have shown more originality and ingenuity than those by which he succeeded in measuring the velocity of the electric current and the duration of the spark. The principle of the rotating mirror employed in these experiments, and by which he was enabled to measure time to the millionth part of a second, admits of application in ways so varied and important that it may be regarded as having placed a new instrument of research in the hands of those employed in delicate physical inquiries of this order." The rotating mirror, subsequently used by Foucauh 57 (1850) and Feddersen 58 (1858) in sensational experiments, became an important

38

P. Krehl element in the later technique of high-speed rotating-mirror cameras. Stimulated after 1945 by the need to study shock wave effects involved in the development of nuclear weapons, work with these cameras resulted in very sophisticated ultrahigh-speed cameras incorporating helium-driven turbines. 59

1838

ILAcadCmie des Sciences, Paris

Arago 6~ publishes an essay on thunder for the Annuaire du Bureau des Longitudes at Paris, in which he gives a masterly historical sketch of the real facts that have hitherto been accumulated. From these he deduces the inferences, scientific and practical, that may legitimately be drawn. He discusses also ball lightning and analyzes a number of evidently reliable observations, pointing out that an observer, viewing the descent of the ball at an angle from the side, is not subject to the optical illusion described. Shortly after, Faraday 61 will give essentially the same explanation, stating that the optical illusion is caused by an afterimage perceived by eyes that just have seen the dazzling flash of an ordinary bolt. 9 Ball lightning has a diameter somewhere between a golf ball and a large beach ball, moves horizontally at low speed and can decay silently or explode violently. Ball lightning has been well documented since the Middle Ages as a natural but rare phenomenon associated with thunder, but still is an enigma to modem science. 62

1839

Ecole des Ponts et Chauss~es, Paris

De Saint-Venant and Wantze163 study compressible flow in a duct of changing area and the exhaust of compressed air from a small opening. Using Poisson's adiabatic law ( - , 1823) and Bernoulli's energy equation, they assume compressible flowm i.e., p = p(p)--and express the difference of enthalpy by the pressure integral. This leads to their famous fundamental formula relating outflow velocity V at given pressure p in the pressure reservoir by V2 = [1 - (p/po)"]2po/mpo with m - - ( • - 1)/~'. For an outflow into a vacuum (p = 0), the maximum outflow velocity is given by Vma• -(2po/mpo) 1/2, which, in the case of air (to = 1.405), amounts to 757 m/s.

1840

Chair of Physics, Kings College, London

Wheatstone 64 invents the first electric chronoscope to measure projectile velocities by employing an electromagnetically controlled mechanical stopwatch.

1842

Meeting of the Association for the Advancement of Science, Manchester

Russell 65 coins the expressions great solitary wave (or wave of the first order or wave of translation), a single hump of constant shape and constant speed which, moving on the surface of an inviscid incompressible fluid, is capable of traveling in a uniform channel a considerable distance with almost no change. Referring to his former studies (18331840), he reports on the reflection of such a wave type at a

History of Shock Waves

39 solid boundary, "when the angle of the ridge with the surface is small, not greater than 30 ~ the reflexion is complete in angle and in quantity. When the ridge of the wave makes an angle greater than 30 ~ the angle of reflexion is still equal to the angle of incidence, but the refected wave is less in quantity than the incident wave.., when the angle of the ridge of the wave is within 15 ~ or 20 ~ of being perpendicular to the plane [i.e., at an angle of incidence within 75 ~ or 70 ~, annotation by the author], reflexion ceases, the size of the wave near the point of incidence and its velocity rapidly increases, and it moves forward rapidly with a high crest at right angles to the resisting surface. Thus at different angles we have the phenomenon of total reflexion, partial reflexion, and, non-reflexion and lateral accumulation; phenomena analogous in name, but dissimilar in condition from the reflexion of heights, &c." 9 His "lateral accumulation" of the reflected wave front, merging with the front of the incident wave, creates a new wave front that extends at a right angle to the boundary. This phenomenon of irregular wave reflection, found for the interaction of hydraulic jumps, was rediscovered by Mach and Wosyka (-+ 1875) for the case of interacting aerial shock waves. It was brought again to light by von Neumann (---~1943), who called it "Mach reflection."

1844

Conservatoire des Arts-etMetiers, Paris

Pouillet 6~ describes an electric circuit to measure the duration of short current pulses by studying its action on the magnetic needle of a galvanometer, a method based on the principle of the ballistic pendulum and later renowned as the ballistic galvanometer. He considers a precise time measurement as essential for the better understanding of high speed events, such as the ignition process of gunpowder and the contact duration of impacting bodies. His concept, later refined by Ramsauer (-+1909), will allow even the measurement of times in microseconds.

1845

Haswell Collieries, Durham District, England

Faraday and Lyell,67 investigating possible causes of a serious explosion at Haswell Collieries, observe many signs of the coal dust being partly burned and partly subjected to a charring or shocking action. Their conclusions that coal dust adds considerably to the disastrous effects of firedamp explosions and that proper ventilation is an effective means of preventing similar accidents will be confirmed later by leading French mining engineers (--+ 1890).

Royal Observatory, Greenwich

Airy, 68 Astronomer Royal, analytically treats the motion of "waves of finite amplitudes" in a uniform water canal of rectangular section and finds, by the method of successive

40

P. Krehl approximation, that in a progressive wave different parts travel with different velocities. In particular, he makes important statement that the crests tend to gain upon hollows so that the anterior slopes become steeper steeper.

1847

1848

will the the and

Chair of Chemistry, University of Basel

Sch6nbein experiments with the nitration of cellulose and invents nitrocellulose. 69 He communicates his process to John Taylor, 7~ who in the following year will be granted an English patent. The detonation of guncotton, however, is difficult to control, and it will take more than 40 years to convert nitrocellulose into a reliable gun propellant. 9 In 1862 von Lenk in Austria will try to use guncotton as an explosive. However, acid residues in guncotton, originating from the production process, provoked dangerous self-ignitions. This problem was not solved until 1866 by Abel 71 in England.

Technical State Academy, Prague

Doppler 72 speculates that the propagation velocity of sound should increase with increasing intensity and reflects on acoustical consequences of his discovered "Doppler effect." He discusses what might happen to a disturbance that, propagating with a velocity u, moves faster than the sound velocity a of the surrounding medium. Assuming a sequence of explosionlike emissions of disturbances, he graphically constructs the cone geometry for the three cases of disturbances propagating with a constant, an increasing, and a decreasing supersonic velocity. Doppler shows that, for a constant velocity u, the half-cone angle ~ of this cone allows one to determine the velocity u by the simple relation sin ~ = a/u. 9 His purely theoretical results were confirmed 40 years later by Mach and Salcher's ballistic experiments (--~ 1887). Mach designated the envelope of this cone as the "head wave" and Prandtl (---~1913) the cone angle ~ as the "Mach angle."

Chair of Applied Chemistry, University of Turin

Sobrero, 73 a former student of von Liebig and Pelouze, reports in a letter to Prof. Pelouze on his discovery of nitroglycerine. The increasing number of new explosive substances discovered in the following years will stimulate physicists and chemists to uncover the puzzle of detonation, which is felt to be somehow closely related to rapidly propagating mechanical waves.

Royal Observatory, Greenwich

Airy 74 shows that "the velocity does not depend on the absolute pressure of the air in its normal state of density, but upon the proportion of the change of pressure to the change of density. This is increased by the suddenness of

History of Shock Waves

41 condensation in one part, which, when the elastic force is great, makes it still greater--and by the suddenness of rarefaction in another part, which, when the elastic force is small, makes it still smaller,--thus in both ways increasing the change of pressure."

Cambridge Observatory

Challis 75 resumes the classical analytical problem of the velocity of disturbances. Obviously not knowing Poisson's previous work (--+ 1808) but commenting on Airy's remarks (---, 1848) on his theory of sound, he finds that for waves of finite amplitudes propagating in a perfect gas the velocity of propagation alters as it advances and tends ultimately to become a series of sudden compressions followed by gradual dilatations. The velocity of propagation is greater than the sound velocity and certain faster parts in the wave profile will take over the slower ones, thus leading to ambiguous mathematical solutions (the "Challis paradox").

Pembroke College, Cambridge

Stokes 76 replies to Challis' claim of a contradiction in the commonly accepted theory of sound. Stokes, assuming an isothermal gas, introduces surfaces of discontinuity in the velocity and density of the medium, thereby eluding the Challis paradox. He indicates that small pressure disturbances might create compression waves with discontinuous fronts, because each subsequent sound wave will propagate in a medium with a slightly higher sound velocity. He writes, "Of course, after the instant at which the expression (A) becomes infinite, some motion or other will go on, and we might wish to know what the nature of the motion was. Perhaps the most natural supposition to make for trial is, that a surface of discontinuity is formed, in passing across which there is an abrupt change of density and velocity. The existence of such a surface will presently be shown to be possible . . . . The strange results at which I have arrived appear to be fairly deducible from the two hypotheses already mentioned. It does not follow that the discontinuous motion considered can ever take place in nature, for we have all along been reasoning on an ideal elastic fluid which does not exist in nature. In the first place, it is not true that the pressure varies as the density, in consequence of the heat and cold produced by condensation and rarefaction respectively. But it will be easily seen that the discontinuous motion remains possible when we take account of the variation of temperature due to condensation and rarefaction, neglecting, however, the communication of heat from one part of the fluid to another. Indeed, so far as the possibility of discontinuity is concerned, it is immaterial according to what law the pressure may increase with the

42

P. Krehl density . . . . " He also first derives the conservation relations of mass and momentum that are now usually attributed to Rankine and Hugoniot.

1849

Royal Observatory, Greenwich

Airy 77 first points out the analogy between the velocity change in waves of sound of finite amplitudes and that which takes place in sea waves when they roll into shallow water.

1850

University of Edinburgh

Maxwell 7s publishes a paper on the theory of elasticity. He shows that two elastic constants are necessary to describe the elastic behavior of an isotropic solid, and completely develops the technique of photoelastic stress analysis. 9 Because it permits the determination of the entire stress field, his method proved very useful in the study of impact-induced shock wave propagation in 2-D birefringent solid specimens. 79

1851

Private laboratory at Lacock Abbey, U.K.

Fox-Talbot s~ performs the first microsecond snapshot photo from a page of the London Times rotating at high speed on a revolving disk by using an electric spark from a Leiden jar as a flash light source. He states, "it is in our power to obtain the pictures of all moving objects, no matter in how rapid motion they may be, provided we have the means of sufficiently illuminating them with a sudden electric flash." To obtain the necessary high sensitivity, he uses albumine plates, which he exposes immediately after sensitization. 9 This experiment was an important step toward single-shot photography because it first proved the excellent property of film to freeze high-speed events for a later detailed analysis.

Consultant Engineering, Edinburgh

Rankine, sl civil engineer and independant scholar, addresses the sound problem and previous arguments given by Laplace (-+ 1816) and Airy (-+ 1848), and states: "Now the velocity with which a disturbance of density is propagated is proportional to the square root, not of the total pressure divided by the total density, but of the variation of pressure divided by the variation of density . . . . It is therefore greater than the result of Newton's calculation, and this, whether the disturbance is a condensation or a dilatation, or compounded of both."

Parish of Sheffield

Earnshaw, mathematician and chaplain, observes unusual sound phenomena that he later s2 will describe as follows: "a thunder-storm which lasted about half an hour was terminated by a flash of lightning of great vividness, which was instantly (i.e., without any appreciable interval between) followed by an awful crash, that seemed as if by atmospheric concussion alone it would crush the cottages to ruins. Every one in the village had felt at the moment of the crash that the electric fluid had certainly fallen somewhere in the village . . . .

History of Shock Waves

43 But, to the surprise of everybody, it turned out that no damage had been done in the village, but that that flash of lightning had killed three sheep, knocked down a cow, and injured the milkmaid at a distance of more than a mile from the village... " . Since sound needs about 41 seconds to cover an English mile ( = 1523m) and Earnshaw noticed that lightning flash and thunder was felt almost simultaneously even though the strike happened more than a mile away, he correctly stated that intense sound, such as originating from a thunderclap, must propagate with supersonic velocity. Seven years later he will present his "theory of sound of finite amplitudes" (Earnshaw---~ 1858).

Pembroke College, Cambridge

Stokes s3 submits the view that during the propagation of pulses in an elastic fluid compressions and expansions of the particles take place so rapidly that there is no time for any appreciable transmission of heat between different particles, thus showing that Challis' supposition 84 that the developed heat is lost by radiation is untenable, and that Laplace's view (--, 1816) has a real physical foundation.

1854

Bethelehem Zinc Works, PA

First unusual explosion accident of finely powdered zinc ("metal-dust explosion"). 85

1856

Ecole Polytechnique, Paris

Jamin 86 invents the first optical interferometer, the archetype of many subsequent interferometer constructions, and applies it to measure the refractive index of gases. 9 Already 14 years later A. Toepler and Boltzmann 87 introduced optical interferometry in fluid dynamics (acoustics) to determine the amplitude at the threshold of heating, a masterpiece of experimental physics.

KOnigliche Realschule, Berlin

Kr6nig 88 publishes the first theory of gases. Following D. Bernoulli's model (1738), he assumed that a gas consists of discrete particles (molecules), each of which behaves according to universal mechanical laws. 9 Subsequently, Clausius 89 (1857), Maxwell 9~ (1859-1879), and Bohzmann 91 (18681904) made important improvements and today are regarded as the main founders of the kinetic theory of gases. 92

Private laboratory in Joule's brewery at Salford, Manchester & Chair of Physics, University of Glasgow

Joule and Thomson 93 treat thermal effects of bodies moving through air (aerodynamic heating) and conclude "that a body round which air is flowing rapidly acquires a higher temperature than the average temperature of the air close to it all round." In addition, they note that "the same phenomenon must take place universally whenever air flows against a solid or a solid is carried through air. If the velocity of 1780 feet per second in the foregoing experiment gave 137~ difference of temperature between the air and

44

e. Krehl the solid, how probable is it that meteors moving at from six to thirty miles per second, even through a rarefied atmosphere, really acquire, in accordance with the same law, all the heat which they manifest! On the other hand, it seemed worth while to look for the same kind of effect on a much smaller scale in bodies moving at moderate velocities through the ordinary atmosphere.., we have tried and found, with thermometers of different sizes and variously shaped bulbs, whiled through the air at the end of a string, with velocities of from 80 to 120 feet per second, temperatures always higher than when the same thermometers are whirled in exactly the same circumstances at smaller velocities." In the case where the velocity of translation of the body, v, is a small fraction of the velocity of sound, a (-- 1115 ft/sec at 17~ they estimate for the "hot spots" at the body's surface--i.e., at those points where the flow velocity is slowed down to zeroma temperature increase AO [~C] -- 58.8(v/a) 2. For a bulb thermometer moving at v - 183ft/sec, they measure a temperature rise of AO = I~ Their theoretical value, according to the formula given above, would yield a temperature increase of 1.5~ 9 Aerothermodynamics (G. A. Crocco--,1931), at Joule's time rather a subject of academic curiosity, became immediately important after World War II when supersonic flight could be realized not only in the military realm but later also in civil aviation (Tupolev Tu-144 and Concorde).

1857

Allegheny Arsenal, PA

Rodman 94 invents his "indentation gauge" to measure the maximum internal pressure in a gun. It consists of a piston working in a hole bored into the wall of a gun and acting on an indenting tool, for the purpose of determining the pressure in the bore at different points. With the help of this gauge, he discovers that the maximum pressure in a gun decreases with increasing grain size of the gunpowder (termed "mammoth powder" or "Rodman powder"). This finding becomes important for large-caliber guns to reduce the danger of damaging the barrel.. 15 years later, Noble 9~ who first critically studied the pressure data obtained by the Rodman gauge, stated; "It is curious that so distinguished an artillerist as Major Rodman should never have taken the trouble to calculate what energies the pressure which his instrument gave would have generated in a projectile; had he done so he would have found that many of the results indicated by his instrument were not only improbable but were absolutely impossible." Contrary to Rodman, Noble first correlated measured pressure data in the bore with theory using measured kinematic data of the projectile (Noble -+ 1872).

History of Shock Waves 1858

45

Herzogliche Realschule, Meiningen, Saxony

Knochenhauer 96 studies an electric discharge circuit that consists of two Leiden jars coupled to each other. It will be modified later by A. Toepler (---~1864) and further improved by E. Mach (---~1878) to control a delay pulse in the microsecond regime, an important requirement to stop motion of shock waves within a given field of view for recording purposes.

British Association for the Advancement of Science, Leeds

Earnshaw 97 presents on November 20 his famous theory of sound of finite amplitudes, which, published two years later, is the most complete. About the objective of his work he writes, "I consider this article as tending to account for the discrepancy between the calculated and observed velocities (which most experimentalists have remarked and wondered at), when allowance is made (as will be done in a future part of this paper) for change of temperature .... " He improves Poisson's one-dimensional theory of finite amplitude disturbances (---~1808), putting the equations into a form, in which the motions of particular particles are followed (Lagrangian coordinates). Using the adiabatic law, he obtains a complete solution for a wave progressing in one direction in a medium in which the pressure is any function of waves of the density, and observes that the differential equations of motion need not necessarily possess a unique solution for the velocity. He assumes that in a real fluid heat conduction and viscosity might prevent the true formation of a discontinuity, and speculates: "I have defined a bore to be a tendency to discontinuity of pressure; and it has been shown that as a wave progresses such a tendency necessarily arises. As, however, discontinuity of pressure is a physical impossibility, it is certain Nature has a way of avoiding its actual occurrence. To examine in what way she does this, let us suppose a discontinuity to have actually occurred at the point A, in a wave which is moving forwards. Imagine a film of fluid at A forming a section at right angles to the tube. Then on the back of this film there is a certain pressure which is discontinuous with respect to the pressure on its front. To restore continuity of pressure, the film at A will rush forward with a sudden increase of velocity, the pressure in the front of the film not being sufficient to preserve continuity of velocity. In so doing the film will play the part of a piston generating a bit of wave in front, and a small regressive wave behind. The result will be a prolongation of the wave's front, thereby increasing the original length of the wave, and producing simultaneously a feeble regressive wave of a negative character . . . . " He draws the important conclusion that "the velocity with which a

46

p. Krehl sound is transmitted through the atmosphere depends on the degree of violence with which it was produced . . . . The report

of fire-arms will travel sensibly faster than a gentle sound, such as the human voice. . . . " . The transactions of this meeting 98 later read: "Fortunately, it transpired at the Meeting, that in Captain Parry's Expedition to the North, whilst making experiments on sound, during which it was necessary to fire a cannon at the word of command given by an officer, it was found that the persons stationed at the distance of three miles to mark the arrival of the report of the gun, always heard the report of the gun before they heard the command to fire; thus proving that the sound of the gun's report had outstripped the sound of the officer's voice; and confirming in a remarkable manner the result of the author's mathematical investigation, that the velocity of sound depends in some degree on its intensity." It was James C. Ross, later becoming a famous South Pole explorer and carrying out important arctic and antarctic magnetic surveys, who was in command of the cannon during Parry's expedition (--+1824-

]825). 1859

Royal Scientific Society, GOttingen

Riemann 99 presents on November 22 his "theory of waves of finite amplitudes," which, not limited to a single progressive wave as was Earnshaw's solution (--+ 1858), is put on a more general basis and suited to calculate the propagation of plane waves of finite amplitude proceeding in both directions. Limiting his study to a steady two-dimensional flow and considering motions occurring at a fixed point in the gas (Eulerian coordinates), he assumes a pressure-density relation p = p(p) that depends only on density and holds for all particles and all time, even across shocks, i.e., limits to adiabatic motion in the case of weak shocks. To find the essential propagation properties of waves of finite amplitudes, he integrates the partial differential equations using Monge's "method of characteristics" (--+ 1770s) which simplifies under the assumption that the sound speed is a function of density alone ("Riemann invariants"). He shows that an original disturbance splits into two opposite waves: the rarefaction wave grows thicker, and the condensation wave (a shock wave) thinner which he calls a "compression shock" [Verdichtungsstofg]., His results formed an important step toward a mathematical treatment of shock wave steepening and formation. However, using the "static adiabate" he incorrectly assumed that the entropy remains unchanged through the shock wave (isentropic process). The total energy content

History of Shock Waves

47 (enthalpy) remains unchanged, whereas the entropy always increases through a shock wave; this was first recognized by Rankine (-+1869) and later, independently, by Hugoniot (-+ 1887).

Private observatory, Redhill, Surrey, England

Carrington, 1~176 using a telescope, observes a violent and rapid eruption near a large sunspot. At that very moment modest, but very marked disturbances of three magnetic elements are observed at Kew Observatory, affecting all the elements simultaneously and commencing quite abruptly. He reports, "While engaged in the forenoon of Thursday, September 1, in taking my customary observation of the forms and positions of the solar spots, an appearance was witnessed which I believe to be exceedingly rare. The image of the sun's disk was, as usual with me, projected on to a plate of glass coated with distemper of a pale straw color, and at a distance and under a power which presented a picture of about 11 inches diameter. I had secured diagrams of all the groups and detached spots, and was engaged at the time in counting from the chronometer and recording the contacts of the spots with the crosswires used in the observation, when within the area of the great north group (the size of which had previously excited great remark), two patches of intensely bright and white light broke out, in the positions indicated in Fig. 1 . . . . My first impression was that by some chance a ray of light had penetrated a hole in the screen attached to the object glass, for the brilliancy was fully equal to that of direct sun-light; but by at once interrupting the current observation, and causing the image to move... I saw I was an unprepared witness of a very different affair. I therefore noted down the time by the chronometer, and seeing the outburst to be very rapidly on the increase, and being somewhat flurried by the surprise, I hastily ran to call some one to witness the exhibition with me, and on returning within 60 seconds, was mortified to find that it was already much changed and enfeebled. Very shortly afterwards the last trace was gone. In this lapse of 5 minutes, the two patches of light traversed a space of about 35,000 miles." m About 17 hours later other researchers observed considerable magnetic disturbances, a so-called "magnetic storm" [magnetisches Ungewitter], a term which was introduced by A. yon Humbold 1~ the year before. Carrington's unique observation made evident for the first time the enormous dimensions and dynamics of solar flare explosions (Chapman and Ferraro--+1931; Gold 1949; Parker 1961) and started much discussion on the coincidence of solar eruptions and magnetic disturbances.

48 1860

E Krehl

Parish of Sheffield, England

Earnshaw 1~ discusses the problem of whether violent sounds would propagate more rapidly than gentle sounds. He distinguishes three kinds of waves, all propagating with different velocities v in regard to the sound velocity a: minute waves (v = 0 to 0.Sa), ordinary waves, (v---0.Sa to a), and violent waves (v -- a to oo). Although this arbitrary classification is rather hypothetical, he draws a very important conclusion: "If the theory here advanced be true, the report of fire-arms

should travel faster than the human voice, and the crash of thunder faster than the report of a cannon." 9 Earnshaw obtained a memoir from Montigny, 1~ professor at Antwerp, who observed that in the case of a thunderclap sound is sometimes propagated with a velocity far greater than the ordinary sound velocity, a phenomenon that Earnshaw (---~1851) had already noticed and that was much discussed among scientists. For example, in the same year Hirn, 1~ French autodidact and independent scholar at Colmar, speculated on possible reasons why the velocity of sound depends on intensity and assumed a pressure-dependent ratio of the specific heats at constant pressure and volume. Raillard, 1~ French abbot and amateur naturalist, referred to Biot, who had previously had a discussion with Poisson on irregular propagation phenomena of thunder. The latter, however, although essentially supporting this idea, did not resume it in his M~noires sur la theorie du son (1808). Raillard speculated also on the propagation velocity of thunder but estimated abnormally high velocities (5000-6600m/s). He wrote, "I heard the first outbursts of thunder three or four seconds after the lightning had appeared; however, according to the delay of the reinforcement of the noise originating from the stem of the lightning, and to its orientation, I estimated that the fire was lit in the vicinity of Gray, about 20 km from Courchamp where I was . . . . " 1862

Nitroglycerin Ltd., Heleneborg, Sweden

Nobel 1~ applies for a patent on the improvements in the process of manufacturing Nitroglycerin which is called Pyroglycerin, then Glonoine Oil, and later Nobel's Blasting Oil. He erects works at Heleneborg, an isolated area outside Stockholm, where nitroglycerine is manufactured for the first time on a commercial scale. 9 Two years later they were entirely wrecked by an explosion which cost the lives of Nobel's youngest brother and his chemist Hertzmann.

1863

Ecole Pyrotechnique, Brttxelles

Le Boulenge 1~ invents an electrically triggerable dropping weight timing system (the Le-Bouleng~-chronograph) that after some improvements will become a robust and accurate chronograph with a temporal resolution of less than i ms. It

History of Shock Waves

49 will prove its applicability even for ballistic "open range" measurements.

University of Cambridge

Airy 1~ reviews previous theoretical and experimental attempts to calculate the destructive energy of steam boiler explosions. He concludes that one cubic foot of water at 60psi is equal to the destructive energy of one pound of gunpowder. 9 Various hypotheses for possible causes of steam boiler explosions 1~176 were (i) generation and ignition of oxyhydrogen when, at low water level in the boiler, the water chemically reacts with the overheated iron walls; (ii) sudden destruction of the initial isolation of water from the boiler walls, nullifying the protecting "Leidenfrost layer"; (iii) reduction of mechanical strength of the boiler material at high temperature; (iv) sudden generation of large quantities of steam by the phenomenon of "delay of boiling"; and (v) increasing unyieldingness of the boiler walls when firing sulfurous coal. The accidents prompted engineers and metallurgists to study dynamic material behavior under thermal and mechanical stress and to improve production technology. They also provoked the foundations of the first official safety inspection authorities.

Colli~ge de France, Paris

Regnault 111 begins a five-year campaign of measuring the sound velocities in air and other gases. To exclude negative side effects such as wind he performs his experiments in long pipes with lengths up to 20 km and diameters ranging from 0.1 to 1.1 m, using the gas pipeline and sewage channel system of Paris. This allows long base lines to compensate for the low accuracy of available chronoscopes. Discharging a small quantity of gunpowder (about i g) at the pipe entrance, he determines the average blast velocity by mechanically recording the arriving pressure signal at the pipe end using a membrane microphone, combined with a rotating drum chronograph. He is the first to confirm experimentally that the sound velocity also depends on the sound intensity, thereby touching an essential feature of a shock wave. Since his remarkable achievements have barely been acknowledged by the modem shock physics community, he is cited here in more detail: "the theoretical calculation assumes that the excess of compression which exists in the wave is infinitely small compared with the barometric pressure supported by the gas. But the experiments made to determine the rate of sound in free air have been hitherto made by means of a cannon, and the wave has been reckoned from its source, namely the cannon's mouth. Now this wave as it leaves the cannon is under enormous compressionma compression, it is

50

P. Krehl true, which diminishes very rapidly as the wave spreads spherically through space; but during the first part of its course it cannot be supposed that its compression is infinitely small. When the excess of compression in the wave is a sensible fraction of the compression of the gaseous medium at rest, we can no longer employ Laplace's formula, but must have recourse to a more complex formula embracing the true elements of the problem. Even the formula which I have given in my Memoir [MCm. Acad. Roy. Paris 37 (1868)] is only an approximation; for it implicitly admits Mariotte's law and all its consequences. In short, the mathematical theory has as yet only touched upon the propagation of waves in a perfect gasuthat is to say, in an ideal fluid possessing all the properties which had been introduced hypothetically into the calculation. It is therefore not surprising that the results of my experiments often disagree from theory . . . . " 9 His remarkable result, however, that intense sound propagates faster than with sound velocity, was not immediately accepted. 112 E. Mach and Sommer (---~1877) first confirmed Regnauh's observations.

1864

Royal Agricultural Academy, Poppelsdorf, Germany

Toepler 113 publishes his "schlieren method." Although its principle was previously discovered by Hooke 114 (1665) and Foucauh 115 (1859), Toepler uses an arrangement that will prove extremely useful in the study of compressible flow. He directly visualizes the propagation and reflection of shock waves in air and first notices the sharp wave front, but is at first confused by the appearance of several shock fronts: "Apart from the envelope and little clouds, the spark seems to be surrounded by concentric spheroids a b c with rather sharp boundaries. They are never disrupted or bulged; with increasing size they approach a spherical geometry. Closely to the spark they resemble a cylinder which is bounded by two hemispheres. Operating the induction coil at high repetition rate they give the impression of soap bubbles which, formed around the spark, immediately disappear again. It makes one believe that always several, usually three or four, are visible simultaneously in the field of view. However, in the case that the coil is working at the lowest possible rate so that the ear is capable of clearly differentiating between each stroke, it is obvious that each discharge corresponds to only a single one of the above described spheroids, but that from spark to spark, the phenomenon strongly varies in size and formation." To illustrate this discontinuous wave phenomenon, he first uses the correct terms shock wave [Stoj~welle] and air percussion wave [Lufterschfitterungswelle], but likewise also the incorrect term sound wave [Schallwelle]. Since high-

History of Shock Waves

51 sensitive films are not yet available to him, he studies the shocks subjectively by using a sophisticated stroboscopic arrangement and a modification of Knochenhauer's circuit (---~ 1858) to delay the illumination spark relative to the spark generating the shock wave. He also inspects the spark channel and notices that it is not a homogeneous cylindrical plasma column but rather is pinched and shows constrictions in the axial direction.

Heleneborg, Sweden

Nobel 116 finds that nitroglycerine (Sobrero--~1847) can be fired by an initial explosion such as can be produced by a small charge of gunpowder, and soon experiments with small metal receptacles loaded with fulminate of mercury mixed with gunpowder or nitrate of potash. His invention of the blasting cap ("detonator") initiates the explosive reaction in a column of explosive by percussion, or the local heat of an electric spark or an electrically heated w i r e . , The introduction of the initial ignition principle, using a strong blast wave rather than heating, was a significant achievement in the technique of blasting. Ten years after having perfected his famous invention, Nobel 117 stated with plain words: "but the real era of nitroglycerine opened with the year 1864, when a charge of pure nitroglycerine was first set off by means of a minute charge of gunpowder."

Chair of Natural Philosophy, South Carolina College, Columbia

Le Conte 118 reviews the large body of international literature relating to the obvious discrepancy between the velocity of sound as given by the physical theory and by direct experiment. He addresses also the theories of violent sound given by Airy (--+ 1849), Earnshaw (--+ 1858), Challis (--+ 1848,1851), Stokes (--+1848,1851), and Parry's experiments (-->18241825). Previous observations on thunder by Earnshaw (---->1851,1860) and Montigny (--+1860) he considers as a psychological illusion. Rejecting all hypotheses of wave propagation attributed to the peculiarities of large amplitudes, he writes, "It is true there may be nothing a priori improbable in the assumption that the velocity of sound might be related to the violence of the disturbance; but the fact that the analytical investigations conduct to such extreme results as to set at nought all our physical conceptions, originate a strong presumption that they belong to that class of mathematical fictions which have frequently sharpened the ingenuity and brightened the imagination of some of the most eminent geometers." He supports Laplace's view "...that the accuracy of the physical reasoning upon which Laplace's formula is based has not been invalidated by the recent discussions on the mathematical theory of sound." 9 The paper is very interesting from the historical point of view,

52

P. Krehl because the large number of reasons discussed illustrates not only the keen interest of contemporary naturalists in this subject, but also reveals the difficulties to accept hitherto unknown mechanisms of generating supersonic velocities of aerial waves.

