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CHAPTER 2EXPLOSIVES

What Is An Explosive?

An explosive [1]-[12] is any substance, or mixture of substances, that is capable ofundergoing a rapid exothermic (energy-releasing) chemical reaction without the participation ofexternal reactants. In this context, gasoline is not an explosive because it requires an externalreactant (oxygen) to burn. However, a mixture of gasoline and air does constitute an explosive(because the oxygen is no longer external – it is part of the mixture). Most combinations of fuelsand oxidizers are explosives and indeed many explosives are combinations of separate fuel andoxidizer components. In many of the chemicals that we traditionally call explosives, both the fuelcomponent and the oxidizer component are incorporated into the same molecule. For example,nitroglycerine contains both a fuel component (the hydrocarbon backbone of glycerine) and anoxidizer component (oxygen derived from the attached nitrate groups).

The exothermic chemical reaction that provides the energy for an explosive can proceed inone of three fashions. If the reaction occurs at a rate slow enough that no appreciable temperaturerise occurs, or if one does occur, it does not affect the rate of reaction, then we describe the reactionas simple oxidation (if fuel and oxidizer are separate molecules) or decomposition (if fuel andoxidizer are combined in the same molecule). If the reaction propagates through the material at asubsonic velocity determined by the rate at which energy is transferred as heat from the products tothe reactants, the reaction is termed a deflagration. Deflagration is simply a rapid burning process.However, if the exothermic reaction provides such violent release of energy that the temperature andpressure of the reaction products cause a supersonic shock wave to be driven into the adjacentunreacted material and if the heating produced by this shock is sufficient to initiate the chemicalreaction in the unreacted material at a rate sufficient to maintain the undiminished propagation ofthe shock, the reaction is termed a detonation. The propagation velocity of the shock frontproduced in a detonation is called the detonation velocity. Detonation velocity is a characteristicproperty of an explosive.

High explosives are defined as those explosives that undergo detonation under “normal” useconditions. Some high explosives may undergo deflagration under some ignition conditions anddetonation under other ignition conditions. For example, the plastic explosive C-4 will burn(deflagrate) if initiated by a flame. Small amounts of C-4 were commonly used as heating fuelduring the Vietnam conflict. However, if C-4 is initiated by a strong impact (shock initiated), it willdetonate. Since the blast effect is usually the desired attribute, not its heating ability, C-4 isconsidered a high explosive.

Low explosives are defined as those explosives that undergo deflagration under normal useconditions. Low explosives are commonly used as propellants or gas generators. Propellants areused to provide a controlled release of gas to perform useful work. Most solid rocket and gun

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propellants are low explosives. In such propellants the fuel and oxidizer are intimately mixed andtherefore satisfy the defining requirement of an explosive. It should be noted that some propellantsmay detonate under certain conditions. For example, gunpowder will deflagrate at normal densities(loosely-packed powder) but can detonate if densely packed or if the burning is tightly confined.As a result, gunpowder can be used as both the propellant and the main charge in an artillery shell.High-performance solid rocket propellants may be borderline between high explosive and lowexplosive. More than one rocket motor test has turned catastrophic when the engine pressure roseto levels that caused the deflagration to transition to a full-scale detonation. This is sometimescalled “going high order” as the reaction changes from a relatively linear burning process to anonlinear detonation process (and nonlinear processes require higher order terms in anymathematical description of the rates).

Pyrotechnics are explosives used to create smoke, light, heat, and sound. Fireworks, smokegrenades, and flash-bang grenades are pyrotechnic devices. Pyrotechnic devices may employ bothlow and high-explosive components.

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Explosive Trains and Fuzes

Explosives are almost never used in a stand-alone configuration. Without a detonator, mostexplosives would not reliably explode at the desired time. Without safety & arming devices, theexplosives would have an unacceptably high probability of exploding at times that would bedisastrous to the users. When explosives are combined with other devices, an explosive train isestablished.

An explosive train is an arrangement of a series of combustible and explosive elementsconsisting of [13]:

* a primer,* a detonator,* a delay,* a relay,* a booster charge,* a lead, and * a main charge,

one or more of which may be omitted, duplicated, or combined. The function of the explosive trainis to accomplish the controlled augmentation of a relatively small impulse into one of sufficientenergy to cause the main charge to detonate.

Explosive trains are invariably used in combination with fuze agents. A fuze agent is anymechanism or phenomenon that may be used as a means to accomplish the initiation of detonationof the explosive train. Fuze agents are sometimes called stimuli or insults. The latter term isusually reserved for unintended stimuli producing undesired results (i.e., “If you insult an explosive,it blows its top!”). The following are all examples of viable fuze agents:

* percussion (shock) from the impact of a spring-loaded firing pin,* percussion (shock) from the impact of an explosively accelerated “slapper” plate* flame (heat) from a safety fuze, * flame (heat) from a “bomblet” in a fuel-air explosive,* heat from a chemical reaction, such as the action of an acid on a reactive metal, * heat from friction in motion of an object against a rough surface, * heat and shock from an electric spark,* heat and shock from a vaporizing bridgewire when heated by an electric discharge.

The fuze agent is produced by a fuze, which is a device that determines if and when the explosivetrain should be inititated. Figure 6-1 illustrates the elements and nominal ordering of elements inan explosive train.

Figure 6-1. Elements of an explosive train.

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Regardless of the type of warhead, the precise timing of when that warhead detonates isdetermined by a fuze. The fuze interacts with the external environment and when conditions areappropriate, the fuze produces the fuze agent that triggers the initiation of detonation in theexplosive train. There are many different types of fuzes that can be used in virtually everyimaginable application. Table 2-1 lists most of the more important types of fuze.

Table 2-1. Types of Fuzes.

* Impact – Electrical– Chemical– Pyrotechnic

* Influence – Magnetic– Electric Field– Acoustic– Pressure– Cosmic Ray Distribution

* Proximity – Radar Range– Radar Doppler– Electro-Optical– Acoustic– Infrared– Image-Based– Gravimetric

* Fixed Delay – Pyrotechnic (Safety Fuze)– Chemical– Electronic– Mechanical

* Delayed Action – Fixed Delay– Inertial-based

* Chronometric – Analog– Digital

* Location-Sensing – GPS– Inertial– Laser Radar

* Altimetric – Barometric– Radar

* Environmental – Barometric– Thermometric– Hygrometric

* Motion-Sensing – Microwave– Infrared– Ultrasonic

* Command Detonated – Hard-Wired– Radiofrequency– Telephone

* Anti-Tamper – Circuit Closure– Circuit Breakage– Tilt/Jiggle– Optical Circuit Breakage (Laser Beams)– Temperature Change– Pressure Change

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Impact fuzes are among the simplest and more commonly used kinds of fuze. In anelectrical impact fuze the forces of impact either crush a physical body or drive a mass against aspring forcing one contact of an electrical switch against another. When the contacts touch, anelectrical circuit is closed that contains a battery and an electrical initiator. Electric current flowingthrough the initiator produces sufficient heat to cause the primary explosive to detonate. In chemicalimpact fuzes, the impact causes the breaking of a vial of reactive chemical. The reactive chemicalmay cause the primary explosive to detonate directly. More commonly, the reactive chemical eithercauses an electrical circuit to be closed or provides the missing ingredient (e.g., the electrolyte) ina battery in an otherwise closed circuit containing an electrical detonator.

Influence fuzes are commonly used in naval mines. The fuze senses variations in one ormore physical properties of the external environment and triggers if an appropriate pattern ofvariations is observed. Common signatures examined include magnetic field, acoustic intensity, andhydrostatic pressure. Typical magnetic, acoustic, and pressure signatures of a ship are shown inFigure 2-2, 2-3, and 2-4, respectively. Combinations of these signatures may also be used to makeminesweeping more difficult. Less commonly used influence signatures include electric fields andthe angular distribution of cosmic rays. In the latter, the passage of a ship attenuates cosmic rayscoming from above relative to those passing through the earth and arriving from below.

Proximity fuzes are used when it is desired to detonate the warhead at some distance fromthe target[4]. Such detonation at a distance is desirable when the warhead is unlikely to actually hitthe target (as in anti-aircraft missile or ant-aircraft artillery warheads) or when detonation at adistance will permit a fragmentation warhead to scatter its fragments over a larger area (commonlydesired with anti-personnel artillery warheads). Proximity to a target can be determined in severalways: significant change in signal level, determination of range, or detection of a Doppler-shiftedsignal. Microwave radiation, infrared/visible radiation, and acoustic radiation can be and are usedto produce the signal, depending on the application.

Perhaps the simplest form of proximity fuze transmits a signal (microwave, infrared, oracoustic – typically radiated into the forward hemisphere) and triggers when it detects a back-reflected signal that exceeds some predetermined threshold. Under normal conditions, there isnothing to reflect the radiated signal unless the target is present. When the target approachessufficiently closely, the detected signal will rise to a level that exceeds the threshold. Such fuzesare essentially simple radars or sonars. Analysis of required thresholds, detection probability as afunction of range, and false alarm probabilities follows the standard approaches pertinent to the kindof sensor employed. Such fuzes experience problems when the projectile is fired at shallowtrajectories. Potential returns from high terrain features or vegetation may cause prematuretriggering. The large area of the surface features can produce signals at significant distances thatrival the signals produced by targets at shorter distances. Determination of range can eliminatemany such premature detonations. The radar or sonar transmits a signal permitting high resolutionrange measurements. When a sufficiently strong signal with an acceptably close range is detected,the fuze detonates the warhead. The Doppler shift may also be used to discriminate ground returnsfrom target returns. Targets are often moving with respect to the ground and will have adistinctively different Doppler shift. Image-based fuzes use data derived from imaging seekers todetermine the rate of closure and distance to the target to predict the appropriate time of detonation.

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Figure 2-2. Typical magnetic signature of a ship as seen by an influence fuze of a naval mines.[2]

Figure 2-3. Typical acoustic signature of a ship as seen by an influence fuze of a naval mine.[2]

Figure 2-4. Typical pressure signature of a ship as seen by an influence fuze of a naval mine.[2]

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Fixed delay fuzes trigger the detonator at a preset delay after initiation. One of the mostcommon fixed delay fuzes is commercial safety fuze (made from a core of black powder woundwith yarn, impregnated with bitumen, and coated with plastic).[7] This pyrotechnic material burnsat a relatively constant velocity (nominally 120 seconds to burn one meter of length). The delaydesired is selected by cutting the safety fuze to the appropriate length. Chemical delays can beobtained by initiating slow chemical reactions. For example, the time required for a strong acid toeat through a zinc plate and react with a primary explosive is determined by the thickness of theplate and the strength of the acid. Electronic fixed delays use timing circuits. After triggering, thetiming circuit counts the time until the elapsed time equals a preset value at which time Mechanicalmechanisms employing escapements can also provide fixed delays for fuze applications.

Chronometric fuzes use clock circuits or mechanical clocks. When the time calculated bythe clock equals a preset time, the detonator is triggered. In a mechanical chronometric fuze, onelead of an electrical circuit is connected to the minute hand (or hour hand) of a clock while thesecond lead is connected to a pin placed at the appropriate time on the clock face. When the clockmoves to the present time, the clock hand contacts the pin, closing an electrical circuit and triggeringthe detonator. Clocks can also be used to produce fixed delays.

Position-sensing fuzes measure the position of the fuze in space. When that positionmatches the position of the target to within some tolerance, then the fuze detonates the warhead.The optimum detonation position might be a specific location inside a structure or it might be at aprecise location beneath or above a target. For example, a bridge might be destroyed with minimumordnance expenditure by detonating a warhead a few meters below the center point of the main span.A command post might be destroyed with minimum ordnance by detonating a warhead in the centerof a specific room in the center of the facility. Several sensor systems exist with the potential foruse in position-sensing fuzing. For example, the global positioning system (GPS) measures absoluteposition relative to an earth-centered coordinate system. GPS can be used to guide a projectile tothe general vicinity of a target. Laser radars can also provide position information adequate forfuzing. A three-dimensional imaging laser radar can determine its position relative to somereference point to accuracies as small as a few centimeters. The author remembers one programwhere the objective (paraphrased as a joke) was to be able to “guide a missile through the thirdwindow on the fourth floor of a specific building on a particular block, then through the door on theopposite side of the room, and detonate the warhead outside the third door on the left in the hallbeyond the door”. This is not impossible to do.

Barometric fuzes measure the ambient pressure and trigger the detonators when the pressurepasses through a preset pressure. The fuze can be triggered by rising or falling pressure. A favoriteuse (at least in fiction) is in terrorist aircraft bombs. The fuze is armed when the pressure falls belowa preset value (as the aircraft climbs above a certain altitude). The fuze detonates when the pressurerises above the preset value (as when the aircraft tries to land). Depth charges commonly usebarometric fuzing to detonate at a preset depth (hydrostatic pressure increases by one atmospherefor each 33.9 feet of depth). Altimetric fuzes differ from barometric fuzes in that the formerdirectly measure the height of the weapon above the ground and detonate when the height of theweapons is equal to some desired “trigger height”. There is no need to assume any relationshipbetween pressure and altitude.

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Thermometric fuzes respond to changes in temperature. The fuze may measure thetemperature directly or it may undergo a change at some desired temperature that can act as atrigger. For example, potassium metal melts at about 336.5 K. This is well above ambienttemperature. When the potassium melts it can flow and close an electrical circuit. Such a fuzemight be used to trigger a bomb that is designed to detonate when the engine to which it is attachedhas been run for an extended period of time.

