Physics of Air Raids

J. D. Bernal1

The field considered in this lecture is limited to only one aspect of air raids, namely the effects produced by high-explosive bombs. A large number of physical problems arise in connection with other aspects of air raids—for example, in the matter of the outbreak of fires; however, these questions are not so close to our everyday experience as questions concerning the effects caused by bomb explosions.

The terrifying effect of high-explosive bombs is to a considerable extent connected with insufficient knowledge of the processes that occur when these bombs burst. It is perfectly natural that the study of phenomena proceeding at the speeds of explosions is difficult; nevertheless, it is still possible. Thanks to the work of physicists in many countries, and especially of English physicists during the war (chiefly in the laboratory of the Department of Scientific and Industrial Research), we may say that the main features of the physical processes connected with an explosion are already emerging quite clearly. Of course, because of the complexity of the phenomenon, and also because of the requirements of secrecy, in the present article we can outline only the general contours of the results of these investigations.

The action of all explosives is based on the liberation of energy over very short intervals of time. The quantities of energy released are large, but they do not substantially exceed the quantities released in ordinary energy production. If referred to unit mass, explosives contain scarcely more energy than coal or gasoline; but whereas 10 gallons of gasoline can keep an engine running for 5 hours, the same quantity of explosive (approximately that contained in a 50-kilogram German bomb) releases its energy in the course of \(1/20\,000\) sec. Accordingly, the power liberated in an explosion proves to be many times greater. Another consequence of the brevity of the interval of energy release is that the mechanical effects of explosions are far more important than the thermal effects. An explosion is a very effective method of converting chemical energy into mechanical—

release at very small losses in the form of heat. Unfortunately, in wartime, in any case, all mechanical effects have a destructive character.

The enormous rate of release of the energy contained in an explosive means that the action exerted on surrounding bodies—whether they are solid, liquid, or gaseous—is not determined by their ordinary mechanical properties. In considering explosions, simple static pressures have almost no significance, and only the dynamic properties of materials prove essential. In general this is expressed in an increase in the resistance of materials. Most materials have a much greater resistance to sudden loads than to loads observed under a gradual increase of stresses; but the stresses arising in explosions, at least near the site of the explosion, prove to be much greater than those that can be produced in laboratories, and in essence they can be studied only in connection with explosions.

A large part of the action of explosives on the surrounding medium can be well explained if one assumes that explosives form a wave of exceptional intensity, propagating at very high speed through bodies. An ordinary mechanical disturbance is transmitted in a substance at the speed of sound. This latter is determined by the square root of the ratio of the density of the body to its elasticity. If the density is large and the elasticity small, the wave propagates slowly, and conversely. The limits of these speeds are 150 m/sec in gaseous carbon tetrachloride and 5,000 m/sec in steel. Owing to the high pressures developing at the site of the explosion, the speeds obtained are much greater. This occurs as a consequence of the dependence of the elasticity of a body on pressure; the internal layers of the atom are more elastic than the external ones. Under strong compression the elasticity increases, and the speed of propagation of the wave increases. This increase in speed is more noticeable in gases than in solids or liquids. Thus, for example, the speed of sound in water may vary from 1,825 m/sec to 3,650 m/sec near an explosion; the corresponding figures for the speed of sound in air will vary from 330 to 6,000 m/sec.

At the same time the character of the wave itself will change. High-pressure waves do not have the smooth form of ordinary sound waves. Indeed, the pressure in the wave front rises instantaneously to its maximum and then gradually falls, passing through values lower than atmospheric pressure, or the phase of “suction” (suction) (Fig. 1).

The formation of this wave with a steep front, or shock wave, resembles the formation of surf waves in the sea; the high-pressure phase, always transmitted faster than the low-pressure phase, forms the front just as the crest of a surf wave does, which is delayed less than its base, which experiences friction against the ground. This crest moves forward and, overturning, destroys the wave. A shock wave is always destroyed, since its frontal parts lose energy faster than the following parts, as a result of which, as it propagates—

As the wave spreads, its frontal part decreases more and more, and the whole wave degenerates into an ordinary sound wave.