1865

1866

Athenaeum, Deventer, The Netherlands

SchrOder van der Kolk, 119 correctly assuming that intense sound propagates faster than weak sound, tries to derive a formula for the sound velocity s in terms of the ratio of the specific heats, 7; the sound velocity at infinitely small amplitude, So; and the specific volume reduction, AV = V0 - Va, caused by the intense sound. - Since he assumed compression along the static adiabate (Poisson's law) and not along the dynamic adiabate (Hugoniot curve)--which is steeper in the p,V-diagrammhis equation gives too small a velocity increase. The problem was first solved in a general manner by Hugoniot (--+ 1887) and later put in a practicable equation known today as the "Hugoniot relation" by Vieille (--~ 1900).

Stockholm

Nobel 12~ addressing the advantage and multi-purpose applications of nitroglycerine in the mining industry, writes: "The greatest advantage of nitroglycerine consists in the fact that when it is used a force can be introduced into the blast-hole of a mine ten times as great as when powder is used. Hence arises a great economy in manual labor, the importance of which is understood when it is remembered that the labor of the miner represents, according to the hardness of the rock, from five to twenty times the value of the powder required, a saving therefore which will often amount to 50 per cent. The use of this substance is very simple. If the blast-hole of the mine is fissured, it must be lined with clay in order to render it tight. Nitroglycerine is then poured in, and the upper part of the hole is filled with water; in the nitroglycerine is then introduced a safety-match of suitable length, at the end of which is pressed a strong percussion-cap. The operation is finished, and it is only necessary to put fire to the match."

The Napier Brothers, Glasgow

Napier, 121 a Scottish mechanical engineer, studies the flow characteristics of a gas, from a vessel in which it is compressed, through an orifice into the atmosphere. He observes that the rate of discharge increases as the ratio of the receiver pressure to the initial pressure diminishes from unity to about 0.5, but that when the latter stage is reached, a further reduction in the receiver pressure has no effect on the rate of discharge, which remains constant (the "choking effect").. An important step in the theory of orifice discharge was made not until 1885 by Reynolds, a22 who assumed a continuous fall of pressure along the axis of the jet.

History of Shock Waves 1867

53

Humboldt UniversitFzt, Berlin

Magnus receives Toepler's paper on schlieren observations of spark waves (--~ 1864). He criticizes Toepler's use of the term sound wave [Schallwelle] for the visualized spark (--shock) wave. In a letter 123 to Toepler he states, "I was never in doubt about the correctness of your observations...however, I have declared myself against the expression 'sound wave' as, I suppose, I already did previously. Now you state in your kind letter that the air is expanded by the spark which causes a compression propagating with the speed of sound: this is clear and nobody will contest it, just as little as this compression was reflected. However, visible is not the sound, but rather the air which, heated and perhaps colored by the spark, expands from the position of the spark and is reflected, because the compressed air itself is visible with your apparatus . . . . A designation can easily give reason for a misinterpretation. Who will not imagine waves emitted by a sounding body when hearing about 'sound w a v e s ' ? . . . " . This stimulated ToepleP 24 to give a more detailed definition in his next paper: "the electric spark is a very favorable source of sound; it can be used to provide single shocks which [at increasing repetition rate] can be driven up to the generation of a tone. The expression 'sound' has been used for any perceptible impression to the sense of hearing, likewise the word 'sound wave,' also in case that the air particles do not experience a full oscillation .... "

Nitroglycerin Ltd., Heleneborg, Stockholm

Nobel 125 invents Dynamite [after the Greek dynamis, meaning power], which he also calls Guhr Dynamite. It is a mixture of nitroglycerine and a suitable nonexplosive porous absorbent [Kieselguhr], which fully establishes nitroglycerine as the leading blasting agent. To explode it safely and under all conditions, it is ignited by a detonator cap (A. Nobel---~ 1864). 9 The invention of Dynamite was a large commercial success: From 1867 to 1874 Nobel founded 15 factories worldwide, which increased dynamite production from 11 tons in 1867 to 3120 tons in 1874.126

Chair of Chemistry [Allgemeine Experimentalchemie], University of Heidelberg

Bunsen 127 determines the explosion pressure of oxyhydrogen in a closed vessel to be around 9.5 atm. He speculates that in a gaseous explosion the total gaseous mass does not explode at once, but rather successively in discontinuous partial explosions that propagate stepwise through the gas ["e/ne discontinuierliche, gleichsam stufenweise erfolgende Verbrennung"]. To measure the rate at which an explosion is propagated in a gas he first releases highly pressurized gas from a narrow opening only 1.2 mm in diameter and ignites it in free air. Then he slowly reduces the pressure until the flame backfires, which he regards as a criterion that the explosion velocity has just

54

e Krehl surpassed the outflow velocity. He determines an explosion velocity for oxyhydrogen of only 34 m/s and for a mixture of CO-O 2 of only i m/s. 9 His puzzling results stimulated Berthelot and Vieille (--+1881), Mallard and Le Ch~telier (-+ 1881), and von Oettingen and von Gernet (--+ 1888). Their results revealed that Bunsen did not provoke an explosion but rather a deflagration, which explained his obtained low velocities.

1868

1869

4th International World Fair, Paris

Toepler 128 displays his improved schlieren apparatus and demonstrates the propagation of spark (=shock) waves to the public.

Private study at VilleporcherSaintOuen/VendOme, France

De Saint-Venant ~29 treats the longitudinal impact of elongated bars, which, for simplicity, are assumed to be of the same material and thickness but of different length. He shows that, except when the lengths are equal, a considerable fraction of the original energy takes the form of vibrations in the longer bar so that the translational velocities after impact are less than those calculated by Newton for bodies that he calls "perfect elastic." He observes that after impact the short bar will take the initial velocity of the longer bar and becomes free of tension.

St. Petersburg, Russia

The International Treatise of Petersburg is proposed on December 11, with the goal to ban the use of explosive bullets for small arms. It is signed by all European and North American countries.

University of Heidelberg

Kirchhoff, 13~ after having read Toepler's paper, on the visualization of shock waves, 131 writes to him: "without doubt the expression 'sound wave' as you use it is justified, and an air quake [Lufierschfaterung] makes an impression on the ear even if it is of only very short duration but of sufficiently high intensity."

Royal Military Academy, Woolwich, Arsenal, London

AbeP 32 shows that unconfined charges of guncotton, nitroglycerine, dynamite, and mercury fulminate only burn if ignited by a flame or a hot-wire, but detonate if subjected to an impulsive force such as applied by a hammer blow, a detonator cap, or the impact of a projectile. 9 It appears that Abel was the first who used the term detonation in the modem sense. Hitherto the terms explosion and detonation, in use since the late 17th century, 133 were applied interchangeably.

Chair of Civil Engineering & Mechanics, University of Glasgow

Rankine TM submits a paper to the London Royal Society on "adiabatic waves, that is waves of longitudinal disturbance in which there is no transfer of heat..." and on the problem of how "to determine the relations which must exist between the laws of the elasticity and heat of any substance, gaseous,

History of Shock Waves

55 liquid or solid, and those of the wave-like propagation of a finite longitudinal disturbance in that substance." His significant achievements can be summarized as follows: (i) Treating the shock wave as a two-dimensional discontinuity, he assumes a dissipative fluidmi.e., conductive but nonviscous--and applies the conservation laws of mass, momentum and energy to both states far up- and downstream from the shock front, thus obtaining three equations which, however, are only equivalent to those of Hugoniot (--~ 1887) in the case of a perfect gas, later to be referred to as the Rankine-Hugoniot equations (or conditions). (ii) He coins the expression adiabatic [derived from the Greek ~ ~ i v ~ z v - to pass through] to characterize a change in the volume and pressure of the contents of an enclosure without exchange between the enclosure and its surroundings. He also uses the term adiabatic curve for a p(v)-diagram, obtained by plotting the pressure p against the specific volume v in the adiabatic equation. In contrast, GIBBS135 will shortly after propose the expression isotropic curve, since in an adiabatic process the entropy remains constant. (iii) RAN~INE addresses also the rarefaction wave phenomenon which he calls sudden rarefaction. Referring to a discussion with Sir Thomson, he annotates: "Sir William Thomson has pointed out to the author, that a wave of sudden rarefaction, though mathematically possible, is an unstable condition of motion; any deviation from absolute suddenness tending to make the disturbance become more and more gradual. Hence the only wave of sudden disturbance whose permanency of type is physically possible, is one of sudden compression; and this is to be taken into account in connexion with all that is stated in the paper respecting such waves." (iv) Rankine also measures the ratio of specific heats, ~/ and finds that "7 is nearly 1.41 for air, oxygen, nitrogen and hydrogen, and for steam-gas nearly 1.3." Asked by the editor of the Proceedings of the Royal Society to give credit also to previous investigators on waves of finite disturbances and to point out to what extent the results arrived at his paper are identical with their researches, Rankine 136 cites the works of Poisson, Stokes, Airy, and Earnshaw, and claims: "The new results, then, obtained in the present paper may be considered to be the following: the conditions as to transformation and transfer of heat which must be fulfilled, in order that permanence of type may be realized, exactly or approximately; the types of wave which enable such conditions to be fulfilled, with a given law of the conduction of heat; and the velocity of advance of such waves. The method of investigation in the present paper, by

56

P. Krehl the aid of mass-velocity to express the speed of advance of a wave, is new, so far as I know; and it seems to me to have great advantages in point of simplicity." War

Department, U.K.

Abel 137 reports on his observation that one detonating dynamite cartridge can trigger another that is positioned in the vicinity and speculates that detonation is transmitted by means of some "synchronous vibrations." He states, "The vibrations produced by a particular explosion, if synchronous with those which would result from the explosion of a neighboring substance which is in a state of high chemical tension, will, by their tendency to develop those vibrations, either determine the explosion of that substance, or at any rate greatly aid the disturbing effect of mechanical force suddenly applied, while, in the case of another explosion which produces vibrations of different character, the mechanical force applied by its agency has to operate with little or no aid . . . . " 9 E. Mach and Wentzel (--+1885) refused Abel's "queer" hypothesis and correctly attributed this phenomenon to the mechanical effect of the shock wave.

Chair of Organic Chemistry, College de France, Paris

Berthelot 138 defines the "strength" of condensed and gaseous explosives and emphasizes the role of a mechanical shock, which during detonation propagates "from layer to layer," thus anticipating an important assumption of the ChapmanJouguet theory (Jouguet-+1905). He writes, "In order to transmit the transformation of a detonating bulk which is not subjected in all parts to the same action, it is necessary that the same conditions of temperature, pressure etc. which have provoked the phenomenon in one point propagate successively, layer to layer [couche par couche], through all parts of the bulk . . . . "

1871

England

Maddox 139 prepares emulsions of silver bromide in essentially the same manner as that used for making colloidal emulsions but replaces collodion by gelatin. Further improvements of this new photographic process were made by Bennet (1878), van Monkhoven (1879), and Eder (1880) which, leading to the so-called "high sensitive photo-gelantine dry plate" in the 1880s, were a basic requirement to make the first photograph of a shock wave (E. Mach and Wentzel--> 1884).

1872

Royal Academy of Sciences, Brussels

Melsens 14~ reports on the severe injuries observed in the recent Prussian-French War (1870-1871). He comes to the conclusion that they were not caused by explosive projectiles banned by the St. Petersburg Treatise (--+1868), but rather by air compression phenomena in front of the projectile. 9 Nine years later, he addressed the same subject in a lecture

History of Shock Waves

57 presented at Paris. His hypothesis inspired E. Mach to investigate these possible ballistic phenomena in more detail. TM However, he had to wait almost six years before his photographic technique was matured enough to catch the motion of high-speed bullets in flight (E. Mach and Salcher--~ 1887).

Expedition of H.M.S. "Challenger," England

A prolonged oceanographic exploration 142 is carried out by the British Admiralty and the Royal Society from 1872-1876. The expedition performs scientific research such as depth sounding, dredging, and measuring currents, depths, and contours of the ocean basin. Tait (-~ 1878) participates and measures deep-sea temperatures.

Trinity College, Cambridge

John Hopkinson 143 measures the strength of steel wires when they are suddenly stretched by a falling weight. He observes that the minimum height from which a weight has to be dropped to break the wire is independent of the size of the weight. He explains this surprising result in terms of the propagation of elastic waves up and down the wire.

Elswick Ordnance Company, U.K.

Noble 144 first reports on his "crusher gauge," a by-product of his investigation into the behavior of explosives and artillery that will render his name famous. Introductorily he compares previous estimations on the elastic force of fired gunpowder in cannons, which not only widely range in historic studies between 100 and 100,000 atmospheresmfor example, 100 by John Bernoulli; 145 1000 by Robins (1743); 2000 by Hutton; 10,000 by Daniel Bernoulli; 12,400 by Rodman (1857-1859); and 100,000 by Rumford (1797)rebut also in modern "reliable" handbooks between 2200 by Bloxam (1867) and Owen (1871), and 29,000 atmospheres by Plobert (1859). 146 With the help of his crusher gauge, a modification and improvement of the indentation gauge (Rodman-~ 1857), Noble determines the maximum pressure produced when a charge of gunpowder is exploded in a confined space (such as in a cannon) and finds a value of about 5500 atmospheres which well correlates with theoretical estimations based on measurements of in-barrel projectile velocities. 9 In the early period of shock and explosion research the crusher gauge was the instrument most used to evaluate the maximum pressure of high-rate thermodynamic phenomena such as explosion and detonation. Since the gauge is simple in construction, inexpensive, and insensitive to electromagnetic radiation, it saw a renaissance in World War II: Penney 147 used his "five-gallon-can blast pressure gauges" to map the overpressure in the "Mach stem" region of an atomic explosion. Blast pressures were computed from the degrees of

58

P. Krehl crushing in the cans. To measure maximum pressures generated in underwater explosions, Abboth 148 used crusher gauges in which a steel piston acted on a small lead cylinder fixed on a massive support.

Woolwich, Arsenal, London

Abel and Brown, ]49 using the Noble-chronograph, measure the detonation velocity of guncotton to be around 20,000ft/sec and state: "Recent experiment has shown that the rapidity with which gun-cotton detonates is altogether unprecedented, the swiftness of the action being truly marvelous. Indeed, with the exception of light and electricity, the detonation of gun-cotton travels faster than anything else we are cognizant of . . . . "

Laboratoire Central des Poudres, Paris

Roux and Sarrau 15~ confirm Abel's observation (---~1869) and differentiate between an "explosion of the first kind" (detonation) and an "explosion of the second kind" (deflagration). 9 In a deflagrationma rapid combustion process that gives off heat and light--the flame speed is below the velocity of sound in the burnt gases; in a detonation, burning takes place at or above the velocity of sound in the burnt gases. A detonation is always associated with a high-pressure and high-temperature shock wave that is sustained by the liberated energy via shock compression rather than via heat transfer as in the case of combustion. The energy of this reaction maintains constant conditions at the front of the detonation wave, thus leading to a constant detonation velocity. Detonation and deflagration are words derived from the Latin verbs detonare (to thunder out) and deflagrare (to burn down), respectively.

1874

Realschule Kaschau, AustroHungarian Empire

Antolik TM publishes his "soot method" and records with this method strange interference patterns in the vicinity of gliding spark discharges. He observes that conically shaped branches [kegelartige "AuslFzufer"] originate from the concave parts of a spark path, which disappear when the discharge occurs in a vacuum. Antolik explains this phenomenon by the behavior of the gliding spark, which in a vacuum prefers to follow a straight rather than a given crooked path. In reality, however, the soot figures are the very first records of irregular interactions of shock waves.

1875

Chair of Experimental Physics, KarlFerdinandUniversitFzt, Prague

E. Mach, 152 together with his student Wosyka, immediately repeats Antolik's experiments (---~1874). They verify that his soot pictures are indeed of acoustic and not of electric origin. Mach and Wosyka are the first to study Mach reflection. They record the trajectories of the triple point (Mach funnel) and stop the Mach disk by using two oppositely facing V-shaped gliding sparks. 153 They also arrive at the following important

History of Shock Waves

59 conclusion: "It should be pointed out that Antolik's simple and ingenious method of preliminary tracing of the spark enables various applications in the field of acoustics, because it can be used to create intense sound waves with an arbitrary initial shape.". The soot method, although in principle very simple, is somewhat tricky to handle, particularly to provide a homogeneous and well-adhering soot layer reliable enough to obtain a high spatial resolution and wide dynamic range of pressure recording. By increasing the adhesion of the soot layer on the glass plate, it is also possible to record even double Mach reflection, which results in two concentric Mach funnels. 154 The soot method was also used to record periodic cell structures in gaseous detonations (Shchelkin and Troshin 1965; Schultz-Grunow 1969).

Royal Society for the Encouragement of Arts, Manufactures & Commerce, London

Nobel 155 reads before the Society a paper entitled "Modem blasting agents." Giving information regarding his invention of Dynamite and the difficulties of its introduction into practical use, he states, "the concentration of power, velocity of explosion, and immunity from danger, are the three points on which mainly depend the success or non-success of a new explosive substrate." Speaking of gunpowder he says, "That old mixture possesses a truly admirable elasticity which permits its adaptation to purposes of the most varied nature. Thus, in a mine it is wanted to blast without propelling; in a gun to propel without blasting; in a shell it serves both purposes combined; in a fuse, as in fireworks, it burns quite slowly without exploding. Its pressure exercised in those numerous operations, varies between 1 oz. (more or less) to the square inch in a fuse, and 85,000 lb. to the square inch in a shell. But like a servant for all work, it lacks perfection in each department, and modem science armed with better tools, is gradually encroaching on its old domain."

Ordnance Company, Elswick; Woolwich Arsenal, London

Noble and Abel 156 start an ambitious program on researches on gunpowder and its explosive effects in guns with the following goals: (i) To ascertain the products of combustion of gunpowder fired under circumstances similar to those which exist when it is exploded in guns or mines; (ii) to ascertain the "tension" of the products of combustion at the moment of explosion, and to determine the law according to which the tension varies with the gravimetric density of the powder; (iii) to ascertain whether any, and if so what, well defined variation in the nature or proportions of the products accompanies a change in the density or size of grains of the powder; (iv) to determine whether any, and if so what, influence is exerted on the nature of the metamorphosis by

60

P. Krehl the pressure under which the gunpowder is fired; (v) to determine the volume of permanent gases liberated by the explosion; (vi) to compare the explosion of gunpowder fired in a close vessel with that of similar gunpowder when fired in the bore of a gun; (vii) to determine the heat generated by the combustion of gunpowder, and thence to deduce the temperature at the instant of explosion; and (viii) to determine the work which the gunpowder is capable of performing on a shot in the bore of a gun, and thence to ascertain the total theoretical work if the bore be supposed of indefinite length. 9 Their results became the basis of modern internal ballistics.

1876

1877

Jabin de SaintEtienne, Graissessac

Two serious firedamp explosions in the French hard coal mining industry (231 miners killed) will initiate the foundation of a governmental research commission (---~1878).

British Telegraph Manufactory, London

Sabine, 157 chief engineer, measures the shock contact time of elastic bodies using an ingenious electric method that allows the measurement of the time between two successive mechanical movements with a considerable degree of accuracy. The method is based on the fact that a charged capacitor can only be discharged at a certain definite rate through a given circuit. For the duration of a blow of a light hammer (weighing about 1 oz) against a steel anvil, he finds contact times around 50~ts. Further experiments reveal that the contact time decreases with increasing impact velocity. 9 His important results reliably proved for the first time that the contact time of impacting elastic bodies is indeed extremely short, which was later found theoretically by Hertz (-~ 1882) and reconfirmed experimentally by Tait (-~ 1892).

KarlFerdinandUniversiti~t, Prague

Rosicky,15s a coworker of E. Mach, visualizes shock-focusing phenomena in an elliptic reflector.. Today ellipsoidal reflectors are also used for focusing spark-generated shock waves in extracorporeal shock wave lithotripsy. 159"16~

Cambridge University

Lord Rayleigh, being in the final phase of his book The Theory of 5ound, has a controversy 161 with Stokes who previously published a paper on sounds of finite amplitudes. Rayleigh writes to him on June 2, 1877: "In consequence of our conversation the other evening I have been looking at your paper 'On a difficulty in the theory of sound,' Phil. Mag. Nov. 1848. The latter half of the paper appears to me to be liable to an objection, as to which (if you have time to look at the matter) I should be glad to hear your opinion . . . . It would appear therefore that on the hypotheses made, no discontinuous change is possible . . . . " Stokes admits that Thomson

History of Shock Waves

61 (later Lord Kelvin) had already made similar objections that the proposed motion would violate the conservation of energy. Avoiding a confrontation with his former student, he kindly replies to Lord Rayleigh on June 5, 1877: "It seemed, however, hardly worth while to write a criticism on a passage in a paper which was buried among other scientific antiquities. PS: You will observe I wrote somewhat doubtfully about the possibility of the queer motion . . . . "

Karl-Ferdinand Universitat, Prague

E. Mach and Sommer 162 measure the propagation of shock waves on a laboratory scale and confirm that indeed a shock wave travels faster than a sound wave and that the shock velocity increases with shock strength. Their results confirm previous large-scale measurements by Regnauh (-~1863), thus reaching therewith an important milestone in shock wave physics. Using a linear percussion model--a row of gas molecules arranged two by two along a straight line--they illustrate that the velocity of percussion must also increase when the velocity of sound increases, such as in the case of violent sound, and state, "It does not contradict the theory to assume that the velocity of sound increases with the intensity of the impulse. Only for very small vibrations does the velocity of sound not depend on the amplitude. But this is not valid for vibrations of finite amplitude as has been proved by Riemann in his paper Uber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite, 1860. 'Velocity of sound' receives hereby a quite different meaning; it is different at every point of the wave and alters during the wave motion. It appears that we deal in our experiments with such waves as described by Riemann."

Chair of Mathematics, University of Straj~burg

Christoffe1163 extends Riemann's theory on shock waves (--~1859) to the case of a three-dimensional propagation. He also treats the propagation of percussion through an elastic solid medium.

Philosophical Society of Washington, DC

A committee formed by the society publishes 164 the observations of 48 people who witnessed the fall of the Washington Meteor on Dec. 24, 1873. Descriptions of observed acoustic phenomena range between "no sound" and "very violent sound" (for example, "short, hard reports like heavy cannon and continued resounding"). The committee concludes that the sound could have been generated by sound focusing and the Doppler effect. 9 Later E. Mach and Doss (-,1893), referring to this "queer theory," explained the loud report not as the result of any explosion or focusing effects, but due to the head wave phenomenon alone.

62 1878

e. Krehl

Karl-Ferdinand-Universitat, Prague

E. Mach and Weltrubsky 165 use the "Jamin interferometer" (Jamin--~ 1856) and first record the density jump at the shock front. E. Mach, Tumlirz, and K6gler 166 measure thoroughly the velocity-distance profile of a blast wave, which they generate by an electric spark discharge. They confirm previous observations by E. Mach and Sommer (--+ 1877) that the blast wave velocity approaches the sound velocity at greater distance from its center of origin. E. Mach and Gruss 167 study Mach reflection in a V-shaped gliding-spark arrangement E. Mach and Wosyka (--+ 1875) in more detail. They give an ingenious interpretation of the propagating and temporarily increasing width of the Mach disk. Their publication contains correct drawings of the interaction phenomenon, but not photographs.

Chair of Natural Philosophy, University of Edinburgh

TaR begins his research on the corrections of deep-sea temperatures obtained during the "Challenger" expedition (--+ 1872). His research will lead to important experimental studies of the compressibility of liquids (TAR-+ 1888) and the behavior of solid materials under impact (Tait-+ 1892).

Paris

Foundation of the French Fire-Damp Commission [Commis-

sion d'~tude des moyens propres a prevenir les explosions du grisou] to uncover the so-far mysterious phenomenon of detonation and to investigate how firedamp explosions can be prevented. Prominent members are Berthelot (president), Le Chatelier, Mallard, and Vieille (secretary). Shortly after, similar commissions will be formed in Prussia, Belgium, and England (president Abel). 9 The results of the investigations initiated by the French commission became an important milestone toward a theory of detonation (Berthelot-+ 1881).

Cambridge University

Lord Rayleigh publishes his monograph The Theory of Sound. In vol. 2 he returns to the point of his previous controversy with Stokes (-+ 1877) and writes, "but it would be improper to pass over in silence an error on the subject of discontinuous motion into which Riemann and other writers have fallen. It has been held that a state of motion is possible in which the fluid is divided into two parts by a surface of discontinuity . . . . " There follows a proof of the impossibility of such motions based on a "violation" of the conservation of energy. 168 9 Rayleigh held to this statement in the 2nd edition (1896) of his book, although at that time the existence of a sharply pronounced discontinuity at the shock front had been proven by using both the schlieren (Toepler--+ 1865; E. Mach and Wentzel-+ 1884) and the interferometer techniques (E. Mach and Wehrubsky-+ 1878).

History of Shock Waves

63

1880

University of Agram, Kingdom of CroatiaSlovenia [now Zagreb, Croatia]

Dvof~ik 169 describes "a simple kind of schlieren observation," which, later called shadowgraphy, does not require any lenses or concave mirrors and allows a large field of view.- The change of illumination is roughly proportional to the rate of change of density gradient. For this reason the method is sometimes superior to the schlieren method (TOEPLER-+1864)--in which the change of illumination is roughly proportional to the density gradient--for observing certain flow phenomena. 17~

1881

Ecole des Mines, Paris

Mallard and Le Chfitelier 171 measure the propagation of the flame front in gaseous mixtures of H2-O2, CO-O2, and CH 402 using the Deprez-chronograph.172 In short tubes with a length of 1.35 m, they observe a speed of 5 7 0 m / s in oxyhydrogen, which reduces to only 7 0 m / s when the length is 1 However, similar to Davy (-+ 1816) they reduced to about 5" notice that the flame is not propagated in narrow tubes.

Russian Artillery Academy, St. Petersburg

Maiyevskii, 173 studying the ballistics of cannon shells, publishes a work on the resistance of projectiles at high speeds, w, that exceed the sound velocity, a. For velocities up to w/a < 1.1 he finds the formula for the ballistic resistance Cx: Cx = 0.19211 + 3.34(w/a)2].. Although subsequent measurements have shown that the air resistance does not steadily increase from transonics to supersonics, it is interesting to note that Maiyevskii, very similar to his forerunner Euler (1745), considered the ratio w/a--later termed the Mach number (Ackeret --+ 1929)--an important quantity governing air resistance at high speed. 174

U.S. Army Corps of Engineers, Washington, DC

Abbot 175 reports on strange surface phenomena of an underwater explosion, which he observed 0.1 s after the explosion. He writes, "The surface of the water around the torpedo over a distance of 200 feet is covered by a misty spray resembling rain, which has been thrown upward from the surface by the shock. Over the torpedo appears a dome of water of which the diameter is about 100 feet and the extreme height about 20 feet. The surface of this dome is a fleecy texture, and through the top are bursting upward many spearlike jets, which cover a space about 50 feet in diameter and attain in the middle an extreme height of 105 feet.". A correct explanation of this phenomenon was first given by Blochmann (--+ 1898).

Coll~ge de France, Paris

Berthelot 176 studies the propagation of the flame speed in essentially the same gaseous mixtures as Mallard and Le Chfitelier (-+ 1881), however, contrary to them he announces the discovery of enormous velocities of explosion. Berthelot, using long tubes (up to 5 m in length, 8 mm in diameter),

64

P. Krehl measures flame velocities of up to 2500m/s. He makes the important observation that the initially slow flame speed approaches a characteristic high limiting value after propagating a sufficiently long distance in the tube. That value is independent of the pressure of the gases, the material of the tube, and the tube's diameter above a small limit, but is a constant of each gaseous mixture. Calling this new thermochemical phenomenon an "explosion wave" [l'onde explosive], he does not explain this supersonic velocity of combustion by any thermal conductivity and diffusion process that governs the propagation of a slow flame, but rather by a transfer of gas compression from layer to layer (Berthelot---~1870), herewith reaching an important milestone toward a theory of detonation. He also states that its velocity could be predicted if the heat of combustion and the density and specific heat of the products are known. Berthelot 177 first demonstrates that a shock wave, generated by an explosive (mercury fulminate), can chemically decompose a gas into its elements. Using the example of acetylene (C2H2), he shows that the violent explosion that is accompanied by a flash emission transforms the initial gas into fine carbon particles dispersed in a hydrogen atmosphere. He draws the important conclusion that "these phenomena give evidence that direct thermodynamic relations exist between chemical and mechanical actions.", More recent studies by Aten and Greene 178 using infrared analysis of quenched products have shown that diacetylene (C4H 2) is the most important product of acetylene pyrolysis by shock heating: it may form over 5% of the total and decomposes into hydrogen and carbon (C4H2--~ C4 + H2).

Royal Commission on Accidents in Mines, U.K.

Abel and associates, stimulated by the calamitous accident in the Seaham Colliery at Durham in the autumn of 1880, show that the finely divided particles suspended in air are a source of danger similar to that occasionally experienced in flour mills. They begin to carry out explosion experiments with coal dust in large mine galleries and demonstrate that, with a very highly inflammable dust suspended in the air in which no trace of hydrocarbon gas (firedamp) is present, a blownout shot can produce ignitions that extend as far as the mixture of air with sufficient dust to maintain flame extends. 9 Some years later their results were thoroughly confirmed and also considerably extended by large-scale experiments carried out by the Prussian Fire-Damp Commission at Neunkirchen in the Saarbrucken District.

History of Shock Waves

65

Service des Poudres et Salp(.tres, Paris

Foundation of the journal Memorial des Poudres et Salp~tres ( 1 . 1 8 8 2 / 8 3 - 17.1913/14; continued as Memorial des Poudres, 18.1921 + 29.1939, 30.1948 + 46/47.1964/65) by the order of a ministerial decree. The editorial board consists of E. Sarrau, Ch. Arnould and E. Desortaux. 9 It was the first professional journal exclusively dedicating to the communication of results on the research of explosives, and its applications for civil and military purposes. Initially created with the intension to improve communications between French researchers on explosion technology, it soon advanced to an international scientific forum.

Physikalisches Institut, Humboldt UniversitFlt, Berlin

Hertz 179 treats the collision of bodies analytically and applies the potential theory to calculate stress and strain as a result of the acting force in the contact area. He first makes the important assumption that the duration of collision is much longer than the time that the elastic wave needs to travel the colliding body. Later this will be confirmed experimentally by Berger (--+ 1924). For straight, elastic collision of two spheres colliding with the relative velocity v, he derives simple formula for the maximum pressure P and duration of collision T, given by P - k iv 6/5 and T - k2 v-1/5. Here the coefficients k 1 and k 2 depend on mass, radius, and E-module of the spheres. For steel spheres 3 cm in diameter colliding at 100 m/s, the contact time T is about 36 ~ts, which is a multiple of the transit time of the excited longitudinal waves in the spheres. Hertz measures the outline of the surface of contact by covering one of the colliding bodies with soot, thus giving an experimental proof of his theory. He also calculates the elastic stress distribution for contact of a hard sphere on a plate, which, for low impact velocities, results in conical cracks (Hertzian cone fracture).. The Hertzian cone is best observed in glass and can be generated either statically by pressing a hard sphere on the surface or dynamically by impact (Kerkhof and Mailer-Beck 1969). In glass it extends from the point of contact under a cone angle of about 130 ~. However, it exists also in flint stone, obsidian, and other hard (and rather isotropic) materials. In prehistoric times, stone fragments [Absplif~] split off by Hertzian cone fracture were used for further processing into handaxes, arrowheads, knives, etc.

Laboratoire Central, Service des Poudres et Salp~tres, Paris

Vieille 18~ first applies a dynamic method to determine the accelerating force of an explosion. Arranging a small piston in the wall of the test vessel, he records its displacement-time profile under the action of the expanding gases on a sootcovered rotating drum and obtains the acceleration by double differentiation.