Delayed action fuzes are fuzes designed to detonate at a point in time after some other fuzemechanism has activated. There are two primary reasons for using delayed action fuzes. The firstis to permit penetration into the interior of an object. An impact fuze may be used to ignite a short-time fixed delay fuze so that a fraction of a second is permitted to pass after impact beforedetonation. A more sophisticated delayed action fuze for penetration measures acceleration versustime using an accelerometer. When a fixed number of decelerations of sufficient magnitude havebeen encountered or when the projectile stops (decelerations cease entirely), the warhead willdetonate. This option is attractive when penetration to a specific level of a complex buried structureis desired. The second reason for employing delayed action fuzes is the complication of repair andrecovery efforts. Delayed action fuzes were incorporated in a substantial fraction of Germanaircraft-delivered bombs during the London “Blitz”. Immediately after a large bombing raid,precious fire fighting resources, rescue personnel, and medical personnel would respond to thebombed areas. Combining delayed action bombs with immediate action bombs guaranteed that asignificant number of these hard-to-replace assets would be drawn out of bomb-proof shelters intoareas where they could be killed or injured by the delayed explosions. Delayed action bombletsscattered over airfields, bridges, barracks areas, etc. can significantly hinder repair efforts. At aminimum, the frequent random explosions exert a considerable harassing effect. The anti-personneluse of delayed action fuzes is usually implemented by combining a long-time fixed delay fuze orchronometric fuze with an impact fuze. Anti-tamper mechanisms are also typically incorporated intoto delayed action fuzes.

Anti-tamper fuze mechanisms are designed to prevent warheads from being disarmed. Thatis, when traditional approaches to disarming weapons are attempted, the anti-tamper fuze willactivate and detonate the warhead. Most warheads do not have anti-tamper fuze devices. However,bombs with delayed action fuzes, boobytraps,[8] and demolition charges (military, nuclear, orterrorist -- commercial demolition charges will not) will commonly have anti-tamper devices toensure that the charges will go off regardless of any actions by disarmers on the other side. Thereare many different kinds of anti-tamper mechanism. The number and type employed depends mostlyon the ingenuity of the warhead designer. Most, however, can be reduced to closing an electricalcircuit that was open or opening an electrical circuit that was closed. Circuits that sense significantbut not on-off changes in current or voltage are sufficiently close relatives to be included in the opencircuit or closed circuit categories.

In open circuit anti-tamper devices, when the disarmer intentionally or inadvertently closesthe circuit, current is able to flow through a device that activates other circuit elements in the fuze.Often this other element is the detonator and the charge is fired immediately. In others, a timingcircuit may be activated (for example, to give legitimate disarmers the time to perform the correctsequence of disarming steps before detonation). Typical actions that open circuit anti-tamper

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devices are designed to prevent include making electrical contact with two pieces of an assemblyat the same time, placing jumper wires across supposedly closed switches or supposedly continuouscircuit elements, etc.

In closed-circuit anti-tamper devices, the closed circuit includes an element that reacts whencurrent ceases to flow. For example, a magnetic relay may hold open a second electrical circuit aslong as current flows through the relay. When the current is shut off, the relay closes the secondcircuit firing the detonator. Alternatively, a dc current flowing through one arm of a transformerproduces no output. However, if the current is abruptly cut off, the transformer produces an outputpulse of sufficient magnitude to trigger the detonator. Typical actions that closed-circuit anti-tamperdevices are designed to prevent include cutting battery leads, opening the lid or removing a panelof an enclosure, cutting or breaking electrical wires, etc.

Open and closed circuit anti-tamper devices can include non-electronic elements. Forexample, laser diodes and photocells can implement an optical link in an electronic circuit. Insertionof a body part or tool into the beam will break the circuit. Alternatively, opening an airtightcompartment and releasing an absorbing gas can close an optical circuit. Mechanical motion ofcomponents can open or close switches in circuits.

Tilt or jiggle anti-tamper devices are designed to prevent movement of the warhead afterarming. A mercury switch (or switches) can close a circuit and trigger the warhead if the assemblyis tilted more than a few degrees from its original position. Pendulum switch switches can triggerthe warhead if accelerations are encountered. Pressure sensors can measure the weight of an objectand detonate the warhead if that weight is increased or decreased.

Anti-tamper devices need not have any electronic parts. A breakable ball containing areactive chemical placed in an elevated shallow cup can perform both anti-tilt and anti-jigglefunctions without need for electrical circuitry. Depressurization (upon opening) of a pressurizedcompartment can permit a mechanical firing pin to impact the detonator. Similarly, removing apanel or opening the lid may permit a spring-loaded firing pin to strike the detonator (in the sameway that the lever on a hand-grenade permits its firing as soon as it is released).

Command detonated fuzes detonate when they receive a command from an external source.The command may come over a hard-wired link, such as wires connected to a commercial blastingmachine. A blasting machine is the manually-operated plunger-based or rotary-based generator usedto supply current to detonate electrical blasting caps. A “dead man switch”, i.e., a hand-held switchthat automatically closes when hand-pressure ceases (as often happens when the holder is killed),is also a form of command detonated fuze. Command links may also operate at radio frequenciesor use telephone circuits. Radio command links permit detonation from distances as far as 5 to 10kilometers. Telephone command links permit detonation from anywhere.

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The primer is a relatively small and sensitive initial explosive train component, which onbeing actuated initiates functioning of the explosive train, and which by itself will not reliablyinitiate high explosive charges. Primers are generally classified in accordance with the method ofinitiation, such as percussion, stab, electric, friction, flash, chemical, etc. The explosive element inprimers is usually a member of the class of primary explosives. Primary explosives are highexplosives of such high sensitivity that they nearly always detonate by simple ignition from suchmeans as spark, flame, or impact. Their high sensitivity generally makes them unsuitable for usein large amounts. They are unsafe. However, in small amounts initiation can be prevented untilsuch time as it is desired. Blasting caps contain primary explosives. Secondary explosives are highexplosives that are less sensitive than primary explosives. Secondary explosives can be detonatedby the action of primary explosives or by other secondary explosives. Tertiary explosives are theleast sensitive kind of explosives. They cannot be detonated by the action of primary explosives (asare used in blasting caps). The more violent effect of detonation of a secondary explosive isrequired to detonate a tertiary explosive. Ammonium nitrate-based explosives are examples oftertiary explosives.

A detonator is an explosive train component which can be activated by either a non-explosive impulse or the action of a primer, and which is capable of reliably initiating high-orderdetonation in a subsequent high explosive component of the train. When actuated by a non-explosive impulse, a detonator includes the function of a primer. Detonators are generally classifiedin accordance with the method of initiation, such as, percussion, stab, electric, friction, flash,chemical, etc. Detonators contain secondary explosives.

A lead is an explosive train component that consists of a column of high explosive, usuallysmall in diameter, used to transfer detonation from one detonating component to a succeeding highexplosive component. It is generally used to transmit the detonation from a detonator to a boostercharge. Primacord (cloth-encased PETN or RDX explosives), Detacord (extruded flexible plasticexplosive), and shock tube (plastic tubing coated on the inside with a mix of aluminum and HMX)are examples of leads. Leads contain secondary explosives. A relay is an element of an explosivetrain that augments a physically-separated and otherwise inadequate output of a prior explosivecomponent so as to reliably initiate a succeeding train component. Relays, in general, contain asmall single charge of a primary explosive material such as lead azide, and are not usually employedto initiate main high explosive charges.

A safety & arming device is a device that prevents accidental detonation of the main chargeof an explosive train by physically interrupting the path of the detonation in the explosive train untilit has been ascertained that detonation will not be harmful to friendly forces; and which removes theinterruption from the path of the explosive train (thus arming the device) after it is determined thatsafety is no longer required. A common location for the safety & arming device is between thedetonator and the lead or relay leading to the larger explosive charges.

It is traditional that safety & arming devices have at least two separate mechanisms requiringat least two independent physical conditions to be satisfied in order for the device to be armed. Ingeneral the required physical conditions are conditions that are not encountered except in normaloperation after a firing decision has been made. For example, the safety & arming mechanism of

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an artillery shell might require the sustained presence of an acceleration in excess of 1000 g’scoupled with the simultaneous attainment of an angular spin rate (established by the rifling in thegun barrel) in excess of 120 rpm. The linear accelerations could cause a spring-loaded pin to beforced out of a hole, permitting a spring-loaded pendulum to swing away from its rest position underthe influence of the centrifugal force produced by the high spin rate. See Figure 2-5. When thependulum swings away from its normal position, it opens a direct air path between the detonator andthe relay charge. With the pendulum in normal position, the metal of the pendulum would preventthe weak detonator shock (in the event the detonator fired) from reaching the relay charge. Neitherthe acceleration nor the spinning by themselves can actuate the mechanism. An acceleration willcause the pin to retract but as soon as the acceleration is removed, the pin will return to a positionthat locks the pendulum. Spinning alone cannot move the pendulum because it is locked intoposition by the pin. However, if the pin is retracted by the acceleration, then simultaneous spinningwill allow the pendulum to move. Once the pendulum has moved, subsequent deceleration will notaffect the armed state that has been established. In fact it can allow the pin to lock the pendulumin the armed position.

Many other safe and arm devices, some quite clever, can and have been used. World WarII aircraft bombs often had propellers attached to the tail fin assemblies. A pin prevented thepropeller from turning. When the bomb was dropped, a cord pulled out the pin. As the bomb fell,airflow rotated the propeller, which in turn rotated a screw mechanism, that aligned the explosivetrain arming the bomb only after a certain number of rotations had occurred. Some ship-launchedtorpedoes have a salt-water battery that provides the voltage necessary to fire the detonator. Thebattery is kept dry by a plug that keeps out the seawater (the electrolyte). When fired, the plug isyanked free by a cord. As the torpedo enters the water, the sea water enters the plug hole andactivates the battery. This, in turn, arms the warhead.

Figure 2-5. A safe and arm mechanism for artillery shells that requires simultaneous rotation and acceleration for warhead arming.

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Military explosive weapons are required (by virtually all militaries) to contain safe and armmechanisms. This provides safety for the operating forces. It also makes it harder to use theweapons in an unauthorized fashion. Unless all of the proper conditions are met, the bomb will notarm. Simply pushing an improperly prepared military aircraft bomb out of the door of an airplanewill result in a bomb buried in the ground, not an explosion. Permissive action links (PAL – highlyencoded electronic devices that prevent the weapon from being armed unless the specific codes forthat weapon are entered) on nuclear explosives makes them almost impossible to detonate properlyif stolen. Fewer people have access to the codes than have access to the weapons themselves.Without the arming codes, the only way the nuclear explosive could be detonated successfully is toremove the firing circuitry and replace it with a new firing circuit that produced all of the necessarystimuli in the requisite order at the required times. Improvised explosive devices (IED) are“home-made” explosive weapons. They will seldom include safe and arm devices in their explosivetrains.

A booster charge is an explosive train component that augments the detonation of a priorexplosive train component amplifying its strength to a level capable of reliably initiating detonationof a succeeding explosive charge. Booster charges may contain sizable quantities of moderatelyinsensitive high explosive. However, booster charges are usually still secondary explosives. Themain charge is the explosive train component that provides the primary explosive energy outputof the explosive device. Generally, it contains insensitive (or less sensitive) high explosivecompounds that will not detonate without the action of an explosive train. Main charges may beeither secondary or tertiary explosives.

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Characteristics of Explosives

There are hundreds of explosive chemicals, thousands of fuel-oxidizer mixtures that formexplosives, and tens of thousands of combinations of two or more explosive chemicals. Hundredsof formulations find commercial or military use. Some are powerful; some are weak. Some aresensitive; some are insensitive. Some are useful for shattering objects; others are useful fordisplacing large masses of material. It is not practical to list all of the possibilities and theirproperties, and even less practical to remember all of those properties. Common safety estimatesare usually based on the properties of a “standard” explosive (e.g., TNT). How does one estimatethe damage that a non-standard explosive can produce? If given a known mixture of chemicals howdoes one estimate whether the material is explosive, and if so, how strong an explosive the mixtureis likely to be? The purpose of this section is provide a glimpse at how such determinations aremade. Relatively simple calculations can provide rough estimates of properties, and these roughestimates are usually adequate for understanding real world problems.

In order to predict the effects of a quantity of explosive, it is necessary to know a numberof important characteristics about the explosive itself. For example, the amount of work (or damage)that an explosive can perform, will be limited by the amount of energy that the explosive releaseswhen it explodes and by how rapidly the material explodes.

An explosion is a fast chemical reaction. Reactant molecules combine or dissociate toproduce product molecules. The reaction between i different reactant species to form j differentproduct species can be expressed mathematically by

,[ ] [ ]i ji j

EXPLOSION EXPLOSIONREACTANTS PRODUCTS

n REACTANT i n PRODUCT j⇒∑ ∑

where the quantities ni and nj represent the quantities of reactant i and product j, respectively. Thesequantities may have any consistent set of units (although the values will depend on the units). Theyare usually chosen to have units of individual molecules or units of moles. For those whose highschool chemistry is rusty, a mole is a number of molecules equal to Avogadro’s number NA = 6.02x 1023. A mole of any substance has a weight in grams equal to its molecular weight. Themolecular weight M of a molecule is just the sum of the atomic weights of its constituent atoms. Theatomic weights can be found in almost any version of the “periodic table of the elements”. Theatomic weights and chemical symbols of the atoms found in common explosives are:

Hydrogen H 1Carbon C 12Nitrogen N 14Oxygen O 16Aluminum Al 27.

The molecular weight of water (H2O) is M = 18 (= (2 x 1) + (1 x 16)) while the molecular weightof carbon dioxide (CO2) is M = 44 (= (1 x 12) + (2 x 16)).

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By way of example, consider the explosion methyl nitrate CH3ONO2. The explosivedecomposition of two moles (or two molecules) of methyl nitrate yields 3 moles (molecules) ofwater + 1 mole (molecule) of carbon dioxide + 1 mole (molecule) of carbon monoxide + 1 mole(molecule) of nitrogen according to the reaction

.3 2 2 2 22 3CH ONO H O CO CO N⇒ + + +

Any quantity value might be substituted for one species (for example, 4 CH3ONO2) and the reactionequation would still be valid IF the other quantities are adjusted proportionally. For methyl nitrate,there must always be 1.5 times more water molecules produced than methyl nitrate moleculesconsumed and 3 times more water molecules produced than CO2 molecules produced. Thequantitative relationships (fixed ratios) between components of a reaction is called stoichiometry.

