Explosives
Residue: Origin and Distribution
John D. Kelleher
Team Leader
Fire and Explosion Investigation Section
Victoria Forensic Science Center
Victoria Police
Melbourne, Australia
Introduction.......Unexploded
Material.......Origin of
Explosives Residue.......Distribution
of Explosives Residue: Empirical Relationships.......Distribution
of Explosives Residue: Mathematical Relationships.......Application
to Explosion Scenes.......Summary.......
References
Introduction
Whereas the
occurrence of explosives residue has been studied extensively, there
are few direct references in scientific literature to the principles
underlying the origin and distribution of explosives residue. Where
does it come from? How does it spread? Does it form a pattern? Why
do we look for residue near the blast seat?
In any explosion,
there are two distinct sources of explosives residue to considerresidue
attached to or associated with fragments of a device, container,
or nearby object, and residue gleaned from surfaces or items that
are not associated with the explosive itself. Fragmentation is a
known source of unexploded material; however, for a bare, or effectively
bare charge, experience shows that there is still explosives residue
that can be collected. Where does this unexploded material come
from? How can it be that explosives material can survive in the
unreacted state so close to a detonation? These issues are the basis
of a more complete understanding of explosives residue distribution.
This paper explores some of the fundamental mathematical and physical
principles determining that distribution.
Unexploded
Material: Bulk Material and Explosives Residue
A trivial case
can be an explosive charge that fails to detonate completely due
to a failure of the detonator, some inhomogeneity in the main charge,
or some other reason. This may result in the explosives material,
in whole or part, being disrupted by a fire, a loworder explosion,
or a partial detonation. In these circumstances, the explosives
material distributed about the scene is bulk material, visible to
the naked eye or under modest magnification. Occasionally the detonation
wave fails to "turn the corners" near the detonator or
booster, so a small amount of unreacted explosive is left to be
ejected in a direction determined by its position relative to the
main charge.
Whereas this
bulk material is certainly residual, the term explosives residue
generally refers to submicroscopic particles whose presence can
be identified with sensitive chemical analysis but is not visible
except through highpower microscopes (Strobel 1998). The distribution
of bulk material is variable because the process itself may be erratic
and have relatively few large particles involved. However, explosives
residue in the form of unexploded material is detected even in cases
when there is no failure in the detonator, no inhomogeneity in the
main charge, or no obvious reason for anything other than complete
detonation.
Origin
of Explosives Residue
The concept
of critical diameter is recognized with small cylindrical charges
when surface effects lower the detonation pressure in the reaction
zone (Johannson and Persson 1970). In a larger charge, the shock
wave does not die out from an unstable wave front, but there may
be some effect due to the partial reflection of the wave at the
chargeair or chargecontainer interface (Figure 1). Whether the
shock front passes from explosives material into air
or from explosives material into a solid container wall, the shock
wave will be partially reflected at the discontinuity (Davis 1998).
As the shock front approaches, then reflects back into the reaction
zone, the surface layers may not react completely.
It can be suggested
that explosives residue is derived from this thin, partly reacted,
outer layer of the charge, and it is not unreasonable to consider
residue as fragments of a container, albeit extremely small, light
fragments, where the outer layer from which residue is derived corresponds
to the shell of the container. If this approach is correct and reflects
the actual course of events, the mathematical consequences are that
the proportion of explosives residue, that is the weight percent
of the charge, which survives as residue, as distinct from the total
weight of residue, will:
 Decrease
with increasing charge weight because for any explosives charge,
the amount of residue is proportional to the surface area, whereas
the charge weight is proportional to the explosive volume (for
most charge shapes, the volume increases at twice the rate of
the surface area).
 Decrease
with increasing velocity of detonation because the reaction zone
and the interaction zone at the explosive air boundary are narrower,
and less material remains in the unreacted or partly reacted state.
Residue from high velocity of detonation explosives, such as cyclotrimethylene
trinitramine (RDX) and pentaerythritol (PETN), have in practice
proven more difficult to detect than residue from lower velocity
of detonation explosives, such as ammonium nitratebased explosives.
 Increase
with increasing curvature of the shock front with smaller diameter
charges (Figure 1). As the charge diameter decreases, so does
the velocity of detonation (Johannson and Persson 1970), increasing
the size of the reaction zone.
 Increase
with an increasing number of interfaces so that stacked cartridges
or bags of explosives may be expected to produce more residue
than a uniformly packed container of equal explosive weight. Stacked
cartridges provide many interfaces and have a much greater surface
area than a single large charge.