1882

66

1883

p Krehl

Coll~ge de France & Laboratoire Central, Service des Poudres et Salpttres, Paris

Berthelot and Vieille, 181 using the Desprez-chronograph (Maillard and Le Chatelier-~ 1881) and later the Le-Bouleng4 chronograph (Le Boulenge--~ 1863), measure the detonation velocity in about 50 mixtures of fuels and oxidizers, diluted by different amounts of nitrogen. They observe a uniform detonation velocity that only depends on the mixture composition, not on the tube material and diameter (as long as the latter is not too small). 9 Both electromechanical chronographs require electrical pulses for start/stop activation. The start pulse was provided by simultaneously igniting the gaseous mixture via a spark, and the stop pulse was generated by suspending perpendicularly to the tube axis a thin foil strip that, covered with a small amount of fulminate, exploded at the moment of arrival of the detonation front, thus breaking the holding current in the chronograph.

Nitrocellulose Fabrik Wolff & Co., Walsrode, Germany

Von Foerster, 182 chief engineer of the company, rediscovers the hollow cavity effect for high explosives without inlet (yon Baader-~ 1 7 9 2 ) . . The important discovery of the hollow charge effect, in Europe also called the von Foerster effect, can be ascribed to various inventors of different nationalities. A retrospect on this phenomenon was published in Germany by Freiwald 183 during World War II and more recently in the U.S.A. by Kennedy 184 to commemorate the 100th anniversary of von Foerster's discovery of the shaped charge effect. The shaped charge lined cavity effect, for both military and civil applications being of greater importance than the unlined cavity, was discovered much later (Thomanek--~ 1938).

France

Moisson, 185 naval captain and ballistician, investigates theoretically the air resistance of projectiles of cylindrical, spherical, and ogival geometry at speed u as a function of the ratio u/a = 0.2 to 2, where a is the sound velocity. This ratio will later be called the Mach number (Ackeret--~ 1929).

Ecole des Mines, Paris

Mallard and Le Chatelier 186 study detonation in gases and make streak records of flames from explosions in glass tubes 10-20ram in diameter and 1-3m in length. They use a rotating drum covered with film upon which the flame image is projected. Depending on the tube length and boundary conditions at the tube exit, they observe (i) a constant slow propagation velocity (deflagration), (ii) a phase of vibrations (intermediate state), and (iii) a rapid wave propagation (explosive wave).

Krakatao Island, Sunda Strait, Java

Explosion of volcano Perbuatan on August 27. The enormous mass of spilled lava into the ocean produces the greatest steam explosion in history. 187 9 The mighty blast came in as a

History of Shock Waves

67 "roar" at Batavia, 160 km away, and was said to be still audible at a distance of 3500km in Australia. Tidal waves were observed on four continents and residues of the blast wave recorded as barometric fluctuations around the globe.

1884

Stockholm

De Lava118s invents the first steam turbine. He uses steam jets, which, issuing from nozzles, give up their energy by impulsive action on a moving vane (reaction turbine). This principle, based on the idea of Heron's steam ball [aeolipile, A.D. 100], requires steam jets of very high velocity and will eventually lead to the invention of the "Laval nozzle" (---~1888), which will considerably stimulate supersonic aerodynamics.

Clark, Chapman, Parsons & Co., Gateshead, U.K.

Parsons invents the first multistage steam turbine, which is based on the principle of the reaction that a steam jet exerts on the orifice from which it issues. His machine utilizes several stages in series. In each stage, the expansion of the steam is restricted to allow the greatest extraction of kinetic energy without causing the turbine blades to overspeed. Immediate applications for marine propulsion purposes, however, will uncover serious limitations set by cavitation problems at the propeller, which will stimulate systematic studies of cavitation phenomena. 189

Ecole d'Artillerie de la Marine, Lorient, France

Hugoniot and Sebert 19~ examine a one-dimensional discontinuous gas flow and assume that the flow parameters before and after the discontinuity behave adiabatically (Poisson's law). 9 These studies--later significantly improved by Hugoniot, who assumed a steeper equation of state (his "dynamic adiabate," later called by others the Hugoniot curve)--led to the first general shock theory (Hugoniot---~ 1887).

Karl-Ferdinand Universitat, Prague

E. Mach and Wentze1191 succeed in making the first photograph of a shock wave. They select the most sensitive silver bromide gelantin dry plates then commercially available (Maddox--+1871). As a first test, they generate a shock wave by discharging a Leiden jar and use the spark of a second one, which is fired with a delay of about 20 ~s, as a light source. 9A large number of Mach's original photo plates have survived. They were donated to the Ernst-Mach-Institut at Freiburg/Breisgau by Karma Mach, Ernst Mach's daughter inlaw. Together with his notebooks and correspondence they are now kept at the archives of the Deutsches Museum, Mfmchen.

Brighton, U.K.

Phillips 192 constructs the first wind tunnel. Instead of being operated by a ventilator, it is operated by a steady stream of vapor emerging from a system of fine nozzles. The wind tunnel has a cross section of 0.43 x 0.43 m 2 and consists of a 1.83-m-long test section, which, most remarkably, is followed

68

e. Krehl by a 1.83-m-long diffuser. Using a mechanical balance, he measures for the first time the resistance of curved air foils up to a velocity of 18m/s.

1885

College de France, Paris

Berthelot and Vieille 193 invent the "bomb calorimeter" and measure with this new thermochemical method the specific heat of various gases up to above 2000~ with an accuracy hitherto unattainable.

Laboratoire Central, Service des Poudres et Salp~.tres, Paris

u

Karl-

E. Mach and Wentze1195 publish a study on blast waves originated from chemical explosions. Setting up a pair of parallel line charges of silver fulminate, they record, with the help of the soot method (Antolik --+ 1875), the interference of the two head waves drawn by the detonation fronts and find a detonation velocity ranging from 1700 to 2000m/s. It is interesting to note that they use here the correct term shock wave [Stofiwellel to appropriately describe the observed abrupt pressure increase and write, "The propagation of the shock wave can be felt by the hand, and optically (using the schlieren method) it can be proved that this wave consists of a single shock (without periodicity).". Before that time, Mach and coworkers had experimented with spark discharges and chemical explosives, thus using the terms spark wave [Funkenwelle] and explosion wave [Explosionswelle], as well as the terms percussion wave [Knallwelle] and compression shock [Verdichtungsstofg], the latter having adopting from Riemann (--+ 1859).

Ferdinand, Universitat, Prague

1887

invents "smokeless powder" [poudre B = poudre blanche, meaning white powder whereas poudre N = poudre noir, black powder]. In December of the same year test shots

with a 65 mm cannon are performed to show that the new powder permits the ballistic effect of black powder to be secured with the same pressure and with the charge reduced to only about a third, thus allowing a significant increase of the power of fire arms. Details of his invention were not published in the open literature until six years later. 194

University of KOnigsberg, Germany

Von Neumann 196 publishes a treatise on the longitudinal impact of two thin cylindrical rods, a subject on which he lectured previously (1857-1858). His approach, based on D'Alembert's solution of the wave equation, allows one to evaluate the normal velocity and axial stress in the rods as a function of time.

Private laboratory at Terling Place, Essex, U.K.

Lord Rayleigh 197 shows theoretically that waves passing along the surface of an elastic body probably play an important part in earthquakes, inasmuch as, spreading only in two dimensions, their intensity will gain the upper hand at great

History of Shock Waves

69 distances compared with waves spreading through the interior of the Earth. 9 His surmise was fully confirmed (and called Rayleigh waves). For example, in the great Messina earthquake (1908), Prince Galitzin 198 at Petrograd traced the seismic surface shocks that had traveled around in the Earth in opposite directions. His measured data of the surface wave velocity showed good agreement with Rayleigh's theory. Generally, seismographic records show three separate groups of waves: (i) longitudinal waves with the highest velocity of propagation velocity; (ii) distortion waves with mainly transverse motion; and (iii) surface or Rayleigh waves with the smallest propagation velocity but largest amplitudes.

Karl-

Ferdinand, Universitat, Prague, & Imperial AustroHungarian Marine Academy, Fiume [now Rijeka], Croatia

E. Mach and Salcher 199 start a long series of very successful and unique ballistic experiments. Salcher, who performs the experiments at the Adriatic Naval Test Station in Fiume together with his colleague Riegler, discusses with Mach via correspondence the progress of his work. Using two supersonic infantry riflesmthe Austrian Werndl (438 m/s) and later the Portuguese Guedes (530m/s)mSalcher photographs for the first time supersonic projectiles in flight. The photos reveal that a supersonic projectile, similar to a "bow wave" [Bugwelle] of a ship, produces a hyperbolic-like "head wave" [Kopfwelle] (a shock wave), which is followed by a "tail wave" [Achterwelle] (an expansion wave) and, depending on the projectile geometry, a series of intermediate waves. Addressing also the analogy to the motion of a body in water, they write, "It is possible to reproduce this phenomenon if we take a rod of cross section AB in a large water tank and move it at a velocity which exceeds the velocity of wave propagation." To find the density distribution around the supersonic projectile, they also propose Nobili-Guebhard's electrolytic method by using "a silver-coated copper sheet on the bottom of a container filled with an electrolyte, placing a non-conducting model projectile on the sheet and dipping metal probes connected to a battery to find the equipotentials." ,, This method was indeed used successfully by Taylor and Sharman 2~176 to investigate the field of flow of a compressible fluid past a cylinder. Unfortunately, Mach and Salcher did not consider themselves obliged to cite Doppler (---~1847) as the spiritual originator of the head wave phenomenon. In the 20th century the cone geometry was termed Mach cone and the head wave Mach wave. In the case of the sonic boom, resulting for example from an aircraft flying with supersonic speed, the region outside of the Mach cone was be called the

zone of silence.

70

P. Krehl Tumlirz, 2~ a coworker of E. Mach, presents his shock wave theory, which is based on Riemann's mathematical model (--~ 1859) and assumes an adiabatic law. To avoid Riemann's error, he explicitly uses the principle of energy applicable to continuous motion, in place of the principle of momentum. He concludes that as soon as a discontinuity is formed, it immediately disappears again, this effect being accompanied by a lengthening of the wave and a more rapid advance of the disturbance. He takes this process to be an explanation for the increased velocity of the wave.

Ecole Polytechnique, Paris

Hugoniot 2~ obviously not knowing Rankine's previous work (---~1869), formulates a general theory of discontinuous flow and, following the behavior of a point in the fluid (Lagrangian coordinates), being initially at rest, he uses the laws of conservation of mass, momentum and energy. His most remarkable results an be summarized as follows: (i) He shows that Riemann's assumption that a shock wave is an isentropic process is not correct and that the p,v data are not positioned along the static adiabate [Poisson's law, p - po(Vo/V);], but rather along a dynamic adiabate, later called the Hugoniot curve. Under the consideration that, at the discontinuity, kinetic energy is transformed into internal energy, he derives the famous relation el - e0 1 -~(Po + Pl)(Vo- vl). Later to be called the Rankine-Hugoniot relation (Rankine--~ 1869), it contains no velocity terms, only thermodynamic quantities. Here e0, P0, v0 and e l, Pl, Vl denote the thermodynamic states before and after such a discontinuity, respectively. (ii) Hugoniot shows that for a perfect gas of constant ratio of specific heats, m, the maximum shock compression is given by (m + 1 ) / ( m - 1), which for air with m = 1.4 is equal to 6. He uses the letter m instead of ~, which, coined by Poisson (--~ 1808) and also used by Rankine (---~1869), will later generally be adopted throughout. (iii) Hugoniot also addresses the propagation of shock waves in solids. Considering the conditions at the contact area of two colliding bodies, he states, "It is doubtful whether the discontinuities which are described by the theory of wave propagation are only a simplified analytical fiction or whether they correspond to the physical reality. This is an open question which is difficult to answer at the present state of science.". For an ideal gas the dynamic adiabate, not explicitly given by him in his memoirs, was later derived by Hadamard (--+1903). If the initial state is the standard laboratory state (25~ and 1 bar), the Hugoniot curve is called the principal Hugoniot. Sometimes the term Hugoniot

History of Shock Waves

71

relation is also used in the literature, meaning the dependency of the shock front velocity in terms of the overpressure at the shock front. Apparently, it was first derived by Vieille (--->1900). In the modern literature the Rankine-Hugoniot equations (conservation of mass, momentum and energy) are often given in the Eulerian representation which is preferable both from a mathematical and from a physical point of view: (i) (U - up)v o = Uv; (ii) p - P0 = Uup/vo; and (iii) e - e0 = 1/2(p + po)(Vo - v). Here e, e0; p, P0; and v, v0 are the specific internal energy, pressure and specific volume at the disturbed and undisturbed state, respectively; U is the shock front velocity and u r the particle velocity to which the shock-compressed material is accelerated. From (i) and (ii) the following expressions for U and up can be derived: u = v 0 [ ( p - po)/(Vo - v)] ~/'-" up = [ ( p - po)/(Vo - v)] ~/~. Depending on the particular application, the Lagrangian representation might be more convenient. 2~

1888

University of Edinburgh

Tait 2~ suggests his empirical isothermal equation of state (the "Tait equation") to fit data for the compressibility of sea water up to 500 bar. 9 Kirkwood and Richardson 2~ modified the Tait equation of sea-water for use from initial conditions (r0, P0) up to 25 kbar. Their form (p + B)/( po + B) = (p/po) A, resembles an isentropic in a perfect gas. Here A and B are two empirical functions of temperature, and p and p are pressure and density, respectively. The Tait equation has also been used to describe the p(p)-relation of organic liquids. 2~ Tait and Lord Kelvin publish their book Treatise on Natural Philosophy, in which they also treat the collision of spherical bodies. They introduce a "restitution coefficient," which they define as the quotient of velocities after and before impact.

Ecole Normale, Tir du Champ de Chalon; Artillerie de la Marine

Journee, 2~ De Labouret, 2~ and Sebert 2~ perform supersonic ballistic experiments that essentially confirm Mach and Salcher's observed head wave phenomenon (--+ 1887). They do not use high-speed photography, but rather measure the front velocity of the head (shock) wave along a line perpendicular to the Mach cone periphery and compare the data with Doppler's cone model of wave propagation (---~1847).

U.S. Naval Torpedo Station, Newport, RI

Munroe 21~ discovers by accident how to shape explosives to concentrate energy. He observes that, by increasing the depth of the cavity in the explosive, greater and greater effects on a metal plate facing the explosive can be generated. The phenomenon, later to be called the Munroe effect and caused by an oblique collision of explosive waves, will be used by him to imprint designs on iron plates by interposing a

72

P. Krehl stencil between the explosive and plates of iron (explosive engraving). 9 His discovery was partly a rediscovery of the hollow cavity effect of an unlined shaped charge (von Baader---~ 1792; von Foerster--+ 1883).

University of Dorpat, Russia [now Tarpu, Estonia]

Von Oettingen and yon Gernet 211 resume Bunsen's hypothesis (---~1867) on the discontinuous nature of oxyhydrogen explosions. Using a high-speed rotating mirror and a still camera, they produce time-resolved records from the propagation of the flame front originating from an oxyhydrogen explosion in a straight, 40-cm-long tube. To visualize the otherwise dark oxyhydrogen explosion, they add a small quantity of salt. With this unique streak diagnostics they determine an initial explosion velocity of 2560m/s, thus confirming Berthelot's previous result (--* 1881). After several reflections the shock wave diminished to a velocity of 600m/s. They call the explosion wave the "main wave" [Hauptwelle] or "Berthelot wave" and its reflection at the tube end the "shock wave" [Stoj~welle]. They also observe various secondary waves, which they call "Bunsen waves".

AB Separator Company, Stockholm

De Lava1212 receives a Swedish patent for his "Laval nozzle". Apparently knowing that previous studies on straight nozzles had shown that the gas can be expanded best with sound velocity (critical speed, de Saint Venant and Wantzel---~ 1839) and following his intuition, he uses a convergent-divergent nozzle geometry. This expands the gas isentropically from subsonic to supersonic speeds, thus increasing the efficiency of steam turbines. In his patent he claims: "At rotating steam engines, a steam inlet channel, having cross sections in the vicinity of the rotating part of the steam engine that are increasing in the direction of the said rotating part with the objective to expand the steam in that way that the steam will achieve its highest possible speed before its contact with the rotating, working part of the steam engine.", De Laval had experimented with nozzles 12 years before. As recorded in his personal notes of 1876, he observed that the severe shock behind a nozzle consumes a lot of energy. 213 It appears that he resumed this subject when he experimented with the Sshaped turbine (Heron's steam ball). In his notebook of 1886, there are entries on a 10-inch turbine "with conically widened nozzles at the orifice." However, the idea did not appear to be new: Traupe1214 annotates in his book on thermal turbines that K6rting, owner of a factory for steam apparatus in Hannover, already used this principle in 1878 for steam ejectors.

History of Shock Waves

73

Imperial AustroHungarian Navy Academy, Fiume, Croatia

Salcher and Whitehead 215 study the discharge parameters of a "free-air jet" exhausting from a pressure reservoir through a small opening and compare their experimental data with various existing theories. Salcher performs the experiments at Whitehead's torpedo factory at Flume. Whitehead gained much experience in the generation and storage of highpressure gases, because the torpedoes are propelled by pressurized air up to 100 bar. Illuminating the free air jet with a flash light source of short duration (such as an electric spark) or of long duration (such as by the Geisler discharge tube or using even sun light), which allows the visualization of nonstationary or stationary flow characteristics, respectively, they first make the startling observation that a jet emerging from a pressurized nozzle contains a crossed wave pattern. Since this interference pattern reminds Salcher of an ancient Greek harp, he calls it a lyre [Lyra] in a letter to E. Mach. 216 They correctly interpret this as a superposition of reflected shock waves.. Later this structure--a sequence of pairs of oblique shock fronts, each irregularly interacting and creating a sequence of Mach disks--was coined shock diamonds. Today this is a frequently observable phenomenon in the exhaust of jet engines. The jet experiments described above were later resumed by L. Mach (-~1897), who also first obtained interferograms of excellent quality.

Navy Academy, Fiume & KarlFerdinandUniversitat, Prague

The study of free-air jets inspires Salcher to suggest a supersonic blow-down wind tunnel with the air flowing and the test body being at rest. In a paper written with E. Mach, 217 he says, "On the occasion of the experiments on projectiles Salcher hit upon the idea of likewise investigating the inverse case of the flow of air against a body at rest in order to confirm the results already obtained." They confirm that the inverse case is indeed possible, but with the existing equipment head wave studies of model projectiles were not practicable because of the available small jet diameter. Obviously, Huguenard and Sainte kague in France were the first who realized Salcher's idea for drag measurements of projectiles at supersonic speeds (kangevin and Chilowsky --~ 1918).

Karl-Ferdinand Universitdt, Prague

E. Mach, together with his son L. Mach, first applies interferometry to visualize the flow field around a supersonic bullet. 218 They also apply schlieren photography to visualize the interaction phenomena of two shock waves emerging from two closely spaced point sparks and get the first schlieren photos of the Mach disk. Their experiments fully confirm the triple-point model that they had only assumed hitherto on the basis of soot records (E. Mach and Wosyka

1889

74

P. Krehl --~1875, E. Mach and Gruss - ~ 1 8 7 8 ) . . 54 years later, Campbell, Spitzer, and Price (-~ 1943), using two detonator caps in a very similar geometry, first proved that Mach reflection also exists in water.

1890

French FireDamp Commission, Paris

Charpy 219 and Le Ch~telier 22~ review the first results of experiments the commission had performed to study possible causes of firedamp explosions [le grisou] in coal mines. To avoid such explosions the commission recommends: (i) provision of an effective ventilation system to prevent sudden outbursts of firedamp, to reduce the concentration of methane in the air below 5%, particularly in all higher gallery sections; (ii) use of safe explosives; (iii) avoidance of open fire, sparks, etc.; and (iv) exclusive use of such miner's lamps as remain safe even at higher air speeds. 9 Pure coaldust explosions (without any presence of firedamp), hitherto frequently observed in England but only rarely by French mining engineers, were not yet considered a real hazard.

1891

BerlinLichterfelde

Man's longest flight (300m) to date is performed by von Lilienthal. At this date the basics of supersonics are understood, but practical aviation is still in its infancy.

Chemische Fabrih Griesheim, Germany

Haeussermann 221 discovers the explosive properties of trinitrotoluene (TNT), a substance that had already been synthesized by Wilbrand (1865) by the nitration of toluene with mixed acid. 222 9 Haeussermann first suggested the military use of TNT in shells and undertook its manufacture on an industrial scale. TNT, indeed, gained great military importance in both world wars and remains important today.

Newport Torpedo Station, RI

Munroe 223 invents a smokeless powder. He calls it Indurite because the final powder when dried is exceedingly hard.

Universiti~t Wf~rzburg & Karl-Ferdinand Universitiit

Zehnder 224 and L. Mach 225 independently invent a special type of interferometer that will later be called the MachZehnder interferometer. Consisting of two beam splitters and two mirrors, it divides the source beam into two different parallel light paths (object beam and reference beam) of arbitrary distance. 9 This optical setup proved to be most worthwhile to measure variations of refractive index in compressible gas flow. Zehnder 226 invented and applied this new type of interferometer prior to L. Mach in his Ph.D. thesis at the University of Worzburg under the guidance of R6ntgen in order to investigate the pressure dependency of the refractive index of water. L. Mach, first using it in nonstationary gas dynamics, commercialized his invention and became a wealthy man.

University of Edinburgh

To measure the shock duration between an impinging block and the material to be studied, T a i t 227 builds a simple but very

1892

History of Shock Waves

75 effective percussion apparatus that he humorously calls the "guillotine." The impactor, a block sliding freely between vertical guide rails (precisely like the axe of a guillotine), is attached with a pointer to continuously record the block movement on a revolving plate-glass wheel that is coated with soot. For time measurement he uses a tuning fork that simultaneously produces a second trace on the revolving plate. He also estimates the duration of impact between hammer and nail (200 Its) and the associated time-average force (300 lb-wt). 9 One year later Tait 228 wrote to Hertz: "Some months ago, I was told by Lord Kelvin that you had brilliantly attacked the problem of the impact of elastic spheres. Being very busy at the time, I glanced over your paper in Crellos 92 [J. Reine & Angew. Math. 92 (1881)], but did not attempt to read it. I had been working for some years at direct experiments on impact, but I used a mass of 2; 4; and 8 kg falling through i m or so, and the elastic body on which it fell was a cylinder whose upper surface was very slightly convex. The amount of longitudinal distortion was, in some cases, as much as 30mm. I found, by a graphical method, that the force called into play was at the power 3 of the distortion thus measured. On lately reading your paper with some care, I found to my great surprise that this is the same law which you have theoretically deduced for spherical bodies . . . . " Unfortunately, we do not know today whether Hertz answered this letter. Tait's records, now kept at the Archives of the University of Edinburgh, do not contain any such letters.

Ecole

Sup~rieure de Pharmacie, Paris & C. A. Parsons Co., Newcastleupon-Tyne, U.K.

Royal College of Science, South Kensington, U.K.

The first attempts are made to produce artificial diamonds. However, there is no clear evidence of any incipient transformation of carbon into diamond. Moissan 229 at Paris uses a solution of carbon in a suitable molten metal at high temperature, which he quenches rapidly in water. 9 Later Parsons, 23~ used a 0.303-inch caliber rifle to fire steel bullets at 1500m/sec into an armored press steel house filled with graphite powder. All his attempts, however, gave negative results. Moissan and his contemporaries believed that diamonds could be synthesized successfully by this method, but later investigations rejected this conclusion. TM The spectacular shock synthesis of diamonds did not succeed until about 70 years later by DeCarli and Jamieson at Stamford Research Institute, Menlo Park, CA and the Dept. of Geology of the University of Chicago, IL, respectively. 232 Boys 233 studies flow about bullets and interaction processes of multiple shock waves by using the shadow method (Dvorak--+ 1880). He succeeds also in measuring the spin rate of a shot by using photography. Since a professional ballistic range is not available to him, he performs his shot

76

P. Krehl experiments in a long public hallway in his institute. Boys, who repeated E. Mach and Salcher's ballistic experiments (--> 1887) and promoted the spreading of their method in England, writes 234 to Mach, "I am much obliged to you for your kindly sending me copies of your papers and the two photographs. I have when speaking on bullet photography thoroughly recognized that the whole credit of bullet photography is yours, as you were the first, to carry it out successfully and that your apparatus answers perfectly i.e. so far as I can judge from your account of them. In the English papers were inaccurate reports and in one case of a scientific paper ! corrected it, as stated, what you had done. The daily papers are always so untrustworthy that it is absurd to credit them. I do not think I have failed to appreciate or to recognize what you have done . . . . If you should think I have not properly recognized your work, I am exceedingly sorry, that it should be so, but I am sure if you had heard what I have said at the Royal Society and elsewhere, that you would not think so... " . In the same year E. Mach 23~ wrote, "Boys' method is certainly a simplification when using it merely for demonstration purposes in a lecture. However, I suppose that everybody who wants to study this matter in more detail, will prefer an optical image which allows to estimate the condensation by its shading, rather than a mere silhouette which only reveals the contours of the air waves . . . . Nevertheless, I am grateful to Mr. Boys that he has taken over this assignment hitherto not touched by others, and I hope that he intends to continue it in future." Today, however, in most outdoor ballistic facilities shadowgraphy is used more frequently than the schlieren method because of its simplicity and minor sensitivity toward temperature fluctuations.

Washington, DC

1893

University of Manchester

U.S. President Harrison states 236 in his farewell message to Congress, "I consider one of the great achievements of my administration the invention of smokeless powder by Charles E. Munroe." 9 However, the chief obstacle that eventually prevented the general employment of Indurite (---~ 1891) by the U.S. military was its inconsistency of composition due to the use of improperly nitrated guncotton and to difficulties in removing the residual solvent. Schuster 237 derives a simple formula to calculate the velocity V of the detonation front, which, based on Riemann's theory (-+ 1859), is given by V - [(P/Po)(P - Po)/(P - P0)]1/2He observes a good agreement with experimentally determined rates of explosion in various explosive gaseous mixtures and writes, "Lord Rayleigh criticizing his

History of Shock Waves

77 [Riemann's] investigation, draws attention to the fact that a steady wave is only possible for a particular relation between the pressure and density of the gas, which is different from the one actually holding. In the case of the explosion-waves it seems possible, however, that the temperature, pressure, and density of the gas should so adjust themselves as to make Riemann's equations applicable. In fact, they must do so if the front of the wave keeps its type, which it probably does when the velocity has become constant . . . . In the strict sense of the word I do not think the explosion-wave can be steady, because if the motion is, as assumed, linear, compression must precede the explosion, and Lord Rayleigh's objection would hold for the front part of the wave in which no combination takes place. But it seems possible to me that the motion may not strictly be a linear one, and that yet taking the average velocities over a cross-section of the tube the ordinary equations would apply. It seems probable that jets of hot gases are projected bodily forward from that part of the wave in which the combination takes place, and that these jets, which would correspond to the spray of a breaking wave really fire the mixture.". His correct supposition of a steadily moving detonation wave, made previously in a similar manner by Berthelot 238 and in the same year worked out in more detail by Dixon (-+1893), led to the first theory of detonation (Chapman--+ 1899).

England

Burton 239 resumes Lord Rayleigh's critiques on Riemann's theory (see also his Theory of Sound, vol. II, p. 41, -+ 1878). He also tackles the difficult problem of whether in the absence of viscosity the motion of spherical waves of finite amplitude can become discontinuous, as in the case of plane waves.

Karl-Ferdinand Universitat, Prague, & Polytechnikum Riga

E. Mach and Doss 240 assume that the sharp bang of a meteorite approaching the Earth is a supersonic phenomenon, thus creating a head wave. Mach's motivation to treat the phenomenon of meteoric showers was a letter by C. Abbe, an employee at the Washington Weather Bureau who belonged to a committee of the Philosophical Society of Washington, which had analyzed the fall of the Washington Meteor (-+ 1877). Abbe claims to have already given in 1877 a "true theory of thunder and meteorite explosions" and states, "We are disposed to consider the so-called 'explosion', and subsequent 'rumbling' not as due to a definite explosion of the meteor, but as a result of the concentration at the observer's ear of the vast volume of sound emanating, almost simultaneously, from a large part of the meteor's path, being, in that respect, not dissimilar to

78

p. Krehl ordinary thunder." Abbe then tries to explain the violent sound by the Doppler effect and concludes: "we may remark that it requires only comparatively feeble noises distributed along the entire path of the meteor to produce, by their concentration at the observer's station, a sound equal to that of loud thunder." Mach, rejecting Abbe's theory and his prior claim, replies that only the head wave phenomenon is the true cause of the explosionlike sound effects. 9 Mach's interpretation was indeed correct; however, although pioneering supersonics and being far-sighted, he could not yet realize that the head wave of meteoroite which enter the Earth's atmosphere at speeds up to several 10 km/s, is closely wrapped around the meteorite and forms the so-called "hypersonic boundary layer," thus creating hitherto unknown surface heating and erosion effects.

World Colombian Exposition, Chicago

De Laval displays his reversible single-stage steam turbine. The engine (15 hp at 16,000rpm) is designed for marine use and has been tested on Lake MOlaren in the vicinity of Stockholm to drive a launch. Its novelty is that the turbine blades are driven by a stream of hot, high-pressure steam emerging from a series of unique convergent-divergent nozzles (De Laval-+ 1888). 9 Today his turbine is part of the collection of the Smithsonian Institution and on display in the History of Technology Building at Washington, DC.

University of Moscow

Mikhel'son 241 first proposes a linear law in his theory of detonation and assumes steady propagation of the reaction products--i.e., equal velocities at which any of the intermediate states propagate. Starting from the equations of mass and momentum, he derives the elementary relation P--Po 4-(U/vo)2(Vo- v), which, also derived in the same year in England (Schuster-+ 1893), represents a straight line in the p, v-plane. Here U denotes the shock front velocity, and v and vo are the specific volume at pressure p and P0, respectively. 9 In the western world this line is called Rayleigh line, referring to the work of Lord Rayleigh (--~ 1910) on aerial shock waves. Zeldovich 242 coined this line the Mikhel'son-line in honor of Mikhel'son's early contribution to the theory of detonation, which was unknown among contemporary scientists outside Russia. The theory of detonation was established independently six years later by Chapman (--+ 1899).

Chair of Chemistry, Owens College, Manchester

reports on his observations of the high velocity of explosions in gases. He put forth the view that the detonation wave travels with the velocity of sound in the burning gases, essentially supporting Schuster's view of an unsteady motion of the detonation front (Schuster-~ 1893). Using a coiled-up D i x o n 243

History of Shock Waves

79 lead pipe (length, 55 m; inner diameter, 8 mm), he measures in oxyhydrogen a velocity of 2821 m/s, thus essentially confirming Berthelot's previous measurements (Berthelot-+ 1881).

1895

1896

Institution of Naval Architects, London

Thornycroft 244 and Barnaby 245 investigate reasons for the failure of a British destroyer to meet its design speed. They observe that a marine screw propeller, if turned too fast, might waste its effort by creating vacuous spaces in the water, which afterward suddenly collapse. They also coin this phenomenon cavitation. 9 The systematic search for the origin of erosion by cavitation bubbles was initiated by the finding of severe destructive effects on the propellers of the British ocean liners "Lusitania" and "Mauretania". 246 A committee was appointed in 1915 by the British Admiralty to determine the cause of erosion of propeller blades which resulted in pioneering results (Lord Rayleigh-+1917, Cook--+ 1928).

