THE JULIUS MESZAROS LECTURE
53 YEARS OF BLAST WAVE RESEARCH - A PERSONAL HISTORY
John M. Dewey
Dewey McMillin & Associates, 1741 Feltham Road, Victoria, BC V8N 2A4, Canada
Professor Emeritus, Dept. Physics & Astronomy, University of Victoria, BC Canada
ABSTRACT
I began my studies of the physical properties of blast waves in 1957 when the Moratorium on the Atmospheric
Testing of Nuclear Weapons initiated a renewed cooperation between Canada, US and UK. My fascination with
this subject continues to the present day, and I would like to take the opportunity, at what will undoubtedly be
my last scientific conference, to share with you a few of the topics of blast wave research that I continue to find
interesting. Some of these may be well known to you, but I hope that you will find others to be of interest,
especially those that we do not yet fully understand.
The following topics are discussed: the non-isentropy that characterizes a blast wave; the piston-path method for
calculating the physical properties of a blast wave; the Hopkinson and Sachs scaling laws; the Rankine-Hugoniot
relationships; height-of-burst effects, and our emphasis of hydrostatic pressure as a blast wave descriptor.
THE ENTROPY PROBLEM
The expanding spherical shock wave from a centred explosion causes large changes of
entropy in the air close to the centre, and progressively smaller changes as the shock wave
expands and weakens. This leaves the air in a state of radially decreasing entropy. As a
result, the blast-wave-flow past a fixed location is non-isentropic so that the simple
thermodynamic relationships cannot be applied to a time-resolved measurement made at that
position. For example, a measurement of the pressure-time history at a point in a blast wave
cannot be used to calculate the time history of any other physical property, such as density or
particle velocity, at that location. To fully describe the physical properties of the blast wave
flow past a fixed position, three independent, simultaneous measurements must be made, such
as hydrostatic pressure, density and total pressure, as was achieved by the Suffield Blast
Station (Ritzel, 1985; Slater et al, 1995).
This problem can be simplified if the blast wave is studied in Lagrangian rather than Eulerian
co-ordinates. In Lagrangian co-ordinates the flow is followed along the particle paths. When
an element of air is traversed by the primary shock of a blast wave all its physical properties,
including the entropy, undergo a virtually instantaneous change, and these changes can be
simply calculated using the Rankine-Hugoniot equations in terms of the easily measured
shock Mach number. From that point on, the element of air moves at constant entropy, until it
is overtaken by the second shock, and the simple thermodynamic relationships, such as
P  RT and P /    const , can be used to relate the various physical properties of the air
element at different places and times.
It was for this reason that we started to use smoke tracers and high-speed photography to map
the particle trajectories within blast waves. The technique was first developed to measure just
the particle velocities, but it soon became apparent that knowledge of the particle trajectories
was sufficient to determine all the physical properties of a blast wave, without reference to
any other measurement. The method, known as Particle Trajectory Analysis (PTA) (Dewey,
1971), is illustrated in Fig. 1, in which the particle trajectories, measured using high-speed
photography of smoke tracers, are plotted in the radius-time plane. The time-of-arrival of the
primary shock at each smoke tracer provides the radius-time history of the shock from which
the shock Mach number can be calculate and used in the Rankine-Hugoniot equations to
provide all the physical properties of the gas immediately behind the shock.
Particle
Trajectories
ΔR
Time
Primary
Shock
ΔRo
Radius
Figure 1. Primary shock and particle trajectories in the radius-time plane
The distance between the tracers, ΔR, at any part of the flow field gives the density, ρ, from
the relationship,
  R0  R0
,
 
 0  R  R
2
(1)
where ΔR0 is the original spacing between the tracers, and ρ0 is the ambient density. This
maps the density throughout the flow field. The isentropic relationship
P PS    S 

(2)
can then be applied along the particle trajectories to map the hydrostatic pressure, where PS
and ρS are the pressure and density, respectively, behind the primary shock and γ is the ratio of
specific heats. The hydrostatic pressure and density can then be used with the particle,
velocity
u  dR dt ,
(3)
to map all the other physical properties throughout the flow field. The Particle Trajectory
Analysis technique was extensively used on many of the explosive test series carried out at
Suffield and White Sands between 1961 and 1995, with charges ranging from 500 kg to 4
ktonnes. The PTA technique provided a complete mapping of all the physical properties of
the blast wave, and since it depended only on high-speed photography of smoke tracers, it
was an invaluable backup in the event of any failure of the electronic gauge measurements.