A shock wave in air is precisely what we usually call an explosion; it accounts for the greater part of the collateral phenomena associated with an air raid, such as, for example, the destruction of windows. The pressures required in order to force out window panes are not especially great. A pressure of 60–600 g/cm² (6 atm.) is sufficient to become dangerous to a person. This can occur only in the immediate vicinity of the place of explosion, so that in fact direct injury to people by an explosion occurs comparatively rarely. The shock wave, however, is not merely an increase in pressure; immediately behind the front the air moves forward, creating an initial impulse. It is accompanied by a subsequent reverse impulse. These sharp oscillations of the air can move loose objects, knock people over, etc. The greater part of the damage in explosions is precisely a secondary effect in this sense, and is usually not so serious.

Fig. 1. Pressure–time curves for the explosion of a charge of 2 pounds of explosive substance.

Accordingly, in view of the relatively small pressures with which one has to deal in the case of an explosive wave in air, it is precisely in this case that safety measures achieve the greatest successes, especially when the matter concerns such light structures as windows. It has proved possible to determine, by calculation, the effective strength of materials with respect to their resistance to blast waves. This determination

is not a simple matter, since the behavior of an elastic structure under the action of a shock wave depends not only on the character of the latter, but also on the elastic properties of the structure itself. A shock wave, encountering an obstacle such as a window, sets it into oscillation, and the resulting effect proves to depend on the relation between the window’s natural period and the time characteristics of the wave.

For any wave and for any known structure, the effective pressure can be reduced to a certain static pressure producing the same effect. This pressure is known as the “equivalent static pressure” (Fig. 2). The fact that the action of a wave depends on the elastic properties of the obstacle is manifested in the different behavior of different windows and doors located at the same distance from the site of an explosion. One window may be blown out, while the neighboring one remains intact solely because it has a different natural period. The behavior of windows under explosive waves is well illustrated by the accompanying photographs (see the insert). When an explosion occurs far from a window, the glass first bends in the direction of the shock wave, then moves in the opposite direction and cracks (if it cracks at all), so that the fragments fly outward. In the case of a closer explosion, the glass cracks during the first motion, and the fragments fly into the building. When the explosion has occurred very close by, the window oscillates with the frequency of one of its harmonics, and the periphery of the glass cracks, while the middle part often remains entirely intact until it is shattered by striking some obstacle (insert, Fig. B).

One might think that windows could be protected by increasing their strength. Unfortunately, however, almost all methods of strengthening windows simultaneously increase their natural frequencies, and consequently also the equivalent static pressure; thus, since the two effects usually almost balance one another, only the illusion of increased strength is obtained. In reality, almost nothing can be done to prevent glass from cracking, but very much can be done to prevent the scattering of fragments.

Cinematographic study of the process of destruction of window glass in explosions has shown the great usefulness of such protective devices as transparent viscose films and screens.

The peculiar action of an explosion on windows depends not only on the great variety in the sizes of windows. A shock wave behaves like other waves: it may be reflected with greater or lesser absorption, depending on what it strikes. In streets, especially those with tall buildings, this reflection will be complex. A bomb explosion produces a series of reflected waves which, at a considerable distance from the site of the explosion, combine into a periodic disturbance. Glass panes whose natural frequency coincides with the frequency of this disturbance will be destroyed as a result of resonance. As a consequence of this effect, individual windows may be blown out at a great distance from the site of the explosion.

PHYSICS OF AIR RAIDS

A. Radial cracking. Explosion at a moderate distance.
B. Circular cracking. Close to the explosion.

Frames from a motion picture of a breaking window:
C. 0.03 sec after the explosion. First appearance of cracks.
D. 0.01 sec later. The radial cracks have fully developed. Small fragments fly out.
E. 0.08 sec later. Fragments are carried in the direction toward the bomb.

Fig. 2.