Komaishi,

Tsunamis originating from a seaquake in the Pacific destroy the coastal town of Komaishimabout 27,000 people die and 5000 are w o u n d e d . . Then this puzzling wave phenomenon was a subject of much discussion some years before this disaster, Rudolph 247 had reviewed previous hypotheses on the origin of seaquakes and associated tidal waves, and had speculated that they are caused by submarine gaseous detonations at the sea bottom. Rottok, 248 another German scientist, had assumed that they might be caused by submarine volcanic eruptions. In the past, tsunamis were often referred to as tidal waves in the English literature. However, they are not created by gravitation as are tidal waves, but rather by tectonic displacements associated with earthquakes. Occasionally, tsunamis can also be generated when a huge body of water is displaced impulsively, e.g., by exploding islands (Krakatao--+ 1883), landslides, and underwater explosions of nuclear devices. Tsunamis cannot be felt aboard ships on the open sea. When they approach the coastline and enter shallow water, their velocity diminishes and their wave amplitudes can increase to heights of up to 30 m. Tsunamis then become very similar to hydraulic jumps of large amplitudes. The term tsunami is a Japanese word composed of two characters meaning "harbor" [tsul and "long wave" [nami], or "long-wave-in-harbor." The term was adapted in the 1960s for general use, in preference to either of the terms tidal wave or seismic sea wave. An equivalent phenomenon, encountered in rivers and confined waters and known as bores, attracted many early naturalists such as Airy, Challis, Earnshaw, Jouguet, Lord Rayleigh, Russell, and de Saint-Venant.

Japan

80

1897

1898

P. Krehl

Pressburg, Hungary

Siersch, 249 director of the Dynamite AG, Wien and concerned about the safe use of explosive in coal mines, applies photography to classify the nature and intensity of the flash emitted by an exploding charge. [He concludes that the shape and dimensions of the flash afford a clue to the eventual security of the explosive, since the smaller the flash the greater the relative security of an explosive for use in the mining industry. Using a still camera and photographing the flash with an open shutter during night, he observes that the flash intensity from an explosive depends on the geometry, the mode of stemming, and the density and admixtures]. 9 On the whole, this straight-forward method proved to be useful, however, he was not yet aware that shock wave reflection and interaction phenomena can also contribute considerably to the geometry and intensity of the flash (Michel-L~vy and Muraour--~ 1934).

C.A. Parsons Co., Newcastleupon-Tyne, U.K.

Parsons 25~ begins a three-decade study of marine propulsion. High propeller speeds are generally advantageous for the steam turbine, but if too high, they lead to much cavitation. With the help of flow visualization he minimizes cavitation effects, thus also improving the propulsive efficiency. He ascribes cavitation to the "water-hammer of collapsing vortices" and compares this phenomenon to whip cracking "whereby nearly all the energy of the arm that swings the whip is finally concentrated in the tag.". The first mathematical treatment of cavitation was performed by Lord Rayleigh (---~1917).

KarlFerdinandUniversitF~t, Prague

L. Mach, 25~ resuming previous experiments by his father and Salcher (--~1889), visualizes free air jets emerging from nozzles of various exit geometry. He applies not only the schlieren but also the interferometer technique, and makes the important observation that with increasing driving pressure (i) the jet diameter surmounts the nozzle diameter, and (ii) the reflected wave fronts no longer intersect in a point (regular reflection) but rather form a new wave, which later will be called Mach reflection (von Neumann---~ 1943).

Laboratoire Central, Service des Poudres et Salp(.tres, Paris

Vieille 252 ignites small amounts of explosives at one end of an air-filled tube with a length of 4 m and a diameter of 22 mm. He measures the shock propagation velocity using chronography and obtains supersonic velocities for both gunpowder (337-1268 m/s) and mercuric fulminate (359-1138m/s). His measurements of a fast-propagating discontinuity confirm theoretical models provided by Riemann (---~1859) and Hugoniot (---~1885, --~ 1887) as well as observations by E.

History of Shock Waves

81 Mach, who generated supersonic waves from both explosives (E. Mach--+1877) and electric sparks (E. Mach--,1875, --,1878).

Aleksejew Water Line Station, Moscow

Kareljskich and associates study the propagation of hydraulic shocks in water pipes. They use water pipes with diameters of up to 6in. and lengths of up to 2494ft. The pipes are connected with Moscow's main water line (24-in. in diameter) via a fast-closing valve. For pipes ranging between 2-in. and 6-in. in diameter, they record pressure jumps between 3 and 4 bar. With the aid of an electrical chronograph they measure speeds ranging between 4200 and 3290ft/s, regardless of whether the shock is generated by a sudden opening or closing of the valve. Zhukovsky, 253 supervising and analyzing the experiments, notices that water hammer waves in plumbing systems are related to shock discontinuities that propagate with constant speed, being dependent only on the wall material and thickness of the pipe and independent of the shock intensity. He draws the following conclusions: (i) The pressure jump p can be estimated by the simple relation p = p0c0V, where P0 and co represent the ambient density and sound velocity of the liquid, respectively, and V is the velocity of the discontinuity carried by the wave, which he assumes is moving with the acoustic speed. (ii) Reflected shocks can generate detrimental periodic oscillations in the pipe system. (iii) At transitions from large to small pipe diameters, the shock intensity can double and, under unfavorable reflection conditions, even further increase up to a fatal level of shock loading. (iv) Hydraulic shocks can be prevented by using slowly closing valves, with a closing time proportional to the length of the water pipe, and by installing wind tanks in the vicinity of the valves. 9 The problem of water hammer, a steady companion in the extension of urban infrastructures, was also tackled in the 1890s in England by Church 254 and in the United States by Carpenter. 25~ Zhukovsky and associates, however, were the first to thoroughly treat this subject both experimentally and theoretically.

German Imperial Navy, Torpedo Inspection Organization, Kiel

Blochmann 256 first correlates the numerous underwater explosion phenomena under local, temporal, and causal aspects. Based on pressure-time profiles recorded with a mechanical apparatus [Dynamometer], he develops a theory of underwater explosion that, along with gas bubble oscillation, allows the prediction of the shock pressure in the water at any distance from the explosive. His analytical results explain hitherto strange surface phenomena (Abbot-+ 1881), such as the dome of spray thrown up from the surface

82

P. Krehl (which he explains by reflection of the incident shock wave at the surface) and, shortly after, the formation of spearlike plumes of spray (which occur during breakthrough of the gaseous explosion products).

1899

Physical Laboratory, University of Wisconsin, Madison

Wood 257 repeats Toepler's shock propagation and reflection experiments (---~1864), but instead of observing the phenomena through a schlieren telescope he uses film for recording. In the introduction he states, "I have always felt that the very beautiful method derived in 1867 by Toepler for the study of 'schlieren' or stri~e, is not as well known outside of Germany as it deserves to be, and trust that the photographs illustrating this paper are sufficient excuse for bringing it before the readers of the Philosophical Magazine. Sound waves in air were observed by Toepler, but they have never to my knowledge been photographed. When seen subjectively, the wavefronts, if at all complicated, cannot be very carefully studied, as they are only illuminated for an instant, and appear in rapid succession in different parts of the fields of the viewingtelescope.". Wood failed to notice that 15 years before E. Mach and Wentzel (---~1884) had successfully photographed the shock wave emerging from a spark discharge. Nevertheless, Wood, who extended his experiments in the following years, obtained interesting results of the reflection, refraction, and diffraction of spark (weak shock) waves, which made widely known the great potentials of shock wave photography to the Anglo-American public.

Universities of Leipzig and Munich

The Emden Brothers, 258 studying in detail gas jets emerging from orifices, make the important observation that stationary waves are generated in the jet as soon as the driving pressure exceeds a critical value for provoking a gas flow propagating with sound velocity.

Laboratoire Central, Service des Poudres et Salpdtres, Paris

Vieille 259 constructs the first bursting diaphragm shock tube to demonstrate that a shock wave propagates with a speed greater than the speed of sound. His device consists of steel tubes with a constant cross section 22 mm in diameter. The driver section has a length of 2 m, followed by a 4-m-long expansion tube. As diaphragms he uses collodion, paper, glass, and steel. The diaphragm ruptures automatically at reaching a certain overpressure, for example, at 35 bar for a 1.5-mm-thick glass plate. In air he achieves shocks with Mach numbers up to M -- 2 and concludes with plain words that "explosives do not play any essential role in phenomena of propagation at great speeds," meaning that the phenomenon of supersonics is not limited to the use of explosives, but for

History of Shock Waves

83 example can be generated also by a bursting membrane. ,, The "shock tube", a term coined much later (Bleakney, Wimar and Fletcher 1949) became an important diagnostic tool for a variety of scientific disciplines, such as for aerodynamic purposes, to study the kinetics of chemical reactions and vibrational and rotational energy transfer, for plasma spectroscopy, to investigate vapor bubble dynamics in two-phase flow, and even for fertilizer production. 26~

University of Manchester

Chapman, 261 assistant to Prof. Dixon, treats an unsupported detonation by assuming that, once the maximum velocity is reached, the detonation frontmi.e., the front of the explosive wave--is of such a character that (i) it moves steadily; (ii) the flow is planar; (iii) the chemical reaction occurs instantaneously; and (iv) the flow, following immediately behind the discontinuous shock, is exactly sonic. He analyzes the solutions to the shock jump conditions for explosive gases and observes that the minimum-wave-speed solution agrees with experimental measurements previously made by Dixon (41893). He concludes, "When an explosion starts, its character and velocity are continually changing until it becomes a wave permanent in type and of uniform velocity. I think it is reasonable to assume that this wave--i.e., the wave of which the velocity has been measured by Prof. Dixon--is that steady wave which possesses minimum velocity; for, once it has become a permanent wave with uniform velocity, no reason can be discovered for its changing to another permanent wave having a greater uniform velocity and a greater maximum pressure . . . . ",, His lasting contributions, which were later independently made by Jouguet (--~1905), have been commemorated by the state of the exploded gas immediately behind the explosion wave being called the Chapman-Jouguet state.

Ballistic Test Range, BerlinCummersdorf

Wolf 262 first investigates large-scale explosions by order of the Prussian Ministry of War. He (i) measures the velocity of the spherical blast wave emerging from the explosion of large quantities of trinitrophenol and uses an electrical contactmicrophone, which triggers a "Le-Bouleng~-chronograph"; (ii) studies the blast response on structures; and (iii) records the pressure-time profile of blast waves using a thin rubber membrane directly coupled to a drum chronograph. His observations fully confirm Mach's previous observations that the blast wave is supersonic close to the charge but rapidly decreases with increasing distance. For a charge weight of 1500kg, he measures a velocity of 858m/s at a distance of 10m. His mechanically recorded pressure-time

84

v. Krehl profiles of blast waves show all the typical characteristics, such as the steep rise, the rapid decay, and the phase of negative pressure.

1900

Laboratoire Central, Service des Poudres et Salp~.tres, Paris

Vieille, 263 starting from Hugoniot's theory (---~1887), first derives a relation between the shock front velocity, V, as a function of the overpressure, (p - P0), at the shock front. This relation, V -- a [1 4- (m 4- 1)/2m x (p - po)/Po] 1/2, will later be known as the Hugoniot relation. Here P0 and a denote the pressure and sound velocity at rest, respectively, and m is the constant ratio of specific heats. He also confirms this relationship experimentally. In another study, Vieille 264 speculates on hypersonic flight, predicting stagnation pressure and temperature for flight in ideal air at speeds up to M ~ 30, and associated surface phenomena such as incandescence and erosion, leading for example in meteorite falls to thermal ruptures. He concludes, "Without admitting these numbers an absolute value, one can imagine that the incandescence of meteorites, the erosion of the surface and the rupture which accompanies their passage through our atmosphere are explicable by pressures and temperatures predictable by the law of the propagation of discontinuities, even when taking into account of the rarefaction of the medium passing through."

University of Wisconsin, Madison

Wood 26~ photographs focused spark (weak shock) waves by using spherical, parabolic, and elliptical mirrors.

Royal Institution, London

In an evening lecture entitled Some Modern Explosives, Noble 266 reports on the physical and chemical effects of detonating explosives in the bore of a gun and states, "I am not without hope that the experiments I have been describing may, in some small degree, add to our knowledge of the kinetic theory of gas . . . . The kinetic theory of gases has, however, for us artillerists a special charm, because it indicates that the velocity communicated to a projectile in the bore of a gun is due to the bombardment of that projectile by myriads of small projectiles moving at enormous speeds, and parting with the energy they possess by impact to the projectile . . . . But in the particular gun under discussion, when the charge was exploded there were no less than 20,500 cubic centimetres of gas, and each centimetre at the density of explosion contained 580 times the quantity of gas, that is, 580 times the number in the exploded charge is 8 31 quadrillions, or let us say approximately for the total number eight-followed by twenty-four cyphers . . . . "

History of Shock Waves

85

1901

Chair of Mathematics, University of Stra~burg

Weber 267 presents his revised edition of Riemann's lectures on mathematics, which he had delivered in the period 18551866 at the University of G6ttingen. He extends Riemann's theory (--->1859) and treats shock waves in two chapters entitled "Propagation of Shocks in a Gas" and "Aerial Vibrations of Finite Amplitude." Returning to Lord Rayleigh's previous objection (---~1878) on Riemann's theory (see also his Theory of Sound, vol. II, p. 41), he demonstrates that Riemann's theory is indeed correct and compatible with the law of energy. 268 Lord Rayleigh (-->1910) will resume this problem in his classic review paper on the evolution of shock wave theories.

1903

Coll~.ge de France, Paris

Hadamard 269 treats discontinuities mathematically and in a general form. For an ideal gas he derives the "Hugoniot curve" [loi adiabatique dynamique] as 1/2(p I + po)(Vo - vl) = (ply1-poVo)/(7 - 1) which, plotted in the p,v-plane, is steeper than Poisson's adiabatic law [loi adiabatique statique]. While studying the works of Riemann (-~ 1859) and Hugoniot (--~ 1887), he noticed that the shock front problem can be considered separately and can be mathematically transformed by a particular simple procedure not connected with any specific problems and that can be fully described by the so-called "identity and kinematic conditions" and their derivations. He postulates, "If a function of the coordinates and of time, together with all its derivatives, is defined both outside of and at the surface of discontinuity, then the rule for compound differentiation can be applied to it at the surface of discontinuity . . . . " . Referring to Hadamand's theorem, v o n Karman 27~ later annotated, "According to his theorem, a vortex-free flow ahead of a shock wave can remain vortexfree after passing through the shock only when the wave is straight. If the shock wave is curved, it produces vorticity. This is a fact which makes the analysis of motion behind a shock wave rather complicated." Hadamard used also the terms shock wave [onde de choc] to illustrate the wave-type character of this phenomenon and acceleration wave [onde d'accglgration] to elucidate the steepening process behind the shock. He distinguished the characteristics as propagation paths of vanishingly small shock waves, as the energy defect across them becomes zero.

Institut fftr Thermische Maschinen, ETH Zftrich

Stodola 271 publishes his famous book on steam turbines, which contains the first studies of flow characteristics through a supersonic (Laval) nozzle. He measures the pressure distribution along the nozzle axis at different back pressures and, noticing a sequence of steep pressure increases,

86

P. Krehl states, "I see in these extraordinary heavy increases of pressure a realization of the 'compression shock' theoretically derived by Riemann, because steam particles of great velocity strike against a slower moving steam mass and are therefore compressed to a higher degree . . . . " 9 Each zone of maximum pressure is visible in a photograph as a vertical line in respect to the nozzle axis, which was called by Cranz 272 the "barrier line" [Staulinie]. A historical review on the outflow of gases and steam from orifices was given by Prandtl. 273

1904

Kitty Hawk, North Carolina

The Wright Brothers start their wind tunnel experiments to optimize the design of wings and propeller blades. On December 17, Wilbur Wright performs the first controlled motor flight over a distance of 260m; total duration is 59 s (i.e., average velocity 4.4 m/s). 9 Later v o n K a r m a n 274 stated in his memoirs, "The peak event of this part of my visit to the U.S.A. was my meeting in Dayton, Ohio, with Orville Wright . . . . To my surprise and enormous interest, I found that Orville Wright was familiar with the fundamentals of aerodynamic theory. He told me that before the historic flight at Kitty Hawk, he and his brother spen~almost two thousand hours with their small wind tunnel, studying the relative merits of various wing shapes."

Technische Hochschule Dresden

M. Toepler 275 visualizes and photographs spark (weak shock) waves by using the schlieren method of his father (A. Toepler --+ 1864).

Owens College, Manchester

Lamb 276 solves the theoretical problem of surface waves excited by impulsive line or point loads. He finds that the surface disturbance may be divided roughly into two parts: (i) a minor tremor, composed of both longitudinal and transverse waves, which starts with some abruptness and may be described as a long undulation leading up to the main shock and decaying gradually after this has passed; and (ii) the main shock propagating as a solitary wave with the velocity found by Lord Rayleigh (--+1887). Lamb's contribution is of fundamental significance to theoretical seismology.

Institut far angewandte Mechanik, Universitiit G6ttingen

Prandt1277 begins a study on wave propagation phenomena inside and ouside of nozzles of various geometry when stored high pressure air is exhausted through them. Starting from Riemann's theory (---~1859), he gives a quantitative explanation on the periodic formation of stationary waves in free jets (Salcher---~ 1889): Expansion waves originating at the edge of the outlet are reflected at the boundary of the free jet as compression waves, which in turn are reflected as expansion waves. This process repeats periodically, thus resulting in

History of Shock Waves

87 crossed lines (later to be called "shock diamonds"). He also deduces the "wavelength" of the crossed wave pattern in the photograph from the ratio c/w (w - supersonic flow velocity along the axis, c = sound velocity at that state) which can be estimated with sufficient accuracy from the inclination of the characteristic lines with respect to the axis of the jet using Mach's law sin a = c/w. Later he will coin this angle 0~ the "Mach angle" ( P r a n d t l ~ 1913).

1905

University of Bordeaux, France

Jouguet 27s derives an expression for the entropy change in a small-amplitude shock wave in terms of the second derivative (~2v/~p2)s. Since the adiabatic curve p(v) in the pressurevolume diagram is concave down for practically all substances--i.e., this expression is always positivemJouguet concludes that a rarefaction shock is impossible. Zeldovich 279, however, theoretically showed that rarefaction shocks are indeed possible, which later was also proven experimentally by Kutateladze 2s~ at the Institute of Heat Physics, Novosibirsk.

III. Internationaler MathematikerKongref~, Heidelberg

Prandtl 2sl proposes his concept of a "boundary layer" [Grenzschicht] near the surface of a body moving through a fluid. This concept will prove extraordinarily fruitful in the development of fluid m e c h a n i c s . . During World War II, some aerodynamicists considered the removal of a part of the boundary layer air by suction through a porous surface or a number of slots to increase the laminar stability, to delay transition, and to reduce drag. 2s2 The flow in a boundary layer may likewise be laminar or turbulent, and the flow pattern and location of shock waves are dependent on the type of flow in the boundary layer. 283

Breslau University, Germany

Lummer TM publishes his shock theory [Theorie des Knalls], which, outlined only briefly by him, approaches the shock problem by using the Huygens principle of wave front propagation and referring to the Doppler principle. Lummer also first speculates on whip cracking as being a supersonic phenomenon. First successful attempts to tackle this puzzle experimentally were undertaken in France by Carri/~re (--~ 1927). 9 It seems that von Neumann (-->1942) had a similar approach of modeling shock wave propagation in mind, but obviously did not follow it up.

Humboldt Universitat, Berlin

Nernst, 2s5 an avid automobile fan and in the late 1890s the owner of one of the first automobiles in G6ttingen, indicates that the shock phenomenon of knocking [Klopfen, Schlagzandung] in reciprocating internal combustion engines might be due to the buildup of a detonation wave. 9 His correct

88

P. Krehl hypothesis later initiated a long period of international research on this important practical problem.

University of Bordeaux, France

Jouguet 286 after having studied detonation in more detail, concludes, independelty of Chapman (-+ 1899), that (i) the chemical reaction at the detonation front occurs instantaneously from unburnt into burnt gas, (ii) the detonation products propagate at constant velocity; and (iii) behind the detonation front the velocity of detonation products with respect to this front is equal to the local velocity of sound. JOUGUET correctly postulates that a detonation wave comprises a shock wave followed by a combustion wave and arrives at very similar conclusions as Chapman (thus the Chapman-Jouguet hypothesis 1899/1905). Assuming that the detonation products are at thermodynamic equilibrium and using previously measured data of heat capacities at high temperatures, Jouguet calculates the velocity of the detonation wave for various gaseous mixtures and obtains good agreement with previously measured values (Berthelot and Vielle---~ 1883; Dixon--~ 1893). 9 The Chapman-Jouguet model assumes a homogeneous layer of reaction; however, most surprisingly, later studies of detonation waves in gases rather showed complicated patterns, such as a "spin" structure (Bone, Fraser and Wheeler-+1936) or a "periodic cell" strucutre (Shchelkin and Troshin 1965).

New York City

Percy Maxim, 287 an American gunsmith, invents the first silencer for small fire arms. He founds the Maxim Silent Firearms Company and will obtain a German patent in 1910. His design is based on the modern concept of a multiple baffle arrangement, which is screwed onto the barrel. In his legendary indoor demonstrations, he proves the efficient reduction of muzzle blast. 9 However, the commercial success failed, because the interest of military circles to introduce "silent firearms" into the army was small--perhaps since in the use of common firearms the sound of explosion is also an effective physiological factor.

Cambridge Engineering School, University of Cambridge, U.K.

Hopkinson 288 repeats previous experiments of his father John Hopkinson (-~ 1872) and reconfirms that the tensile strength of metal wires is indeed much greater under rapid conditions than when measured statically. 9 This important result stimulated research on the dynamic elastic behavior of solids as well as that of shock-loaded materials, and initiated the "onedimensional finite-amplitude theory" on dynamic plasticity of metals derived by Taylor 289 (1942), von Karman zg~ (1942), and Rakhmatulin 291 (1945).

History of Shock Waves

1906

89

University of Gi~ttingen

Zemplen 292 considers an ideal gas with constant specific heat and shows that entropy changes in a shock wave: It rises with increasing pressure and falls with decreasing pressure. From this he concludes that a rarefaction shock is impossible (the Zempl~n theorem). In his paper he gives the first concise and modern definition of a shock wave: "A shock wave is a surface of discontinuity propagating in a gas at which density and velocity experience abrupt changes. One can imagine two types of shock waves: (positive) compression shocks which propagate into the direction where the density of the gas is a minimum, and (negative) rarefaction waves which propagate into the direction of maximum density."

Institut fur angewandte Mechanik, Universiti~t GOttingen

Prandt1293 obtains a first estimate of the shock front thickness for an ideal gas of constant viscosity and heat conductivity. Starting from heat conduction processes in the transition layer, he calculates for an aerial shock wave with a pressure jump of 0.2 atm a shock front thickness of 0.5 ~tm and states that "the thickness of shock layers range within the wavelengths of visible light.".

University of Bordeaux, France

Duhem 294 demonstrates that true shock waves--i.e., waves having a discontinuous front according to Riemann's and Hugoniot's theory--are only stable in perfect fluids. In real fluids, however, only "quasi shock waves" are possible.

Lehmanns Verlag, M~nchen

Foundation of the German journal Zeitschrift far das gesamte SchieJ~- und Slprengstoffwesen ( 1 . 1 9 0 6 - 3 9 . 1 9 4 4 ) with the goal to "improve and promote the communication between science and industry, and to advance the development and application of explosives and propellants." Editor-in-chief is R. Escales. 9 It was the second international journal that exclusively dedicated to the quickly growing field of explosives, ballistics and shock waves (cf. Memorial des Poudres & Salp~tres-~ 1882).

Laboratoire de la Commission des Substances Explosives, Paris

Dautriche 295 describes a simple method of measuring the detonation velocity of a test explosive. His "difference method" uses a match [cordeau] of known detonation velocity (6500m/s) placed on a lead plate, their two ends being inserted into the test cartridge at a known distance are ignited subsequently by the passage of the detonation wave in the cartridge. When the two waves in the cordeau meet, they make a sharp furrow in the lead plate that, shifted from the midpoint of cordeau, is a measure of the detonation velocity in the cartridge. For confined dynamite he measures detonation velocities ranging from 1991 to 6794 m/s, depending on the initial density of the cartridges. 9 His method much

90

P. Krehl resembles E. Mach and Sommer's interference method (---~1877), which they used to determine the propagation of velocity of explosion waves.

1907

1908

EcoleNationale des Mines, Saint-Etienne, France

Crussard 296 first applies the Rankine-Hugoniot equations (--~1887) on a reactive fluid, thereby using a graphical representation. He shows that the explosion wave is composed of a shock and a combustion wave that propagates with a velocity equal to the speed of sound in the medium that follows them, thus anticipating the supplementary Chapman-Jouguet relation (Jouguet---~ 1917).

Institut ffir angewandte Mechanik, Universitdt GOttingen

Prandt1297 resumes his previous studies (---~1904) on supersonic wave propagation of gases and steam exhausting from nozzles. The use of plane nozzles confined between two glass plates allows the visualization of wave phenomena of the free jet as well as of the nozzle interior. Schlieren photography clearly shows the formation of a shock wave inside the nozzle, indicating the need for considering area ratio distribution to obtain uniform supersonic flow.

Institutfflr angewandte Mechanik, University of GOttingen

Meyer, 298 one of Prandtl's Ph.D. students, visualizes the propagation of Mach waves inside the divergent section of a supersonic nozzle and theoretically treats the oblique interaction of shock waves. He presents shock wave tables of pressure ratios at various angles of incidence and reflection and derives the "Prandtl-Meyer function."

Podkamennaja Tunguska, Siberia, Russia

On June 30, at about 7 a.m. local time, an asteroid, impacts the Earth's surface in the Stony Tunguska, about 3400 km east of Moscow. It generates a huge blast wave, equivalent to the energy liberated by the explosion of about 107 tons of TNT and devastates an unpopulated, 720-square-mile area of forests, but does not form a crater. 299 Accounts from the town of Kansk (about 600 km south from the impact site) and from Kuriski-Popovich Village, District of Kansk state that "a first shock caused the doors, windows and votive lamp to shake, a minute later a second shock followed, accompanied by subterranean rumbling,", and "a severe earthquake and two loud bursts, like the firing of a large caliber gun, were observed in the vicinity," respectively. 9 Seismic shocks and air pressure waves were recorded as far away as Central Europe, but the fall of the meteor was not brought immediately to the notice of the scientific world, although strange barometric phenomena were recorded in England.3~176 Napier, discussing wave motion at the meeting of the British Association at Dublin in the same year, showed microbarograms of a series of waves which were taken on the day of the

History of Shock Waves

91 meteorite fall and remarked, "the succession of four undulations, commencing with a range of about five thousandths of an inch, lasting about a quarter of an hour and then violently interrupted by a sudden, though slight explosive disturbance, which set up different, and much faster oscillations for a similar interval . . . . It would seem that the disturbance, if not simultaneous at the different places, traveled faster than 100 miles per hour."

1909

University of Jena, Germany

Auerbach, 3~ reviewing the present state of the art of physical acoustics, addresses also the enormous progress achieved in supersonics since Antolik's soot experiments. Under the headings "Aeromechanics" [Aeromechanik] and "Anomalies of the Propagation Velocity" [Anomalien der Fortpflanzungsgeschwindigkeit], he discussed many most notable early contributions to gas dynamics., Subsequent handbook articles covering this rapidly growing field of compressible flows were given by Prandtl 3~ (1905), Prandtl 3~ (1913), Ackeret TM (1927), and Busemann 3~ (1931). It appears that the term gas dynamics [Gasdynamik], to some extent forming a link between thermodynamics and hydrodynamics, 3~ was first used in Ackeret's handbook article.

Pittsburgh, PA

Several severe accidents in the American coal mining industry in the previous year, partly attributed to dust explosions, result in the establishment of the U.S. Bureau of Mines. Focusing also on the nature of dust explosions, it will study over a period of 60 years the properties of hundreds of different powders.

Compagnie des Omnibus, Paris

Lorin, 3~ a French engineer, obtains a patent on a "propulsive duct" [propulseur a reaction], a compressor-less jet engine that, shortly after, he proposes for use in aeronautics. 3~ Based on the ram effect and later to be called ramjet, it derives its thrust by the addition and combustion of fuel with air compressed solely as a result of forward speed. 9 At that time, only five years after the first motor flight (Wright Bros. -~ 1903), the application of this engine type was far out of sight. The first successful application of ramjet to flight was not made until 1945, when supersonic flight was maintained by a ramjet developed by the Applied Physics Laboratory at Johns Hopkins University and associated contractors under the sponsorship of the U.S. Navy Bureau of Ordnance. A review of early ramjet developments was given by Avery. 3~ The principle of ramjet was later extended to scramjet (Billig 1959).

University of Heidelberg

Ramsauer 31~ investigates the phenomenon of percussion and shows that discrepancies with de Saint-Venant's theory

92

e Krehl (--+ 1867) are due to the nonperfect elastic behavior. He also shows that the resulting complex interaction process can be divided into a shock due to the actual collision and another (impairing) shock due to oscillation.

1910

Technische Hochschule Wien

Kobes 311 investigates the question of whether the application of shock waves could improve the performance of railway airsuction brakes, then an important practicle problem particularly on long trains to avoid overrunning by the last cars. Kobes publishes the first shock tube theory. 9 His "shock tube," [a term not yet coined until Bleakney et al. 312 (1949)] was not a laboratory-type, smooth and straight pipe, but rather consisted of a test train with 71 cars (total length 746m) with the common arrangement of brake hoses, elbows, joints, and valves. He determined an average shock wave velocity of 370m/s from the measured shock arrival time at the last car.

Militartechnische Akademie, Berlin

Bensberg and Cranz 313 provide a series of quantified drag measurements on projectiles that reveal that the drag coefficient gradually decreases after passing the sound barrier.

Royal Colonial Institute, London

Cornish, 314 publishes photographs of all kinds of wave phenomena in nature--such as the oblique interaction of hydraulic jumps in very shallow water--thereby also observing by chance Mach reflection. 9 In addition, he published propagation phenomena of snow and sand waves and waves in rivers, which apparently are barely known among modern fluid dynamicists.

Private laboratory at Terling Place, Essex, U.K.

Lord Rayleigh 315 thoroughly reviews and comments on previous theories of "sound of finite amplitudes." Starting from the Navier-Stokes equations, he investigates possible influences of heat conduction on the shape of the discontinuity. He resumes his earlier critiques (-~ 1877, --~ 1878) and states, "The problem now under discussion is closely related to one which has given rise to a serious difference of opinion. In his paper of 1848 Stokes considered the sudden transition from one constant velocity to another, and concluded that the necessary conditions for a permanent regime could be satisfied . . . . Similar conclusions were put forward by Riemann in 1860. Commenting on these results in the Theory of Sound (1878), I pointed out that, although the conditions of mass and momentum were satisfied, the condition of energy was violated, and that therefore the motion was not possible; and in republishing this paper Stokes admitted the criticism, which had indeed already been made privately

History of Shock Waves

93 by Kelvin. On the other hand, Burton and H. Weber maintain, at least to some extent, the original view . . . . Inasmuch as they ignored the question of energy, it was natural that Stokes and Riemann made no distinction between the cases where energy is gained or lost. As I understand, Weber abandons Riemann's solution for the discontinuous wave (or bore, as it is sometimes called for brevity) of rarefaction, but still maintains it for the case of the bore of condensation. No doubt there is an important distinction between the two cases; nevertheless, I fail to understand how a loss of energy can be admitted in a motion which is supposed to be the subject to the isothermal or adiabatic laws, in which no dissipative action is contemplated. In the present paper the discussion proceeds upon the supposition of a gradual transition between the two velocities or densities. It does not appear how a solution which violates mechanical principles, however rapid the transition, can become valid when the transition is supposed to become absolutely abrupt. All that I am able to admit is that under these circumstances dissipative forces (such as viscosity) that are infinitely small may be competent to produce a finite effect . . . . " He derives a simple formula to estimate the shock front thickness x, which is on the order of p/pu, where u is the velocity of the wave and/~/p is the specific gas viscosity. He writes, "For the present purpose we may take u as equal to the usual velocity of sound, i.e., 3 x 104 cm per second. For air under ordinary conditions the value of pip in C.G.S. measure is 0.13; so that x is of the order ~1 x 10 -5 cm. That the transitional layer is in fact extremely thin is proved by such photographs as those of Boys, of the aerial wave of approximate discontinuity which advances in front of a m o d e m rifle bullet; but that according to calculation this thickness should be well below the microscopic limit may well occasion surprise."