THE SPHERICAL PISTON
Although PTA proved to be a powerful technique for measuring the physical properties of
blast waves, it required the deployment of extensive arrays of smoke tracers. To overcome
this problem, Professor Gottlieb of UTIAS reminded us of a paper by G. I. Taylor (1946),
which shows that any centred blast wave can be generated by a spherical piston with the
appropriate radius-time trajectory. The appropriate piston path can be determined from highspeed photography of a single smoke tracer established close to the charge just before
detonation. Ideally, the piston path would be that of the contact surface between the
detonation products and the ambient atmosphere, but due to Rayleigh-Taylor and RichtmyerMeshkov instabilities such a contact surface does not exist, and there is an extensive region of
turbulent mixing. However, it is not necessary to go far beyond the mixing region to find a
stable piston path, as illustrated in Fig. 2.
Figure 2. A multi-ktonne ANFO explosion. The second (white) smoke tracer from the left shows that a stable
flow soon develops outside the turbulent contact zone, and this can be used to define a piston path trajectory
from which all the properties of the subsequent blast wave can be calculated. (Photo courtesy the MABS web
site)
The trajectory of a smoke tracer, initially formed just beyond the turbulent contact region,
provides the radius-time history of a spherical piston that can be used in any suitable hydrocode to generate a blast wave identical to that produced by the explosion. When this
technique was first used, the particle trajectories generated by the piston at various distances
from the centre of the explosion, were compared with the observed trajectories at those
distances, and slight adjustments were made to the piston path until an optimum match
between the calculated and observed smoke trajectories was achieved. However, for the
MINOR UNCLE and MISERS GOLD tests, no adjustment of the original piston path was
required, and all the physical properties of the blast waves were mapped using the trajectory
of a single smoke tracer. A comparison of pressure-time histories obtained using the pistonpath method and electronic gauges is shown in Fig. 3. It is very satisfying to a physicist to see
such a validation of the simple laws of physics which provide identical pressure-time histories
in a blast wave obtained from the amplified signal from a piezo-electric crystal or from the
high-speed photography of a single puff of smoke.
(a)
)b(
Figure 3. A comparison of the (a) hydrostatic and (b) dynamic pressure time-histories measured by electronic
gauges (the noisy curves) and by the smoke puff – piston path method (smooth curves) on MINOR UNCLE (2 kt
ANFO surface burst).
The smoke tracer – piston path technique is not so useful for the study of the complex thermobaric, non-centred, multi-reflection explosions, which are of primary interest these days, but it
remain as the simplest, cheapest and most powerful technique for characterizing all the
physical properties of blast waves produced by newly developed explosives.
THE SCALING LAWS
If the radially varying entropy in a blast wave provides a challenge for the researcher, there
are two features of blast waves that simplify our task. One of these is the validity of the
scaling laws developed by Hopkinson (1915) and Sachs (1944). Hopkinson suggested that if
a peak physical property behind the primary shock, PS, occurs at a distance R1 from a charge
of mass W1, and at a distance R2 from a charge of the same material of mass W2, then
R1 R2  W1 W2  3 .
1
(4)
Sachs extended this relationship to allow for differences in the atmospheric pressure, P0, and
absolute temperature, T0, viz.,
R1 R2  W1 W2 
13
t1 t 2  W1 W2 
13
P02
P02
P01  , and
13
P01 
13
T2
T1  ,
12
(5)
(6)
where t is a time-of-arrival, or a duration within the blast wave. A US, British and Canadian
Tripartite Agreement in the late 1950s, suggested that these relationships be used to report all
blast measurements relative to a unit charge mass in an atmosphere at NTP, viz. pressure
P0 = 101.325 kPa, temperature T0 = 288.16 K (15 C) and density ρ0 = 1.225 kg/m3.
With a few exceptions, these simple relationships allow the comparison of blast waves from
different size charges detonated in different atmospheric conditions, and more importantly,
permit a reliable prediction of the physical properties of blast waves from any charge size in
any atmospheric conditions. The validity of these scaling laws over many orders of magnitude
of charge mass was not fully established until 1964 (Dewey, 1964). Figures 4 and 5 are
reproduced from that paper, and demonstrate the validity of the laws both for the physical
properties immediately behind the primary shock as a function of radius, and more
importantly, the physical properties as a function of time at a fixed location.
Figure 4. Peak particle velocity versus scaled distance for surface-burst hemispherical TNT charges ranging in
mass from 30 kg to 100 tonne (Dewey, 1964).