The energy ∆Hexpl released per mole of explosive is termed the heat of explosion.[7] Theheat of explosion may be calculated from the heats of formation of the reactants and the products,according to the equation

(2.1)expl j f j i f i ij i i

EXPLOSION EXPLOSIVE EXPLOSIONPRODUCTS REACTANTS REACTANTS

H n H n H n

∆ = ∆ − ∆

∑ ∑ ∑

The heat of formation (or enthalpy) ∆Hf is the energy required to assemble one mole of a chemicalfrom its fundamental elemental constituents. Elements in their natural state have zero heat offormation by definition. Heats of formation of many compounds including a number of explosivesand almost all explosive products can be found in standard chemistry handbooks such as Lange’s[15]. Table 2-2 lists a number of common explosive reaction products and their heats of formation.The heat of explosion is often given in units of Joules released per gram of explosive. This form ofthe heat of explosion is labeled Q and is given by

(2.2)

i ji j

EXPLOSION EXPLOSIVEREACTANTS PRODUCTS

expl expli i j j

i jEXPLOSION EXPLOSIVEREACTANTS PRODUCTS

n n

Q H Hn M n M

= ∆ = ∆

∑ ∑

∑ ∑

The heat of explosion expressed in units of megajoules per kilogram of explosive is sometimescalled the energy content.

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Table 2-2. Heats of formation of typical explosion products.

HEAT OF FORMATION ∆Hf

PRODUCT STATE (kcal/mol) (kJ/mol)

C Solid 0.00 0.0 CO Gas -26.42 -110.5 CO2 Gas -94.05 -393.5 N2 Gas 0.00 0.0 H2O Gas -59.56 -241.8 HCl Gas -22.06 -92.3 HF Gas -64.2 -268.6 Al2S3 Solid -121.6 -508.8 SF6 Gas -262 -1096.2 AlCl3 Solid -166.2 -695.4 AlF3 Solid -311 -1301.2 Al2O3 Solid -399.1 -1669.8 MgCl2 Solid -153.4 -641.8 MgF2 Solid -263.5 -1102.5 MgO Solid -143.84 -601.8 O2 Gas 0.00 0.0 MgS Solid -83.0 -347.3 SO2 Gas -70.96 -296.9

Given the complex organic molecules and mixtures that comprise typical high explosives,it may not be obvious what are the reaction products. To a very limited degree almost every possibleproduct will be produced. In most cases, however, only a few specific products will be producedin sufficient quantities to affect the performance of the explosive. For example, toluene is a possibleproduct of the explosion of TNT (trinitrotoluene). However, toluene is produced in such smallquantities that it is virtually undetectable. Methane, ethylene, nitrous oxides, and other similarproducts are also produced in minuscule amounts. Surprisingly even carbon dioxide is not animportant product. On the other hand, water, carbon, carbon monoxide, and nitrogen gas areproduced in such quantities that they comprise almost 100% of the total.

The products produced by an explosion are determined by a combination of kinetics andthermodynamics. For the simplest molecules, the products that release the most chemical energyare favored. For more complex molecules, those that must be built by successive reactions (suchas carbon dioxide, which is produced by sequential oxidation of carbon to carbon monoxide tocarbon dioxide), kinetics and the availability of reactants will affect the yield. Empirical study ofnumerous explosives has yielded an algorithm that predicts the products of any explosion withreasonable accuracy for performance computation and comparison. This algorithm is embodied ina concept of reaction priorities. One list of priorities (expanded by the author based on earlier liststo encompass the widest range of explosive compounds) is shown in Table 2-3.

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Table 2-3. Reaction priorities in explosives and propellants.

PRIORITY EXPLOSIVE COMPONENT REACTION & REACTION PRODUCT1 Any Metal + Fluorine M + x F –> MFx (solid) 2 Hydrogen + Fluorine H + F –> HF (gas)3 Sulfur + Fluorine S + 6 F –> SF6 (gas)4 Nitrogen + Fluorine N + 3 F –> NF3 (gas)5 Any Metal + Chlorine M + x Cl –> MClx (solid)6 Hydrogen + Chlorine H + Cl –> HCl (gas)7 Sulfur + Chlorine 2 S + 2 Cl –> S2Cl2 (gas)8 Any Metal + Oxygen y M + x O –> MyOx (solid)9 Hydrogen + Oxygen 2 H + O –> H2O (gas)10 Carbon + Oxygen C + O –> CO (gas)11 Carbon Monoxide + Oxygen CO + O –> CO2 (gas)12 Any Metal + Sulfur y M + x S –> MySx (solid)13 Sulfur + Oxygen S + 2 O –> SO2 (gas)14 Sulfur + Hydrogen S + 2 H –> H2S (gas)15 Nitrogen N + N –> N2 (gas)16 Excess Sulfur (if any) S –> S (solid)17 Excess Oxygen (if any) O + O –> O2 (gas)18 Excess Hydrogen (if any) H + H –> H2 (gas)19 Excess Carbon Monoxide (if any) CO –> CO (gas)

Reactions are assumed to proceed to completion in priority order until all componentsare used up.

The explosive formulation is first assumed to break up into constituent atoms. These atomsare then consumed according to the listed priorities until all atoms are accounted for. Consider thesimple explosive: methyl nitrate with chemical formula CH3ONO2. The compound yields 1 C atom,3 H atoms, 1 N atom, and 3 O atoms. Looking at Table 6-2, we see that the reaction with the highestpriority is Reaction 9. Two atoms of H combine with one atom of O to produce H2O. The 3 Hatoms will thus produce 1.5 molecules of H2O consuming 1.5 O atoms in the process. Fractions areacceptable because in truth we are dealing with trillions of trillions of explosive molecules. Atomsneeded to complete any process will be obtained from neighboring decomposing molecules. Someoxygen is not consumed (1.5 O atoms per molecule). This is now available to react via the reactionwith the next highest priority (Reaction 10). The 1 C atom reacts with 1 of the remaining 1.5 Oatoms to produce 1 molecule of carbon monoxide (CO). There is still 0.5 atoms of O unaccountedfor. According to the next highest priority reaction (Reaction 12), 0.5 molecules of CO will reactwith the remaining 0.5 O atoms to produce 0.5 molecules of CO2. Some of the CO (0.5 molecules)remains unreacted and forms part of the final product. Since there is no fluorine in this explosive,the lone N atom forms 0.5 molecules of nitrogen (N2). At this point there are no unreacted atomsleft and the overall reaction may be written as

3 2 2 2 21.5 0.5 0.5 0.5CH ONO H O CO CO N⇒ + + + or, after eliminating the fractions, as

111

.3 2 2 2 22 3CH ONO H O CO CO N⇒ + + +

Using the same approach the explosion products of even the most complex explosive formulationcan be predicted with reasonable accuracy.

Many explosives are similar to methyl nitrate in that they contain only C, H, N, and O atoms.Not surprisingly, these are known as CHNO explosives. More specifically, CHNO explosives havethe chemical formula

CaHbNcOd

where a, b, c, and d are integers. A quantity called oxygen balance Ω may be defined for CHNOexplosives [7]

(2.3)Ω ≡ − −FHG

IKJd a b

M2

21600

in terms of the numbers of each type of atom. If the oxygen balance is zero, then the explosiveproducts are only CO2, H2O, and N2. There is no C, no CO, no H2, and no O2. If the oxygen balanceis negative, there is not enough O atoms to oxidize all the C atoms to CO2 and all the H atoms toH2O. The explosion products will contain CO, C, and possibly even H2, in addition to H2O, N2, andpossibly CO2, . If the oxygen balance is very negative, there will be insufficient O to oxidize all ofthe C atoms to CO. The products will then contain a large amount of C dust and the explosive cloudwill be dark and persist for a considerable length of time. If the oxygen balance is positive, thereis more oxygen than needed. There will be no C, CO, or H2. There will be considerable O2 inaddition to CO2, H2O, and N2.

In CHNO explosives, it is the oxidation of C and H atoms that release much of the storedenergy. Incomplete oxidation (negative oxygen balance) means that the explosive containsconsiderable weight in unreacted C and H atoms). Excess oxygen (positive oxygen balance) meansthat the explosive contains considerable weight in unreacted O atoms. The energy release per unitmass, the energy content, is maximized when there is no unreacted mass. That is, energy contentis maximized when the oxygen balance is zero. It should be noted that oxygen balance is not theonly determinant of the energy content of an explosive. Bond strain and multiple bonds can alsocontain chemical energy. For example, azide groups (N3-) do not contribute to anything to oxygenbalance (because the products are only nitrogen) but contain considerable energy. These othersources account for the lack of perfect correlation between energy content and oxygen balance.

Table 2-4 shows the oxygen balance of a number of common CHNO explosives. Of theexplosives listed nitroglycerine (with standard abbreviation NG – see Tables 2-11 through 2-13 fordescriptions of the explosives associated with the standardly used abbreviations) has the oxygenbalance nearest to zero. It is also one of the most energy efficient of all explosives. HMX and RDXall also very energy efficient explosives and they too have small absolute oxygen balances.

112

Ammonium nitrate has a very large positive oxygen balance. It is a relatively poor explosive byitself. However, addition of a small amount of fuel oil (to consume the excess oxygen) and theexplosive performance improves considerably. TNT has a very negative oxygen balance. Theoxygen deficiency makes TNT less powerful than many other CHNO explosives with smallerabsolute oxygen balances. It also accounts for the black smoke produced when TNT explodes. Theoxygen deficiency is so large that large amounts of carbon soot are produced that cannot be oxidizedto carbon monoxide.

Table 2-4. Oxygen balance of some common CHNO explosives.

MOLECULAR OXYGEN EXPLOSIVE WEIGHT CaHbNcOd BALANCE

Ammonium Nitrate 80.0 C0H4N2O3 +20%HMX 296.2 C4H8N8O8 -22%NG 227.1 C3H5N3O9 +3.5%NM 61.0 C1H3N1O2 -39%PETN 316.1 C5H8N4O12 -10%Picric Acid 229.1 C6H3N3O7 -45%RDX 222.1 C3H6N6O6 -22%TATB 258.1 C6H6N6O6 -56%Tetryl 287.1 C7H5N5O8 -47%TNT 227.1 C7H5N3O6 -74%

Given an estimate of the energy content (or the heat of explosion), the temperature of thegases produced may be estimated. This explosion temperature Te will be determined by a balanceof the energy released in the explosion and the absorption of that heat by the products (due to theirheat capacities) as those products approach equilibrium. The explosion temperature may beestimated from the relation [7]

(2.4)exple a

j jj

HT T

n c∆

= +∑

where Ta is the ambient temperature prior to the explosion, Q is the heat of explosion, ni is thenumber of moles of product molecule j, and <cj> is the average molar heat capacity of the jth productspecies over the temperature range from Ta to Te. Detailed thermodynamic data is available instandard reference works. However, if the products can be assumed to be ideal gases, then the heatcapacities may be approximated by [14]

, (2.5)j j jc c x R= =

113

where R = 8.3145 J/mole-K is the ideal gas constant, and

x ~ 2.5 for monatomic species, ~ 3.5 for diatomic molecules (e.g., nitrogen and carbon monoxide), ~ 4.0 for nonlinear triatomic molecules (e.g., water), and ~ 4.5 for carbon dioxide

we have

(2.6)exple a

j jj

HT T

R n x∆

= +∑

The assumption of ideal gas behavior is not very good at the densities (near solid density) found inan explosion. Unfortunately, any other assumption fails to yield easily calculated results. Thisequation is a crude estimate at best.

Another measurable characteristic of explosives is the volume of gas that they generate. Thegas volume Vg is defined as the volume of gas produced at 1 atm and 273 K by 1 gram of explosive.If two explosives have comparable energy contents, then the explosive with the larger gas volumewill produce a higher pressure. For an explosive consisting of a single molecular species (e.g.,TNT), the gas volume in liters per gram may be determined by the relation [7]

(2.7)22.4 22.4

g jji i i

GASEOUS

nV nM M n

= = ∑

where n is the number of moles of gaseous products generated per mole of explosive, Mi is themolecular weight of the explosive, ni is the number of moles of explosive in the reaction equationand the nj are the numbers of moles of each product species (that is formed as a gas). If theexplosive has multiple reactants, then the gas volume of the multi-reactant explosive can be foundusing the relation

(2.8)22.4g j i ij i

GASEOUS REACTANTSPRODUCTS

V n n M= ∑ ∑

This same equation is adaptable to explosives made by combining two or more explosivecompounds, such as octol, which is made from HMX and TNT. The overall reaction for the mixtureis used to determine the ni and nj .

The force constant is a measure of the motive force that can be produced by an explosive.The force constant F can be estimated from the explosion temperature by [7]

114

(2.9)F nM

RTe=

where n is the number of moles of gaseous products produced per mole of explosive, M is themolecular weight of the explosive, R is the molar gas constant, and Te is the explosion temperature.It should be noted that because n/M is used in the equation, the force constant is determined pergram of explosive.

The power index is a measure of the rate at which motive work can be performed by theexplosive. The power index is based on the Berthelot approximation of the amount of mechanicalwork performed by the explosion.[4] Berthelot assumed that the strength of an explosive was givenby a characteristic product of the volume of gas produced Vg and the change in internal energy Q [7],that is,

(2.10)P I QVg. .∝

where Q is the heat of explosion (in J/g) and Vg is the gas volume (in cm3/g). Typically power indexis normalized to the value for picric acid, which is arbitrarily defined to have a power index of 100.Thus

. (2.11)P IQV

Q VQVg

Picric Acid gPicric Acid

g. .= =100

29211

Power index is a good measure of relative utility (from an energy perspective) in blasting fordisplacing large quantities of material. Some groups prefer to use a slight variation of power indexcalled the relative strength which uses TNT as the reference explosive. Thus,

. (2.12)

100. .