Cavendish Laboratory, Cambridge

G. I. Taylor 316 investigates the thermodynamic conditions at the shock front. He extends Lord Rayleigh's approach (---> 1910) by including not only heat conduction, but viscosity as well, and establishes theoretically that a propagating sharp transition layer of permanent type is possible only when the pressure increases across the layer and when diffusion processes operate in its interior. To obtain an estimate of the thickness of a shock wave, he set up the continuum equations for the perfect gas with constant viscosity p and heat conductivity ~ and shows that they can be solved exactly if either p - 0 or ~c = 0 and approximately if the velocity jump across the layer is relatively small.

94

P. Krehl

1911

Harvard University, Cambridge, MA

Bridgman 317 describes a gauge for the measurement of static pressures based on the electrical properties of manganin, an alloy consisting of Cu (84%), Mn (12%), and Ni (4%). The resistance of manganin is shown to be a linear function of pressure up to 12 kbar and, by extrapolation, enables pressure measurements to be made with some certitude to 20 kbar. Later he will extend 31s the linear gauge response up to 30kbar. 318 9 After World War II manganin gauges became an important diagnostic tool to measure the pressure (or stress) in shock-loaded samples (Hauver 1960).

1912

Royal Institution, London

In an evening discussion with Lord Rayleigh in the chair, B. Hopkinson 31~ reports on new fracture phenomena that occur in metal specimens when small quantities of explosive are detonated in contact with them. Using charges of guncotton placed upon steel plates, he observes that for plates with a thickness greater than 1 inch a circular disk of metal from the opposite side of the plate is broken away and thrown off; he calls this "scabbing.". This phenomenon of separation, today also called "back spalling" or the "Hopkinson effect", occurs when a strong compressive shock of short duration is reflected from the back surface of a body, thus producing a tensile wave.

1913

Point Hawkins, MD

The British cargo ship "Alum Chine", destined to transport explosives to the Panama Canal for use in blasting operations and having 285 tons of dynamite on board, explodes during loading of freight at Point Hawkins (about 6.5 km southeast of Baltimore). The disaster leaves 62 dead and 60 wounded. The explosion is felt as a blast and/or seismic shock, depending on the distance and the direction from the origin of the explosion. 9 Analyzing a large number of observations at distances ranging from 6.4 to 160km, Munroe 32~ later concluded that these differences are attributed to the acoustic phenomenon of zones of silence and the orientation of the ship at the moment of the explosion. 321 This study is important as it was the first detailed documentation on the destructive effects of a large-yield explosion.

Elektrochemisches Institut, TH, Hannover

Bodenstein, 322 studying the photochemical-induced chlorinehydrogen explosion (Gay-Lussac and Thenard--~ 1807), finds that the reaction velocity is proportional to the square of the chlorine concentration and inversely proportional to the oxygen concentration. Through the concept of a chain reaction he correctly explains this law and, simultaneously, the fact that the photochemical yield exceeds the Einstein law of equivalents by a factor of 104. The concept of atomic "chain

History of Shock Waves

95 reaction" [Kettenreaktion] will gain great importance in detonation and combustion physics. 9 In the example of a detonating chlorine-hydrogen mixture, a long-time puzzle to physicochemists [Nernst (1918): "die boshafte Chlorknallgasexplosion"], the chain reaction occurs in three steps: initiation propagation and termination. 323

Institut ff~r angewandte Mechanik, Universitat G6ttingen

PRANDTL,324 reviewing the progress of gas dynamics and supersonics, coins the term Mach angle" [Machscher Winkel].

1914

Cambridge Engineering School, University of Cambridge

B. Hopkinson 325 describes a novel and ingenious variant of the ballistic pendulum to analyze the force and time of a blow. Instead of a pendulum, he uses a long, thin steel rod of high strength (the "Hopkinson pressure bar"), divided by a transverse joint into a long and a short portion. The rod takes the blow longitudinally and transmits it as a wave of elastic compression, which proceeds from the long piece to the short one. At the extreme end of the short piece, the wave of compression is reflected back along the rod as a wave of tension. When the reflected wave reaches the joint, the short piece flies off and carries with it a fraction of the whole momentum, which depends on the length of the short piece. This enables the length of the pressure wave to be determined, and from that the duration of the blow is readily inferred. Moreover, by using a very short length for the detachable piece, the maximum pressure is also measured. He examines the blows given by a bullet striking the end of the rod normally and by the detonation of guncotton positioned at or close to one end of the rod.

1915

University of Cambridge

B. Hopkinson 326 proposes his cube-root law (the "Hopkinson law") for scaling the blast field about conventional explosive charges under sea-level conditions. He states that self-similar blast (shock) waves are produced at identical scaled distances when two explosive charges of similar geometry and the same explosive but different sizes are detonated in the same atmosphere.

1917

Private laboratory at Terling Place, Essex, U.K.

Lord Rayleigh 327 solves the problem of the collapse of a spherical empty cavity in a large mass of liquid and calculates the velocity of contraction. Introductorily he writes, "I learned from Sir C. Parsons that he also was interested in the same question in connection with cavitation behind screw-propellers, and that at his instigation Mr. S. Cook, on the basis of an investigation by Besant, had calculated the pressure devel-

96

P. Krehl oped when the collapse is suddenly arrested by impact against a rigid concentric obstacle . . . . It appears that before the cavity is closed these pressures may rise very high in the fluid near the inner boundary." To find the pressure in the interior of the fluid during the collapse, he extends Besant's calculation and shows that the final volume is extremely small when the initial pressure of the gas is only a small fraction of that of the surrounding fluid. In reality, however, the bubble undergoes isentropic compression, and a high temeprature as well as a high dynamic pressure should be reached. In the same paper he also considers the problem that the cavity contains a small amount of gas, which is isothermally compressed and converts the energy of collapse into the pressure of this imprisoned gas. (cf. also Parsons---~1884, 1897; and Cook--+ 1928). 9 Rayleigh's famous paper stimulated many subsequent researches on caivtation. The first experimental evidence of the high-pressure pulse originating from a collapsing bubble was given by Harrison (1952) using acoustic diagnostics and by Giith (1954) using optical schlieren technique. Bubble jet formation, a result of unstable, asymmetric bubble wall collapsing, was suggested by Kornfeld and Suvorov (1944) as a possible damaging mechanism in cavitation erosion. It was first experimentally confirmed by Naud~ and Ellis (1961). A review of cavitation-generated erosion phenomena was given recently by Philipp and Lauterborn. 328 Ecole

Polytechnique, Paris

1918

Mac Cook Field, Dayton, OH

Jouguet, 329 resuming previous studies on detonation (Chapman--1899; Jouguet-~1905) and referring to Crussard's graphical method (--~ 1907), assumes that the RankineHugoniot relation is not only valid to describe discontinuities (shock waves) propagating in the same fluid but also to describe two separate, chemically distinct environments (reactive waves). Jouguet explains the mechanism of detonation at constant speed by considering the detonation front as a shock wave of a special kind to which the RankineHugoniot relation can be applied by inducing in the energy balance the part due to chemical reaction (the "supplementary Chapman-Jouguet condition"). Caldwell and Fales 33~ design and build the first American high-speed wind tunnel (14-inch diameter, 200m/s) and study compressibility effects on airfoils. They note that at a "critical speed" there is a large decrease in lift coefficient accompanied by a large increase in drag coefficient.. Their wind tunnel can be seen in the USAF Museum at Dayton, OH.

History of Shock Waves

1919

97

Moscow

Tupolev organizes, together with Zhukovsky (the "Father of Russian Aviation"), the Centralized Aerohydrodynamic Institute [LIAFId]. In 1922 he will become head of the institute's design bureau.

Coll~ge de France Governmental Laboratory, France

Langevin and Chilowsky suggest the first supersonic wind tunnel using a high-speed current of air at supersonic velocity emerging from a Laval nozzle to test a new type of projectile. Hugenard and Sainte Lagu/~ carry out such experiments on a stationary high-speed current of air at velocities greater than the velocity of sound TM. Initially using a Laval working section 8cm in diameter obtain a Mach number barely above 1 (M = 1.07). Later, however, after changing the diffuser angle, they will reach Mach numbers up to 1.4. The drag is measured by a torsion balance. 332 9A British ballistic commission, paying a visit to them, initiated similar studies at the National Physical Laboratory (NPL) in Teddington. 333

U.K.

British researchers begin to study propeller tip phenomena and recognize that a propeller is a wing whose flow characteristics and, therefore, propulsion efficiency vary along the span. They observe a loss in thrust and a large increase in blade drag when the rotational speed of the blade tips approaches or even exceeds the sound velocity. Contemporary theories of the airscrew, however, are still limited to subsonic tip speeds, and even seven years later Glauert TM will write, "Little is known on the effect of the compressibility of the air on the characteristics of an aerofoil moving with high velocity and further progress, both in theory and in experiment, is necessary before the theory of the airscrew can be modified to take account of this effect." This important practical problem is rather complex and can be divided in three cases: (i) subsonic tip velocity; (ii) subsonic flight and supersonic tip velocity; and (iii) supersonic flight velocity. 9 Doppler (--, 1847) had already shown that a body moving in a circle at supersonic speed produces a rotating Mach wave. This was later investigated theoretically by Prandt1335 and experimentally by Hihon. 336 A theory of high-speed propellers, referring to all three cases mentioned above, was first worked out by Frankl. 337

1920s National

Physics Laboratory, Teddington, U.K.

Stanton 338 and coworkers set up a supersonic wind channel, probably the first in the world with a Mach number significantly above 1. The mini blow-down facility, having only a diameter of 0.8 in. but approaching M = 2, is used initially to investigate the drag, lift, and upsetting moment of projectile models of diameters not exceeding 0.09 in. Later Stanton 339

98

P. Krehl will study airfoils of various geometric configurations at supersonic speed in a more advanced, continuously driven wind channel with a 3.07-in. diameter and speeds up to M - 3.25. 9 This wind tunnel has survived and is now kept in the NPL Museum at Teddington.

1920

1921

Ecole Polytechnique, Paris

Jouguet 34~ discusses the similarity between shooting channel flow and supersonic compressible flow and suggests this analogy to study two-dimensional gas flows by means of experiments with a rectangular water channel. An extension for three-dimensional motion will be given later by Riabouchinsky 341 (1932).

France

Fauchon-Villepl~e 342 obtains a German patent on his "electromagnetic rail gun," which he invented during World War I by order of the Minist~re de l'armement et des fabrications de guerre (1916-1918). His idea was resumed after World War II by various research institutions to possibly generate ultrahigh velocities.

Mount Wilson Observatory, CA

Anderson, 343 father of scientific exploding wire research, uses exploding wires to produce temperatures in excess of the 3000~ available at that time for high temeprature spectroscopic studies. He investigates the pressure shift of spectral lines in exploding wires and concludes that the brilliant flash has an intrinsic intensity that corresponds to a temperature of about one hundred times the intrinsic brilliancy of the sun. Using a rotating mirror, he visualizes the dynamics of the flash size, apparently the emitted shock wave, and measures a speed of propagation in open air of about 3300m/s. 9 The visualization of the shock and flow field around exploding wires, a small-size phenomenon that requires optical magnification and therefore virtually increases the velocity on the film plane, requires ambitious ultrahigh-speed diagnostics 344 and was not realized until the late 1950s.

Humboldt Universit~t, Berlin

Becker 345 presents his thesis entitled Stoj~welle und Detonation for the certificate of habilitation. Published one year later, this thesis will become renowned for its clarity. His achievements can be summarized as follows: (i) To illustrate on a qualitative basis how shock waves in gases are formed, he proposes his simple "Becker piston model" which, assuming a stepwise motion of a piston in a tube and the coalescence of pressure pulses, explains on a qualitative basis how shock waves in fluids are formed; (ii) Treating the Navier-Stokes equations for non-weak shocks, he obtains the first solution involving both viscosity and heat conduction. (iii) He calculates the thickness of a shock front in air

History of Shock Waves

99 by assuming constant values for the transport coefficient and the specific heats. For air (1 bar, 0~ he finds for a shock pressure of 8 bar that the front thickness becomes already smaller than the mean free path length (about 90nm) and for strong shocks at 2000 bar even remains under the mean distance of two molecules (about 3.3 nm). He concludes that classical kinetic theory is inapplicable to very intense shock waves in gases, because in the shock front the temperature increase is the result of only a few collision processes. (iv) Starting from the Tamman equation of state, he also estimates shock wave data in liquids. For example, for a strong shock wave propagating in ethyl ether at 10 kbar the calculated shock front thickness amounts to 0.65nm which is comparable to 0.55 nm, the mean distance of two molecules. (v) He calculates the detonation velocity in gases and essentially confirms Jouguet's theory (---~1905). For liquid and solid explosives, however, similar calculations are not yet possible, because the equation of state of the hot burnt gases are still unknown.

1922

Lynn Works, General Electric Company, United States

Briggs, Hall, and Dryden 346 begin with measurements of the characteristics of wing sections at sonic and supersonic speeds, with the wing sections corresponding to tip sections of propeller blades. They do not use a wind tunnel but rather open-air jets from 2 to 12 in. in diameter, thus following Salcher's suggested principle of supersonic testing (Mach and Salcher--. 1889).

1923

University of Danzig, Germany

Ramsauer 347 studies systematically full-scale underwater explosions with charges of gun-cotton up to 2 kg fired at depths up to 30 ft in 40 ft of water and first determines the position of the gas bubble boundary. He uses an ingenious "electrolytic probe method" which consists of an arrangement of electrodes supported at suitable distances from the charge by a rigid frame and together with a common electrode forms conducting circuits with the seawater acting as an electrolyte. The bubble radius expansion, interrupting the electrode circuits successively, is recorded with a mechanical chronograph. He finds that the maximum radius rmax (M/P)1/3, with M being the mass of the explosive and P the total static pressure at the depth of the explosion. He also makes the important observation that the bubble migrates upwards. 9 His method was limited to the recording of the bubble expansion, but could not detect its oscillation which during World War II was recognized as a further source of underwater shock waves endangering submarines (--.1941). "~

100

P. Krehl

1924

SiemensSchuckert Werke, Wien

Berger 348 investigates collision phenomena in solid bodies and proves experimentally that the shocked contact surface of collision moves impulsively. This phenomenon is attributed to the rarefaction wave, which is created by reflection of the compression wave at the free surface (surface shock unloading).

1925

Harvard University, Cambridge, MA

Bridgman 349 makes first systematic measurements of the piezoresistivity of metals and recognizes the tensor nature of this effect in crystals. In the 1960s this "piezoresistive effect" will become important in solid-state shock physics as a diagnostic tool to measure the response of shock-loaded materials.

Aerodynamische Versuchsanstalt, GOttingen

Ackeret 35~ publishes his famous "two-dimensional linearized wing theory," where he considers a thin wing exposed to a uniform and parallel supersonic flow. According to his theory, the deflection of the stream causes a pressure increase at a concave corner and a pressure drop at a convex corner. Consequently, in the case of supersonic flow, a shock wave emanates from the concave corner and an expansion (rarefaction) wave from the convex corner. Both wave types had already been observed by Mach and Salcher (--+ 1887) in their pioneering supersonic ballistic experiments.

1926

PhysikalischTechnische Reichsanstalt, Berlin

Grfineisen 351 proposes an equation of state for solid matter based on his "lattice vibration theory," which he derived from previous investigations by Mie 352 and himself. 353 The so-called "Mie-Gruneisen equation" can be written as pv + G ( v ) - F(v)e, where e is the specific internal energy, v is the specific volume, F(v) is the Gruneisen coefficient for the material, and G(v) is related to the lattice potential. First applied to shock-compressed solids by Walsh, Rice, McQueen, and Yarger, 354 it proved most worthwhile to describe the thermodynamic state of shock-compressed matter.

1927

Institut Catholique de Toulouse, France

Carri/~re 355 studies the phenomenon of whip cracking, the oldest means of man to generate shock waves. He uses a machine-driven whip and high-speed schlieren photography 9 The first pictures showing the shock wave emerging from a real whip were not obtained until 1958 by Bernstein et al. at the U.S. Naval Research Laboratory. 356 More recent investigations using high-speed videography and laser stroboscopy, however, revealed that for generating strong shocks the supersonic motion of the tuft is only a conditio sine qua non, but that the essential mechanism of shock generation occurs in the final stage of acceleration and is due to the abrupt flapping of the tuft at the turning point. 3~7

History of Shock Waves

101

TH BerlinCharlottenburg

Hildebrandt, 358 investigating the nonstationary flow in long lines of railway airbrake systems, extends Kobes' shock tube theory (--~ 1910).

General Electric Company, Schenectady, NY

Langmuir, who had studied gas discharges in electron tubes with his colleagues since the early 1920s, coins the term plasma for a quasi-neutral system of ionized gas that he considers to be the fourth state of matter, consisting of neutrals, ions, and electrons. Mott-Smith, 359 a coworker of Langmuir for many years, will later remember, "We noticed the similarity of the discharge structures [between mercury vapor discharges, Geissler tubes and gas-filled thermionic tubes] they revealed. Langmuir pointed out the importance and probable wide bearing of this fact. We struggled to find a name for it. For all members of the team realized that the credit for a discovery goes not to the man who makes it, but to the man who names it . . . . We tossed around names.., but one day Langmuir came in triumphantly and said he had it. He pointed out that the 'equilibrium' part of the discharge acted as a sort of sub-stratum carrying particles of special kinds, like high-velocity electrons from thermionic filaments, molecules and ions of gas impurities. This reminds him of the way blood plasma carries around red and white corpuscles and germs . . . . So he proposed to call our 'uniform discharge' a "plasma".... Langmuir 36~ will not use the word plasma in a scientific paper until 1929. 9 Shock waves propagating in a plasma without an applied external magnetic field behave much like shock waves propagating in a neutral gas, because submicroscopic forces among the electrically charged particles can be neglected in the first order. In the case of strong shock waves, collision processes at the shock front provoke an ionization of the neutral gas particles leading to luminous phenomena (Michel-L~vy, Muraour, and Vassy-~ 1941).

Swampscott, MA

The first Symposium on Combustion is held at the 76th Meeting of the American Chemical Society with the goal "to emphasize the practical significance of combustion research, particularly in the area of high-output combustion in aviation power plants." General chairman is

1928

Brown.

Royal Aircraft Establishment, Farnborough, U.K.

Glauert 361 gives the first interpretation of Prandtrs aerodynamic theory of airfoils in England and thereupon derives a rule, the so-called "Prandtl-Glauert rule", that enables designers to calculate the amount of lift needed at high speed---up to the speed of sound but not beyond.

102

1929

P. Krehl

Parsons Marine Steam Turbine Co., Wallsendon-Tyne, U.K.

C o o k 362 reports on his investigations of the hydrodynamic properties of collapsing cavities in an incompressible fluid and his calculations of the pressures that might arise from the collapsing vortices of cavitating propellers. His studies, verified by experimental methods, convince the Committee of Erosion Research that the deterioration of propeller blades of cruisers and destroyers by erosion is indeed caused by the water-hammer effect, i.e., is resulting from cavitation, thus essentially confirming Parsons' previous hypothesis (-->1897).

Budapest

Fono, 363 a Hungarian engineer, obtains a German Patent for a propulsive device. Furnishing a design for a convergentdivergent inlet, he describes its use specifically for supersonic flight. ~ His engine is clearly recognizable as a prototype of today's ramjet.

KaiserWilhelmInstitut fur StrOmungsforschung, GOttingen

Prandtl and Busemann 364 develop a graphical method based on the method of characteristics to approximately determine smooth supersonic flows at arbitrary initial and boundary conditions. Their method replaces the stationary two-dimensional supersonic potential flow by a crossing system of stationary sound waves. 9 Busemann later mentioned that Prandtl had already used a primitive form of the characteristics method as early as 1906 to shape the exit of his Laval nozzles for parallel supersonic jets. 365

ETH Zurich & Escher Wyss AG, Zf~rich

Ackeret 366 delivers his inaugural lecture [Privatdozent], thereby coining the term Mach number [Machsche Zahl] with the argument "since the well-known physicist E. Mach clearly recognized the fundamental significance of this ratio in our field and confirmed it by clever experimental methods." 9 The term Mach number denotes the ratio of the velocity of a body or disturbance to the velocity of sound and was introduced into the English literature in the late 1930s. However, it was not immediately accepted by the Russians, who at one time preferred Bairstow 367 number, or the French, who proposed Moisson 368 number 369 (-~Moisson 1883). Nowadays Mach's name is used by almost anyone describing something that is very fast. In fact, Mach is more known for this than for his numerous contributions to the philosophy of science.

University of Cambridge

G. I. Taylor 37~ investigates long gravity waves in the atmosphere. These waves can result from extraordinary strong blast waves, such as those observed during the huge volcanic eruption of Krakatao (--~ 1883) that traveled at great height with a velocity of about 320m/s around the Earth. Taylor's

History of Shock Waves

103 results, presented at the 4th Pacific Science Congress in Java, show good agreement with recorded data of 1883.

Institut fiir Technische Physik, Berlin

Cranz and Schardin 371 invent the "Cranz-Schardin multiple spark camera," the prototype of which provides 8 frames of excellent quality at a maximum frame rate of 3 x 105 frames per second. They immediately apply the camera to record head waves and the oblique interaction of shock waves (Mach reflection). They also investigate the well-known phenomenon of why an implosion is always accompanied by a sharp report and show that it is not caused by the rarefaction wave itself but rather by the blast wave created shortly after the implosion. They demonstrate this phenomenon by using a 34-m-long evacuated tube that they suddenly open at one end. The air masses, then rushing in violently and being reflected at the other end of the tube, return to the open end of the tube after about 0.2 s, thereby perceptible as a report. Zornig from the United States, later becoming Colonel of the U.S. Army and involved in the Manhattan Project (---~1943), apparently discusses with Schardin the historic soot recording experiments of irregular shock reflection (Mach and Wosyka---~1875), their possible interpretation, and related problems of nonacoustic reflection of air shocks. 372 9 This subject became important for selecting the optimum height of burst (von Neumann---~1943, 1945) of the two nuclear explosions in Japan (---~1945).

1930

Mount Wilson Observatory, Pasadena, CA

Hubble 373 publishes a plot of the "Doppler shift" of light versus distance for 22 galaxies and reports that all distant galaxies recede from us and more distant galaxies recede faster (Hubble's l a w ) . . Two years later, after having compiled more data on velocities of nebulae, he stated 374 (together with Humason), "The relation [between radial velocity and distance] is a linear increase in the velocity amounting to about +500km/sec per million parsecs of distance." This simple statement had an enormous impact on cosmology: It suggested the idea that the expanding universe may have its origin in a huge explosion (the Big Bang theory). Estimates on the age of the universe range from 10 to 20 billion years.

Maschinenund Apparatebau Mfinchen

Schmidt, stimulated by previous works of the Frenchmen de Karavodin (1906-1909) and Marconnet (1909), develops his "Schmidt tube" [Schmidtrohr], a pulse jet engine, and obtains German and British patents. 375 Using a tube resonator with a length of about 3.6 m, a valve matrix at the entrance and a

104

P. Krehl Laval nozzle at the exit, it applies the reflected shock wave for periodical reignition (at about 50 Hz). 9 Further developed in Berlin by the Argus Motoren GmbH [Argus-Schmidtrohr], it served in World War II to power the V-l, the world's first cruise missile ( M - 0.47),

1931

Applied Mechanics Division, University of Michigan, Ann Arbor, MI

Donnel1376 studies longitudinal shock wave transmission in solid bodies when impacted and the dimensions are no longer very small compared to the velocities of such waves. He theoretically treats various cases of practical importance, such as the impact of thin bars with free or fixed ends, effects of a sudden change in the cross section or material of a bar, and waves due to a force applied at an intermediate section.

Television Laboratories Inc., San Francisco, CA

Farnsworth 377 suggests the continuous dynode "electron multiplier.". This simple but most effective and versatile device led in the 1960s to the development of the microchannel plate (MCP) at Bendix Research Laboratories. Its outstanding features, such as high intensification and fast shuttering, allowed CCD cameras to be used in the 1990s at ultrashort exposure times down to only a few nanoseconds (intensified CCD or ICCD), an important requirement for applications to shock wave recording in solids and hightemperature plasmas. In addition, MCPs provided trace intensity multiplication of about 1000 times, which allowed single-sweep viewing up to the oscilloscope's rise-time specification at bandwidths of as much as 1 GHz.

Harvard University, Cambridge, MA

Bridgman publishes his book The Physics of High Pressures, which will earn him the Nobel Prize in physics in 1946. Although exclusively dealing with static pressure phenomena, his book will stimulate following generations of solid-state shock physicists to study also the dynamic properties of materials beyond pressures not accessible by static compression techniques.

Imperial College, London

Chapman and Ferraro 378 suggest that the "sudden commencement" impulse coming from the sun is the front of a plasma cloud emitted from the sun and hitting the Earth's magnetic field. Their hypothesis will lead to the discovery of planetary shock waves by Gold 379 and planetary bow waves by Axford 38~ and Kellog. 3sl

School of Aeronautical Engineering, University of Rome

General Gaetano A. Crocco, 382 a former pioneer of Italian aviation and director of research of the Italian Air Force, coins the term aerothermodynamics, a combination of fluid mechanics and thermodynamics, to take account of aerodynamic heating at supersonic speeds that at this time are only

History of Shock Waves

105 reached by the propeller tips of high-speed aircraft. 9 This particular branch of super/hypersonic flow, later introduced and propagated by yon I~rman, 383 still is a serious problem in the design of high-speed air- and spacecraft, because one has to meet with the reduction of materials strength at elevated temperatures, which already begins at rather low Mach numbers. For the example of the Soviet SST Tu-144 (1968), it was observed that, when it flew for hours at Mach 2, air friction heated up the airframe over 300~ (150~ above the surrounding air with heat concentrations on the nose and leading edges of the wings. TM

1932

Zeiss-Ikon AG, Dresden

Joachim and Illgen 385 measure the gas pressure of rifles by using their "piezo-indicator," an instrument consisting of a piezo-crystal, an amplifier, and an oscilloscope with a cathode ray tube. Time sweeping occurs with a rotating drum covered with photo paper. Being the archetype of modern shock pressure recording techniques, it allows for the first time the recording of pressure-time profiles with a high temporal resolution.

Institut far Technische Physik, Berlin

Schardin 386 investigates theoretically the shock propagation in tubes and the condition for ignition of hydrogen-oxygen mixtures by incident and reflected shocks. His work, together with that of Kobes (-~ 1910) and Hildebrand (--~ 1927), form the basis of modern shock tube theory.

Milan, Italy

G. A. Crocco 387 reads a paper at the 20th Meeting of the Italian Association for the Advancement of Science that discusses future possibilities of superaviation, i.e., flight at very high altitudes (above 37,000 feet) up to about M = 3. He addresses the particular problems of high-speed flights in the stratosphere--such as lift and propulsion--and illustrates the economic efficiency.

Flugwissenschaftliches Institut, TH BerlinCharlottenburg

Wagner 388 studies the fundamental processes of percussion and gliding when a body at high speed hits the free surface of a fluid. 9 The water impact of a body under a small angle of incidence leads to a periodic bouncing along the surface, which can easily be demonstrated by throwing a small stone on a pond's surface under a low angle. This phenomenon, called ricocheting, had already attracted some early percussion pioneers, such as Marci (1639) who explained this effect by the law of reflection [De proportione motus, Propositio XXXX]. The skipping effect to which seaplanes are subject when they land on water is of great practical importance for the float construction and was tackled also in the United States 389 and the Soviet Union. 39~

106

1933

P. Krehl

Guggenheim Aeronautical Laboratory at CalTech, Pasadena, CA

Von K,4rm/m and Moore 391 perform a pioneering study on the resistance of slender, spindle-like bodies (such as projectiles) at supersonic speed. Their study takes into account a new type of drag (wave drag) that occurs when the body approaches the sound velocity. Later their study will be generally considered as the starting point of supersonic aerodynamics. ,, In the following year Taylor and Maccol1392 extended the study to the more general case of axisymmetric cones having any semivertical angle that is less than a certain critical angle under which the shock wave detaches from the body (Mach angle). For narrow cones both methods showed consistency.

Cavendish Laboratory, Cambridge

G. I. Taylor 393 calculates the forces on a thin biconvex airfoil moving at supersonic speed and compares his result with Stanton's drag data obtained in the wind tunnel at NPL, Teddington (Stanton-+ 1920s).

Langley Aeronautical Laboratory of NACA, Hampton, VA

Stack and Jacobs first photograph the transonic flow field over airfoils at speeds above the critical Mach number. They use the schlieren technique and correlate their flow analysis with detailed pressure measurements. 394 9 In 1951 Stack and his colleagues were awarded the prestigious Collier Trophy for their pioneering transonic wind tunnel work.

Institut ff~r Aerodynamik, ETH Zf~rich

Ackeret 395 operates the world's first continuous-flow supersonic wind tunnel with a closed loop using a kaval nozzle (M = 2; 40 x 40 cm2). It is anticipated not only for the testing of model aircraft but for use in ballistic research, and steam and gas turbine design as well. He designed the facility when he was still working at Brown-Boveri Company, which also built the device.

British Museum of Natural History, London

Spencer, 396 keeper of minerals, summarizes the available information on meteorite craters and cites five craters or crater clusters with associated meteoritic material: the Arizona Meteor Crater, the Odessa Crater of Texas, the Henbury craters of Australia, the Wahar craters of Arabia, and the Campo del Cielo craters of Argentina. 9 Since 1931 various authors have appealed to the impact and explosion of meteorites to account for the Ries and Steinheim basins of Germany, the Ashani Crater of the African Gold Coast, the K6fels Crater of the Tyrolian Alps, and the Pretoria Salt-Pan of South Africa. Most contemporary theoreticians, however, still favored some form of cryptovolcanic hypothesis, maintaining that the explosions were due to expansion of gases associated with ascending magmas.

University of Cincinnati, OH

Bucher 397 discovers in a large quarry, about two miles east of Kentland [Newton County, Indiana] curious striated cup-and-

History of Shock Waves

107 cone structures, so-called "shatter cones," with apical angles ranging from 75 to nearly 90 degrees, and as long as 2 meters in limestone and 12 meters in shale. Considering these unusual "cryptovolcanic structures" (Branca and Fraas 1905) as disturbances in deranged Paleozoic beds, he ascribes their origin to a deep-seated explosion of gases derived from an igneous intrusion.