Figure 5. Particle velocity versus scaled time at a scaled distance of 1.77 m from surface-burst hemispherical
TNT charges ranging in mass from 30 kg to 100 tonne. Due to the afterburning of TNT, the particle velocity
never falls to zero, but the scaling laws still appear to apply (Dewey, 1964)
The physical property shown in these figures is particle velocity, measured using high-speed
photography of smoke tracers, which in those days was a more reliable measure than
hydrostatic overpressure using piezo-electric gauges. The results in Figure 5 are of special
significance because particle velocity is the property most affected by the afterburning of
TNT. It can be seen that because of this affect, the flow velocity does not fall to zero, even
past the minimum of the negative phase. Serendipitously, this figure shows that the effect of
the afterburning of TNT also obeys the Hopkinson and Sachs scaling laws.
In order to use the scaling laws it is necessary to know only the charge mass, and the ambient
pressure and temperature at the time of the explosion. Experience shows, unfortunately, that
these parameters are frequently not measured accurately. The nominal charge mass is often
the only value available. This may be provided by the manufacturer and is sometimes based
on the volume of the mold rather than the weighed charge. Also, the quoted atmospheric
pressure and temperature may be that provided by the closest weather station, and not
measured on the test site at the time of the detonation.
Although the scaling laws have been shown to be valid over many orders of magnitude of
charge mass for most explosives, there are limits in some cases. For example, it has been
shown (Kleine, Dewey et al, 2003) that the scaling laws are valid for silver azide charges as
small as 0.5 mg, and no upper limit appears to have been found. In contrast, uncased cast
TNT charges less than about 4 kg may fail to detonate completely. Similarly, uncased ANFO
will not detonate in amounts less than a few 100 kg, which is one of the reasons it is such a
useful explosive because it can be safely handled in relatively large amounts. With bigger
charge masses, the detonation efficiency of ANFO gradually increases with charge size due to
the increased loading density of the prill-oil mixture. In large scale field trials the energy
release may also depend on the enthusiasm of the Test Director when the charge is built. For
very large charges, in the megaton range, the scaling laws at low overpressures would be
expected to break down at ground level due to atmospheric diffraction caused by the lapse
rate. It is for this reason there are zones of silence around large energy releases such as
volcanic eruptions (Dewey, 1985).
REANKINE-HUGONIOT EQUATIONS
In addition to the reliability of the scaling laws, blast wave research is aided by the very
reliable Rankine-Hugoniot relationships. These relationships were developed independently
(Rankine, 1870a, b, Hugoniot, 1887, 1889), before the concept of a shock was known, in an
attempt to find the compressible gas equivalent of the hydraulic jump of incompressible
flows. The equations relate the physical properties on the two sides of a shock in terms of the
other physical properties, or more usefully, in terms of the easily measured shock Mach
number. The ratio of specific heats must also be known, and γ = 1.401 can be used for shock
waves in air with strengths less than 7 atm (MS < 2.6). The equations were discussed in detail
at MABS19 (Dewey, 2006) and do not require further elaboration here.
SHOCK REFLECTION
It has been known, certainly since WWII, that an explosion at an appropriate altitude can
produce more damage at ground level than the same charge detonated on the surface. It was
in order to optimize this effect that John von Neumann, who was the scientific advisor to the
targeting committee for the atomic bomb attacks on Hiroshima and Nagasaki, developed his
two- and three-shock theories. To his surprise, the theories predicted that there would be a
significant increase of hydrostatic pressure at the point of transition from regular to Mach
reflection, which produced extensive “knees” in the height-of-burst curves, as shown in
Figure 6. Subsequent pressure measurements of blast waves from air-burst nuclear test
explosions failed to show this enhancement effect. Nor was it observed by Reichenbach and
Khul in their extensive experiments using 1 g charges. The present generally accepted
position appears to be that “height-of-burst curves do not have knees”.
Figure 6. Theoretical height-of-burst curves of peak hydrostatic overpressure for a 1 kt nuclear explosion,
showing extended regions of high pressures at transition from regular to Mach reflection (von Neumann, 1943).
The enhanced pressure in the region of transition from RR to MR has been demonstrated in
the pseudo-stationary case of reflections from plane wedges, and in the case of non-stationary
reflections from cylinders in shock tubes. The enhancement is also shown in hydro-code
calculations if sufficiently high spatial and temporal resolutions are used. The pressure
increase at transition for an air-burst explosion was first observed by Reisler et al (1987) and
can be seen in the results from the AirBlast database, illustrated in Fig. 7. The enhancement
occurs over a relatively short distance and the high amplitudes predicted by the von Neumann
2-shock theory have not been measured.