Tests by the
U.S. Bureau of Mines on small cartridge charges which included granular
and gelatinous explosives incorporating nitric esters showed a strong
positive correlation between velocity of detonation and the proportion
of the explosive consumed, and a slight positive correlation between
charge weight and proportion consumed. (The overall proportion of
residue recovered, from all types of explosives tested, was surprisingly
high at around 40 percent, which reflects both the small charge
size and the positioning of the detonator.) (Miron et al.1983).
Distribution
of Explosives Residue: Empirical Relationships
Distribution
of residue associated with fragments
In a bare charge,
there is an interface at the charge surface where unreacted or partly
reacted explosives material may survive and become residue. This
material may leave the charge as residue. It can be formed from
an explosives device with a casing in two ways. It may leave the
charge surface independently or may be associated with casing fragments,
in which case its path will be determined by the fragment path.
Considering
residue associated with fragments, R. H. Bishop at Sandia National
Laboratories in Albuquerque, New Mexico, investigated the flight
of fragments from bomb casings and found that the flight was predictable
for regular fragments. He found that for cubic, tumbling (to minimize
aerodynamic effects) steel and aluminum fragments, maximum range
could be predicted with reasonable accuracy (Bishop 1958).
Assuming they
are homogenous, fragment thickness for metal cubes is effectively
a function of weight. In this case, the significant difference between
the types of metals is the variation in density. From Bishop's chart
(Figure 2), an equation can be derived which approximates the maximum
fragment range, with fragment thickness converted to a function
of density and maximum fragment weight.
R_{max} = 190r^{.112}w + 52r^{.858}
Equation
1
r = fragment density (grams per cubic
centimeter)
w = maximum fragment weight
(kilograms)
For
a bomb casing of an improvised explosives device with a typical
small pipe bomb maximum fragment size of 100 grams, this equation
predicts R_{max} for steel fragments to be 320 meters and
R_{max} for aluminum fragments to be 139 meters.
Perhaps more
importantly, as w decreases, the final term becomes more
significant.
Table 1 can be constructed showing R_{max} in meters
for steel and aluminum fragments of various maximum fragment weights
(in kilograms). The table shows that as the maximum fragment weight
decreases, the maximum fragment range decreases to a limiting value;
thus, the final term in Equation 1 becomes 52r^{.858}. This
suggests that the spread of residue for scenes involving metallic
fragmentation is likely to be many times the radius of scenes involving
bare or lightly cased charges. Confinement or environmental factors
can have some effect, but for simplicity, these factors are assumed
to be negligible.
Distribution
of residue from bare or lightly encased charges
There
is little published information about the spread of fragments and
residue from explosives devices. If it is assumed that the equation
can be applied equally to plastic (a mean density of 0.8 grams per
cubic centimeter) and to explosives (densities commonly range from
0.8 to 1.2 grams per cubic centimeter), Table
1 can be extended into Table 2
to include distances for various weights of those materials. The
application of the equation to explosives and plastic is, at this
stage, hypothetical. However, the computer models developed by Baker
(Baker et al. 1978) produce similar results for fragments in the
range of 0.8 to 1.2 grams per cubic centimeter. This suggests that
as estimates for maximum fragment range, the figures for smaller
fragments in Table 2 are realistic.
This
implies that at a large scene with negligible external factors such
as wind and terrain, there will be an inner field radius of about
60 meters essentially covered with explosives residue and light
fragments, and an outer field radius up to 320 meters having isolated
areas of residue associated with particular metallic fragments.
Fragments with a high sectional density, ballistic shape, or efficient
aerodynamic profile can be projected to greater ranges.
Note that in
Equation 1, there is a term for fragment weight but not for explosives
type or charge weight. The derived equation predicts that, regardless
of the charge weight, for a large unconfined charge that detonates
evenly, there is a limiting radius on the order of 60 meters (depending
on charge density), beyond which explosives residue concentration
drops effectively to zero. (This should not be confused with projectile
trajectories from weapons where the effect of the charge is directed,
and the projectile shape and rotation are designed to maximize range.)
The velocity with which particles leave the surface is dependent
on the local particle velocity, which is independent of the charge
size.