1934

Institute of Chemical Physics of the Soviet Union, Leningrad

Semenov 398 publishes his monograph Chain Reactions, which contains the development of a theory of nonbranching chain reactions. It is the result of previous discoveries that he and his team made on the basis of the study of critical phenomenamsuch as the limit of ignition--during oxidation of vapors of phosphorus, hydrogen, carbon monoxide, and other compounds. He writes, "In 1927 and 1928 in Oxford, Leningrad and partly at Princeton the chain theory was applied to a study of the reactions leading to inflammation and explosion. What is particularly important, the theory has advanced here hand in hand with new experiments, which led to a discovery of new and the explanation of old, long ago forgotten, and quite unintelligible phenomena, and they have outlined the field of those reactions which are specific in the new conception. They have aroused a broad interest in this new reaction field and have brought to life in 1930, 1931, 1932, and 1933 a wave of new kinetical investigation . . . . It is hoped that the analysis given here will enable us to make some new generalization and thus to advance somewhat further in the question of the classification of reactions and of finding new laws common to wide classes of chemical change." J His thorough and continuous investigations earned him the 1956 Nobel Prize in chemistry which he shared with the British Hinshelwood.

Lehrstuhl fur Luftfahrttechnik, TH Aachen

The first German supersonic wind tunnel 399 is installed at Wieselsberger's institute under the leadership of R. Hermann. The Laval nozzle is covered with a layer of plaster of Paris, which ensures a sufficient surface smoothness and is easier to form than wood or metal. The ideal nozzle geometry was determined graphically using the method of characteristics. The 10 • 10 cm 2 wind tunnel can be operated up to M = 3 and will be used in 1936 to test models of the liquidpropellant rocket A-3 (short for Aggregat 3), the forerunner of the V-2 (Peenem~nde -~ 1942).

Mt. Wilson Observatory and CalTech, Pasadena, CA

Only 18 months after Chadwick's discovery of the neutron in England, Baade and Zwicky 4~176 connect supernova explosions to the formation of neutron stars, stating, "With all reserve, we advance the view that a supernova represents the transition

108

e Krehl of an ordinary star into a neutron star." 9 The first observational evidence was given 33 years later with the discovery of a rapidly rotating magnetic neutron star, a so-called "pulsar," in the center of the Crab Nebula, which is a remnant of an explosion seen by the Chinese (1054). Further evidence was given by the spectacular event 4~ of the Supernova 1987a.

1935

Institute of Physics, U.S.S.R. Academy of Sciences

(2erenkov, 4~ then a postgraduate student, observes that radiation of blue light is emitted when an energetic charged particle passes through a transparent nonconductive material at a velocity greater than the velocity of light within the m a t e r i a l . . Later Tamm and Frank (1937) theoretically treated this "Cerenkov effect" and concluded that velocity phenomena, similar to a head wave in supersonic aerodynamics, exist also in the micro cosmos when an energetic particle moves through a medium at a velocity greater than the phase velocity of light in this medium. For this unique discovery and interpretation, the three Soviet scientists earned together the 1958 Nobel Prize in physics. 4~

Services des Poudres, France

Michel-L~vy and Muraour 4~ study the interaction of a single shock wave generated by an explosive with a solid boundary or of two shock waves generated by two simultaneously fired explosives and observe in both cases an intense luminosity. This effect is also observed when a shock wave is reflected from a very light obstacle, such as cigarette paper. They give a correct interpretation that the luminosity is solely attributed to the shock wave itself and not to any phenomena due to the explosion processmfor example by the emission of burnt particle--thus rejecting a previous hypothesis (Siersch-+ 1896).

5th Volta Conference, Rome

G. A. Crocco is president of this international meeting with the topic High Velocity in Aviation. It is the first time that leading supersonic aerodynamic engineers from around the world discuss together the possibilities of supersonic flight. Shortly afterward, however, some nations, starting with Germany and Italy, will classify this topic because of its military relevance. Busemann 4~ extends the existing linear airfoil theory to include terms of higher orders. In his famous concept of "sweepback wings," he predicts that his "arrow wings," with a geometry such that they remain within the shock cone at supersonic speed, would have less drag than straight wings exposed to the head wave (a shock wave). However, since propeller-driven aircraft of the 1930s still lack the ability to enter supersonics, his idea cannot be realized immediately, but will influence most future high-speed aircraft designs. Prandtl 4~ reports on strange shock-like

History of Shock Waves

109 phenomena that he has observed in his supersonic nozzle. Wiese|sberger first suggests that this phenomenon, later named condensation shock, might be caused by condensed water vapor when using atmospheric (moist) air. 4~ Studies by Oswatitsch 4~ and Hermann 4~ will prove that this supposition is indeed correct. Ackeret 41~ discusses the supersonic wind tunnel he has just completed for the Italians at Guidonia. Von K , q r m a n 411 presents a new theory of supersonic flow from the viewpoint of drag.

1936

Princeton University, NJ

Wigner and Huntington 412 suggest that insulating diatomic molecular solid hydrogen, subjected to very high pressures, might transform into a metallic monatomic solid phase, and estimate a pressure of transition to be not less than 250 kbar. 9 Their hypothesis stimulated numerous static and dynamic high-pressure studies. An experimental evidence for the existence of "metallic hydrogen" would be important not only fundamentally in condensed matter physics and astrophysics, but also technologically for possibly producing a high-temperature superconductor. 413

School of Aeronautical Engineering, University of Rome

Luigi C r o c c o 414 publishes a fundamental theoretical study on the relative merits of different types of supersonic wind tunnels. Later von Karm~in referred to this review article as the "bible of supersonic wind tunnels."

Chair of Chemical Technology, Imperial College of Science & Technology, London

Bone, Fraser, and Wheeler 415 study "spin detonation" in a moist 2CO + 0 2 medium and use a high-speed rotating mirror camera to measure the flame speed of detonation phenomena in tubes. They observe a periodic structure in the detonation wave and come to the following important conclusion: "A new view of the detonation-wave in gaseous explosions is advanced. For it can no longer be regarded as simply a homogeneous 'shock wave,' in which an abrupt change in pressure in the vicinity of the wave-front is maintained by the adiabatic combustion of the explosive medium through which it is propagated; but it must now be viewed as a more or less stable association, or coalescence, of two separate and separable components, namely of an intensively radiating flame-front with an invisible shock wave immediately ahead of it; and whether persistent 'spin' is developed or not depends upon the stability or otherwise of their association . . . . " 9 Their observations stimulated other researchers who, although coming to a different explanation of the origin of the periodic phenomena, essentially confirmed the inhomogeneity of the detonation front.

110

1937

1938

P. Krehl

Supersonic Wind Tunnel Division, Institute of Aerodynamics, TH Aachen

Hermann, Wieselsberger's assistant at the supersonic wind tunnel facility (M -- 3.3, working section 10 x 10 cm2), performs aerodynamic tests on models of the A-3 rocket, the first large liquid-fuel rocket (length 6.74m, weight 740kg) and antecedent of the A-4, later renamed V-2 (Peenemfinde--~ 1942). 416 By increasing the length of the tail unit he verifies a stable flight even at high Mach numbers. 9 In the following year plans were worked out "to build an aerodynamic-ballistic research institute, capable of furnishing all aerodynamic, stability, aerodynamic control, and heat transfer data needed for the development of numerous projects, such as supersonic projectiles (fired from guns), rocket-powered vehicles without wings, stabilized by fins (called missiles) and rocket-powered supersonic vehicles with wings and fin-assemblies or with delta wings. ''417

Safety in Mines Research Board, Sheffield, U.K.

Payman and Shepherd 418 rediscover the shock tube (although this term was not yet coined) as a powerful tool to study combustion processes in air-methane mixtures and to clarify whether a shock wave alone could start an explosion in a firedamp/air atmosphere.

5&ool of Aeronautical Engineering, University of Rome

L. Crocco 419 investigates fluids in chemical equilibrium and, combining the entropy equation with the momentum equation, obtains a relation between flow velocity V, vorticity V x V, and thermodynamic properties. The "Crocco equation" contains the important result that a vortex-free flow behaves isentropically in the whole flowfield. 9 His equation was later extended by Vazsonyi 42~ to take into account fluid viscosity and became known as the "Crocco-Vazsonyi equation."

General Electric Company, Schenectady, NY

Tonks, 421 studying high-current-density phenomena in lowpressure arcs, coins the designation "pinch effect.". In the dynamic pinch, the radius of the plasma column decreases with time and the cylindrical current shell moves inward, thus acting like a magnetic piston and sweeping up all of the charged particles it encounters (the snowplow concept). The pinch effect is mostly used to compress gaseous matter. Bless, 422 however, using pinched hollow metal conductors, first demonstrated the suitability of the pinch method for shock compression of solid miniature specimens as well.

Luftkriegsakademie Berlin-Gatow

O. von Schmidt 423 treats wave propagation at the boundary between two media of different wave speeds. He observes that any wave that enters a material with a higher wave propagation velocity produces a "von Schmidt head wave" [von Schmidt'sche Kopfwelle] in the material with the lower propagation velocity that appears similar to a head wave produced

History of Shock Waves

111 by a supersonic bullet. Other wave types in solids, such as transversal and bending waves, can produce head waves under different angles as well. The von Schmidt head wave, however, is a pseudo-supersonic phenomenon, independent of the presence of any shock waves and observable also with sound wave. Nevertheless, it is of great importance for seismology. 424

Southern Methodist University, Dallas, TX

Boon and Albritton 425 show that geologic structures of the Kentland type ("shatter cones", Bucher--+1933) are the product of a meteorite impact. According to their theory, high-velocity impact~many times faster than the velocity of a shock wave in any type of rock--compressed the rocks elastically, rather than deforming them plastically, after which they were "backfired" into a damped-wave disturbance. They assumed that the shatter-cones, typically pointing toward the impinging body, were formed during the initial or compressional stage of such a meteorite i m p a c t . . Later Dietz 426 suggested shatter cones as useful field criteria ("index fossil") for shock-wave fracturing in the geological past, thus constituting presumptive evidence for astroblemes-ancient meteorite impact scars.

U.S.S.R.

Belajev 427 first applies an exploding wire to produce detonation in nitrogen chloride and nitroglycerine. Subsequently Johnston 428 in the United States found that the shock wave, generated by an exploding wire, could also produce detonation in PETN (pentaerythritol tetranitrate), a less sensitive explosive in which detonation cannot normally be effected by a heated wire. This important discovery allowed one to replace the pill of primary explosive in the conventional detonator (Nobel---, 1863) with a secondary explosive, thus substantially reducing the handling hazards. The "safety detonator" became a much-applied device in missile and space vehicle technology, where exploding bridge-wire detonatorsmsuch as in state separators, cable cutters, and explosive bolts--are widely used. Another great advantage is the reduction in the time delay from milliseconds to microseconds, which allows an exact synchronization.

S iemens- Werke Berlin; Research Laboratory, General Electric Company, Schenectady, NY

The flash X-ray technique--the generation of high intensity X-ray pulses of microsecond durationmis introduced. Steenbeck, 429 who invented the method the year before at the Siemens-werke Berlin, uses a capacitor discharge through a mercury-vapor-filled capillary discharge tube, which provides a small focus. He immediately recognizes flash radiography as an outstanding diagnostic tool to stop motion of projectiles in

112

p. Krehl flight, shock waves in optically nontransparent media, and self-luminous events such as detonation waves. In the same year this new method is applied to make flash radiographs of detonating hemisphere-shaped charges (Thomanek-+ 1938). Kingdon and Tanis 43~ in the United States independently generate flash X-rays by using a different diode type to study mutation effects in biological samples.

Luftkriegsakademie Berlin-Gatow

Thomanek 431 discovers the importance of the cavity liner and documents the "shaped charge lined cavity effect." He started his studies on Schardin's hypothesis that the cavity effect might be caused by the Mach effect (Mach and Wosyka--+ 1875). Thomanek's first liner material is the glass recipient used in experiments to evacuate the cavity. His colleague Thomer 432 visualizes for the first time the jet formation by using the recently developed flash radiography technique (Steenbeck -+ 1938). This method allows the study of the collapse of the liner without the interference of smoke and flame associated with the explosion. 9 After World War II, the Swiss Mohaupt 433 claimed in an article to have already discovered the lined cavity effect as early as 1935.

Institut fiir Aerodynamik, ETH Zfirich

Preiswerk 434 investigates the applicability and limitations of the analogy between a two-dimensional shock wave and a hydraulic jump (i.e., a horizontal water flow at low depths and with a free surface). With examples of a hydraulic jump propagating through a plane Laval nozzle or being reflected obliquely at a solid boundary, he notices that with increasing strength of the hydraulic jump the water flow measurements increasingly deviate from the gas dynamic solution. 9 At this time this analogy was of particular interest because it would have allowed the replacement of expensive highspeed diagnostics--such as are required in the case of shock wave diagnostics--by relatively simple water-table installations.

KaiserWilhelmInstitut far Chemie, Berlin

Hahn and Strassmann 435 perform the first artificial nuclear fission of uranium using neutrons. They cautiously annotate that their results (published Jan. 6, 1939) "are in opposition to all the phenomena observed up to the present in nuclear physics.",, In the following year, their colleague Fl~igge436 first estimated the released energy of the uranium fission process and stated that one cubic meter of uranium oxide (corresponding to approximately 4.2 tons of pitchblende) contains sufficient fission energy to cover the consumption of electric energy of central Germany for a period of 11 years. He also speculated on the huge quantity of explosive energy

History of Shock Waves

113 that could be released artificially by nuclear fission within milliseconds. In nature, however, this event is quite unlikely because the concentration of uranium, even in highly enriched deposits, is far too low to maintain a chain reaction. Shortly thereafter, he states 437 in a Berlin newspaper that the fission energy of about 4 tons of uranium oxide would be sufficient "to throw the water mass of Lake Wannsee [a renowned lake in the Southwest of Berlin with a length of about 3 km] into the stratosphere." Given in a popular-science manner, it is the earliest example of illustrating the huge amount of energy that could be released explosively by nuclear fission. Less than six years later it will be realized in the first American atomic bomb. It is interesting here to note that in the same year when FLOGGE published his estimations, Zeldovich and Khariton delivered a report on this topic at a seminar held at the Leningrad Physico-Technical Institute, in which they elucidated the conditions for a nuclear explosion and estimated its destructive force. 438 Later they both contributed mainly to the developmenht of the first Soviet atomic bomb (1949).

1939

Heeresversuchsanstalt Peenemfinde, Baltic Sea, Germany

The world's most advanced supersonic wind tunnel is installed under the leadership of R. Hermann. It is a blowdown-to-vacuum complex (M----4.4, later extended to 5.3; working section 4 0 • 4 0 c m 2) with a three-component balance for measuring drag, lift, and pitching moment. Its main task will be the aerodynamic optimization of the rockets A-4, A-5, and the guided missile Wasserfall. Aerodynamic characteristics of these models, such as drag and lift, can be measured using an electromagnetic balance. Operation above M = 5, however, reveals that condensation effects of the air become significant and impair visualization. This discovery eventually will led to the installation of the first dryer system to take moisture out of the air before it enters the nozzle. 9 After the war the famous Peenem(inde wind tunnel was confiscated by the U.S. Army, dismantled and shipped to the Naval Ordnance Laboratory (NOL) at White Oak, MD. Later the facility was operated by the Naval Surface Warfare Center (NSWC), now defunct.

Heinkel Factory, Warnemfinde

The first successful flight of the Heinkel He-178 occurs (max. velocity 700 kin/h), the world's first turbojet aircraft which leads to an aviation revolution. It was designed by Pabst von Ohain, a graduate from the University of GOttingen.

114

P. Krehl

Aerodynamische Versuchsanstalt GOttingen

The first measurements are carried out on sweepback wings in a high-speed tunnel (cross section 11 • 11 cm 2) at velocities close to the sound velocity, thus following suggestions made by Busemann (--+ 1935) and Betz. 439 These studies were not published until after World War II and caused considerable sensation among foreign aerodynamic experts. 44~

1940

New York City

The Manhattan Project--code name for the U.S. effort during World War II to produce the atomic bomb--is initiated. 441 The initially slow-growing project was named after the Manhattan Engineer District of the U.S. Army Corps of Engineers, because much of the research was done in New York City. 442 O n April 1943 Serber, one of Oppenheimer's assistants, defines the goal more specifically: "The object of the project is to produce a practical military weapon in the form of a bomb in which the energy is released by a fast neutron chain reaction in one or more of the materials to show nuclear fission.",, The project had an enormous impact on the further evolution of shock wave physics and detonics. It led to the installation of a large number of special laboratories and test sites, operated by both governmental agencies, private research organizations and universities.

1940

United States

Von Form~in and Dryden, both on a business trip to Washington DC, discuss shock phenomena in planes that occurred at transonic speeds. In his memoirs von Karman 443 writes, "We talked about the phenomenon and decided that if we invented a word, it had to be something between subsonic and supersonic to indicate that the body travels 'through' the speed of sound and back. We chose 'trans-sonic'. However, there was an argument as to whether to spell it with one s or with two s's. My choice was one s. Dr. Dryden favored two s's ..... We agreed on the illogical single s and thus it has remained. Incidentally, I used this new expression in a report to Wright Field. Although we just made up the word, nobody asked me what it meant. They just accepted transonic as if it had always belonged to the language . . . . " . The transonic regime was then of great practical importance because pilots of the Lockheed P-38 reported that around Mach 0.8 their aircraft was shaken wildly and lost equilibrium. At high flight speed, the air moved over certain parts of the wing and tail at a speed greater than the speed of the plane because of the curvature of these sections. This phenomenon created shock waves that, dancing forward and back, caused dangerous vibrations of the skin structure (shock stall). In 1941 a Lockheed test pilot died when shock waves from the plane's wings

History of Shock Waves

115 created turbulence that tore away the horizontal stabilizer, sending the plane into a fatal plunge.

1941

Safety in Mines Research Establishment, Sheffield, U.K.

Payman and Shepherd 444 continue their shock tube combustion studies (---,1937) and make schlieren pictures of the shock wave with different driver gases. They notice that hydrogen as a driver gas results in higher shock pressures in the test chamber.

Institute of Chemical Physics, Leningrad [now Petersburg]

Zeldovich 445 presents his steady detonation model, assuming that a nonreactive shock wave is the leading element in the detonation, followed by a reaction zone in which detonation is initiated and completed, thereafter followed by the nonreactive flow. 9 Shortly thereafter the same idea was worked out independently by von Neumann 446 in the United States and by D6ring 447 in Germany, and is known today as the

Messerschmitt AG, Augsburg

Zeldovich-von-Neumann-DOring (ZND) theory. The Messerschmitt Me-262 becomes the world's first sweepback jet fighter. It is the fastest aircraft of that time (870 k m / h at an altitude of 6100m). Prior to this, the usefulness of sweepback wings was first proven at the Messerschmitt Company by wind tunnel tests. 448 9 In the same year the Me-163, a rocket plane that already approached the deltawing geometry, made its maiden flight (M = 0.84). At the end of the war, the plane was built with a 45 ~ sweepback in its wings.

Services des Poudres, France

Michel-Levy, Muraour, and Vassy 449 study luminous phenomena in various gases behind the shock front. They generate strong shock waves by head-on collision of shock waves emitted by explosives, and in argon they observe an intense light emission that increases toward the ultraviolet.

Abteilung fur Technische Physik & Ballistik, Luftkriesakademie Berlin-Gatow

Schardin 45~ first suggests the possibility that phase transformations might be induced by shock waves (shock-induced freezing). He fired bullets into a tank filled with carbon tetrachloride and water at speeds varying from 800 to 1800m/s and photographed the process. He found the region surrounding the bullet to be opaque in tetrachloride at 1200m/s and in water at 1800m/s, whereas water remained transparent at 800m/s.

Cavendish Laboratory, Cambridge

G. I. Taylor TM assumes a high-intensity point explosion and calculates the propagation law of the blast wave. 9 His results, then of greatest military importance and top secret, were not published in the open literature until 1950. At the beginning of his paper he stated, "This paper was written early in 1941 and circulated to the Civil Defense Research Committee of the Ministry of Home Security in June of that year. The present

116

e. Krehl writer had been told that it might be possible to produce a bomb in which a very large amount of energy would be released by nuclear fission--the name atomic bomb had not been used---and the work here described represents his first attempt to form an idea of what mechanical effects might be expected if such an explosion could occur. In the thencommon explosive bomb mechanical effects were produced by the sudden generation of a large amount of gas at a high temperature in a confined space. The practical question which required an answer was: Would similar effects be produced if energy could be released in a highly concentrated form unaccompanied by the generation of gas? This paper has now been declassified, and though it has been superseded by more complete calculations, it seems appropriate to publish it as it was first written, without alterations . . . . " He found that only for a point explosion with an instantaneous energy release (the ideal case) the shock wave moves with a steady speed (D = const), analogous to the case of a plane detonation, but that the pressure p with increasing distance r very rapidly decreases (p "- 1/r3). Independently from Taylor, an analogous solution for a point explosion was also obtained in the Soviet Union by Sedov. 452 The corresponding cylindrical problem was solved by Lin, 453 (1954), he obtained similar results (D = const, but p "~ l/r2).

1941

David W. Taylor Model Basin, Carderock Division, MD

[now NSWCCD]; ChemischPhysikalische Versuchsanstalt der Kriegsmarine, Kiel

Studies in the United States 454 and Germany 455 are initiated to study the oscillation of the gas globe ("bubble") of an underwater explosion, beginning on a laboratory-scale using Edgerton-stroboscopy and high-speed cinematography, respectively. The experimental investigations stimulate theoretical studies in the United States and England on the bubble motion and shock wave generation, leading throughout the war to a wealth of new data on underwater shock wave propagation and interaction phenomena with boundary surfaces (published in 1950 as UNDEX Reports). Berthe and Kirkwood 456 will demonstrate that after reaching the rebound point in bubble dynamics, a shock wave is emitted into the surrounding liquid, thus essentially confirming the photography studies. 9 Early investigations of an explosion from a single charge had revealed that the main shock is followed by a second large pulse and further small ones (Blochmann --~ 1898). Probably not later than in submarine warfare of WWI this phenomenon was recognized as a particular threat to a submarine's hull. Campbell 457 appropriately wrote in his report, "For some time, submarine personnel have noticed that more than one impact results from a single nearby

History of Shock Waves

11 7 underwater explosion, such as a depth charge. Successive shocks were noted, and it was believed that the intensity and the time between blows decreased with each successive blow. Motion pictures of the action of floating models subjected to underwater explosions corroborated this impression."

1942

Heeresver-

suchsanstalt Peenemfinde, Germany

On October 3 the rocket A-4 (later named V-2) covers a range of 191 km and reaches a record height of 84.5 km, thus being the first man-made vehicle to penetrate into space. 458 The missile has a total length of almost 14 meters and was capable of transporting a payload of 750 kg with a velocity of up to Mach 4.

LASL, Los Alamos, NM

The Los Alamos Scientific Laboratory (LASL) is established by the U.S. government to centralize nuclear bomb research and development for the Manhattan Project (---~1940s), which had hitherto been performed at the Universities of Chicago, Cornell, Minnesota, Purdue, Stanford and Wisconsin, and the Carnegie Institution of Washington. 459

Institut far Gasdynamik, LFA, Braunschweig

Guderley, 46~ treating the implosion of cylindrical and spherical shock waves mathematically, predicts infinite shock strengths at the implosion center. Real gas effects, however, furnish a natural limit to these theoretical singularities.

Institute for Advanced Study, Princeton, NJ

Von Neumann speculates on a method to find an equivalent Huygens principle for waves of finite amplitude (shock waves). 461 9 Unfortunately, details of this interesting approach have not been passed onto us.

Dept. of Physics, Cornell University, Ithaca, NY

Bethe 462 calculates the stability of shock waves for an arbitrary equation of state and deals with the case when a phase transition is induced by the shock, at that time a phenomenon thought to be possible in strong underwater explosions. In his introduction he circumscribes the goal of his study: "The theory of shock waves thus far has been developed mainly for ideal gases. Even for these, the question of stability of shock waves has received little attention. Recently, the problem of shock waves in water has gained much practical importance. Therefore, it seems worthwhile to investigate the properties of shock waves under conditions as general as possible . . . . " He treats the Hugoniot curve H(v, s) in terms of volume per unit mass, v, and entropy per unit mass, s, and derives the following three stability conditions of a shock wave: (i) 32p(v,s)/3v2>O; (ii) v Op(v,e)/3e>-2; and (iii) 3p(v, e)/Ov < 0 He concludes that the transition from solid to liquid, from solid to gas, and from liquid to gas, as well as the reverse transitions, should not affect the stability of the shock, while in the solid-solid transitions the shock front

118

P. Krehl would split into successive shocks, the first one raising the medium to a metastable state and the second one transforming it into the new stable phase.

1943

Applied Mathematics Group, Institute for Advanced Study, Princeton, NJ

Von Neumann 463 develops a "two-shock theory" of regular reflection and a "three-shock theory" of Mach reflection. He also coins the term Mach effect to denote such a three-shock configuration. 9 The quantitative experimental evidence of his theory of oblique reflection of shock waves came mainly from the four following sources (all provided in 1943): (i) Aberdeen ballistic photographs; (ii) Princeton shock-wave tube photographs; (iii) Teddington supersonic wind-tunnel photographs; and (iv) Prof. Wood's model shock interaction experiments at Johns Hopkins University using Mach and Wosyka's method of shock generation and soot recording (--->1875). The Mach effect was actually used in the bombing of Hiroshima and Nagasaki (--+ 1945) to determine the position (height of burst, HOB) of the atomic bomb best suited for optimum damage. 464

The Johns Hopkins University, Baltimore, MD

Wood 465 repeats E. Mach and Wosyka's soot experiments (-+ 1875) and E. Mach's and L. Mach's schlieren photography of two interacting spark waves (-+ 1889). Wood's results fully confirm the existence of "Mach disk" (or "Mach bridge") formation.

Ballistic Research Laboratories (BRL), Aberdeen, MD

Charters 466 analyses Wood's soot experiments (--+1943) and discovers in E. Mach's "opposite V-gliding-spark" arrangement (--+ 1875) "lines of discontinuity" that separate areas of equal pressuremi.e., are not shock waves. However, they represent discontinuity lines for entropy, temperature and density, 467 = Later they were called contact discontinuity lines (Courant and Friedrichs 1948) or slipstreams (Bleakney and Taub, 1949).

Institut fftr Mechanik, TH Aachen

Schultz-Grunow 468 publishes a pioneering paper on shock wave propagation in ducts having an area change segment. He correctly treats the flow up- and downstream of the area change segment as an unsteady, one-dimensional flow using the theory of characteristics, but approximates the flow in the area change section as being quasi-one-dimensional and steady. 9 His method of approximation was an important achievement for many engineering applications in the precomputer era. For example, it allowed for the first time the determination of the exhaust flow of internal combustion engines, the flow in diffusers such as in shock tunnels and in converging/diverging nozzles used in rockets and jet propulsion engines. Today the flow through ducts with inserted area

History of Shock Waves

1 19 change segments can easily be handled as a truly two- (or three-) dimensional unsteady flow.469

1944

David W. Taylor Model Basin, Carderock Division, MD

Campbell, Spitzer, and Price 470 study interference effects of spherical shock waves resulting from two underwater detonations of small charges and first prove that Mach reflection also exists in water. However, they cannot detect any slipstreams, which is possibly caused by the fact that the pressure level of intersecting shock waves is too low.

Princeton University Station, NJ

Reynolds 471 uses a pressurized "pot" terminated by a diaphragm, which, when pierced, produces a steep pressure pulse with a rise time of only a few nanoseconds. His device, a kind of short shock tube, is very appropriate to calibrate piezoelectric gauges. 9 Since then the piezoelectric gauge has become the standard pressure gauge in most shock tube facilities and is used routinely at most head-on and side-on shock front positions.

Guggenheim Aeronautical Laboratory, Pasadena, CA

Von I~rm~in designs the first large modern American supersonic wind tunnel (working section 15 • 15 in.) for the BRL in Aberdeen, MD. The famous astronomer Hubble will temporarily act as a director of this facility.

BRL, Aberdeen Proving Ground, MD

Sachs 472 extends the Hopkinson scaling law (B. Hopkinson-+1915) to account for effects of altitude or other changes in ambient conditions on air blast waves ("Sachs scaling law").

Heel'esver-

Erdmann 473 modifies the nozzle of the supersonic wind tunnel and performs the first hypersonic wind tunnel tests at a Mach number close to 9. Shortly thereafter the evacuation of the Peenem~inde Supersonic Laboratory to Kochel begins. Plans are worked out to directly use the Walchensee Hydroelectric Plant for providing the required enormous power (about 60 MW) to operate a huge hypersonic wind tunnel (1 • 1 m 2, M = 10) in the future. 9 Hypersonic wind tunnel studies were not resumed until 1947 after the completion of the first American hypersonic facility by the NACA at Langley, VA. The tunnel had an l 1-in. 2 test section, capable of reaching hypersonic flow up to M -- 7.

suchsanstalt Peenemfmde, Kochel, Bavarian Alps

University of GOttingen

Oswatitsch 474 performs for the German Army Ordnance [Heereswaffenamt] the first theoretical and experimental studies to determine the factors influencing muzzle (or recoil) brake efficiency. These brakes recover momentum from the exhausting propellant gases by deflecting the flow away from the direction of fire. However, they also increase significantly the blast overpressure behind the gun in the vicinity of crew members. This problem will remain a

120

e. Krehl permanent challenge to postwar designers of large caliber cannons.

1945

BRL, Aberdeen Proving Ground, MD

Thomas 475 discusses Becker's theory of the shock front (---~1921). He shows that the shock front's thickness is always at least of the order of magnitude of a free path length and that the Boltzmann equation can be applied even for the most violent shocks.

Applied Mathematics Group, Institute for Advanced Study, Princeton, NJ

Von Neumann 476 proposes a new approach to the hydrodynamical shock problem that he applies to the collision of shock and rarefaction waves. His method, based on a simple pressure-density relationship as already proposed by Riemann ( ~ 1859), provides also a computational procedure and will be resumed in the following years by yon Mises and Geiringer (1948).

Palmer Physical Laboratory, Princeton University, NJ

Smith 477 uses a shock tube and photographs the oblique reflection of plane shocks in air, thus giving the first quantitative information about the validity of von Neumann's twoand three-shock solutions (von Neumann --~1943). He discovers that, contrary to the reflection of sound waves, a reflected shock reflects at a larger angle than the angle of incidence. At large shock strengths, the Mach reflection begins at nearly the angles at which the theory says regular reflection is not possible. For weak shocks, regular reflection continues to be seen at larger angles of incidence than where they are theoretically impossible. 478 His discrepancy will later be named the "von Neumann paradox." Smith also first observes complex Mach reflection. 9 In the same year YON NEUMANN,479 treating various shock wave interaction phenomena, termed in the case of Mach reflection the new shock wave--a mergence of the reflected shock with the incident shock in the vicinity of the reflecting wall---the

Mach stem. ISL, SaintLouis, Alsace, France

The Laboratoire de Recherches Balistiques et Ad.rodynamiques de Saint-Louis (LRSL), is founded. The first directors are Prof. H.

LASL, Los Alamos, NM

Goranson and coworkers initiate a program to determine equation-of-state data of shock-compressed materials, a subject of immediate interest for the design of nuclear weapons and their effects. It will stimulate also other laboratories in the United Statesmand shortly after also in the Soviet UnionNto initiate research in shock wave physics on

Schardin and Gen. R. Cassagnou. 9 In 1959 it was transformed into a joint French-German research institute to promote the scientific cooperation between France and Germany and renamed Institut Saint-Louis (ISL).

