A member of the police bomb squad has to be able to assess the type of bomb used in a terrorist activity in order to gain some knowledge that might lead to the capture of the culprit. The most commonly used explosive device is the pipe bomb. Pipe bombs can be made from a variety of explosives ranging from large-grain black powder and gunpowder to more sophisticated compounds, such as PETN or RDX. Identification of the explosive material used in the pipe bomb (after detonation) will tell a bomb squad investigator where the materials might have been purchased, the level of sophistication of the terrorist, and other important identifiers about the criminal.
Four basic types of energetic materials are used in making pipe bombs, each with its own distinctive pattern of post-mortem damage.
1. Explosives. Those that detonate at a velocity equal to the compressional sound speed of the explosive material itself. These materials are by far the most energetic (also the most difficult to acquire) and are characterized (after explosion) by very small pipe fragments, highly discolored (usually bluish in tint) fragments, and extreme collateral damage (especially close to the detonation).
2. Propellants. Usually formed from some compound based on nitrocellulose. These materials do not detonate, but burn very rapidly. Usually propellants are formed in special geometric shapes that allow their surface area to remain constant or increase as they burn, thus causing the burning rate to increase until the compound has been completely exhausted. The destructive force of propellant-based pipe bombs is somewhat less than that of true explosives and is characterized by medium fragment size, little discoloration, and moderate collateral damage.
3. Large-grain black powder. Has been around since about 600 BC , when the Chinese discovered the carbon-sulfur-potassium nitrate mixture. The size of black powder grains can vary tremendously, but the geometry is such that the powder always burns down (the burn rate always decreases once the entire surface of the mixture is burning). Although still very deadly, the damage from these types of pipe bombs is less than that of the other two. The residual fragment size is larger, and the discoloration of the fragments is slight.
4. Gunpowder. A subclass of black powder, usually considered to be homemade. It is characterized by very large fragments (one or two in number), almost no discoloration, and little collateral damage. Black powder is still very common among terrorists.
We can form a table of patterns for each feature:
Assume that the membership space for each feature can be partitioned similarly into four sections on a normalized abscissa, as shown in Fig. P11.24. The other two graphs (for discoloration and collateral damage) would look identical to the one in Fig. P11.24 (with different labels). The weights assigned to each feature are $0.5,0.3$, and 0.2 , respectively. Now, say a new bombing has taken place and the aftereffects measured over three features are denoted as singletons, given as
$$
\mathrm{B}=\left\{\text { fragment size }=\frac{1}{0.7}, \text { fragment color }=\frac{1}{0.6}, \text { damage }=\frac{1}{0.5}\right\}
$$
Determine the composition of the bomb used in the bombing.