Explosives Residue: Origin and Distribution (Forensic Science Communications, April 2002)
April 2002  Volume 4  Number 2 
Research and Technology
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
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.
Figure 1 Shock Wave Reflection at Charge Surface, Air Interface Click to enlarge image.

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).
Figure 2 Bishop's Chart for Calculating Maximum Fragment Range Click to enlarge image. 
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.
Figure 3 Nitrate Residue, 454 kg Charges, Third Order Polynomial Regression Analysis Click to enlarge image. 
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 + ½)^{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 + ½) ^{1/2}
u = D/3 (2C/(2M+C)) ^{½}
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 = ½sin^{1}gR/v^{2}
a = angle of projection
Equation 8
Figure 4 Angle of Projection Versus Range Click to enlarge image. 
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 = ½sin^{1}gR/v^{2 }( a < p/4) + p/4½sin^{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.
Figure 5 Residue Distribution Models, Inverse Square Versus Model 1 Click to englarge image. 
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.
Figure 6 Explosives Residue Trajectories, Model 2 Click to enlarge image. 
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.
 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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