History of Shock Waves

121 a large scale.. At that time some theoretical studies on the behavior of shock waves in solids already existed, provided for example by early pioneers such as Christoffe148~ (1877), Hugoniot 481 (1889), Duhem 482 (1903), Hadamard 483 (1903), and Jouguet 484 (1920)] and some as well as on the theory of plastic waves (B. Hopkinson-+1905). Even so, the longplanned systematic campaign at Los Alamos and other national research laboratories and private research organizations can be regarded as the birth of modem solid state shock wave physics. 485

Trinity Site, Alamogordo, NM

On July 16, the first nuclear fission bomb is ignited at an altitude of 100 ft. The bomb is an implosion-type weapon that uses high explosive lenses to rapidly implode a hollow subcritical sphere of fissionable material into a solid supercritical sphere. Measurements are made by Fastax cameras (i) of the shock wave expansion by positioning cameras at halfmile stations; and (ii) of the mass velocity, using suspended Primacord and magnesium flash powder (upon analysis of the results, a total yield of 19,000 tons TNT equivalent was found). The peak pressure is recorded, using spring-loaded piston gauges. The excess shock velocity in relation to sound velocity is measured with a moving-coil loudspeaker pickup. Fermi 486 devised his own order-of-magnitude method of roughly determining the blast yield: "About 40 seconds after the explosion the air blast reached me. I tried to estimate the strength by dropping from about six feet small pieces of paper before, during, and after passage of the blast wave. Since, at that time, there was no wind, I could observe very distinctly and actually measure the displacement of the pieces of paper that were in the process of falling while the blast was passing. The shift was about 2~ meters, which, at the time, I estimated to correspond to the blast that would be produced by 10,000 tons of TNT . . . . " 9 Later investigations showed that, depending on the height of burst, about 45-55% of the fission energy appears as blast and shock. Since the positive duration of a blast wave from a nuclear explosion is longer than from a chemical one, damage effects to air blast loading are more severe than hitherto observed from conventional explosions.

Japan

On August 6 Hiroshima is bombed (Little Boy, uranium-guntype bomb, equivalent to 15,000 tons of TNT, HOB ~ 1900 ft) and on August 9 Nagasaki is bombed (Fat Man, plutonium implosion bomb, equivalent to 21,000 tons of TNT, HOB ~, 1850ft). Later the crew of the B-29 (Enola Gay), which dropped the bomb and witnessed the explosion from on board, contributed to the following official account 487 of

122

P. Krehl the first atomic air raid in history: "The flash after the explosion was deep purple, then reddish and reached to almost 8,000 feet; the cloud, shaped like a mushroom, was up to 20,000 feet in one minute, at which time the top part broke from the 'stem' and eventually reached 30,000. The stem of the mushroom-like column of smoke, looking now like a giant grave marker, stood one minute after the explosion upon the whole area of the city, excepting the southern dock area. This column was a thick white smoke, darker at the base, and interspersed with deep red. Though about fifteen miles (slant range) from the target when the explosion occurred, both escort aircraft, as well as the strike plane, reported feeling two shock waves jar the aircraft. Approximately 390 statute miles away from the target area, the column of smoke still could be seen piercing the morning sky." The second shock was caused by reflection of the primary shock at the ground. The precise yield of these two bomb explosions was difficult to state for that early type of weapon and remained a subject of later discussions and investigations. 488 In the subsequent long period of Cold War, the knowledge of yields was of particular interest in understanding the mechanism of observed damage on a wide spectrum of civilian targets and radiation effects on man, and in predicting damage scenarios in a possible future nuclear war.

1.9

NOTES

1. C. A. Truesdell. Euler's two letters to Langrange in October, 1759. In Leonardi Euleri Opera Omnia XIII [II]. Teubner, Leipzig (1926). See also Editor's introduction, pp. xxxvii-xli. 2. H. Cavendish. A measurer of explosions of inflammable air (laboratory note). In The scientific papers on the Honorable Henry Cavendish, F.R.S., (E. Thorpe, ed.) Chemical & Dynamical, vol. II, Univ. Press, Cambridge (1921), pp. 318-320. 3. J. Canton. Experiments to prove that water is not incompressible. Phil. Trans. Roy. Soc. London 52:640-643 (1762); Experiments and observations on the compressibility of water and some other fluids. Phil. Trans. Roy. Soc. London 54:261-262 (1764). 4. D. Bernoulli. Examen physico-mechanicum de motu mixto qui laminis elasticis a percussione simul imprimitur. Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae XV: 2931 (1770). 5. G. Monge. M~moire sur la construction des fonctions arbitraires dans les int~grales des equations aux differences partielles. M~noires des mathCmatiques et de physique pr~sent~s l'AcadCmie...par divers sc~avans... 7 [l'ann~e 1773, 2e partie]:267-300, 305-327 (1773). Imprimerie Royale, Paris (1776); Sur la d~termination du fonctions arbitraires dans les int(.grales de quelques (.quations aux differences partielles. Miscellanea taurinensia (Torino) 5, 16--78 (1770-1773).

History of Shock Waves

123

6. R. Taton. ~oeuvre scientifique de Gaspard Monge. Presse Universitaire de France, Paris (1951); Gaspard Monge. Dict. Scient. Biogr. 9: 469-478. Scribner's Sons, New York (1973). 7. K. Oswatitsch. Uber die Charakteristikenverfahren der Hydrodynamik. ZAMM 25//27: 195208, 264-270 (1947). 8. R. Courant and K. O. Friedrichs. Supersonic flow and shock waves. Interscience Publ., New York (1948). 9. M. B. Abbott. An introduction to the method of characteristics. American Elsevier, New York (1966), pp. 35-44, 128-163. 10. E. Nairne. Electrical experiments by Mr. Edward Nairne, of London, mathematical instruJ mentJmaker, made with a machine of his own workmanship, a description of which is prefixed. Phil. Trans. Roy. Soc. London 6 4 : 7 9 - 8 9 (1774). 11. H. Mtiller. Gewehre, Pistolen, Revolver. Kohlhammer, Stuttgart (1979). See also: Windbfchsen und elektrische Zundung, pp. 154-156. 12. J. L. Lagrange: Memoire sur la th~orie du mouvement des fluides. Nouv. M~m. Acad. Roy. Sci. & Belles-Lettres Berlin (1781), pp. 151-198. 13. E R. Gilmore, M. S. Plesset, H. E. Crosley, Jr.: The analogy between hydraulic jumps in liquids and shockwaves in gases. J. Appl. Phys. 21:243-249 (1950). 14. C. Hutton. New experiments in gunnery, for determining the force of fired gunpowder, the initial velocity of cannon ball, the ranges of projectiles at different elevations, the resisatnce of the air to projectiles, the effect of different length of guns, and of different quantities of powder, &c, &c. In: Tracts on mathematical and philosophical subjects. T. Davidson, London (1812). See vol. 2, Tract XXXIV, pp. 306-384. 15. C. Hutton. Theory and practice of gunnery, as dependent on the resistance of the air. In: Tracts on mathematical and philosophical subjects. T. Davidson, London (1812). See vol. 3, Tract XXXVII, pp. 209-315. 16. H. Cavendish. Experiments on air. Phil. Trans. Roy. Soc. London 74: 481-502, 510-514 (1784), 7 5 : 1 5 - 2 2 (1785). 17. Count Morozzo. Account of a violent explosion which happened in a flour~warehouse, at Turin, December 14th, 1785; to which are added some observations on spontaneous inflammations. The Repertory of Arts and Manufactures 2:416-432 (1795). 18. J. L. Lagrange. Sur la percussion des fluides. Mcm. Acad. Roy. Sci. Turin I: 95-108 (17841785). 19. D. Bernoulli: Hydrodynamica, sive de viribus et motibus fluidorum commentarii. Dulsecker, Strassburg (1738); translated into English by T. Carmody, H. Kobus: Hydrodynamics. Dover Publ., New York (1968). 20. J. Goodricke. A series of observations on, and a discovery of the period of the variations of light of the star marked ~ by Bayer, near the head of Cepheus. Phil. Trans. Roy. Soc. London 16: 48-61 (1786). 21. L. I. Sedov. Similarity and dimensional methods in mechanics. Infosearch Ltd., London (1959), pp. 305-353. 22. E yon Baader. Versuch einer Theorie der Sprengarbeit. Bergmannisches J. 1 (No. 3):193-212 (March 1792). 23. D. R. Kennedy. History of the shaped charge effect. The first 1O0 years. Company brochure prepared by D. R. Kennedy & Associates, Inc., Mountain View, CA (1983). 24. G. Pinet: Histoire de l'~cole polytechnique. Baudry, Paris (1887). 25. E. E E Chladni. ~ber den Ursprung der yon Pallas gefundenen und anderer ahnlicher Eisenmassen, und fiber einige damit in Verbindung stehende Naturerscheinungen. J. E Hartknoch, Riga (1794). 26. Journal der Physik 8, 20-21 (1794).

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27. I. I. Glass and J. P. Sislian. Nonstationary flows and shock waves. Clarendon Press, Oxford (1994), pp. 271-275. 28. J. M. Montgolfier: Note sur le belier hydraulique, et sur la maniere d'en calculer les effets. J. des Mines XIII, 42-51 (1802-1803). 29. Weinmann Sondermaschinen- und Steuerungsbau GmbH, 91217 Hersbruck, Germany. 30. J. B. Biot. Theorie mathematique de la propagation du son. J. Phys. 55:173-182 (1802). 31. J. B. Biot. Account of a fire-ball which fell in the neighborhood of EAigle: In a letter to the French Minister of the Interior. Phil. Mag. 16 [I]:224-228 (1803). 32. Brockhaus Konversationslexikon. Brockhaus, Leipzig (1908). See vol. 11, p. 815. 33. E L. Neher. Die Erfindung der Photographie. Kosmos, Stuttgart (1938), p. 36. 34. S. D. Poisson. Memoire sur la theorie du son. J. Ecole Polytech. (Paris) 7:319-392 (1808). 35. J. L. Lagrange. Sur une nouvelle methode de calcul integral pour les differentielles affectees d'un radical carre, sous lequel la variable ne passe pas le 4 e degre. Mem. Acad. Roy. Sci. Turin II: 218-290 (1784-1785). 36. J. L. Gay-Lussac and L. J. Thenard. De la nature et des proprietes de racide muriatique et de l'acide muriatique oxigene. M~n. Soc. Arcueil 2:339-358 (1809). 37. G.J. Singer and A. Crosse. An account of some electrical experiments by M. De Nelis. Phil. Mag. 46 [I]:161-166 (1815). 38. P. S. Laplace. Sur la vitesse du son dans l'air et dans l'eau. Ann. Chim. & Phys. 3:238-241 (1816). 39. H. Davy. (I) On the fire-damp of coal mines, and on methods of lighting the mines so as to prevent its explosion. Phil. Trans. Roy. Soc. London 106:1-22 (1816); (II) An account of an invention for giving light in explosive mixtures of fire-damp in coal mines by consuming the fire-damp. Phil. Trans. Roy. Soc. London 106:23-24 (1816). 40. Technisches Museum Wien, A-1140 Vienna, Austria. 41. L. M. H. Navier. Memoire sur les lois du mouvement des fluides. Mem. Acad. Roy. Sci. Paris 6: 389-440 (1823). 42. S. D. Poisson. Memoire sur les equations generales de l'equilibre et du mouvement des corps solides elastiques et des fluides. J. Ecole Polytech. (Paris) 13 (Cahier 20):1-174 (1831). 43. A. J. C. de Saint-Venant. Note sur l'ecoulement de l'air. C. R. Acad. Sci. Paris 21:366-369 (1845). 44. G. G. Stokes. On the theory of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids. Trans. Cambridge Phil. Soc. 8:287-319 (1845). 45. J. C. Maxwell. On the dynamical theory of gases. Phil. Trans. Roy. Soc. London 157:49-88 (1867). 46. S. D. Poisson. Sur la vitesse du son. Ann. Chim. & Phys. 2 3 : 5 - 1 6 (1823). 47. S. D. Poisson. Sur la chaleur des gaz et des vapeurs. Ann. Chim. & Phys. 23:337-353 (1823). 48. W. E. Parry. Journal of the third voyage for the discovery of a North-West Passage from the

Atlantic to the Pacific; performed in the years 1824-25, in His Majesty's ships Hecla and Fury, under the orders of...W.E. Parry. J. Murray, London (1826). See Experiments to determine the rate at which sound travels at various temperatures and pressures of the atmosphere, Appendix, p. 86. 49. W. E. Parry. Journal of a second voyage for the discovery of a North-West Passage from the

Atlantic to the Pacific; performed in the years 1821-22-23, in His Majesty's ships Fury and Hecla, under the orders of...W.E. Parry. J. Murray, London (1824-25). See p. 140; and Abstract of experiments to determine the velocity of sound at low temperature, Appendix, pp. 237-239. 50. W. E. Parry and H. Foster. Reply to Mr. Galbraith's remarks on the experiments for ascertaining the velocity of sound at Port Bowen. Phil. Mag. 1 [II]:12-13 (1827).

History of Shock Waves

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51. D. Colladon and C. E Sturm. Ober die Zusammendruckbarkeit der Flussigkeiten. Ann. Phys. 12 [II]:161-197 (1828). 52. J. B. C. B~langer. Essai sur la solution num~rique de quelques problCmes relatifs au mouvement permanent des eaux courantes. Carilian-Gceury, Paris (1828). 53. E. Jouguet. Quelques probl~mes d'hydrodynamique g~n~rale. J. Math. Pures & Appl. 3 [VIII]:1-63 (1920). See p. 12. 54. D. E C. Arago. Uber die Explosionen der Dampfmaschinen. Ann. Phys. 18 [II]:287-314, 415436 (1830). 55. C. Wheatstone. An account of some experiments to measure the velocity of electric light. Proc. Roy. Soc. London 3:299-300 (1834). 56. E. Sabine. President's address. Proc. Roy. Soc. London 18:145-147 (1869). 57. L. Foucault. M~thode g~neral pour mesurer la vitesse de la lumi~re dans l'air et dans les milieux transparents. C. R. Acad. Sci. Paris 30:551-560 (1850). 58. B. W. Feddersen. Beitrage zur Kenntnis des elektrischen Funkens. Ann. Phys. 103 [II]:69-88 (1858). 59. P. W W. Fuller and J. T. Rendell. The development of high speed photography. In High speed photography and photonics, S. E Ray, ed. Focal Press, Oxford (1997), pp. 21-23; V. Parker and C. Roberts: Rotating mirror and drum cameras. Ibid. pp. 167-180. 60. D. E J. Arago. On thunder and lightning. Edinburgh New Phil. J. 26: 81-144, 275-291 (1839); Meteorological essays, with an introduction by A. yon Humboldt (translated by R. A. Sabine). Longman & Co, London (1855). 61. M. Faraday. On some supposed forms of lightning. Phil. Mag. 19 [III]:104-106 (1841). 62. G. K. Hubler. Fluff balls of fire. Nature 403:487-488 (2000). 63. A.J.C. de Saint-Venant and P. L. Wantzel. M4moire et exp4riences sur l'4coulement de l'air. J. Ecole Polytech. (Paris) 16:85-122 (1839). 64. C. Wheatstone. Description of the electromagnetic clock. Proc. Roy. Soc. London 4 : 2 4 9 - 2 7 8 (1840). 65. J. S. Russell. The wave of translation in the oceans of water, air and ether. Trubner & Co., London (1885), p. 315. 66. C. S. M. Pouillet. Note sur un moyen de mesurer des intervalles de temps extremement courts, comme la duree du choc des corps ~lastiques, cell du debondement des ressorts, de l'inflammation de la poudre etc.; et sur un moyen nouveau de comparer les intensit~s des courants ~lectriques, soit permanents, soit instantan~s. C. R. Acad. Sci. Paris 19:1384-1389 (1844). 67. M. Faraday and C. Lyell. On explosions in coal mines. Phil. Mag. 26 [III]:16-35 (1845). 68. G. B. Airy. Tides and waves. In Encyclopaedia Metropolitana. Fellowes, London (1845). 69. C. Haeussermann: Gedachtnisrede auf Christian Friedrich SCHONBEIN [Referat]. Z. f. d. gesamte Scheit~- und Sprengstoffwesen 4, 433-434 (1909). 70. J. Taylor. "Improvements in the manufacture of explosive compounds, communicated to me from a certain foreigner residing abroad." Brit. Patent No. 11,407 (Oct. 8, 1846). 71. E A. Abel. On the manufacture and composition of gun-cotton. Phil. Trans. Roy. Soc. London 156:269-308 (1866). 72. J. C. Doppler. Uber den Einflut~ der Bewegung des Fortpflanzungsmittels auf die Erscheinungen der ,~ther-, Luft- und Wasserwellen (presented in 1847). Abhandl. BOhm. Gesellsch. Wiss. Prag 5 [V]:293-306 (1848). 73. A. Sobrero. Sur plusieurs composes d~tonants produits avec l'acide nitrique et le sucre, la dextrine, la lactine, la marnite, et la glycerine. C. R. Acad. Sci. Paris 25:247-248 (1847). 74. G. B. Airy. The Astronomer Royal's remarks on Prof. Challis' theoretical determination of the velocity of sound. Phil. Mag. 32 [III]:339-343 (1848).

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J. Challis. On the velocity of sound. Phil. Mag. 32 [III]:494-499 (1848). G. G. Stokes. On a difficulty in the theory of sound. Phil. Mag. 33 [III]:349-356 (1848). G. B. Airy. On a difficulty in the problem of sound. Phil. Mag. 34 [III]:401-405 (1849). J. C. Maxwell. On the equilibrium of elastic solids. Trans. Roy. Soc. Edinburgh 20:87-120 (1850). 79. W. Goldsmith. Dynamic photoelasticity. In Kurzzeitphysik, K. Vollrath and G. Thomer, eds. Springer, Wien (1967), pp. 579-619. 80. W. H. E Talbot. On the production of instantaneous images. Phil. Mag. 3 [IV]:73-77 (1852). 81. W.J.M. Rankine. On Laplace's theory of sound. Phil. Mag. 1 [IV]:225-227 (1851). 82. S. Earnshaw. On the velocity of the sound of thunder. Phil. Mag. 20 [IV]:37-41 (1860). 83. G. G. Stokes. An examination of the possible effect of the radiation of heat on the propagation of sound. Phil. Mag. 1 [IV]:305-317 (1851). 84. J. Challis. Theoretical determination of the velocity of sound. Phil. Mag. 32 [III]:276-284 (1848); On the theory of the velocity of sound. Phil. Mag. 1 [IV]:405-408 (1851). 85. C. E. Munroe. Modern explosives. Scribner's Mag. 3:563-576 (1888). 86. J. Jamin. Description d'un nouvel appareil de recherches, fondr sur les interferences. C. R. Acad. Sci. Paris 42:482-485 (1856). 87. A. Toepler and L. Bohzmann. Uber eine neue optische Methode, die Schwingungen t6nender Luftsaulen zu analysieren. Ann. Phys. 141 [II]:321-352 (1870). 88. A. Kr6nig. Grundz~ge einer Theorie der Gase. Ann. Phys. 99 [II]:315-322 (1856). 89. R. Clausius. Uber die Art der Bewegung, welche wir Warme nennen. Ann. Phys. 100 [II]:353380 (1857). 90. J. C. Maxwell: Illustrations of the dynamical theory of gases. Part I: On the motion and collisions of perfectly elastic spheres. Phil. Mag. 19 [IV], 19-32 (1860); Part II: On the process of diffusion of two or more moving particles among one another. Ibid. 20 [IV], 21-37 (1860); On the dynamical theory of gases. Phil. Trans. Roy. Soc. London 157, 49-88 (1867). 91. L. Boltzmann. Weitere Studien tiber das Warmegleichgewicht unter Gasmolekulen. Sitzungsber. Akad. Wiss. Wien 66 [II]:275-370 (1872). 92. T. Koga: Introduction to kinetic theory stochastic processes in gaseous systems. Pergamon Press, Oxford etc. (1970). Cf. Appendix G: An historical sketch of kinetic theory, pp. 261-277. 93. J. P. Joule and W. Thomson. On the thermal effects of fluids in motion. (I) On the temperature of solids exposed to currents of air. Proc. Roy. Soc. 8:178-185 (1856-1857); (II) Temperature of a body moving through air. Proc. Roy. Soc. 8: 41-42, 556-567 (1856-1857). 94. T.J. Rodman. Reports of experiments on the properties of metals for cannon, and the qualities of cannon powder; with an account of the fabrication and trial of a 15-inch gun. Crosby, Boston, MA (1861); Mitteilungen fiber Gegenstande des Artillerie- und Geniewesens (Wien). Notizen S. 57 (1881); C. Cranz: Lehrbuch der Ballistik III. Springer, Berlin (1927). 95. A. Noble. On methods that have been adopted for measuring pressures in the bores of guns. Rept. Meet. Brit. Assoc. 64:523-540 (1894). 96. K. W. Knochenhauer. Uber den elektrischen Zustand der Nebenbatterie wahrend ihres Stromes. Sitzungsber. Akad. Wiss. Wien 33 [II]:163-204 (1858). 97. S. Earnshaw. On the mathematical theory of sound (communicated in Nov. 1858). Phil. Trans. Roy. Soc. London 150:133-148 (1860). 98. S. Earnshaw. "On the mathematical theory of sound." Rpt. Meet. Brit. Assoc. 28:34-35 (1858). 99. B. Riemann. Uber die Fortpflanzung ebener Luftwellen yon endlicher Schwingungsweite. Abhandl. KOnigl. Ges. Wiss. GOttingen 8 (Math. Physik. Kl.):243-265 (1860). 100. R. Carrington. Description of a singular appearance seen in the sun on Sept 1, 1859. Month. Not. Astron. Soc. 20:14-16 (1860); On two cases of solar spots in high latitudes, and on the surface currents indicated by the observation. Month. Not. Astron. Soc. 20:255-259 (1860). 75. 76. 77. 78.

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101. A. von Humbold. Kosmos. Entwurf einer physischen Weltbeschreibung, vol. III. Cotta, Stuttgart & Augsburg (1858), p. 127. 102. S. Earnshaw. On the velocity of the sound of thunder. Phil. Mag. 20: [IV] 37-41 (1860); On the triplicity of sound. Phil. Mag. 20 [IV]:186-192 (1860). 103. C. Montigny. Note sur la vitesse du bruit du tonnerre. Bull. Acad. Roy. Belg. 27 [II]:36-46 (1860); Observations sur l'acc~l~ration de la vitesse du bruit du tonnerre. Bull. Acad. Roy. Belg. 27 [II]:62-63 (1860); Fortschritte der Physik 16:165-167 (1860). 104. G. A. Hirn. Sur le bruit du tonnerre. Cosmos (Paris) 16:651-655 (1860). 105. E Raillard. Sur le bruit du tonnerre. Cosmos (Paris) 1 6 : 3 7 2 - 3 7 4 (1860); Du bruit du tonnerre, de ses variations ou de ses roulements, de sa vitesse &. Cosmos (Paris) 17: 166-172, 675-677 (1860). 106. A. B. Nobel. "Nitroglycerin" (manufacturing and fining). Brit. Patent No. 1813 (1864). 107. P. E. Le Bouleng~. M~moire sur un chronographe r (prCsentr 5 Dr 1863). MCm. Couronn. & M~'m. Savants Etrangers de l'Acad. Roy. (Bruxelles) 3 2 : 3 9 pages (18641865). 108. G. B. Airy. "Report on steam boiler explosions." Rpt. Meet. Brit. Assoc. 33:686-688 (1863). 109. R. Armstrong and J. Bourne. The modern practice of boiler engineering, containing observations on the construction of steam boilers. Spon, Leipzig (1856). See also chp. III: Explosions: an investigation into some of the causes producing them, and the deterioration of boilers generally. 110. Dampfkesselexplosionen. In Meyers Konversations-Lexikon, vol. IV Verlag Bibliograph. Inst., Leipzig (1875), pp. 954-956. 111. V. Regnault. On the velocity of the propagation of waves in gaseous media. Phil. Mag. 35 [IV]:161-171 (1868). 112. H.J. Rink. l]ber die Geschwindigkeit des Schalls nach Hrn. Regnault's Versuchen. Ann. Phys. 149 [II]:533-546 (1873). 113. A. Toepler. Beobachtungen nach einer neuen optischen Methode. Max Cohen & Sohn, Bonn (1864), p. 43. 114. H.W. Robinson and W. Adams (eds.). The diary ofR. Hooke. Taylor & Francis, London (1953). 115. L. Foucault. M~moire sur la construction des t~lescopes en verre argentS. Ann. de l'Observatoire Imperial de Paris 5:197-237 (1859). 116. A. Nobel. "Improvements in the manufacture of gunpowder and powder for blasting purposes." Brit. Patent No. 2359 (Sept 24, 1863). 117. E. Bergengren. Alfred Nobel. The man and his work. Nelson & Sons, London etc. (1962). 118. J. Le Conte. On the adequacy of Laplace's explanation to account for the discrepancy between the computed and the observed velocity of sound in air and gases. Phil. Mag. 27 [IV]: 1-32 (1864). The paper was written in 1861 but did not arrive in England until two years later because of the interruption of communication incident to the great revolutionary struggle. 119. H.W. Schr6der van der Kolk. On the velocity of sound. Phil. Mag. 30 [IV]:34-49 (1865); Note on the velocity of sound, and on the mechanical energy of chemical actions. Phil. Mag. 30 [IV] :391-392 (1865). 120. A. B. Nobel: Results of blasting experiments made with nitroglycerin at Vieille-Montagne mine. Phil. Mag. 30 [IV], 236-238 (1865). 121. R. D. Napier. On the velocity of steam and other gases, and the true principles of the discharge of fluids. Spon, London (1866). 122. O. Reynolds. On the flow of gases. Manchester Lit. & Phil. Soc. 2 5 : 5 5 - 7 1 (1885). 123. This letter, dated April 29, 1867, is now in the archives of the Technische UniversitFzt Dresden. 124. A. Toepler. Die vom elektrischen Funken in Luft erzeugte Welle. Ann. Phys. 131 [II]:180-215 (1867).

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424. O. von Schmidt. Zur Theorie der Erdbebenwellen. Die "wachsende" Reflexion der Seismik als Analogon zur "Kopfwelle" der Ballistik. Z. Geophysik 12:199-205 (1936). 425. J.D. Boon, C.C. Albritton, Jr.: Established and supposed examples of meteoritic craters and structures. Field & Laboratory (Dallas) 6:44-56 (1938); The impact of large meteorites. Ibid. 6, 57-64 (1938). 426. R. S. Dietz: Meteorite impact suggested by the orientation of shatter-cones at the Kentland, Indiana, disturbance. Science 105:42-43 (1947); Meteorite impact suggested by shatter cones in rock. 131:1781-1784 (1960). 427. A. E Belajev. The production of detonation in explosives under the action of a thermal pulse. Dokl. AN (SSSR) 18(No. 4-5):267-269 (1938). 428. H. Johnston. "Electric initiator with exploding bridge wire." U.S. Patent No. 3,040,660 (filed Nov. 8, 1944, applied June 26, 1962). 429. M. Steenbeck. Uber ein Verfahren zur Erzeugung intensiver ROntgenblitze. Wiss. VeriJff. Siemens 17:363-380 (1938). 430. K. H. Kingdon and H. E. Tanis. Experiments with a condenser discharge. Phys. Rev. 53: 128134 (1938). 431. H. Schardin. Uber die Entwicklung der Hohlladung. Wehrtech. Hefte 51 (No. 4):97-120 (1954). 432. A set of some of the first flash radiographs of the shaped charge were donated to Dr. C. Fauguignon, Adjoint Scientific Director of ISL, upon Dr. G. Thomer's retirement from ISL. See also: D. R. Kennedy. History of the shaped charge effect. The first 100 years. Company brochure prepared by D. R. Kennedy & Associates, Inc., Mountain View, CA (1983). 433. H. Mohaupt. Shaped charges and warheads. In Aero-space Ordnance Handbook, E B. Pollad and J. A. Arnold, eds. Prentice-Hall, Englewood Cliffs, NJ (1966), chp. 11. 434. E. Preiswerk. Anwendungen gasdynamischer Methoden auf Wasserstri~mungen mit freier Oberfliiche. Mitteilungen aus dem Institut ftir Aerodynamik, ETH Zurich (1938). 435. O. Hahn and E Strassmann. Uber den Nachweis und das Verhalten der bei der Bestrahlung des Urans mittels Neutronen entdtehenden Erdalkalimetalle. Die Naturwissenschaften 27: 1115 (1939); Uber die Bruchstiicke beim Zerplatzen des Urans. Ibid., pp. 89-95; Nachweis der Entstehung aktiver Bariumisotope aus Uran und Thorium durch Neutronenbestrahlung. Nachweis weiterer aktiver Bruchstucke bei der Uranspahung. Ibid. 163-164. 436. S. Flugge. Kann der Energieinhalt der Atomkerne technisch nutzbar gemacht werden? Die Naturwissenschaften 27:402-410 (1939). 437. S. Flligge. Die Ausnutzung der Atomenergie. Deutsche Allgemeine Zeitung 78 (No. 387) (Aug. 15, 1939). 438. Y. Khariton, Y. Smimov: The Khariton version. Bull. Atomic Scientists 49(No. 5):20-31 (1993). 439. A. Betz. "Flugzeug mit Geschwindigkeiten in der N/~he der Schallgeschwindigkeit." Top secret German Patent D.R.P. No. 732/42 (1939). 440. R. Smelt. A critical review of German research on high-speed airflow. J. Roy. Aeronaut. Soc. 50: 899-934 (1946). 441. E H. Shehon. Reflections of a nuclear weaponeer. Shelton Enterprise Inc., Colorado Springs (1988), chp. 1: The Manhattan Project. 442. The life and time of the Manhattan Project. See http://www.gis.net/carter/manhattan/project.html. 443. T. von Karman and k. Edson. The wind and beyond. Theodore yon Karman pioneer in aviation and pathfinder in space. Little, Brown and Co., Boston and Toronto (1967), p. 233. 444. W. Payman and W. C. E Shepherd. (VI) The disturbance produced by bursting diaphragms with compressed air. Proc. Roy. Soc. London A186:293-321 (1946). 445. Y. B. Zeldovich. On the theory of the propagation of detonation in gaseous systems. ZETP (SSSR) 10:542-568 (1940).