100. .

. . . .. . /100 1.17

g

TNT gTNT

Picric Acid gPicric Acid Picric Acid gPicric Acidg

TNT gTNT Picric Acid gPicric Acid TNT gTNT

TNT

QVR S

Q V

Q V Q VQVP I

Q V Q V Q V

P I P IP I

=

= =

= =

Table 2-5 lists a number of common explosives along with estimated power indices, relativestrengths, and detonation velocities (which provide a measure of shattering ability).

The power index or relative strength has great practical utility in calculating the blast damageeffects produced by explosive detonations. Effects are often tabulated for a standard weight of areference explosive compound. Scaling laws (see below) permit the radius at which a given effectoccurs to be determined for any arbitrary weight of the reference explosive. If the power indices or

115

Table 2-5. Comparison of the “strengths” of various explosives.

Detonation Explosive Power Index Relative Strength Velocity (km/s)

EGDN 170 145 7.3PETN 161 138 8.26HMX 160 137 9.11Nitroglycerine 159 136 7.70RDX 159 136 8.70C-4 ~145 ~124 8.04Cyclotol 60/40 138 118 ---DATB 132 113 ---Pentolite 50/50 129 110 7.47Tetryl 123 105 7.85ANFO ~123 ~105 2-3TNT 117 100 6.93Picric Acid 100 85 7.35Lead Styphnate 21 18 5.1Mercury Fulminate 14 12 4.7Lead Azide 13 11 5.2

relative strengths of the reference explosive and any other explosive of interest are known, then theeffects produced by an arbitrary weight of the other explosive can also be calculated. The strengthof the other explosive relative to the reference is calculated and the weight of the reference isadjusted to provide equal strength with the known weight of the other explosive. Scaling using theadjusted weight of the reference explosive yields the effects that would be produced by the otherexplosive. For example, the relative strength of C-4 is 124. Thus, only 80.6 kg (= 100 kg/1.24) ofC-4 is needed to produce the same blast damage as 100 kg of TNT.

The detonation velocity is another parameter of considerable significance and utility. TheChapman-Jouguet condition has been determined to be satisfied in most explosions and is expressedas

(2.13)

Speed of sound Expansion velocity Detonation Shock

in the shock- of products behindvelocity velocity

compressed material the shock front

= + =

or

(2.14)pD c u= +

Note: the speed of sound in the shock-compressed material is typically much higher than the speedof sound in the material before compression. An empirical formula for detonation velocity has beenfound to be

116

(2.15)D n T Mein m / sb g b g= + −430 3500 1/ ρ

where n is the number of moles of gaseous products per mole of explosive, M is the molecularweight, Te is the explosion temperature, and ρ is the density of the explosive (in g/cm3). Theempirical formula highlights a significant density effect. If the density of an explosive is reducedby adding an inert component (such as air in the form of small voids) then the detonation velocitywill be reduced. At two different effective densities (g of explosive per cm3), ρ1 and ρ2, theexplosive will have different detonation velocities, D1 and D2, related by

. (2.16)D D2 1 2 13500= + −ρ ρb gIn general, materials with the largest amount of gas produced at the highest temperature vie withmaterials with the highest density to produce high detonation velocities.

Detonation velocity has been shown to correlate with a subjective quantity called brisance.The higher the detonation velocity of an explosive, the higher the brisance. Brisance is theshattering ability (ability to cause strong materials to fracture or break into small pieces) of anexplosive. It is associated with the change in pressure in the shock wave produced in the explosionand not with the outward flow of explosion gases. High brisance (strong shattering power) isrequired to fracture steel structures (as opposed to merely bending them). Demolition of structuresrequire high brisance. Excavation (moving large quantities of material) needs a large power indexnot high brisance. ANFO (ammonium nitrate and fuel oil) has the same power index as tetryl.However, tetryl has a detonation velocity 3 times that of ANFO. Both ANFO and tetryl would begood mining explosives (although ANFO is much cheaper) but tetryl would be much more usefulin demolition of steel reinforced structures.

The sensitivity of an explosive is related to its susceptibility to initiation of detonation bya fuze agent (either produced by a fuze or induced accidentally by the external environment).Impact is a common fuze agent. It is also a common external occurrence. Explosives with higherimpact sensitivity (i.e., able to be detonated by smaller impacts) are more susceptible to accidentaldetonation or detonation by hostile action (bullet or shrapnel impacts). Table 2-6 lists the height offall of a 10 mm diameter, 2 kg weight that will initiate detonation at 50% probability and thecorresponding kinetic energy of that weight. One could interpret the kinetic energy per area as thethreshold for blunt projectile initiation of detonation. Heat is another common fuze agent. Table2-6 also lists the ignition temperatures of these same explosives.

117

Table 2-6. Impact [9] and temperature [7] sensitivity of some common explosives. Sensitivity is measured using the falling weight test.

HEIGHT OF FALL KINETIC IGNITION OF 2 kg WEIGHT ENERGY TEMPERATURE

EXPLOSIVE (cm) (N-m) (C)Nitroglycerine 1 0.2 188Lead Azide 12-20 2.5-4 350Lead Styphnate 12-25 2.5-5 250Tetrazene 5 1 160Mercury Fulminate 5-10 1-2 ---PETN 15 3 205Tetryl 15 3 180Picric Acid 37 7.4 ---RDX 38 7.5 213HMX 37 7.4 ---TNT 75 15 240Ammonium Picrate (Expl. D) >90 >19 ---TATB 250 50 359

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Blast Damage

Explosions produce damage via three distinct mechanisms: blast, heat, and projectiles. Wewill first investigate the effects due to blast. Consider a mass of explosive in air as shown in Figure2-6. Before detonation (t < 0) the explosive is a solid mass at ambient temperature. Thesurrounding air has normal atmospheric density ρA and is also at the ambient temperature TA. Theair molecules move in random directions with velocities comparable to the speed of sound in the air.The speed of sound c in any ideal gas is given by

, (2.17)1/ 2RTc

Mγ =

where γ is the ratio of specific heats (γ = 1.4 for air), R (= 8.3145 J/mole-K), T is the temperature

Figure 2-6. Representation of an explosion in air.

119

of the gas, and M is the mass of one mole of gas (M = 0.028964 kg for air). For T = 300 K, thespeed of sound in air is

. (2.18)( )( )( )

( )

1/ 21/ 2 1.4 8.3145 300347.3 m/s

0.028964RTcM

γ = = =

At t = 0 the explosive detonates. The detonation velocity is so fast (typically 5000 to 9000m/s) that the explosive cannot expand significantly before detonation is complete. As a simpleapproximation, let us assume that it does not expand at all. Immediately after detonation, theexplosive mass has been converted into a very dense (essentially the same density as the initialexplosive) and very hot (thousands of K) gas. The surrounding air has not been affected. A densehot gas has a high internal pressure. Typical pressures in the explosion products are in the range of2 to 6 million psi. The pressure in the surrounding air will approximately one atmosphere (14.7 psi).Since there is nothing containing the high pressure explosion products, they will begin to expandinto the surrounding air. Since the temperature (and the sound velocity) in the explosion productsis higher than that in the surrounding air, the expansion will be supersonic. A shock wave will form.A short time after the detonation, this shock wave will be expanding at a velocity D that is equal tothe flow velocity of the expansion u plus the speed of sound c in the hot gas. As the explosion gasescontinue to expand, the pressure will drop and the gases will cool. Both of these effects reduce theshock velocity.

A shock wave in a material can be considered as a moving surface at which the physicalcharacteristics (temperature, pressure, density, etc.) of the material change in what is essentially adiscontinuous fashion. Immediately ahead of the shock surface (called the shock front) thetemperature, pressure, and density each have a ambient value; immediately behind the shock frontthey each have different values. The change in variable values is not truly discontinuous but occursover such a short distance that it can be considered discontinuous.

Figure 2-7 illustrates the passage of a shock front through a stationary material. The shockwave actually moves through the material from left to right with a velocity u. However, byapplication of a principle of relativity, we may assume the shock is stationary and the material flowsinto the shock front from right to left with a velocity ux = u and exits the shock front moving rightto left with a velocity uy.

Damage from an explosive shock wave results from two effects: overpressure and dragforces from shock-induced winds. The overpressure ∆p is the difference in pressure between thegas on the two sides of the shock front

. (2.19)y xp p p∆ = −

Figure 2-8 shows the time variation of the overpressure at a point while Figure 2-9 shows the timeevolution of the spatial distribution of overpressure. At a point, the overpressure is initially zero.When the shock wave arrives, the overpressure jumps instantly to a large value. Immediately after

120

Figure 2-7. Relative motions and physical parameters involve in passage of a shock front.

Figure 2-8. Time-dependence of the overpressure at an arbitrary distance from an explosion.

Figure 2-9. Time evolution of the spatial dependence of the overpressure.

121

the peak overpressure is achieved, the overpressure will fall roughly exponentially towards zero.However, because the overpressure is accompanied by an outflow of gases, the pressure willultimately drop below ambient (the overpressure goes negative). The negative overpressure causesair to flow back towards the explosion point until the pressure equalizes around the original ambientpressure and the overpressure becomes zero. There may be more than one cycle of positive/negativeoverpressure oscillation, see Figure 2-10, the negative phase and following cycles are only importantin underwater explosions and nuclear explosions. As the shock wave expands, it gets weaker (theoverpressure becomes smaller) and the half-pressure width of the overpressure pulse gets wider.

The overpressure will attempt to crush any object that impedes the passage of the shock. Asthe shock impinges on a structure, one side of the object will experience the overpressure before theother side, because air must flow around the structure in order for the pressure on the back side toincrease. Because such flow can only occur at the speed of sound or slower, there will be a period

Figure 2-10. Temporal relationships between the overpressure and the dynamic pressure.

122

of time during which a pressure imbalance occurs. If the pressure on one side becomes too muchhigher than on the other, the pressure difference force FOVERPRESSURE

, (2.20)OVERPRESSUREF A p= ∆

where A is the area exposed to the overpressure ∆p, will cause the structure to buckle or break. Ifa structure prevents the shock from propagating to its interior, then its internal pressure will remainnear ambient pressure. The external pressure will rise relative to the internal pressure by an amountequal to the overpressure. If the overpressure is high enough, the structure will implode.

Behind the shock front, the gases flow outward with a velocity called the particle velocityup having magnitude

. (2.21)p x yu u u= −

The outflow of gases behind the shock front is the equivalent of a strong wind. As we shall see, theparticle (wind) velocity associated with an explosive shock wave can equal or exceed that of ahurricane or even a tornado. The damage that hurricane force winds can produce is visuallydemonstrated many times each year by the natural phenomena. Explosion “wind” damage can bemuch, much worse, although on a more localized scale. The explosion-produced wind produces adynamic pressure q

, (2.22)20.5 y pq uρ=

whose magnitude is related to the air density ρy behind the shock front and the outflow (particle)velocity up.

This particle velocity-related wind will exert a force on any drag-sensitive object. The flowaround the object will result in higher pressures on the upwind side than on the downwind side. Thepassage of a shock front causes a pressure imbalance that lasts only as long as it takes for the shockfront to pass by the structure. The pressure imbalance produced by drag can last orders ofmagnitude longer than the overpressure imbalance. The drag force can be calculated from

, (2.23)2 200.5 0.5DRAG DRAG D D y p D aF A p Ac q Ac u Ac p Mρ γ= ∆ = = =

where the flow velocity is assumed to be the particle velocity up, cD is the drag coefficient of thebody (of the rough order of 1 for blunt objects such as buildings), A is the presented cross-sectionalarea of the body, ρy is the atmospheric density, γ (=1.4) is the ratio of specific heats of air, pa is theambient atmospheric pressure, and M0 is the Mach number of the flow. Mach number is the ratioof the flow velocity to the speed of sound.

The drag force is directed along the flow. This force will try to accelerate objects that arenot attached to the ground. Such accelerated objects can be damaged when they decelerate after

123

hitting the ground again. The same objects can damage any other object they may hit. Flying debriscauses considerable damage in hurricanes and tornados. The same drag force will try to push overand topple objects that are attached to the ground. Structures that are not crushed or shattered bythe overpressure may be destroyed by the wind forces.

The two critical parameters associated with blast damage are the overpressure and thedynamic pressure. As stated earlier, the overpressure is the difference in pressure between the gason the two sides of the shock front. It is relatively easy to show that

(2.24)∆p p pM

pM

py xx

xx

x≡ − =−

+=

−2 11

7 16

2 2γγc h c h

However, such a derivation is irrelevant to the level of understanding desired here and will not bepresented. By rearranging terms, we have

. (2.25)M pp

ppx

x x

2 1 12

1 67

= ++

= +γ

γ∆ ∆

The primary significance of this result lies in the obviousness that the faster the shock velocity, thehigher the overpressure. Using the equation of state and the definition of Mach number, we find

. (2.26)∆p u cxx x=

+−

21

2 2ργc h

The passage of the shock front will accelerate the air molecules in the direction of the shockmotion. The resulting particle velocity is the difference between the flow speed entering the shockfront and the flow speed leaving the shock front. That is,

. (2.27)u u u M c M c c M MTTp x y x x y y x x y

y

x

= − = − = −FHGIKJ

LNMM

OQPP

1 2/

This result can be modified to yield an expression for the particle velocity as a function of the shockspeed

. (2.28)uc

MM

MM

p

x

x

x

x

x

=−

+=

−2 11

5 16

2 2c hb g

c hγ

It is also possible to cast the particle velocity in terms of the pressure ratio

124

(2.29)

( )

2 2

22 25

1 2 42 49

p x x

x

x x

p pu p pc p p

p p

γ

γ γ

∆ ∆ = = ∆ ∆ + + +

The particle velocity is essentially the speed of the net wind produced by passage of the shock wave.Note that for large shock speeds (Mx >>1) it is possible to have phenomenally high winds(approaching 5/6 of the Mach number).