Regular Reflection
Reflection
Mach Reflection
Figure 7. Peak hydrostatic overpressure versus distance for a 1.25 kg charge of TNT at a height-of-burst of
1.7 m, derived from the AirBlast data base of experimental measurements. The increase of pressure in the
transition region is clearly seen.
10
Transition
Dynamic Pressure (atm)
RR
1
R
MR
0.1
0.01
0.1
1
10
100
Ground Radius (m)
Figure 8. Dynamic Pressure versus ground range for a 1.25 kg charge of TNT at a height-of-burst of 1.7 m,
derived from the AirBlast data base of experimental measurements. There is a five fold increase of dynamic
pressure at transition from regular to Mach reflection
One of the reasons that the controversy persists over the changes that occur to the physical
properties at the transition from regular to Mach reflection, is that most workers consider only
changes to the hydrostatic overpressure. In contrast, it is easy to observe the large increase of
dynamic pressure, and particularly the particle displacement, immediately following transition
illustrated in Figure 8. From this evidence, it is concluded that height-of-burst curves do have
knees. The hydrostatic pressure effects are very localized, but the dynamic pressure effects
may be significant, a feature that does not seem to be discussed in the literature.
THE OVER EMPHASIS ON HYDROSTATIC PRESSURE
In conclusion, it seems important to emphasize the importance in the study of blast waves, of
looking at physical properties other than hydrostatic pressure. Because of a blast wave’s
characteristic non-isentropy, it is necessary to know three independent properties of a blast
wave if its flow is to be completely described. For example, if the hydrostatic pressure (P),
the density (ρ) and the particle velocity (u) are measured independently as functions of
distance and time, then all other properties, such as temperature and dynamic pressure, can be
calculated.
Traditionally, hydrostatic pressure has been the parameter most commonly used to define a
blast wave. This is because it was the easiest parameter to measure. Damage criteria are
usually reported in terms of hydrostatic overpressure, although most damage and injury is
caused by forces not related to the hydrostatic but to the dynamic pressure. In fact hydrostatic
pressure is the least sensitive of all the blast properties that can be measured. For example,
there is no change of hydrostatic pressure across a contact surface, such as that produced by a
Mach reflection, or in the boundary layer in which there are extreme gradients of flow
velocity and therefore of dynamic pressure. As a result, phenomena such as these are
undetected by a hydrostatic pressure measurement. The most sensitive and slowest changing
physical property of a blast wave is the particle displacement, such that the time-resolved
measurement of a single particle-flow tracer is sufficient to determine all the other physical
properties of the blast wave as functions of space and time.
In the days when the physical properties of blast waves were determine almost entirely by
direct measurement, the convenience of using pressure as the primary monitor is
understandable. However, today our principal tool for studying blast waves is undoubtedly
numerical simulation using a hydro-code. The results of the hydro-code can be validated by a
minimal amount of direct measurement, but even here, the measurement of any physical
property other than pressure provides a more reliable validation. Once the hydro-code
simulation has been validated, any physical property can be output with equal ease, and it is
important that results be reported, not only in terms of hydrostatic pressure but also the
density, particle velocity, and thus the dynamic pressure, which reveal many interesting
properties of the flow field not shown by hydrostatic pressure alone.
An example that demonstrates the importance of this procedure is the study of blast
penetration into structures. The entrance ways to protective structures are often equipped
with a labyrinth to mitigate the effects of an incident blast wave. The degree of mitigation
can be studied by a hydro-code simulation, and almost all reports of such research compare
only the hydrostatic overpressure in the unprotected to that in the protected structure. In these
simulations the total energy in the blast wave remains constant, which is probably a valid
assumption since the only way in which the entering blast wave can lose energy is by
conduction to the walls of the structure, and that is likely to be very small. The excess energy
1
1
OP  u 2 ) , where γ is the ratio of specific heats; OP
in a blast wave is essentially  (
 1
2
is the hydrostatic overpressure; ρ the density, and u the flow speed (Dewey & McMillin 1980,
1985). If the hydrostatic pressure, OP, is decreased by the labyrinth, it is important to know
what has happened to that part of the energy. The labyrinth may have spread the blast wave
in space and time so that the energy density will have decreased, and this may be a desirable
result. On the other hand, if the labyrinth has converted the energy of the hydrostatic
overpressure into dynamic pressure, then the labyrinth may have increased rather than
decreased the potential for damage and injury.
At the last three MABS Symposia, there were twenty papers dealing with blast mitigation. Of
those, only one discusses the energy of the blast wave and notes that a reduction in
hydrostatic pressure may lead to an increase of dynamic pressure and thus be non-beneficial.