Another peculiar effect is connected with the fact that the blast wave in a narrow street is reflected from its upper open part. It is well known that a compression wave propagating in a tube with an open end, on reaching it, produces a reflected suction wave. If this occurs in a street, the reflected suction wave may turn out to be stronger than the primary suction wave of the bomb itself. It can act on windows and doors, throwing them out into the street.

The blast wave behaves in a characteristic way with respect to restricted obstacles. Ordinary sound waves form “shadows” only behind large obstacles, such as hills or tall houses, since the wavelengths are of the order of 3–30 m. A blast wave may be regarded as the sum of a certain number of waves of different lengths. The part associated with the wave front has a very small wavelength, while the tailing, suction part is associated with a longer wavelength. As a result, a blast wave passing through an opening or bending around an obstacle changes. Roughly speaking, the pressure wave propagates straight ahead and forms a shadow, whereas the reverse suction part of the wave propagates in all directions, easily bending around corners. Therefore, behind obstacles the compression part of the blast wave may decrease to 0.1 of its value, becoming comparable in intensity with its suction part. This circumstance is extremely favorable, since research has shown that it is precisely the compression part of the blast wave that is most harmful to a living organism. Thus, by taking shelter behind a small garden wall, one can protect oneself from the direct action of an explosion. On the other hand, an open door is dangerous and, by protecting the entrances to shelters, we protect ourselves both from fragments and from the blast wave.

The fear caused by bombs is to a considerable extent connected with reports of large numbers of people killed at great distances without external injuries—the mystical effect of the explosion itself. Studies have shown that the effect of the blast wave is a simple impact on an object. Basically, the effect of an explosion acts most strongly on the cavities of our body—especially on the lungs, causing bruises and hemorrhages in them. This action is connected only with the compression part of the wave; the suction part has no influence. Fortunately, the lungs can withstand a large number of bruises without lasting damage, and although a significant number of cases of blast injury is known, most of them ended favorably. Lung injuries could be regarded as noninfectious pneumonias, and their treatment was reduced to keeping the patient in bed for some time.

Besides the blast wave, injuries may occur from fragments and from impacts against the ground. When a bomb bursts, its casing first expands and then breaks up, just as happens in the rupture of gas cylinders at exceptionally high pressures. The rupture occurs under tension along planes situated at an angle of 45° to the surface of the bomb; as a result of the rupture, fragments are formed and are thrown out by the expanding gases. These fragments acquire-

...develop high velocities (up to 100 m/sec), owing to which their penetrating power is also great. The sizes of fragments range from blocks weighing 18 kg to the size of the finest grains of sand. As a result of experiments, carried out on a broad scale since the beginning of the present war, we have understood the mechanism of the penetrating action of fragments and have learned to protect ourselves from them. Fortunately, the cheapest materials have proved sufficiently effective in this respect. Thus, for example, a layer of sand 1 m thick protects against the small fragments usually encountered in practice, and 1/3 m of brickwork is sufficient for protection against all fragments except the very largest.

This, however, is not always sufficient to eliminate the damage caused by fragments. The point is that any rapidly flying object, on striking an obstacle, not only penetrates into it. In addition, it creates within the obstacle a shock wave which, being reflected from the opposite surface, may cause cracks to appear on it and individual pieces to be torn out; if these fly with sufficient velocity, they may cause serious damage. This tearing-out can be prevented by covering the walls from the inside with materials of high tensile strength, such as steel sheets or even steel mesh.

Only some bombs explode on the surface—on pavements or on street sidewalks, etc. Most of them penetrate into buildings or into the ground. Bombs exploding in the earth leave craters 6–12 m in diameter, depending on the size of the bomb and the properties of the soil. The damage inflicted in this case is connected with the blast wave in the earth. When a bomb explodes in a dense medium, as, for example, in the earth, it produces a shock wave that propagates with different velocities in different soils. If the soil above is more yielding than at depth, the shock wave will propagate in a complicated manner. It will be reflected from the lower-lying layers and at some distance will already give a complex sequence of waves resembling earthquake waves. These waves may act upon structures in a rather peculiar way, depending on the relation between the natural frequency of the building and the frequency of the wave; however, damage will be caused only in very old or poorly constructed buildings.