History of Shock Waves

141

446. J. von Neumann. "Theory of stationary detonation waves." Rpt. OSRD-549 (1942). 447. W. D0ring. Ober den Detonationsvorgang in Gasen. Ann. Phys. 43 [V]:421-436 (1943). 448. T. von Karman and L. Edson. The wind and beyond. Theodore von Kdrman, pioneer and pathfinder in space. Little, Brown and Co., Boston and Toronto (1967), p. 224. 449. A. Michel-L~vy, H. Muraour, and E. Vassy. Repartition spectrale ~nerg~tique dans la lumiere Cmise lors de la rencontre d'ondes de choc. Rev. Opt. Th~or. Instrum. 20:149-160 (1941). 450. H. Schardin. Experimentelle Arbeiten zum Problem der Detonation. Jb. dtsch. Akad. Luftfahrtforsch. (1940-1941), pp. 314-334. 451. G. I. Taylor. "The formation of a blast wave by a very intense explosion." Ministry of Home Security, R.C. 210, II-5-153 (1941) and Proc. Roy. Soc. London A201:159-186 (1950). 452. L. I. Sedov. Propagation of strong explosive waves. Prikl. Mat. Mekh. (SSSR) 10 (No. 2):241250 (1946). 453. S. C. Lin. Cylindrical shock waves produced by instantaneous energy release. J. Appl. Phys. 25:54-57 (1954). 454. "A photographic study of small-scale underwater explosions". David W. Taylor Model Basin, Confidential Test Report R-39 (Aug. 1941). 455. Weinert: "Unterwasserzeitlupenaufnahmen von Gasblasenschwingungen". Berichte der chemisch-physikalischen Versuchsanstalt6 der Kriegsmarine (Kiel) 245, Heft VI (1941). 9 This report which was cited by W. DOting and H. Schardin in a post-war review paper on detonations [In: Naturforschung und Medizin in Deutschland 1939-1946, (A. Betz, ed.) Verlag Chemie, Weinheim/Bergstr. (1953). Bd. 11: Hydro- und Aerodynamik pp. 97-125], could not be located in German archives. 456. H. A. Berthe and J. G. Kirkwood: "The pressure wave produced by an underwater explosion." NDRC Div. B, Progr. Rpt. OSRD-588 (1942). 457. D.C. Campbell. "Motions of a pulsating gas globe under waterma photographic study". David W. Taylor Model Basin Rpt. 512 (1943). 458. W. Dornberger. V2mDer Schuj~ ins Weltall. Bechtle, Esslingen (1952). 459. Los Alamos 1943-45; The beginning of an era. Brochure LASL-79-79, Los Alamos Scientific Laboratories, NM. 460. G. Guderley. Starke kugelige und zylindrische Verdichtungsstot~e in der Nahe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrtforsch. 19:302-312 (1942). 461. R.J. Seeger. On Mach's curiosity about shock waves. In Ernst Mach, physicist and philosopher, R. S. Cohen and R. J. Seeger, eds. Boston Studies in the Philosophy of Science 6:42-67 (1970). 462. H. A. Bethe. "On the theory of shock waves for an arbitrary equation of state." NDRC Div. B, Rpt. OSRD-545 (1942). 463. J. von Neumann. "Oblique reflection of shocks." Navy Dept., Bureau of Ordnance, Explosives Res. Rpt. No. 12, Washington, DC (1943). 464. J. von Neumann: The Mach effect and height of burst. In: (A.H. Taub, ed.): J. von Neumann collected works. Pergamon Press, Oxford etc. (1963), vol. VI, pp. 309-347. 465. R. W. Wood. "On the interaction of shock waves." Rpt. OSRD-1996 (1943). 466. R. J. Seeger. On Mach's curiosity about shock waves. In Ernst Mach, physicist and philosopher, R. S. Cohen and R. J. Seeger, eds. Boston Studies in the Philosophy of Science 6:42-67 (1970). 467. (A.H. Taub, ed.): J yon Neumann collected works. Pergamon Press, Oxford etc. (1963), vol. VI, pp. 309-347. 468. E Schuhz-Grunow. Nichtstatiomire, kugelsymmetrische Gasbewegung und nichtstatiomire Gasstromung in Dusen und Diffusoren. Ingenieur-Archiv 14:21-29 (1943). 469. O. Igra, L. Wang, and J. Falcovitz. Nonstationary compressible flow in ducts with varying cross-section. J. Aerospace Eng. 212 [Part G]:225-243 (1998).

142

P. Krehl

470. R. H. Cole. Underwater explosions. Dover Publ., New York (1948), pp. 257-258. 471. E H. Reynolds. "A preliminary study of plane shock waves formed by bursting diaphragms in a tube." Rpt. OSRD-1519 (1943). 472. R. G. Sachs."The dependence of blast on ambient pressure and temperature." BRL Rpt. 466, Aberdeen Proving Ground, MD (1944); Some properties of very intense shock waves. Phys. Rev. 69:514-515 (1946). 473. P. P Wegener. The Peenemunde wind tunnels. A memoir Yale Univ. Press, New Haven (1996), pp. 69-70. 474. K. Oswatitsch. "Flow research to improve the efficiency of muzzle brakes." Heereswaffenamt. Berlin Rpt. R1001 (1944). 475. L. H. Thomas. Note on Becker' theory of the shock front. J. Chem. Phys. 12:449-453 (1944). 476. J. von Neumann. "Proposal and analysis of a new numerical method for the treatment of hydrodynamical shock problems." Applied Mathematics Group, Institute for Advanced Study, Princeton Rpts. OSRD-3617 and NDRC-108 (1944). 477. L. G. Smith. "Photographic investigation of the reflection of plane shocks in air." Palmer Physical Laboratory, Princeton University Rpt. OSRD-6271 (1945); Phys. Rev. 69:678 (1946). 478. P. Colella and L. E Henderson. The von Neumann paradox for the diffraction of weak shock waves. In Proc. 9th Int. Mach Reflection Symp., H. Reichenbach, ed. Ernst Mach-Institut, Freiburg (June 1990). 479. J. von Neumann: Refraction, intersection and reflection of shock waves. In: John von Neumann. Collected Works. (A.H. Taub, ed.) Pergamon Press, Oxford etc. (1963), vol. VI, pp. 300-308. 480. E. B. Christoffel. lJber die Fortpflanzung yon St6gen durch elastische feste KOrper. Ann. di Mat. 8 [II]:193-243 (1877). 481. P. H. Hugoniot. M~moire sur la propagation du mouvement dans les corps et plus sp~cialement dans les gaz parfaits. 1e Partie. J. Ecole Polytech. (Paris) 5 7 : 3 - 9 7 (1887). 482. P. M. M. Duhem. Sur les thgor~mes d'Hugoniot, les lemmes de M. HADAMARD et la propagation des ondes dans les fluides visqueux. C. R. Acad. Sci. Paris 132:1163-1167 (1901); Sur les ondes longitudinales et transversales dans les fluides parfaits. C. R. Acad. Sci. Paris 132:1303-1306 (1901). 483. J. S. Hadamard. Lemon sur la propagation des ondes et les gquations de l'hydrodynamique. A. Hermann, Paris (1903). 484. J. C. E. Jouguet. Sur les ondes de choc dans les corps solides. C. R. Acad. Sci. Paris 171: 461464 (1920); Sur la cr162 des ondes dans les solides ~lastiques. C. R. Acad. Sci. Paris 171: 512-515 (1920); Sur la variation d'entropie dans les ondes de choc des solides r C. R. Acad. Sci. Paris 171:789-791 (1920). 485. C. E. Morris. Shock-wave equation-of-state studies at Los Alamos. Shock Waves 1:213-222 (1991). 486. E H. Shehon. Reflections of a nuclear weaponeer. Shelton Enterprise Inc., Colorado Springs (1988), p. 2:15. 487. From: Administrative History, History of 509th Composite Group, 313th Bombardment Wing, 20th U.S. Air Force, Activation to 15 August 1945. This information was kindly provided by the Smithsonian National Air and Space Museum, Washington, DC. 488. J. Malik. "The yields of the Hiroshima and Nagasaki nuclear explosions." Los Alamos National Laboratory, Rpt. LA-8819 (1985).

CHAPTER

2

General Laws for Propagation of Shock Waves Through Matter LEROYE HENDERSON Professor Emeritus, 8 Damour Avenue, East Lindfield, Sydney, New South Wales 2070, Australia

2.1 2.2 2.3 2.4

Introduction The Riemann Problem Length and Time Scales The Conservation Laws for a Single Shock 2.4.1 Laboratory Frame Coordinates 2.4.2 Shock Fixed Coordinates 2.5 The Hugoniot Adiabatic 2.5.1 The Hugoniot Equation 2.5.2 The Rayleigh Equations 2.5.3 Solution of a Simple Shock Riemann Problem 2.6 Thermodynamic Properties of Materials 2.7 Thermodynamic Constraints on the EOS 2.8 Nonthermodynamic Constraints on the EOS 2.8.1 Convexity 2.8.2 Shock Wave Stability Constraints 2.8.3 Monotonicity Constraints 2.9 The Bethe-Weyl (B-W) Theorem 2.10 Shock Wave Interactions 2.10.1 Dimensions of the Interactions 2.10.2 Two-Dimensional Shock Wave Interactions 2.10.3 Three-Dimensional Shock Wave Interactions 2.11 The Triple-Shock-Entropy and Related Theorems 2.11.1 The Theorems 2.11.2 Application to Shock Wave Interactions 2.12 Crocco's Theorem 2.13 The Refraction Law 2.14 Concluding Remarks References Handbook of Shock Waves, Volume 1 Copyright ~ 2001 by Academic Press. All rights of reproduction in any form reserved. ISBN: 0-12-086431-2/$35.00

143

144 2.1

L. E Henderson

INTRODUCTION

The ideal objective for this chapter would be to present the theory that describes how shock waves propagate, and interact, as they pass through any material in any thermodynamic state. The conservation laws and some other laws and theorems meet this objective for equilibrium states, or other states that can be defined in some useful way. However it is useful to extend the discussion to theory that requires only mild constraints on the material's equation-of-state (EOS). Powerful results can then be applied to a broad class of materials; in particular to any material in a single phase state. An EOS so restricted has a profound effect on the nature of the phenomena that is observed. The seminal paper for multi-shock interactions in general classes of materials is by von Neumann (1963). Often length and time scales are insignificant for shock problems; these are called shock-Riemann problems (Sections 2.2, 2.3). The equations obtained from the conservation laws of mass, momentum, and energy are called the Rankine-Hugoniot (R-H) equations (Section 2.4). These equations contain the material velocities on both sides of a shock. If the equations are manipulated to eliminate the velocities, a single equation containing only state variables is obtained. It is the Hugoniot equation, and is the starting point for many studies. If two other equations, called the Rayleigh equations are appended to the Hugoniot equation, they comprise a set equivalent to the R-H equations (Section 2.5). The material properties that are required are defined in Section 2.6. Those that will be used most often are the adiabatic exponent ~, the Gruneisen coefficient F, and the fundamental derivative G. The EOS constraints required to ensure thermodynamic stability are presented in Section 2.7. Other EOS constraints presented in Sections 2.8 are needed to ensure the existence and uniqueness of shock-Riemann problems. They are also needed to control the monotonicity of state variables along the Hugoniot adiabatic, which is a plot of the Hugoniot in say the (v, p) plane, where v is the specific volume and p is the pressure. Furthermore they are needed to ensure that a shock does not become unstable by splitting, ot through ripple instability. The important admissability conditions are also presented in Section 2.8. They ensure that the shock is physically possilbe, in that it increases the entropy in the material as required by the second law, and that the flow of the material relative to the shock is supersonic on the upstream side and subsonic downstream, as required to prevent the splitting/ripple instabilities. The important Bethe-Weyl Theorem (B-W) is presented in Section 2.9. In its most general form, it guarantees the existence of a solution to the Hugoniot equation, but it is most powerful when the EOS is convex (Section 2.6). The

General Laws for Propagation of Shock Waves Through Matter

145

theorem shows that the solution is then unique; that the admissability conditions are satisfied; and that the entropy is monotonic along the Hugoniot adiabatic. The (l-D) and (2-D) interactions of shocks are discussed in Section 2.10, and the Triple-Shock-Entropy Theorem in Section 2.11. The theorem is useful for 2-D interactions. Next is Crocco's Theorem presented in Section 2.12; it is useful for curved shocks, and when flow gradients are present. Finally we present the Refraction Law in Section 2.13. It can be applied to 2-D shock interactions, especially when several shocks meet at a point; called a wave node."

2.2

THE RIEMANN

PROBLEM

"A Riemann problem is defined for a system of conservation laws such as mass, momentum and energy, as an initial value problem such that the initial data have no length or time scales, or in other words the data is constant along ray paths" (Courant and Friedrichs, 1948). The classic example is the shock tube problem studied by Riemann (1860). Many shock problems have this scale invariant character, but not all.

2.3 LENGTH

AND TIME SCALES

One length scale that is always present is the thickness of the shock wave. The simplest example is that of a monatomic gas. Its shock wave thickness is about four mean free paths, that is, it takes about four molecular collisions to adjust the equilibrium state upstream of the shock to downstream of it. The molecular processes inside the shock wave are not in equilibrium. A shock wave is thicker in polyatomic gases because molecular rotation and vibration require more collisions for equilibrium to be attained. For weak shock waves in the atmosphere the thickness may be of the order of one i km because of the large number of collisions required to attain vibrational equilibrium in nitrogen, especially when moisture is present (Johannesen and Hodgson, 1979). The shock wave thickness is also increased by chemical reactions as with detonations (Fickett and Davis, 1979), and by dissociation and ionization. More generally, the velocity and the thermal gradients inside the shock wave imply the importance of the material transport propertieswparticularly viscosity and heat conductivity (Zeldovich and Raizer; 1966; Thompson, 1972, p. 363). If the shock wave thickness length scale is too small to be of significance to the problem then it is sufficient to consider only the equilibrium states on both sides of the shock. One then has a shock Riemann problem.

146

L. E Henderson

Time scales are often important, but only two occurrences will be mentioned here. First, a time scale is present if the shock wave becomes unstable and splits into two waves moving in the same direction (Section 2.8.2). Suppose that an intense shock wave propagates into a metal, which is initially at atmospheric pressure and temperature, and suppose it also compresses the metal beyond its yield point. It is known that eventually the shock wave will split into two waves. The first is a precursor shock wave that compresses the metal to its yield point, and the second is a compressive plastic wave (Zeldovich and Raizer, 1966). Second, a shock wave may induce a change in phase of the material. A well-known example is the ~ ~ e (body-centeredcubic to hexagonal-close-packed) phase transformation in iron that takes place at 12.8Gpa, which can also cause splitting (Duvall and Graham, 1977). However, in many cases the time to attain equilibrium is orders of magnitude greater than the time for the shock wave to pass through the material. In this case there will be no phase change, and any equilibrium can only be metastable; there will then be no time scale. For example, if a shock wave

'....

VII

'

VIII 20

15

VI

Q

!0

II

"3--/

i I

-- I O0

.

.

.

.

.

Water

\ l

-- 50

,

0

_

I

50

_

_

i

O0

T~ FIGURE 2.1 Ice-water-phase diagram. (adapted with changes from Eisenberg and Kauzman 1969).

General Laws for Propagation of Shock Waves Through Matter

147

compressed water at atmospheric pressure to a pressure P > 104 atm (1000 MPa), and if thermodynamic equilibrium were attained, then ice (VII) would exist downstream of the shock wave (see Fig. 2.1). However, this does not usually happen because of the long time required for attaining equilibrium (Bethe, 1942). Instead, the water remains in the liquid phase but in metastable equilibrium. The time scale for thermodynamic equilibrium reduces rapidly, however, if the compressed state approaches a spinodal condition (Section 2.7).

2.4 THE CONSERVATION SINGLE

LAWS FOR A

SHOCK

2.4.1 LABORATORY FRAME C O O R D I N A T E S Suppose the material is contained in a cylinder of cross-sectional area A. One end of the cylinder is open, but the other is closed by a piston that is in contact with the material. Initially the system is at rest as shown in Fig. 2.2a. Suppose that at time t = 0, the piston impulsively acquires the finite velocity Up in the x-direction; it instantly begins to drive the material to the right at the same velocity Up. This is accomplished by a shock wave S that instantly appears on the face of the piston and propagates into the material with the finite velocity (/s > /alp (see Fig. 2.2b). As Us is finite (it must be less than the velocity of light!), the material to the left of the shock wave moves at the velocity Up, but the material to the right of it remains at rest. The equations from the conservation laws for mass, momentum, and energy can now be derived. It is assumed for simplicity that the system has adiabatic walls, that body forces such as gravity and electromagnetism are negligible and that there is no heat transfer by radiation across the shock.

Conservation of Mass After unit time the piston has moved a distance Up and the shock a distance Us, where Up, Us, are the scalar magnitudes (speeds) of the vectors/dp, (/s. During that time the shock compresses a mass of the material from its initial volume A U s to A ( U s - U p ) . The density therefore increases from P0 to p, so by conservation of mass PoUs = p ( U s - Up) = rh

(2.1)

where rh is the mass flux of material passing through the shock wave. Notice that it is strictly true that Us > Up, for if Us = Up then p = oo, which is physically impossible with the current state of knowledge.

148

L. E Henderson

I

.Po, Po o)

I 0 I

I .Po, Po

I

~

IS

P

jo, P, Up Up _~ '

Po,Po

Us- Up

r l

''

Us

b)

! _1

v !

,p ,P, Up- Us

c)

X

W

L. U -O, -U s

.,,

_ -Us

_____~_~, Po

t

FIGURE 2.2 Shock wave generated by the impulsive motion of a piston, a) Initial state at rest; b) state in unit time after the piston had acquired velocity/Jp impulsively; and c) motion in shock fixed coordinates (p is the piston and S is the shock wave).

Conservation of M o m e n t u m Suppose that P0 is the initial pressure of the material and p is the pressure of its compressed state. The piston applies a driving force ( p - po)A to the material, causing it to acquire a momentum per unit time of (PoUsA)Up - rhAUp. Then from conservation of momentum p - p0 - p0 U~Up

(2.2)

Conservation of Energy The compressive work that the piston does on the material in unit time is

PAUp. The energy gained by the material in unit time is the sum of the kinetic

149

General Laws for Propagation of Shock Waves Through Matter

!(PoUsA)Up2 and the internal energy (PoUsA)(e- %). Thus by conservation of energy pUp -- PoUs(1Up 4 - e - % )

(2.3)

The preceding equations are the conservation laws for a single shock wave. They are of fundamental importance.

2.4.2 SHOCK FIXED COORDINATES It is often convenient to transform the conservation laws into a coordinate system that is at rest with respect to the shock. This is easily accomplished by subtracting the shock wave speed Us from the (zero) particle speed ahead of the shock wave and also from the particle speed Up behind it. Then uo = - U s

(2.4)

u = Up - Us

(2.5)

and

where u 0 and u are the particle (material) speeds ahead of and behind the shock, respectively, and relative to it. The last of these equations can be written as

Up = u - u o

(2.6)

Substituting Eq. (2.4) into Eqs. (2.1), (2.2), (2.3) we acquire, after some algebra, the conservation laws in shock fixed coordinates; these are also called the Rankine-Hugoniot equations.

pu = PoUo p 4- pu 2 -- Po 4- PoU~ 1 u2 Po 1 P-4-e4- - - - 4 - % 4- u~ p 2 po

(2.7) (2.8) (2.9)

Equation (2.9) can also be written in terms of the enthalpy, h p/p + e, as: lu2

h 4.~

1

-- h 0 4.-~1/2 z

ht

which is called Bernoulli's equation. Here, ht is the total enthalpy.

(2.10)

150

2.5 2.5.1

L. E H e n d e r s o n

THE

HUGONIOT

ADIABATIC

THE HUGONIOT

EQUATION

If speeds U s and Up are eliminated from Eqs. (2.1)-(2.3), the conservation laws reduce to a single equation, which is a function only of the variables of state. It is called the Hugoniot equation, and it is fundamental to shock wave theory. 1 e - e o -- -~(p + po)(Vo - v)

(2.11)

Notice that a neater form of it is obtained if the densities P0 and p are replaced by the specific volumes v0 and v, respectively, where v = 1/p. In order to plot the Hugoniot curve in the (v, p)-plane it is necessary to know the initial state (v 0, P0) of the material and its EOS, or its equivalent such as a table of state properties.

2.5.2

THE RAYLEIGH EQUATIONS

If u o or u is eliminated from Eqs. (2.7) and (2.8), we obtain the Rayleigh equations 2

2

2 2

p0U~ - PoUo - p

21,12

Ap -

Av

(2.12)

where Ap = p - Po and Av = v - v0. If the pressure j u m p across a shock becomes vanishingly small, that is p --~ Po, then v ~ v0 and u ~ u0, and one also finds that the specific entropy is s ~ s o [Eq. (2.41) in Section 2.8.1]; then in the limit Eq. (2.12) becomes 22

P~176

[3P] ~ s

(2.13)

S

where a 0 is the speed of sound in the undisturbed material. It follows that - U s = u 0 --~ a 0, so that in the limit the shock wave propagates at the speed of sound, or in other words it is reduced to an acoustic wave. Note that -Vo[3p/3V]s, is the bulk modulus and that a 0 is called the longitudinal sound speed in solid mechanics and is appropriate for an unconstrained material. The sound speed in a thin bar is somewhat smaller (Kolsky, 1953).

151

General Laws for Propagation of Shock Waves Through Matter

Returning to Eqs. (2.1) and (2.2), and replacing Po and p by vo and v and eliminating Us the result, with the help of Eq. (2.6), is 1

1 Up -- (u - Uo)2 -- -~(p - po)(V 4- Vo)

(2.15)

which in laboratory frame coordinates is the gain in the kinetic energy per unit mass of the material by the passage of the shock wave. In shock fixed coordinates there is a loss of kinetic energy across the shock wave, because for a compression v < v0, and by Eq. (2.7) u < u 0, and so ~1/./2 < 89u~. From Eqs. (2.9) and (2.11) we get 1 (u02 _ u2) _ -~(p 1 - po)(V 4- v o) -~

2.5.3

(2.16)

S O L U T I O N OF A SIMPLE S H O C K R I E M A N N

PROBLEM The problem is illustrated in Fig. 2.2. Suppose the initial state (v0, P0) upstream of the shock is given, and also the downstream pressure p. It is required to find the compressed specific volume v and thus the downstream state (v, p). The problem can be solved in the (v, p)-plane when the EOS of the material is known p = p(e, v). The Hugoniot curve can be plotted by using Eq. (2.11) and the EOS, and v can then be found because p is given (see Fig. 2.3). The slope of

R

P

H

P I I I I I

I i I I I

I .... _

FIGURE 2.3

i ...... I

'A

ID

!

v

vo

Y

Hugoniot curve H and Rayleigh line R in the (v, p)-plane.

152

L. E

Henderson

the Rayleigh line A p / A v can now be calculated and it is a constant; this means that the Rayleigh line is straight in this plane. From Eq. (2.12), U2s/v 2 -- A p / A v , from which we find Us. By Eq. (2.11) the gain in the internal energy is represented by the trapezium ABCDA, while by Eq. (2.15) the gain in the kinetic energy per unit mass (laboratory frame) is represented by the triangle BECB. By Eq. (2.3) the total gain in energy per unit mass is represented by the rectangle AECDA.

2.6 THERMODYNAMIC MATERIALS

PROPERTIES

OF

It is important to notice that the conservation laws, the Hugoniot, and the Rayleigh equations are independent of any equation of state. Consequently, these laws and equations can be applied to any material. Nevertheless, the EOS has a decisive effect on the nature of the shock phenomena that appears in it. However, before these effects can be discussed it is necessary to define the thermodynamic properties that will be needed. The fundamental equation e = e(v, s)

(2.17)

contains all the thermodynamic information about the system (Callen, 1985). If by definition T--

~s v

(2.18)

3e]

(2.19)

and -p-

then by using Eqs. (2.18) and (2.19), in differential form, Eq. (2.17) becomes de - Tds - pdv

(2.20)

where T is the temperature. Equations (2.18) and (2.19) are the thermal and mechanical EOS, respectively, and they can also be written T -- T(v, s) and p - p(v, s)

(2.21)

It is often useful to define the EOS in terms of (v, e) rather than in (v, s). By Eqs. (2.18) and (2.19) this is always possible because e is a monotonically increasing function of s, as T > 0 and T - - 0 is unattainable, and so, T = T(v, e) and p = p(v, e)

(2.22)

153

General Laws for Propagation of Shock Waves Through Matter

The specific heats (2.23)

LOTIv and Cp - T -~ e

Cv -

The compressibilities Ks -- - -

(2.24)

and KT -- - V

V

S

T

The coefficient of thermal expansion l~V

(2.25)

p

Because of the thermodynamic relation Ks=

1

KT

fl2vT =

~

CpK T

Cp

CV

(2.26)

only three of these five properties are independent. It is conventional to choose these to be Cp, KT, and fl, as tables of them exist for many materials. In what follows, some of the properties obtained from the second and third derivatives of the energy are of special importance.

The adiabatic exponent

~' - p

Lav2Js

p~:s - p-~ = - p

~v s

where a is the speed of sound. For an ideal gas, 7 reduces to the ratio of the specific heats, 7 - Cp/Cv. Notice that ~ can often be found from Eq. (2.27) because 7 - aZ/P v. Some values of a, p, and p -- 1/v are given in Table 2.1.

The Grfineisen coefficient

r-

v 2e

TO~O~--T ~

] ~v v i i~i v

(228

This can be written to show that F determines the spacing of the isentropic curves in both of the (ln v, In p) and (v, p)-planes

F

l_avJ~ T

as v

pv T

as

ln v

(2.29)

154

L. E Henderson

Some Approximate Values of Shock and Material Properties. (Originally distributed at the 1989 Topical Conference on Shock Waves in Condensed Matter, Sponsored by the American Physical Society) TABLE 2.1

.

Material a

Water NaC1a KC1b

LiF Teflon PMMA Polyethylene Polystyrene

Brass A1-2024 Be Ca Cu

Fe b Pb U

.

.

.

/9

Cp

a

[kg/m3]

[kJ/kgK

[km/s]

1000 2160 1990 2640 2150 1190 920 1040 8450 2790 1850 1550 8930 7850 11350 18950

4.19 0.87 0.68 1.50 1.02 1.20 2.30 1.20 0.38 0.89 0.18 0.66 0.40 0.45 0.13 0.12

1.51 3.53 2.15 5.15 1.84 2.60 2.90 2.75 3.73 5.33 8.00 3.60 3.94 3.57 2.05 2.49

F

0.1 1.6 1.3 2.0 0.6 1.0 1.6 1.2 2.0 2.0 1.2 1.1 2.0 1.8 2.8 2.1

a Superscripts a and b refer to above and below phase transitions.

It follows at once that the isentropics cannot cross each in these planes when F > 0. By further manipulation and also by using Eq. (2.25) the following, useful relation between F and/~ is obtained: F=

vfl

(2.30)

CvKT For a thermodynamically stable system Cv > 0 and KT > 0 (see Menikoff and Plohr, 1989), and because v > 0, it follows that F and fl always have the same sign. When F is a constant then Eq. (2.30) becomes the famous Gruneisen EOS. For most materials, in most states, F and fl are positive. For the alloy Invar, they are almost zero at room temperature, but for water < 3.984 ~ and at 1 atm, both F and fl are negative. There are also many tetrahedrally bonded materials for which these quantities are negative for some domains of state (Table 2.2). For an ideal gas, F - 7 - 1 > 0. Some values of F are presented in Table 2.1, (Collins and White, 1964).

The reciprocal of the dimensionless specific heat pv -

g = T LO~s2Jv-

Cv~:

(2.31)

General Laws for Propagation of Shock Waves Through Matter

155

TABLE 2.2 Temperature Domains of Some Materials that have a Negative fl and F at a Pressure of I atma Material

Temperature domain

Water Diamond Vitreous silica ZnSe CdTe Ice I GaAs Ge InSb 0~-Sn

0, then the EOS must be convex [Eq. (2.33)]. If on the other hand, the inequality equation (2.33) is reversed, so that the EOS is concave, then it is weak expansion shocks that entropically increase for an adiabatic system. For waves of strength, Bethe (1942) found that sufficient conditions for adiabatic compression shocks to be entropy increasing were that the EOS obeyed the convexity constraint as well as a constraint on the Gl~neisen coefficient

arbitrary

2p] > b-V~2j~

0 ==> G > 0

F>-2

(2.42) (2.43)

Bethe (1942) showed that all pure substances in a single-phase state obeyed Eq. (2.42) for practically all thermodynamic states. The final result of his m e t h o d is given in the Appendix at the end of this chapter. A s u m m a r y of convex (G > 0) materials is presented in Table 2.4. The constraint fails, (G < 0) for fluids of sufficiently high molecular weight (i.e., those containing at least seven atoms in their molecule) and when the fluid in the superheated vapor state nears its phase critical point (Bethe, 1942; Zeldovich and Razier, 1996). Many authors have used the van der Waal's EOS to find a locally

TABLE 2.4 Materialsthat have a Convex EOSa .....

9 Dissociating or ionizing gases 9 Single-phasevapors with 0 strictly, and this is also necessary for the thermodynamic stability equation (2.36). As ~ - 0 is forbidden, there are no stationary values for the pressure along an isentropic. Convexity also forbids the speed of sound being zero, such as occurs at phase triple points, for example ice/water/steam, for then by Eqs. (2.27) and (2.42), G - 0, and the material is neither convex nor concave. However when G > 0, then by Eq. (2.27)

p2a2=

-[~]

>0

(2.44)

s

thus an isentropic curve always has a negative slope in the (v, p)-plane when the EOS is convex (compare Figs. 2.4 and 2.6). The only material that Bethe found that did not satisfy Eq. (2.43) was melting ice at - 2 0 ~ which occurs at about 2500atm and then F , ~ - 2 . 1 . However, other examples are now known, such as vitreous silica, which has the remarkably low value of 1-" ,~ - 9 at about 25 K (Collins and White, 1964).

2.8.2

S H O C K W A V E STABILITY C O N S T R A I N T S

Bethe (1942) deduced constraints on the EOS that would be sufficient to prevent a shock wave from splitting into two waves that move in either the same direction, or else in opposite directions. Von Neumann (1943) gave an elegant discussion of the first type of splitting. He supposed the shock being divided into two parts. The first part joins the initial pressure P0 to an intermediate pressure p', and the second joins p' to the final pressure p. The velocity of each part is given by the Rayleigh equation (2.12). The shock wave

161

General Laws for Propagation of Shock Waves Through Matter

S=const.

g-O

9

:

k

\

"

>0

I

',\\

-

\.

..,~

.

.

.

.

.

.

.

.

V FIGURE 2.6 Sketch of nonconvex, G < 0, isentropics near the saturated vapor line in the (v, p,)plane. Note that meta-stable regions SLP, saturated liquid line; SVP, saturated vapor line; CP, critical point (after Menikoff and Plohr, 1989).

cannot split into two waves moving in the same direction if the speed U~ of the following wave is >_ speed U s of the leading wave U~ >_ U s

( P - P') > ( P ' - Po) (v'-

v) -

(2.45)

(Vo - v')

for all p' in p > p ' > P0- In Section 2.9 it is shown that this splitting is impossible with a convex EOS. In order to exclude a shock splitting into two waves moving in opposite directions, Bethe (1942) deduced that sufficient constraints on the EOS were convexity G > 0, and

F~-l[_~__]-p__( Y - F ) < O koY.] e

(2.46)

V

or equivalently F < ~,

(2.47)

162

L. E Henderson

The basis for Bethe's (1942) study of the materials that satisfied Eqs. (2.46) and (2.47) was the thermodynamic identity

o=g,

--

< 0

Bethe (1942) concluded that: 9 "Nearly all materials in a single phase obey this constraint, but that it breaks down for a few phase transformations. 9 This constraint seems to be more generally fulfilled than the convexity constraint. ~ If the constraint is to be fulfilled for phase transformations, it is required that, AeAs > 0, that is, the energy and the entropy must change in the same direction. This is fulfilled for practically all phase transformations, but some exceptions are ice I or ice III to ice V (see Fig. 2.1)." "Later D'Yakov (1956) and Erpenbeck (1962) used a linearized analysis to test shock stability against small 2-D, ripple perturbations. It was concluded that a shock was stable if the following inequalities were satisfied -I 0; hence it may be used as a parameter (Section 2.9). The constraints presented here are necessary for the monotonicity of other properties and for the uniqueness of the solutions to 1-D shock interactions. Numerous theorems can be proved once the monotonicities are established. The strong constraint

pv F <m_+ --

r

1 (V-Vo) F >0

1+

2

(2.52)

V

When this constraint is satisfied, v is a monotonic decreasing quantity along a Hugoniot adiabatic. If also G > 0, then the curve is itself everywhere convex in both the (v, p)- and (u, p)-planes (see Fig. 2.7a). The ideal gas obeys Eq. (2.52) everywhere because from its EOS it is easy to obtain F = 7 - 1, G - 1(7 + 1) and pv/e - 7 - 1 - F, and so G > 0 and F - pv/e. All materials in a single phase obey Eqs. (2.33) and (2.52) for a large domain of states. The most notable exceptions are dissociating and ionizing gases, which violate Eq. (2.52) but still satisfy Eq. (2.33). In such circumstances the Hugoniot curve becomes locally concave in the (v, p)-plane, but still remains convex everywhere in the (u, p)-plane (see Fig. 2.7b). The medium constraint

F