Evidence
for a limited range for explosives residue
The application
of this equation to explosives residue is hypothetical, although
as stated above, there is some evidence that it is applicable to
plastic. The proposal of a limiting radius of about 60 meters for
nonfragment residue is difficult to test. Logistic and economic
considerations have thus far prohibited a suitable test in Australia
because, whereas 60 meters may seem a reasonable residue radius
for charges in the kilogram range, it seems somewhat low for charges
of hundreds or thousands of kilograms.
Fortunately,
recent American and British collaborative work performed in New
Mexico provided an empirical guide to the amount and distribution
of residue that may be encountered in large devices (Phillips et
al. 2000 A and B). The study examined blast effects and residue
from very large charges of improvised explosives material. The nitrate
residue, found in the greatest abundance, was measured at various
ranges. The residue collected was residue deposited on the front
and back of metal signs. Table 3
shows the average nitrate levels, measured in micrograms (mg), at these distances.
With
the obvious anomalies correlating to some extent with wind speed
and direction, there is a drop in residue at 60 meters, even from
very large charges. In Test 6, for example, the wind was from the
southeast, and most of the residue was deposited to the north and
west of the explosion.
Factors not
covered in the test report, such as the varying wind speed and direction,
the arrangement of the explosive, and possible contamination of
the area, limit the significance of the results. However, they can
be used as a guide to the validity of the proposed 60meter limit.
Moreover, the proposed distribution is independent of charge size
and direction of initiation, since neither significantly alters
the local particle velocity at the interface.
Plotting the
average nitrate concentration against range, regardless of direction,
linear regression analysis using both linear and third order polynomial
models produced estimates for the range at which the expected value
of the nitrate concentration falls to zero, of 59±3 and 61±6 meters for the 454 kilogram
and 2268 kilogram charges respectively.
Distribution
of Explosives Residue: Mathematical Relationships
Residue
distribution independent of charge size
The perceived
independence of explosives residue distribution with respect to
charge size can be related to the Gurney velocity (Gurney 1943),
the velocity to which fragments can be accelerated by explosives,
for various explosivecontainer geometric arrangements. R. W. Gurney
and J. E. Kennedy obtained the expressions for Equations 2 and 3
(Kennedy 1970).
u = D/3 (M/C + ˝)^{1/2} for a cylindrical charge
Equation 2
u = D/3 (M/C + ^{3/5})^{1/2} for a spherical charge
Equation 3
where D is velocity
of detonation, M is container weight, C is charge weight.
Cooper and Kurowski
(1996) suggested that D/3 is an estimate of the characteristic Gurney
velocity. Simple expressions of varying accuracy can be derived
for other configurations and can be used to illustrate the effect
of decreasing container thickness.
The effect of
decreasing container thickness can be demonstrated by using the
cylindrical arrangement that is representative of a conventional
bomb or an improvised device such as a pipe bomb. Equation 4 is
derived for the cylinder.
M/C = length x p
(r_{o}^{2}  r_{i}^{2}) r _{container
} / {length x p ( r_{i}^{2}) r explosive}
Equation 4
(where r_{o}
= the outside radius, r_{i} = the inside radius, r = the density of the explosive)
M/C = (r_{o}^{2}/
r_{i}^{2 } 1) x r
_{container} / r _{explosive}
As r_{i} => r_{0 }(i.e., the container becomes thinner,
M/C =>0 and u => D/3 (1/2)^{1/2)}
(substituting 0 for M/C
in Equation 2, hence u => 0.47D).
Whereas Kennedy
recommends that the Gurney equations not be used at M/C < 0.3
because gasdynamic effects dominate, the maximum ejection velocity
remains proportional to the detonation velocity even when gas dynamics
dominate.
Thus,
for an unconfined explosive, the velocity at which residue leaves
the charge surface is dependent only on D, the velocity of detonation.
For a confined explosive using a cylinder equation, with the constant
container weight as M and the varying charge weight C, the fragment
velocity can be calculated from:
u = D/3 (M/C
+ ˝) ^{1/2}
u = D/3 (2C/(2M+C)) ^{˝}
Equation 5
as
C increases, (2C/(2M+C))^{1/2 }=> Ö2,
(substituting in Equation 5) and
u => Ö2.D/3 = 0.47D.
For a confined
explosive, the velocity at which residue leaves the charge surface
is dependent only on D, the velocity of detonation.
The underlying
explanation for this result, which differs markedly from the theory
of projectiles from weapons, is that the velocity with which particles
leave the surface will be dependent on the local particle velocity.