The densities on the two sides of the shock front are related by

. (2.30)( )

( )

2

2

12 1

xy x

x

MM

γρ ρ

γ +

= + −

Substituting the density relation and the particle velocity relation into the expression for the dynamicpressure yields

(2.31)

( )( )

( )( ) ( )

( ) ( )( )

2 22 22 2

2

2 22 22 2

2

2 1 4 10.5 0.5

1 1 2 1

5 1 25 10.5 0.5

6 6 5

x xy x x x

x x

x xy x x x

x x

M Mq c c

M M

M Mc c

M M

ρ ργ γ γ

ρ ρ

− − = = + + + − − − = = +

As the shock velocity increases, the dynamic pressure also increases.

It can be theoretically shown and is experimentally observed that the blast waves ofexplosions scale with the cube root of the explosive yield. That is, two explosions should giveidentical blast waves at relative distances that are proportional to the cube root of the respectiveexplosive yields. If an appropriately scaled distance is defined then all explosions will yieldidentical blast wave characteristics as a function of that distance. The scaled distance Z is relatedto the actual distance z by the relations

(2.32)Z WW

z pp

TT

WW

z=FHGIKJFHGIKJ =FHGIKJFHGIKJFHGIKJ

ρρ0

1 3

01 3

0

1 3

01 3

01 3/ / / / /

where ρ is the ambient atmospheric density, ρ0 is the atmospheric density in which the referenceexplosion occurs, W is the yield of the explosion, W0 is the yield of the reference explosion, p is the

125

ambient atmospheric pressure, p0 is the atmospheric pressure in which the reference explosionoccurs, T is the ambient atmospheric temperature, and T0 is the atmospheric temperature at whichthe reference explosion occurs.

For an explosion of arbitrary yield, the parameters at the scaled distance can be convertedto parameters at the true distance by inverting the scaled distance equation (Eq. (2.32)) to obtain

(2.33)z WW

Z pp

TT

WW

Z=FHGIKJFHGIKJ =FHGIKJFHGIKJFHGIKJ

ρρ

0

1 3

0

1 3

0

1 3

0

1 3

0

1 3/ / / / /

In making rough estimates, there is little need to adjust for temperature or pressure differences.Because of the cube root dependences, a 10% variation in either temperature (± 29 C) or pressure(±101 mbar) will produce only a 3.5% variation in scaled range. However, the yield scaling shouldtake not only the weight WEXP of explosives involved but also the “relative strength” R.S.EXP of theexplosive into account via the relation

. (2.34). .100

EXPEXP

R SW W=

The utility of scaling is that if the characteristics of a reference explosion are known then thecharacteristics of any explosion can be estimated. Table 2-7 shows the characteristics of just sucha reference explosion. [3] The reference explosion is that of 1 kilogram of TNT detonated in anatmosphere with temperature T0 = 288.15 K = 15 C and p0 = 1.01325 bars = 100 kPa. Table 8-3 liststhe scaled distance (which equals the actual distance for the reference explosion), the shock frontvelocity (in Mach number in the undisturbed air), the overpressure ratio, the time of arrival of theshock front at the scaled distance, the average speed of expansion over the distance from theexplosion center to the scaled distance, the duration of the positive pressure phase of the shock atthe scaled distance, the impulse per unit area delivered by the blast wave at the scaled distance, andthe shock waveform parameter. Although some of the quantities have been defined above, thedefinitions are repeated below (sometimes with amplification).

The Mach number of the shock front is just the ratio of the shock velocity to the speed ofsound in the undisturbed air. The overpressure ratio ∆p/pa is the ratio of the overpressure (totalpressure minus ambient pressure) to the ambient pressure. It has been found that the overpressureratio for a chemical explosion can be expressed by the analytical approximation

(2.35)∆pp

Z

Z Z Za

=

+ FHGIKJ

LNMM

OQPP

+ FHGIKJ + FHG

IKJ + FHG

IKJ

808 14 5

10 048

10 32

1135

2

2 2 2

.

. . .

126

Table 2-7. Reference Chemical Explosion of one kilogram of TNT in air at 15 degrees C and 1.01325 bars.[3]

Scaled Shock Over- Arrival Average Shock Impulse WaveformDistance Mach Pressure Time Speed Duration per Area Parameter(meters) Number (atm) (msec) (m/s) (msec) (bar-msec) ------Z Mx ∆p/pa ta σ td I/A α---------- ----------- --------- -------- --------- ---------- ------------ -------------0.053 21.16 528.3 0 — — — — 0.10 16.7 328.6 0.007 13500 7.777 5.72 — 0.15 13.65 219 0.17 8730 2.317 2.71 — 0.20 11.55 156.4 0.029 6920 0.978 1.76 — 0.25 9.99 116.9 0.043 5870 0.501 1.39 — 0.30 8.79 90.1 0.058 5150 0.29 1.23 — 0.35 7.82 71.2 0.076 4610 0.183 1.15 — 0.40 7.04 57.4 0.096 4180 0.125 1.11 — 0.45 6.38 47 0.118 3830 0.095 1.09 — 0.50 5.83 39 0.142 3530 0.084 1.07 — 0.55 5.36 32.8 0.168 3280 0.088 1.06 — 0.60 4.95 27.8 0.196 3060 0.109 1.05 — 0.65 4.6 23.9 0.227 2870 0.144 1.05 — 0.70 4.29 20.6 0.26 2700 0.191 1.04 — 0.75 4.02 18 0.295 2540 0.246 1.03 — 0.80 3.78 15.7 0.332 2410 0.304 1.02 — 0.85 3.57 13.9 0.372 2280 0.363 1.01 — 0.90 3.38 12.3 0.414 2170 0.419 1 — 0.95 3.21 11 0.459 2070 0.471 0.99 — 0.952 3.200 10.924 0.461 2067 0.473 0.993 4.0001.00 3.05 9.83 0.506 1980 0.52 1.015 3.711.05 2.91 8.84 0.555 1890 0.565 1.039 3.461.10 2.78 7.98 0.606 1820 0.608 1.053 3.241.15 2.67 7.23 0.66 1740 0.647 1.058 3.031.20 2.56 6.57 0.716 1680 0.685 1.057 2.851.25 2.46 6 0.774 1620 0.72 1.051 2.681.30 2.38 5.49 0.834 1560 0.755 1.041 2.531.35 2.29 5.04 0.897 1510 0.788 1.028 2.41.40 2.22 4.64 0.962 1460 0.82 1.013 2.271.50 2.08 3.96 1.098 1370 0.882 0.98 2.051.60 1.97 3.41 1.242 1290 0.943 0.943 1.861.70 1.87 2.96 1.395 1220 1.001 0.905 1.71.75 1.83 2.77 1.474 1190 1.03 0.886 1.631.80 1.786 2.59 1.555 1157 1.058 0.867 1.561.85 1.748 2.429 1.638 1129 1.087 0.849 1.51.90 1.712 2.283 1.723 1103 1.115 0.83 1.441.95 1.679 2.148 1.809 1078 1.142 0.812 1.392.00 1.647 2.025 1.897 1054 1.17 0.794 1.342.05 1.618 1.912 1.987 1032 1.197 0.777 1.292.10 1.59 1.808 2.078 1011 1.224 0.76 1.252.15 1.565 1.711 2.171 990 1.251 0.743 1.212.20 1.54 1.622 2.265 971 1.278 0.727 1.172.25 1.518 1.54 2.361 953 1.305 0.712 1.142.30 1.496 1.464 2.458 936 1.331 0.696 1.12.35 1.476 1.393 2.557 919 1.357 0.682 1.072.40 1.457 1.327 2.656 903 1.383 0.667 1.042.50 1.422 1.209 2.86 874 1.434 0.64 0.992.60 1.391 1.105 3.069 847 1.485 0.614 0.942.70 1.363 1.015 3.281 823 1.535 0.59 0.92.80 1.338 0.93 3.498 800 1.584 0.567 0.862.90 1.316 0.865 3.72 780 1.63 0.546 0.823.00 1.296 0.802 3.94 761 1.68 0.526 0.793.10 1.277 0.746 4.17 743 1.73 0.517 0.76

127

Table 2-7 (continued). Reference Chemical Explosion of one kilogram of TNT in air at 15 degrees C and 1.01325 bars. [3]

Scaled Shock Over- Arrival Average Shock Impulse WaveformDistance Mach Pressure Time Speed Duration per Area Parameter(meters) Number (atm) (msec) (m/s) (msec) (bar-msec) ------Z Mx ∆p/pa ta σ td I/A α---------- ----------- --------- -------- --------- ---------- ------------ -------------3.20 1.261 0.697 4.4 727 1.77 0.49 0.743.30 1.246 0.652 4.64 712 1.82 0.473 0.723.50 1.219 0.575 5.11 685 1.91 0.443 0.673.75 1.192 0.498 5.72 655 2.01 0.41 0.634.00 1.17 0.437 6.34 631 2.11 0.382 0.64.25 1.152 0.387 6.98 609 2.21 0.357 0.574.50 1.137 0.347 7.62 591 2.3 0.336 0.544.75 1.125 0.313 8.27 575 2.39 0.317 0.525.00 1.114 0.285 8.92 560 2.47 0.3 0.55.50 1.097 0.24 10.25 537 2.63 0.271 0.475.75 1.09 0.223 10.92 526 2.7 0.259 0.466.00 1.084 0.207 11.6 517 2.76 0.248 0.456.25 1.079 0.194 12.28 509 2.83 0.238 0.446.50 1.074 0.182 12.96 502 2.89 0.229 0.436.75 1.07 0.171 13.64 495 2.95 0.22 0.427.00 1.066 0.162 14.33 488 3 0.213 0.417.50 1.06 0.146 15.71 477 3.1 0.199 0.398.00 1.055 0.132 17.1 468 3.19 0.187 0.388.50 1.05 0.121 18.5 459 3.27 0.176 0.379.00 1.046 0.112 19.9 452 3.34 0.167 0.369.50 1.043 0.104 21.3 446 3.41 0.158 0.3510.00 1.04 0.097 22.7 440 3.47 0.151 0.3411.0 1.036 0.086 25.5 431 3.57 0.138 0.3312.0 1.032 0.077 28.4 423 3.65 0.127 0.3113.0 1.029 0.07 31.2 416 3.72 0.118 0.314.0 1.027 0.064 34.1 411 3.78 0.11 0.2915.0 1.025 0.059 37 406 3.83 0.103 0.2816.0 1.023 0.055 39.8 402 3.87 0.097 0.218.0 1.02 0.048 45.6 395 3.93 0.087 0.2620.0 1.018 0.043 51.4 389 3.98 0.078 0.2522.5 1.016 0.038 58.6 384 4.03 0.07 0.2425.0 1.014 0.034 65.8 380 4.06 0.063 0.2327.5 1.013 0.03 73.1 376 4.09 0.058 0.2230.0 1.012 0.028 80.3 374 4.11 0.053 0.2232.5 1.011 0.026 87.6 371 4.12 0.049 0.2135.0 1.01 0.024 94.9 369 4.13 0.046 0.237.5 1.009 0.022 102.1 367 4.14 0.043 0.240.0 1.009 0.021 109 366 4.15 0.04 0.245.0 1.008 0.018 124 363 4.16 0.036 0.1950.0 1.007 0.016 139 361 4.17 0.032 0.1855.0 1.006 0.015 153 359 4.18 0.0029 0.1860.0 1.006 0.014 168 358 4.19 0.027 0.1770.0 1.005 0.012 197 355 4.19 0.023 0.1780.0 1.004 0.01 226 354 4.2 0.02 0.16100.0 1.003 0.008 285 351 4.2 0.016 0.15125.0 1.003 0.007 358 349 4.21 0.013 0.14150.0 1.002 0.005 431 348 4.21 0.011 0.14200.0 1.002 0.004 578 346 4.21 0.008 0.13250.0 1.001 0.003 725 345 4.21 0.007 0.13300.0 1.001 0.003 871 344 4.21 0.005 0.13400.0 1.001 0.002 1165 343 4.21 0.004 0.12500.0 1.001 0.002 1459 343 4.21 0.003 0.12

128

The arrival time of the shock is obtained by noting that the shock velocity is

(2.36)u drdt

M cx x x= =

where r is the radial distance from the center of the explosion, and integrating to obtain

(2.37)tc

drMa

x xcr

r= z1 1

where rc is the radius of the explosive charge. Recalling Eq.(2.25) for the Mach number as afunction of the overpressure ratio

(2.38)M ppx

x

2 11

2= +

+⋅

γγb g ∆

we can rewrite Eq. (2.37) as

. (2.39)tc

drp

p cdr p

pax ac x acr

r

r

r= +

+FHG

IKJ

LNM

OQP

= +FHG

IKJ

LNM

OQPz z1 1 1

12

1 1 1 67

1 2 1 2γ

γb g∆ ∆

/ /

The average shock speed σ is simply given by the distance traveled divided by the timerequired

. (2.40)σ =rta

The duration td of the positive pressure phase of a chemical explosion is given by the analyticalapproximation

(2.41)t

W

Z

Z Z Zd1 3

10

3 6 2

980 10 54

10 02

10 74

16 9

/

.

. . .