Only two of those papers mention an attempt to measure or report the dynamic pressure. Of
the other papers, most of which rely on hydro-code simulations, only the hydrostatic pressure
is reported or discussed. Two papers note, with surprise, that although the blast, as defined by
hydrostatic pressure, appears to be mitigated in the tunnel system the blast at the end-wall is
enhanced, but no explanation of this is given.
CONCLUSION
In conclusion, may I thank you for the honour of allowing me to present the Julius Meszaros
Lecture, and thus permitting me to share some of my thoughts and ideas, at what will
undoubtedly be my final MABS Symposium. With the exception of the Oslo meeting, which
I was unable to attend due to the sudden illness of my wife, I have attended all the Symposia,
starting with the first at Suffield in 1967. I have learned much from the papers presented, but
the true benefit of a symposium such as this arises from the friendships which are made and
the trust which develops between colleagues from countries around the world. I could end by
presenting a “thank you” list longer than that of the average Oscar winner, but will limit
myself to a single note of appreciation to past and present colleagues at Spiez Laboratory for
the creation and maintenance of the MABS web site, and Spiezbase in particular. This is a
unique facility that deserves to be maintained and used, even more extensively than at present,
as an archive and clearing house for the research results of this community.
REFERENCES
Dewey, J. M., 1964, The air velocity in blast waves from t.n.t. explosions, Proc. Roy. Soc. A 279, 366385.
Dewey, J.M., 1971, The properties of blast waves obtained from an analysis of the particle trajectories,
Proc. Roy. Soc., A 324, 275-299.
Dewey, J. M., 1985, The propagation of sound from the eruption of Mt St Helens on 18 May 1980,
Northwest Science, 59, 2, 79-92.
Dewey, J. M., 2006, The Rankine-Hugoniot equations: their extensions and inversions related to blast
waves, Proc. MABS19, DRDC Suffield, Canada, P008, 1-15.
Dewey, J. M. and McMillin, D. J., 1980, Measurements of energy density in shock and blast waves,
Proc. 12th Int. Symp. Shock Tubes and Waves, Hebrew Univ. Jerusalem, Ed. A. Liftshitz & J. Rom,
695 – 703
Dewey, J. M. and McMillin, D. J., 1985, Efficiency of energy conversion using shock waves, Can. J.
Phys., 63, 3, 339 - 345
Dewey, J. M. and van Netten, A. A., 2000, Height-of-burst curves revisited, Proc. MABS16, 70, 185192
Hopkinson, B., 1915, British Ordnance Board Minutes, 13565.
Hugoniot, P. H., 1887, Mémoire sur la propagation du mouvement dans les corps et ples spécialement
dans les gaz parfaits, 1e Partie, J. Ecole Polytech. (Paris), 57, 3-97.
Hugoniot, P. H., 1889, Mémoire sur la propagation du mouvement dans les corps et plus spécialement
dans les gaz parfaits, 2e Partie, J. Ecole Polytech. (Paris), 58, 1-125.
Kleine, H, Dewey, J. M., Ohashi, K., Mizukaki, T., and Takayama, K., 2003, Studies of the TNT
equivalence of silver azide charges, Shock Waves 13: 123–138.
Rankine, W. J. M., 1870a, On the thermodynamic theory of waves of finite longitudinal disturbance,
(read 16 Dec., 1869), Phil. Trans. Roy. Soc. London, 160, 277-286.
Rankine, W. J. M., 1870b, supplement to "On the thermodynamic theory of waves of finite longitudinal
disturbance", Phil. Trans. Roy. Soc. London, 160, 287-288.
Reisler, R. E., Dixon, L. A. and Keefer, J. H., 1987, HOB experiments and charge development studies,
Proc. MABS10, Bad Reichenhall, 2, 374-406.
Ritzel, D. V., 1985, The DRES blast-gauge station, Proc. 9th MABS, AWRE Foulness, III, 2, 1-13.
Sachs, R. G., 1944, The dependence of blast on ambient pressure and temperature, BRL Rept.466,
Aberdeen Proving Ground, MA.
Slater, J. E., Boechler, D. E. and Edgar, R. C., 1995, DRES Measurement of free-field airblast, Minor
Uncle Symp. Rept., Defense Nuclear Agency, POR 7453-4, Vol. 4, 2, 1-98
Taylor, G. I., 1946, The air wave surrounding an expanding sphere, Proc. Roy. Soc., A 186, pp. 273292.
von Neumann, J., 1943, Oblique reflection of shocks, Explo. Res. Rpt. 12, Navy Dept., Bureau of
Ordnance, Washington, DC.