The local particle velocity is a function of the detonation velocity
and the bulk sound speed (i.e., the speed of sound in the unreacted
explosive [Cooper and Kurowski 1996]), which does not vary widely
through the range of common explosive materials.
Residue
distribution pattern: Model 1
The mass distribution
of residue can be considered along with ranges and initial velocities
when the residue does not adhere to primary fragments. (The question
of residue attached to secondary fragments is a more complex matter
to pursue.) Yallop proposed a model of residue evenly distributed
over the surface of a sphere (Yallop 1980) with residue concentration
c (grams per square centimeter) equal to 10^{4}/pr^{2} (r in meters) (i.e., an inverse
square model). Considering the subsequent path of the residue can
further develop this model. If it is assumed that all fragments
and residue are of equal weight and are projected at equal speeds
at all angles above the horizontal, the basic equations of projectile
motion can be applied to plot range against angle of projection
to develop Figure 4. With the effect of air resistance assumed to
be negligible, the solution of more complex equations incorporating
air resistance is possible but impractical and unnecessary for this
exercise.
The basic ballistic
equations are:
R = (v^{2}/g)sin
2a
v = initial velocity
Equation 6
R_{max}
= v^{2}/g
g = gravitational constant
Equation 7
a = ˝sin^{1}gR/v^{2}
a = angle of projection
Equation 8
For the ideal
explosion considered here, the proportion of mass projected between
two angles equals the proportion of the quadrant covered, (i.e., Sm/M = [a_{2}  a_{1]}/90). Referring to Equation 8, the proportion of the
total mass projected to any range in the crosssectional representation
is
between R=0,1: a=0,p/2, represented by the area
outside the curve R = (v^{2}/g) sin2a or
a = ˝sin^{1}gR/v^{2 }( a < p/4) + p/4˝sin^{1}gR/v^{2}
(p/4 < a < p/2)
Equation 9
or
more simply, since the curve is reflected about the line {y=p/4},
a = sin^{1}gR/v^{2} ( a < p/4).
Equation 10
This
curve is effectively a massrange curve, since Sm/M = (a_{2}  a_{1})/90, so we have
m = k.sin^{1}gR/v^{2} where R_{max}
= v^{2}/g.
Thus,
m
= k.sin^{1}R/R_{max}.
Equation 11
In terms of
the distribution over a surface, this curve forms a solid of revolution
about the m (a) axis, representing
the mass distribution, effectively the residue distribution, about
the origin. Therefore, it must be modified by the factor 1/2pR so
that
m = (1/2pR).k.sin^{1}R/R_{max}
Equation 12
which is at
some variance with the inverse square distribution (the curve M=k/2pR^{2} has been used in Figure 5 to show the difference).
The derived distribution has an increased proportion of the mass,
whether residue or fragments, at greater range and has a distinct
endpoint, a range beyond which residue is not expected to be found.
The result,
in terms of what may be expected at a scene, is complex. With a
real device, not all fragments and residue are identical. There
are ranges of fragment sizes and velocities, and there is likely
to be a geometrical effect, a form factor based on the shape of
the charge that will further skew the distribution. Nevertheless,
each group of similar fragments and residue with similar velocities
can be expected to have a distribution similar to Figure 5, characterized
by the specific values for that group. The end result will be a
distribution that is the sum of many less populous distributions,
with varying total masses, ranges, and fragment sizes.
The overall
effect may vary significantly from case to case. However, the form
of the distribution suggests that the concentration of residue may
be lower at the center and higher at medium to long ranges, possibly
incorporating local maxima in comparison with the inverse square
distribution. For residue, there will be a limiting radius, which
the equation derived from Bishop suggests will be about 60 meters.
The fragments are similarly distributed, to greater ranges, with
the fragment pattern being the sum of the individual fragment distributions
to the maximum range for each weight.
Residue
distribution pattern: Model 2
There are additional
factors affecting the pattern. Air resistance is significant, particularly
for smaller fragments. Calculation of this effect would require
a major computing effort and is only applicable to an individual
explosion. Nevertheless, it is reasonable to suppose that air resistance
would have a foreshortening effect, decreasing the range of fragments.
If a model is
adopted where the residue stops at the surface of the Yallop sphere,
effectively a hemisphere of radius R_{max} (Figure
6), and falls to the ground to assume an even distribution of residue
of equal size, clearly the residue dm distributed over
the segment of the crosssection dx
is proportional to the arc length subtended by dx.