=

+ FHGIKJ

LNMM

OQPP

+ FHGIKJ + FHG

IKJ + FHG

IKJ

Impulse is the product of a force F acting over a specified time ∆t and is proportional to thechange in momentum ∆(mv)

129

. (2.42)F t d mvdt

t mv⋅ = ⋅ =∆ ∆ ∆( ) ( )

Since the force produced by an explosive blast wave is proportional to the overpressure, which isa force per unit area, it is appropriate to estimate the impulse per unit area that can be delivered bythe blast. For our reference explosion, the results can be expressed by the analytical approximation

. (2.43)IA

Z

Z Z=

+ FHGIKJ

LNMM

OQPP

+ FHGIKJ

LNMM

OQPP

0 067 10 23

1155

4 1 2

23 1 3

..

.

/

/

The waveform (time-dependent pressure) of the blast wave is approximately given by thefunction

(2.44)( ) /1ad

dt ttp t p p et

α− − = ∆ −

where p(t) is the instantaneous overpressure at time t, ∆p is the maximum or peak overpressureobserved at t=0, td is the time duration of the positive phase of the overpressure, and α is thewaveform parameter. The impulse per unit area is the simple time integral of the overpressure.Thus,

. (2.45)( )( ) ( )20

1 1 1dt

a dI dt p t p p t eA

α

α α− = − = ∆ − − ∫

From the table and the equations above it is possible to determine the overpressure, dragforce, and/or impulse per unit area of explosions in air of any size of any explosive material at anydistance from the explosive device. By itself, this information has little meaning. To determine thedamaging effects of explosions, it is necessary to obtain hardness data, i.e., data on the damagesensitivity of structures as a function of overpressure. Given the detailed design of a target, finiteelement models could be used to determine the overpressure or drag force at which the weakestelement of the target would fail. This is a valid approach when determining vulnerability of our ownsystems. Unfortunately, the calculations are time-consuming and expensive, the analysis requiressophisticated models and computer software, and every potential target is different. However,thousands of vulnerability “measurements” have been performed under conditions where genericeffects can be quantified. A number of correlations between overpressure and observed failureshave been made. These are summarized in Table 2-8. After determining the level of damagedesired, the appropriate correlation determines the required overpressure.

130

Table 2-8. Correlation of blast damage with side-on overpressure. [3]

OVERPRESSURE

TYPE OF DAMAGE (atm) (psi)Minimum damage to glass panels 0.001 - 0.003 0.02 - 0.04Typical window glass breakage 0.010 - 0.015 0.15 - 0.22Threshold for debris and missile damage 0.015 - 0.025 0.22 - 0.37Windows shattered, plaster cracked, minor damage to some buildings 0.035 - 0.075 0.51 - 1.10Personnel knocked down 0.070 - 0.100 1.03 - 1.47Panels of sheet metal buckled 0.075 - 0.125 1.10 - 1.84Failure of wooden or asbestos siding on conventional homes 0.075 - 0.150 1.10 - 2.20Failure of concrete block or cider block walls 0.125 - 0.200 1.84 - 2.94Collapse of self-framing paneled buildings 0.200 - 0.300 2.94 - 4.41Oil storage tanks ruptured 0.200 - 0.300 2.94 - 4.41Utility poles broken off 0.300 - 0.500 4.41 - 7.35Serious damage to buildings with structural steel framework 0.300 - 0.500 4.41 - 7.35Eardrum rupture 0.350 - 1.000 5.14 - 14.7Reinforced concrete structures severely damaged 0.400 - 0.600 5.88 - 8.82Railroad cars overturned 0.400 - 0.600 5.88 - 8.82Total destruction of most buildings 0.700 - 0.800 10.3 - 11.8Lung damage 2.000 - 5.000 29.4 - 73.5Lethality 7.000 - 15.00 103 - 220Crater formation in average soil (air burst) 20.00 - 30.00 294 - 441

GENERIC DAMAGE TYPE SCALED DISTANCE (m) THRESHOLDMinor damage to light construction (unreinforced) 13.3 0.07 1Substantial damage to light construction (unreinforced) 7.9 0.14 2Significant damage to masonry structures (unreinforced) 5.15 or 4.55 0.27 or 0.34 4 or 5Total destruction of most buildings 3.24 or 2.97 0.68 or 0.82 10 or 12Minor damage to blast-resistant structures 3.24 or 2.97 0.68 or 0.82 10 or 12

(shaped, reinforced concrete)Substantial damage to blast-resistant structures 1.89 2.33 30

The generic thresholds at the bottom of the chart are often used in “cookie cutter” modelsof damage. For example, 5 psi overpressure will destroy most unreinforced structures while 12 psioverpressure will destroy most structures and damage even blast-resistant structures. Theappropriate scaled distances are 4.55 and 2.97 meters respectively. A 10,000 kg explosion of TNT(equivalent to a World War II “blockbuster” bomb) has a cube-root scale factor (10,000)1/3 = 21.54.The actual 5 psi and 12 psi distances are 21.54 x 4.55 = 98 meters and 21.54 x 2.97 = 64 meters,respectively. Such an explosion will destroy everything within a football field sized area. In acookie cutter damage analysis, one would assume that everything within the 64 meter radius(assuming the 12 psi threshold) is destroyed by one bomb. Drawing a circle of 64 meter scaledradius on a map of the target for each bomb delivered would show how much of the total target areawas destroyed and could be used to determine optimum spacing between the bombs to be droppedor optimum locations for bombs to be emplaced.

131

Projectile Damage

Compared with buildings, human beings are relatively difficult to injure with blast. Seriousinjury requires an overpressure 10 times that required to produce substantial building damage.Many electronic assemblies, aircraft, ships, etc., are likewise difficult to damage with the over-pressure from small explosions. However, these structures may be destroyed by penetration of asingle high-velocity fragment. Fragmentation warheads were developed to permit the weapon tohave a high probability of putting one or more fragments through specific target areas.

Basically a fragmentation warhead consists of an explosive charge surrounded by a metalcase. A warhead producing a cylindrical fragment cloud is shown in Figure 2-11. This is a typicalconfiguration for an antiaircraft missile warhead. When detonated the explosive shatters the caseinto a number of small fragments and accelerates those fragments to lethal velocities. The fragmentsfly out from the warhead at high speed in an expanding cloud. If one or more fragments strikes asensitive portion of the target, the target will be damaged and partially destroyed. Fragmentationwarhead design details involve choice of the size and number of fragments that must be produced,the initial velocity of the fragments, the choice of explosive, the relative weight of explosive andtotal fragment mass, and the directionality (if any) of the fragment pattern.

Figure 2-11. A fragmentation warhead.

132

Consider first the velocity imparted to individual fragments.[3] Gurney’s formula is anempirical relation for determining fragment velocity. The average initial fragment velocity (theactual spread in fragment velocities is relatively small) due to an explosion is

, (2.46)v E C WC WE =

+

LNM

OQP

21

1 2

ηb g/

where C is the mass of the explosive charge, W is the total mass of the fragmentable material, (2E)½

is a constant with units of velocity, called the Gurney constant, and η is constant depending on theshape of the fragmentable mass. The constant η = 0.5 for long cylinders, η = 0.6 for spheres, andη = 0.33 for planar sandwiches. In the absence of heat retained as internal energy by the explosiveproducts, heating of the fragmentable material, and other sinks of energy, the Gurney constant wouldbe directly related to the explosion energy E. However, these energy loss effects cause the Gurneyconstant to differ slightly from the square root of twice the explosion energy. The Gurney constanthas been experimentally determined for a number of common explosives. These are summarizedin Table 2-9.

Table 2-9. Gurney constants of major explosives and explosive formulations.[3]

EXPLOSIVE COMPOSITION √2E (km/s)Amatol 80% AN + 20% TNT 2.908Ammonium Nitrate (AN) 1.761AN/Fuel Oil (ANFO) 94% AN + 6% Oil 2.769Ammonium Picrate (Explosive D) 2.137Comp B-3 64% RDX + 36% TNT 2.843Comp C-4 2.801Cyclotol 77% RDX + 23% TNT 2.979Cyclotetramethylenetetranitramine (HMX) 3.198Diaminotrinitrobenzene (DATB) 2.192Dipentaerythritolhexanitrate (DiPEHN) 3.268Ethylene Glycol Dinitrate (EGDN) 3.692Hydrazinium Nitrate 2.796Methyltetranitroaniline (Tetryl) 2.710Nitrocellulose (NC) 13.35% Nitrogen 2.473Nitroglycerine (NG) 3.575Nitroguanidine (NQ) 2.308Nitromethane (NM) 2.978Octol 76% HMX + 24% TNT 2.965Pentolite 50% TNT + 50% PETN 2.970Pentaerythritoltetranitrate (PETN) 3.425Tetranitrodibenzotetrazacyclooctatetraene (TACOT) 2.655Tetranitromethane (TNM) 2.173Trinitrophenol (Picric Acid) 2.439Cyclotrimethylenetrinitramine (RDX) 3.205Triaminotrinitrobenzene (TATB) 2.028Trinitrotoluene (TNT) 2.315

133

For any materials not listed in the table it has been found that there is a reasonably accuratecorrelation between the Gurney constant and the detonation velocity

. (2.47)2 2 97E D≈ / .

The size and velocity that a fragment must have to be effective depend on the target. Ingeneral a fragment must penetrate the skin of the target to be effective. There is no good correlationfor penetration as there was for blast. A crude correlation can be found by considering the mostclassical of all military projectiles, i.e., bullets.[7],[8] Table 2-10 lists the parameters of a numberof standard bullets and a few specific kinds of fragments. The kinetic energy per unit area of theprojectile is arguably the best measure of penetration effectiveness. The small, low velocity bullets(0.22 and 0.38 calibers) will clearly penetrate a human body, but have little or no “stopping power”(a subjective ability to stop a charging individual with a single shot and render him unable tocontinue to fight) and are not considered “sure kills”. Only perfect shots to the head or heart arelikely to be lethal. These two bullets have energies per area of 1.9 and 2.6 J/mm2. It is tempting toequate 2 J/mm2 with a minimally effective projectile. With energies per area of 6.8, 12.7, and 10.3J/mm2, the 9 mm Parabellum and 0.44 Magnum rounds and grenade fragments are generallyconsidered lethal. Thus, an energy per area of 10 J/mm2 might be associated with a projectileacceptably lethal to humans. The modern assault weapon projectiles (7.62 mm and 5.56 mm) arehighly lethal with significant “stopping power” and are capable of penetrating a limited amount ofballistic protection. Energies per area of 50+ J/mm2 are associated with these penetrating, highlethality projectiles. The 0.50 caliber machine gun bullets are capable of penetrating thin armorplate. An energy per area of at least 100 J/mm2 will be necessary for fragments to be highlypenetrating. It should be noted that penetration for bullets will be higher than for randomly shapedfragments. However, the differences should not be that significant.

Table 2-10. Characteristics of typical small projectiles.[7],[8]

ENERGY DIAMETER MASS VELOCITY ENERGY per AREA

PROJECTILE (mm) (g) (m/s) (J) (J/mm2)

0.22 cal Short 5.59 1.88 253 60 1.90.38 cal Pistol 9.65 11.7 180 190 2.6Parabellum 9x19mm 9.0 7.47 340 432 6.8Grenade fragment 2.5 0.07 1200 50 10.30.44 cal Magnum 11.17 15.6 400 1248 12.7Shell fragment 6.2 1.0 1200 720 23.9Soviet 7.62x39mm 7.62 7.9 710 1993 43.0Soviet 5.45x39mm 5.45 3.4 900 1385 59.3NATO 7.62x51mm 7.62 9.3 835 3242 71.2NATO 5.56x45mm 5.56 3.5 948 1796 74.00.50 cal BMG 12.7 42.8 945 19100 118.5

134

Given a specific selection of energy per area, there is still considerable flexibility in how thatenergy per area is achieved. Fragment dimension, fragment material density, and fragment velocityall play a role. The energy per area E/A as a function of these three parameters can be shown to begiven by

(2.48)E A m vd

d vd

d vF/ //

/ //

= = =2

2

3 2

2

224

6 24 3π

ρ ππ

ρc h

where d is the characteristic fragment dimension and D is the fragment material density.

A complication to the design of the perfect fragment is the fact that air resistance (drag)causes the fragments to slow down as they travel. Empirically, for non-aerodynamically-shapedprojectiles at sea level, it is found that the velocity at range R is related to the initial velocity vE byan exponential expression

(2.49)v R v eEFR Cmb g = − / /1 3

where C is a constant and mF is the fragment mass. The inverse cube root dependence on masscomes from the fact that the drag deceleration is inversely proportional to mass and proportional toarea. Since the area of a roughly spherical object is proportional to the square of its dimension andthe mass is proportional to the cube of its dimension, the area should be proportional to the 2/3power of the mass. Thus, area divided by mass should be proportional to the -1/3 power of the mass.Examination of velocity versus range curves in Reference [6] suggests that the velocity of a 1 gramprojectile falls to 1/e of its initial velocity in 26 meters. Thus, we may approximate the constant Cby

. (2.50)C = 26 m / g1/3

Because drag scales linearly with air density, it is expected that the constant C can be obtained foraltitudes other than sea level by dividing by the ratio of atmospheric density at the desired altitudeto the atmospheric density at sea level.

Massive projectiles maintain their velocities for greater distances than light projectiles. Forthe 0.07-gram grenade projectile in Table 8-8, we calculate a 1/e range of 10.7 meters. This iscomparable to the kill radius for a typical grenade. A very crude approximation might assume thatCmF

1/3 is equal to the effective fragment radius. Under this assumption 1-gram fragments wouldhave an effective radius of about 26 meters, while 10-gram fragments would have an effective radiusof about 56 meters. Obviously, if the initial velocity is high enough (vE can be greater than 2000m/s) and the penetration velocity is low enough (the 0.38 cal bullet has a velocity of only 180 m/s),the real effective range might be 2 to 3 times this crude approximation. However, it cannot besignificantly greater than 2 to 3 times CmF

1/3 under any realistic conditions.