The most severe damage near high-explosive bombs that have burst in the ground is connected not with the shock wave, but with the actual motion of the soil near the place of the explosion. When a bomb bursts, the explosive gases, acting on the surrounding soil, form the primary expansion chamber. The earth is displaced outward, and a considerable displacement actually occurs, partly elastic and partly inelastic. The earth may shift by several centimeters and not return exactly to its former place, although the residual deformation will be small (Fig. 3). These movements of the ground are, of course, most dangerous for underground structures. In character, however, this motion is not an instantaneous impulse, since here the duration of the constant pressure is of the order of 0.1 sec. This is not so dangerous for structures that can withstand such pressures without destruction.

Fig. 3. Displacement record.

Labels in the figure:

• Vertical axis: Displacement in inches
• Horizontal axis: Time in sec
• Maximum displacement 1.17 inches
• Permanent displacement 0.14 inches

PHYSICS OF AIR RAIDS

The movement of the ground caused by explosive gases is usually associated with damage to the gas and water-supply network.

The shock wave of a bomb that has burst in the ground reaches the surface and is reflected as a stress wave. If it is sufficiently intense, the soil cracks and a cone of earth is thrown upward, breaking up into separate parts and leaving behind a characteristic crater. The observed picture is always complicated by the presence of fragments that have fallen back. The actual crater is usually almost twice as deep. If the bomb penetrates very deeply, then destruction does not occur at the surface—the ground simply bulges upward and settles back. This is the so-called “camouflet” (underground explosion). Such camouflets are of little importance, except in those cases when they may be confused with unexploded bombs (Figs. 4a–4b).

When a bomb strikes a building, the effect of the explosion will be complex; however, it is associated with a small number of factors. In this case the primary effect of the explosion will be the action of the shock wave, which encounters the walls and brings them down. The effect is greater than in an open explosion, because upon reflection the action of the wave will add to the initial explosion, producing a more prolonged pressure and, correspondingly, a larger external moment.

With the exception of spacious premises (railway stations, hangars), the pressure of the explosion is sufficient to destroy walls and floors, sweeping them away and exposing the structure. What happens next depends on the type of construction. In a favorable case, the result of the explosion will be the formation of breaches in the walls. Much more often, damage to the walls leads to partial or complete destruction of the building. In buildings with a steel framework or in reinforced-concrete structures the skeleton is not destroyed and prevents the fall of the upper parts of the structure, withstanding

Fig. 4a

Figure annotations:

• a) Before the explosion
• b) After 0.002 sec.
• c) After 0.1 sec.
• Gases escaping from the bomb push apart the material of the projectile.
• Layer covering the crater rises and cracks.
• Cracks beginning at the surface.
• Formation of a compression chamber.
• The compression wave is reflected from the surface.

a) After 0.2 sec

e) End of explosion

Fig. 4b

Condensation wave reflected as a tensile wave

Irregularity of the ground-surface layer

Crack reaching the surface

Formation of a condensation chamber

Completely developed condensation chamber

a) Before the explosion

b) After 0.004 sec

c) After 0.1 sec

Fig. 4.

relatively small weight of the fragments formed directly at the site of the explosion.

The present essay, which concerns certain physical aspects of damage from air raids, shows that we already have a quantitative picture of these phenomena, which is the first step in the struggle for rational methods of reducing the effectiveness of air attacks.

Fig. 4d.
a) After 0.2 sec: escaping gases; pressure of the escaping gases.
d) End of the explosion: beginning of collapse; cavity of the chamber after the explosion.

1. Lecture delivered on December 3, 1940, at the Royal Institution of Great Britain, Proceedings of the Royal Institution of Great Britain, 31, 262, 1941. Translated by A. A. Ilyina. ↩