Then
dm = k˘.(dx^{2}
+ dy^{2})^{1/2},
® dm = k˘.(1 + dy^{2}/dx^{2})^{1/2}dx.
Since
dy/dx = x/(R_{max}^{2}  x^{2})^{1/2},
® dm = k˘.R_{max}^{2}/(R_{max}^{2}
 x2)^{1/2}dx, and
m
= k˘.R_{max}sin^{1}(x/R_{max}),
Equation 13
the
point x ( R ) is obviously a point on a circle about the origin,
so
m = (1/2pR).k˘.R_{max} sin^{1}R/R_{max } = (1/2pR).k˘˘sin^{1}R/R_{max},
Equation 14
which is essentially
the same as the equation derived previously for Model 1.
This is not
to suggest that one model is proof of the other, because there is
an inherent mathematical similarity which leads to the similar results.
However, both models support the prediction of a limiting residue
radius and the possibility of residue levels above those that may
be expected from an inverse square distribution at ranges approaching
the limiting range.
Residue
distribution affected by air resistance, wind, and charge size
In this case,
wind and residue initial velocity must be treated as vector quantities,
increasing the complexity of the calculations greatly. Extension
of the models to include these factors is beyond the scope of this
basic discussion, but some general observations can be made.
The shape and
velocity of individual particles will determine the effect of air
resistance. The distances derived from the Bishop chart take into
account air resistance for heavy particles but may be overestimated
for lighter particles. Model 2 can be seen as a simple model incorporating
the effect of air resistance. This model preserves the two important
features of Model 1, a clear limit for the spread of residue and
the increased residue level at close to the maximum range.
Even the simple
case of a constant horizontal wind introduces a major complexity.
The distribution cannot simply be translated downwind because particles
with a greater time of flight will be affected longer. This extends
the distribution in the downwind direction and compresses it in
the upwind direction. For small particles, terminal velocity is
a few meters per second, so even a light breeze can spread the residue
to many times the calculated radius downwind. The significant features
of these simple models are still evident though. Even with a strong
wind, there is a clearly defined (but possibly much longer) maximum
range, and there is still a more even spread of residue than predicted
by an inverse square distribution.
With large charges,
the physical size of the charge will materially affect the distribution.
The calculated residue radius would need to be increased by the
radius of the charge. With smaller charges, this is obviously less
important.
Residue
distribution affected by fragmentation
That primary
and secondary fragments may carry explosives residue adhering to
their surfaces has been established at many reported bomb scenes.
Also, basic aerodynamic considerations suggest that residue may
be entrained behind relatively fast moving fragments. If some of
this residue is shed in flight, it may be found along the fragment
flight path at greater than expected distances from the blast seat.
Effect
of the blast wave and negative pressure
The models proposed
are based on the proposition that the limiting speed of the explosive
residue is the local particle velocity. This is considerably lower
than the velocity of detonation, and hence the speed of the blast
wave as it departs the surface of the charge. The blast wave does
slow to the speed of sound in air, but the shock front speed is
still much greater than the local particle velocity (Johannson and
Persson 1970). Particles from the detonation, whether gaseous or
solid, are not affected by the shock front but may be given some
positive impulse by the positive pressure behind the front. The
negative impulse following the shock wave may similarly act to retard
these particles. These complexities are beyond the scope of the
empiric models presented here.
Application
to Explosion Scenes
The models discussed
do not imply any major change in the current procedures for processing
crime scenes, but they do show that there is a theoretical basis
for the procedures currently undertaken. There is a theoretical
as well as an empirical explanation for the existence of explosives
residue, and there are mathematical models to validate the practice
of residue recovery near the explosion seat. The distribution models
provide a reasonable basis to select controlsampling areas and
offer some guidance for appropriate barrier locations and control
points.
Summary
 There is
evidence to support the suggestion that explosives residue is
derived from a thin outer layer of the charge.
 The proportion
of explosives residue will decrease as both the charge size and
the velocity of detonation increase.
 Simple mathematical
models indicate that residue not associated with fragments is
concentrated within a limiting radius, approximately 60 meters,
regardless of the charge size (excluding wind effects).
 The distribution
of explosives fragments and residue does not follow a simple inverse
square distribution. High concentrations of residue are not only
encountered close to the blast seat; residue may be found in relatively
high concentrations further from the blast seat than would be
expected. These could not happen if the distribution followed
a simple inverse square law.
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