135

If the explosive device is intended to produce fragments, i.e., it is intentionally placed in aheavy metal case, it is likely that the fabricator would like to maximize the number of fragmentsproduced while insuring that they are each large enough to produce the desired degree ofpenetration. There are many solutions to the problem of how to produce fragments of knownnumber and relatively equal known size. Key examples are illustrated in Figure 2-12. For examplethe fragments may be discrete (physically separated from each other). Cubes can be packed into flatplate geometries or cylinders with little problem. Spheres can be close-packed into almost anyshape. These options yield fragments that are all the same size and shape. However, an externalcase or fracturable binder is required to hold the fragments in the desired shape.

Solid metal cases can be designed to fracture into relatively uniform fragments. Metals arestronger under compression than under tension. Interacting shock waves can produce regions oftension separated by regions of compression. The case will fracture where the material is placedunder tension. Consider the effect of grooves etched into the case. It does not matter whether thegrooves are on the outside or the inside of the case. When a shock wave passing through the casereflects off the surface, the grooves reflect the waves diagonally back into the material. As theshock waves collide and pass each other, the space between the flat surface and the groove tips willundergo tension and fracture. A cylindrical case with grooves on the outside of the case is illustratedin Figure 2-13. This type of fragmentable case will produce fragments with essentially rectangularcross section.

Figure 2-12. Generic techniques for producing relative uniform fragments in known quantities.

136

Figure 2-13. Examples of cylindrical fragmentation cases with grooves and dimples.

Dimples are conical or hemispherical (cup) depressions in the case that extend into theexplosive. Dimpled cases combine tensional fracture with a separate effect. As the shock wavepasses through each dimple, the dimple acts like a small shaped charge (see the section on shapedcharges below) and shoots out a high speed jet of metal. The shock then causes the rest of the caseto fracture at the thin points of the remaining web. A cylindrical case with cup dimples arrangedin a hexagonal pattern is shown in Figure 2-13.

Grooves etched into the explosive employ the Munroe effect [9] As the shock wave passesthrough the grooves the shock intensity is focused onto the case. The higher intensity resulting fromthe focusing causes the case to fragment at the position of the grooves.

137

Description of Specific Explosive Formulations

Conventional high explosives can be classified in several different ways. Physical form isone method of classification. Some explosives are solids, some are liquids, and a few are neithersolid nor liquid. The solids may be in loose powder form, powder compressed into a solid mass,powder bonded with plastic to form a solid mass, or a polycrystalline solid formed by casting moltenmaterial. Those which are neither truly liquid nor solid may be in the form of a slurry of solid in aliquid, or in the form of a gel of semi-dissolved solid, or in a deformable solid with characteristicssimilar to putty or modeling clay. The physical form often affects the use of the explosive. Castablesolids are often used in large artillery shells and bombs where casting makes production easier.Liquids are often used in blasting for mining or construction, because the liquid can be pumped intoirregular-shaped holes and will guarantee intimate contact of the explosive with the material to beblasted. The deformable solids are commonly used for field demolition, where the ability to alterthe size and shape of the charge is important. The plastic explosives are often used in precisionexplosive assemblies because the plastic explosive can be precision machined to any shape desired.

The author prefers to classify explosives based on whether they are single-componentexplosives or multi-component (or composite) explosives. Single-component explosives are purechemical species. For example, TNT, nitroglycerine, and lead azide are single-componentexplosives. A unique chemical formula can be assigned to each and their properties can be studiedwithout ambiguity. The single-component explosives can be further separated into primaryexplosives and secondary explosives (explosives which are almost always initiated by otherexplosives). Multi-component explosives are explosives formulated from one or more single-component explosive with the possible addition of fuel components or structural bindingcomponents (which may or may not act as fuel components). For example, the putty-like explosivesare often mixtures of a single-component explosive and oil (a fuel). Multi-component explosives(and their explosive properties) can vary substantially from lot to lot and from manufacturer tomanufacturer. This is because there is rarely a fixed formula to follow. Cyclotol is nominally 75%RDX and 25% TNT. However, mixing RDX and TNT in any ratio results in an explosive ofconsiderable power. Some vendors may sell cyclotol that is 70%/30% or 80%/20% rather than75%/25%. Indeed, some end users may request a different formulation designed to meet specificneeds. Nevertheless, because the composition of cyclotol may vary, its explosive properties mayalso vary.

Despite the potential for variability that is introduced, there are many good reasons forproducing multi-component explosives. For example, the putty-like explosives are putty-likebecause they contain oil as a component. No-single component explosive is putty-like. Dynamiteis made by adding an adsorbing material (sawdust, cellulose, nitrocellulose, diatomaceous earth,etc.) to nitroglycerine. Liquid nitroglycerine has undesirable high sensitivity. The adsorptionprocess stabilizes the high explosive, rendering it relatively safe to handle. Depending on itscharacter, the adsorbent material may be inert, may act as a fuel, or may be explosive itself.Sawdust and cellulose are fuels, nitrocellulose is an explosive, and diatomaceous earth is inert.Multi-component explosives may be formulated to produce specific explosive properties. Forexample, addition of barium nitrate to TNT can not only improve the oxygen balance of the mix, butalso alter the detonation velocity.

138

Most of the castable explosives are mixtures of TNT with other explosives such as HMX orRDX. TNT melts at a relatively low temperature which is well below its initiation temperature. Themelted TNT forms a slurry with the other unmelted explosives. The slurry can be cast into a moldor a hollow artillery shell and allowed to cool and solidify. By itself the other explosive componentcould not be cast. TNT alone is unacceptable for many applications because it has a relativelymediocre energy content, detonation velocity, and Chapman-Jouguet pressure. The other explosivecomponent of the mixture provides the desired explosive characteristics; the TNT provides thecastability.

Table 2-11 lists the properties of the important primary explosives. Table 2-12 lists theproperties of pure (single-component) high explosives. Table 2-13 lists the properties of composite(multi-component) high explosives. Data in these tables have been extracted from numerous sourcesincluding References [1]-[4], [7], and [10]-[12]. NOTE: in Tables 2-11 through 2-13 manyproperties are characterized by question marks. This means that a numerical value of the propertywas not available to the author from open sources. In some instances, the property has not beenmeasured or estimated for the explosive in question. In many cases, the property may have beenmeasured, but the numbers are classified or proprietary. Rather than guess at possible numbers, theauthor has opted for openness in the degree of uncertainty.

139

ON

N

NO2

O2N

NO2

O2N NO2

O O

Pb

N

N N

HN

N N NH

HN

NH

NH2 H2O

Table 2-11. Properties of primary explosives.

MELTING ENERGY DETONATION DEFLAGRATION IMPACT DENSITY POINT CONTENT VELOCITY POINT SENSITIVITY

EXPLOSIVE CHEMICAL FORMULATION FORM (g/cm3) (C) (MJ/kg) (mm/µs) (C) (N-m)

DDNP Diazodinitrophenol (Diazol) Solid 1.63 ? ? 6.6 180 1.5

— Lead Azide Solid 4.8 ? 1.54 5.3 320 - 360 2.5 - 4.0(Wetted) 4.0 ? ? 5.1 ? ?

Pb(N3)3

— Lead Trinitroresorcinate (Lead Styphnate) Solid 3.0 ? 1.55 5.2 275 - 280 2.5 - 5.0 (Wetted) 2.5 ? ? 4.8 ? ?

— Mercury Fulminate Solid 4.42 ? 1.49 ? 330 1 - 2 (Wetted) 3.6 ? ? 4.7 180? ?

Hg(ONC)2

— Silver Azide Solid 5.1 251 ? ? 273 ?

AgN3

Tetrazene Tetrazolyl Guanyltetrazene Hydrate Solid 1.7 ? ? ? 140 1

140

CH2

NH

CH2C

CO2N

O2N

O2N

NO2

O2N

NO2

N N

N N

N N NO2O2N

NO2

NO2O2N

O2N

Table 2-12. Properties of pure single-component high explosives.

MELTING ENERGY DETONATION C-J DENSITY POINT CONTENT VELOCITY PRESSURE

EXPLOSIVE CHEMICAL FORMULATION FORM (g/cm3) (C) (MJ/kg) (mm/µs) (kbar) SENSITIVITY

ADN Ammonium Dinitramide Solid < 1.82 93-95 ? >5.3 ? Medium

NH4N(NO2)2

AN Ammonium Nitrate Solid 1.72 169.6 ? ? ?V. Low

NH4NO3

APC Ammonium Perchlorate Solid 1.95 Decomposes 2.05 ? ? Low

NH4ClO4

BTNENA Bis-(2,2,2-trinitroethyl)nitramine ? ? ? 5.05 ? ? ?

CL-20 Hexanitrohexaazaisowurtzitane ? ? ? ? ? ? ?

141

NH2

NO2

NO2

O2N

NH2

OOO

NO2O2N

OCH2

CH2

CC

H2C

CH2H2C

H2C

CH2

H2C

ONO2

ONO2

ONO2ONO2

ONO2

O2NO

HC CHOO NO2O2N

ONH4

NO2

NO2

O2N

Table 2-12 (continued). Properties of pure single-component high explosives.

MELTING ENERGY DETONATION C-J DENSITY POINT CONTENT VELOCITY PRESSURE

EXPLOSIVE CHEMICAL FORMULATION FORM (g/cm3) (C) (MJ/kg) (mm/µs) (kbar) SENSITIVITY

DATB 1,3-Diamino-2,4,6-trinitrobenzene Solid ? ? ? ? ? ?

— Diethyleneglycol Dinitrate Liquid 1.38 2 4.38 6.60 ? High

DIPEHN Dipentaerythritol Hexanitrate Solid 1.63 72 4.85 7.40 ? Medium

EGDN 1,2-Ethanediol Dinitrate (Nitroglycol) Liquid 1.48 -20 6.85 7.30 ? High

Explosive D Ammonium Picrate Solid 1.72 280 2.88 7.15 ? V. Low

142

H2C

O O

H2C

C

H2C

C

NO2

O2NFF

NO2

O2N

N

H2CN C

H2

N

CH2

NH2C

NO2

NO2

O2N

O2N

O2N

O2N

NO2

NO2

O2N

NO2

Table 2-12 (continued). Properties of pure single-component high explosives.

MELTING ENERGY DETONATION C-J DENSITY POINT CONTENT VELOCITY PRESSURE

EXPLOSIVE CHEMICAL FORMULATION FORM (g/cm3) (C) (MJ/kg) (mm/µs) (kbar) SENSITIVITY

FEFO Bis-(2-fluoro-2,2-dinitroethyl)formal Liquid 1.60 11.3-12.9 5.82 7.50 ? Medium

HMX 1,3,5,7-Tetranitro-1,3,5,7-tetraza- Solid 1.89 285-287 6.19 9.11 387 Mediumcyclooctane (Octogen)

HNE Hexanitroethane Solid 0.91 147 3.10 4.95 ? Low

(NO2)3CC(NO2)3

HNS 2,2',4,4',6,6'-Hexanitrostilbene Solid 1.70 316 5.69 7.00 ? High

— Hydrazine Nitrate Solid 1.63 71 3.83 8.70 ? MediumH2NNH3ONO2

143

O

O

O

O

O

O

HO OH HO OH O2NO OH

OH ONO2 ONO2

O

O

ONO2

O2NO ONO2

OO

ONO2

NO2O2N

NH

NH

H2N

O2N

Table 2-12 (continued). Properties of pure single-component high explosives.

MELTING ENERGY DETONATION C-J DENSITY POINT CONTENT VELOCITY PRESSURE

EXPLOSIVE CHEMICAL FORMULATION FORM (g/cm3) (C) (MJ/kg) (mm/µs) (kbar) SENSITIVITY

— Methyl Nitrate Liquid 1.22 -83 6.17 6.30 ? High

CH3ONO2

NC 13.35%N Nitrocellulose (13.35% N) Solid 1.58 >135 decomp 4.27 7.30 210 High

NG Nitroglycerine Liquid 1.59 13.2 6.19 7.70 253 V. High

NM Nitromethane Liquid 1.14 -29 4.45 6.29 ? ?

CH3NO2

NQ Nitroguanidine Solid 1.70 246-247 3.68 8.27 268 V. Low

144

C

H2C

CH2

CH2H2CO

O

O

NO2

NO2

O2N

NO2

O

OH

NO2

NO2

O2N

H2C

NCH2

N

CH2N

NO2

NO2O2N

N N

NN NO2

NO2

O2N

O2N

Table 2-12 (continued). Properties of pure single-component high explosives.

MELTING ENERGY DETONATION C-J DENSITY POINT CONTENT VELOCITY PRESSURE

EXPLOSIVE CHEMICAL FORMULATION FORM (g/cm3) (C) (MJ/kg) (mm/µs) (kbar) SENSITIVITY

PETN Pentaerythritol Tetranitrate Solid 1.76 139-142 6.32 8.26 340 High

Picric Acid 2,4,6-Trinitrophenol Solid 1.76 122 3.75 7.35 ? Medium

RDX 1,3,5-Trinitro-1,3,5-Triazacyclohexane Solid 1.77 204 6.19 8.70 338 Medium

TACOT Tetranitrodibenzo-1,2,5,6-tetraza- Solid 1.64 378 4.02 7.25 ? V. Lowcyclooctatetraene

145

NH2

NO2

NO2

O2N

NH2H2N

N3

NO2

NO2

O2N

N3N3

N

NO2

NO2

O2N

CH3

NO2

NH2

NO2

NO2

O2N

Table 2-12 (continued). Properties of pure single-component high explosives.

MELTING ENERGY DETONATION C-J DENSITY POINT CONTENT VELOCITY PRESSURE

EXPLOSIVE CHEMICAL FORMULATION FORM (g/cm3) (C) (MJ/kg) (mm/µs) (kbar) SENSITIVITY

TATB 1,3,5-Triamino-2,4,6-trinitrobenzene Solid 1.88 448-449 4.52 7.76 291 V. Low

TATNB 1,3,5-Triazido-2,4,6-trinitrobenzene Solid 1.81 350 1.28 ? ? Medium

Tetryl 2,4,6-Trinitrophenylmethylnitramine Solid 1.72 130 6.07 7.85 260 High

TNA 2,4,6-Trinitroaniline Solid 1.72 188 4.38 7.30 ? V. Low

146

N

NO2

O2N NO2

NO2O2N

NO2

CH3

NO2

NO2

O2N

Table 2-12 (continued). Properties of pure single-component high explosives.

MELTING ENERGY DETONATION C-J DENSITY POINT CONTENT VELOCITY PRESSURE

EXPLOSIVE CHEMICAL FORMULATION FORM (g/cm3) (C) (MJ/kg) (mm/µs) (kbar) SENSITIVITY

TNAZ 1,3,3-Trinitroazetidine ? ? ? ? ? ? ?

TNB 1,3,5-Trinitrobenzene Solid 1.76 123 4.81 7.30 ? Low

TNM Tetranitromethane Liquid 1.60 14.2 2.30 6.40 144 ?

C(NO2)4

TNT 2,4,6-Trinitrotoluene Solid 1.64 80.9 5.40 6.93 190 Low

147

Table 2-13. Properties of multi-component (composite) high explosives.

MELTING ENERGY DETONATION C-J DENSITY POINT CONTENT VELOCITY PRESSURE

EXPLOSIVE CHEMICAL FORMULATION FORM (g/cm3) (C) (MJ/kg) (mm/µs) (kbar) SENSITIVITY

AEREX 94% Nitromethane Liquid ? ? ? 6.2 ? Low6% Aniline

ANFO 94% Ammonium Nitrate Semi-Solid ? ? ? ? ? Medium6% Fuel Oil

Blasting 92-94% Nitroglycerine Semi-Solid ? ? ? ? ? MediumGelatine 6-8% Nitrocellulose

“Homemade 75% Ammonium Nitrate Semi-Solid ? ? ? ? ? Medium C-4" 20% Nitromethane

5% Powdered Aluminum

Astrolite A-1-5 88% Hydrazinium Nitrate Slurry ? ? ? ? ? Medium12% Powdered Aluminum

Baratol 24% TNT Solid 2.61 79-80 3.01 4.87 140 Low76% Barium Nitrate

Composition B, 63% RDX Solid 1.71 ~80 5.86 7.99 295 Medium Grade A 36% TNT

1% Wax

C-4 91% RDX Putty-like 1.59 ? 5.86 8.04 257 Low5.3% Di-(2-ethylhexyl)-sebacate Solid2.1% Polyisobutane1.6% Motor Oil

Cyclotol 75/25 75% RDX Solid 1.76 79-80 6.03 8.30 316 Medium25% TNT

148

Table 2-13 (continued). Properties of multi-component (composite) high explosives.

MELTING ENERGY DETONATION C-J DENSITY POINT CONTENT VELOCITY PRESSURE

EXPLOSIVE CHEMICAL FORMULATION FORM (g/cm3) (C) (MJ/kg) (mm/µs) (kbar) SENSITIVITY

H-6 30% TNT Solid 1.75 79-80 ? ? ? Medium45% RDX20% Aluminum powder5% Wax0.5% CaCl2

HBX-1 38% TNT Solid 1.71 79-80 7.7 7.31 220 Medium40% RDX17% Aluminum powder5% Wax0.5% CaCl2

HBX-3 29% TNT Solid 1.84 79-80 8.83 7.12 ? Medium31% RDX35% Aluminum powder5% Wax0.5% CaCl2

Octol 75% HMX Solid 1.81 79-80 5.98 8.48 342 Medium25% TNT

PBX-9007 90% RDX Solid 1.66 >200 decomp 5.82 8.09 265 Medium9.1% Polystyrene0.5% Di-(2-ethylhexyl)-phthalate0.4% Rosin

PBX-9404 94% HMX Solid 1.84 >250 decomp 5.94 8.80 375 Medium3% Nitrocellulose3% Tris-β-chloroethylphosphate

PBX-9501 95% HMX Rubbery 1.84 >240 decomp 6.03 8.83 358 Medium2.5% Estane Solid1.25% Bis-(2,2-dinitropropyl)acetal1.25% Bis-(2,2-dinitropropyl)formal

149

Table 2-13 (continued). Properties of multi-component (composite) high explosives.

MELTING ENERGY DETONATION C-J DENSITY POINT CONTENT VELOCITY PRESSURE

EXPLOSIVE CHEMICAL FORMULATION FORM (g/cm3) (C) (MJ/kg) (mm/µs) (kbar) SENSITIVITY

PBX-9502 95% TATB Solid 1.89 448-449 4.29 7.70 >150 V. Low5% Kel-F 800 (CFClCF2CH2CF2)n

PBXN-1 68% RDX Solid ? ? ? ? ? ?20% Aluminum powder12% Nylon

PLX 95% Nitromethane Liquid ? ? ? 6.2 ? Low5% Ethylenediamine

Pentolite 50/50 50% PETN Solid 1.67 76 5.86 7.47 280 Medium 50% TNT

Semtex 1A 76.9% PETN Putty-like ? ? ? 6.2 ? Low4.7% RDX Solid9.0% n-Octyl phthalate butyl citrate

+ N-phenyl-2-naphthalamine9.4% Styrene-butadiene rubber

Semtex H 41.4% PETN Putty-like ? ? ? 6.2 ? Low41.7% RDX Solid7.9% n-Octyl phthalate butyl citrate

+ N-phenyl-2-naphthalamine9.0% Styrene-butadiene rubber

Torpex 40.5% RDX Solid 1.81 ? ? 7.60 ? Medium40.5% TNT18% Aluminum powder1% Wax

XTX-3003 80% PETN Rubbery 1.53 129-135 4.39 7.30 170 High20% Silicone rubber Solid

150

Fuel-Air Explosives, Dispersed Explosives, and Thermobaric Weapons

One disadvantage of weapons using conventional explosives is that the warhead must containboth the fuel and oxidizer components. Given common reaction products of N2, H2O, and CO2 forCHNO explosives, one can estimate that the oxidizer fraction (assumed to be oxygen) can be asmuch as 80% of the total weight, although 50-60% is perhaps more typical. If the warhead couldcarry only fuel and obtain its oxidizer (from the air) at the target, then the effective yield of thewarhead per kg of warhead weight could be doubled, tripled, or even quadrupled. This is onemotivation behind fuel-air explosives.

A fuel-air explosive (FAE) is a mixture of fuel (usually vapor or small particulates) and anadequate amount of air. If the relative concentration of fuel and air lies between well-establishedlimits (called the upper and lower explosion limits), then ignition of the mixture will result indetonation. If there is too little fuel for the given volume of air, then the limited energy released bythe reaction will not be able to fuel the shock wave needed to continue the detonation process. Thissets the lower explosion limit. Below the lower explosion limit, the fuel may burn but it will notdetonate. At very low concentrations, the fuel-air mixture may not even support combustion. Mostlower explosion limits are in the range of 1-10% by volume. On the other hand, if there is too muchfuel for the given volume of air, then only part of the fuel may react with the air and much of theenergy released by the reaction goes into heating the unreacted fuel. This reduces the intensity ofthe shock wave and prevents the shock itself from igniting the unreacted portions of the mixture.This sets the upper explosion limit. Only “fuels” that are explosives in their own rights (e.g.,hydrazine and ethylene oxide) have no upper explosion limit. Upper explosion limits vary from lessthan 10% to 100%.

Table 11-14 lists a number of fuels which form explosive mixtures with air and theconditions under which explosions can occur.[16] Ethylene oxide and propylene oxide are theamong the fuels that have been used in early U.S. fuel-air explosive weapons.[17] Fuel-airexplosives work by dispersing the fuel into the air around the target and igniting the mixture whilethe concentration is somewhere between the explosive limits. Obviously, the wider the rangebetween the lower and upper explosive limits, the less tightly controlled and monitored the fueldispersal needs to be. Similarly since the fuel is almost always dispensed into the air above thetarget, it is desirable for the fuel vapor to be heavier than air, so that the vapor cloud sinks to theground around the target, rather than rising and dissipating rapidly.

Fuel-air explosions occur naturally by accident and can also be produced by acts of sabotageor terrorism, as well by employment of a fuel-air weapon. A massive fuel-air explosion can beproduced in situ by igniting the vapor-air mixture produced by a leaking (or appropriatelysabotaged) liquefied petroleum gas (LPG – a generic term, but often propane or butane), liquifiednatural gas (LNG – mostly methane), ethylene oxide, acetylene, or gasoline storage tank. LPGtanks of sufficient size to level a city block or more are scattered by the thousands throughoutsuburban and rural America and many other countries. Since many explosive vapors are denser thanair, they will settle and accumulate in low spots, such as sewers or storm drains. Large quantitiesof gasoline or LPG leaking into storm drains have the potential for confined fuel-air explosionsinvolving enormous geographic areas. For example, an LNG leak into the storm drains in Cleveland

151

Table 11-14. Chemicals forming explosive mixtures with air.[16] Revised & expanded by the author.

BOILING VAPOR DENSITY SPECIFIC EXPLOSION LIMIT IGNITION HEAT OF SPECIFIC HEAT OF POINT PRESSURE RELATIVE VOLUME LOWER UPPER TEMP. FORMATION HEAT COMBUSTION

FUEL °C MPa @ 21°C TO AIR m3/kg vol.% vol.% °C kJ/mol J/deg/mol MJ/mol MJ/kg

Acetylene -84 4.38 0.905 0.918 2.5 81 305 -226.7 44.1 -0.8022 -30.81

Ammonia -33.35 0.786 0.60 1.411 15 28 651 -45.9 35.65 -0.3169 -18.61

n-Butane -0.5 0.110 2.08 0.400 1.8 8.4 420 -125.6 97.5 -2.6577 -45.73

Carbon Monoxide -191.5 * 0.97 0.862 12.5 74 651 -110.53 29.14 -0.2930 -10.46

Ethane -88.6 3.74 1.047 0.799 3 12.4 530 -83.8 52.5 -1.4288 -47.52 Ethylene -103.7 * 0.974 0.862 3.1 32 543 +52.5 42.9 -1.3232 -47.17

Ethylene Oxide 10.4 0.146 1.52 0.548 2.6 100 429 -52.6 48.3 -1.2181 -27.65 Hydrazine 113 0.00133 1.1 0.75 4.7 100 <270 +50.6 98.9 -0.5343 -16.67

Hydrogen -252.8 * 0.0696 11.99 4 75 585 -0.0 28.84 -0.2418 -119.95

Isobutane -11.6 0.212 2.0 0.405 1.8 8.4 462 -125.6 97.5 -2.6577 -45.73

Methane -164 * 0.555 1.480 5 15 538 -74.9 35.6 -0.8023 -50.02

Methyl Chloride -24.2 0.405 1.74 0.475 10.7 17.4 632 -81.9 40.8 -0.7667 -15.19

**Natural Gas >-164 * 0.55–0.65 <1.48 <5 <15 <538 ~-75 36 – 38 ~-0.85 ~-50

Octane (Gasoline) 122 0.00147 3.86 0.21 1.0 6.5 ? -208.6 188.9 -5.1161 -44.79

Propane -42.1 0.752 1.55 0.531 2.1 9.5 468 -104.7 73.6 -2.0432 -46.34

Propylene Oxide 34 0.0589 2.0 0.42 2.1 37 449 -92.8 72.3 -1.8133 -31.22

* Above the fluid’s critical temperature at 21 °C. ** 70-99% Methane, 1-12% Ethane, 0-18% Other hydrocarbons

152

OH on 21 October 1944 produced a fire and explosion that killed at least 128 people and destroyed165 homes and hundreds of automobiles in a nearby parking lot.[18],[19] On 19 November 1984an LPG leak at the Petroleos Mexicanos (PEMEX) plant in the San Juan Eixhuatepec suburb ofMexico City, Mexico, produced a fire storm that killed an estimated 540 people and injured over2000.[19] On 31 October 1963 a leak from a small 24-gallon LPG tank produced an explosion atthe Indianapolis (Indiana) State Fairgrounds Coliseum that killed 64 people and injured an additional385.[19]

LPG tanks as small as 5 gallons (the small tank carried on many mobile homes, recreationalvehicles, and gas barbecues) are prohibited from many tunnels because of their explosion hazard.Mid-sized tanks of 500 gallon capacity can be found at thousands of gasoline stations and ruralpropane supply companies. Semi-trailer tanks and railroad tank cars are at least ten times larger still.All of these pose the threat of major fuel-air explosions. In fact the threat of disaster from the largeseagoing LNG tankers is so great that when such a tanker enters Boston Harbor, it must first passa stringent safety inspection, then it may proceed only during daylight and good visibility, all otherships are required to stand clear by at least 2 miles ahead and 1 mile astern, and air traffic at LoganAirport is rerouted to avoid overflying the tanker.[20]

Fuel-air explosives need not employ vapor-air mixtures. Mixtures of small particles (dusts)of flammable materials can also be explosive. For example, in the Great Plains of the United States,grain elevators are often considered to be "explosions waiting to happen". Hundreds of dust-airexplosions (more than 260 in the U.S. alone between 1974 and 1991) have occurred in the past from"natural causes" such as electrostatic discharge, lightning strikes, electrical equipment shorts, andunauthorized smoking.[21] Although modern safety and “housekeeping” techniques have reducedthe dangers from natural causes, it would take only the smallest of well-timed explosive devicesplanted by a terrorist or special warfare operator to initiate a massive explosion in many functioningelevators. Fortunately, most previous instances of grain elevator explosions have produced only afew casualties each (although still more than 700 total in the 260 explosions cited above).[21] Forexample, one of the more recent explosions (on 8 June 1998 in Haysville, Kansas) killed six andinjured eleven others.[22] However, unfortunate timing of the blast (such as during a local festival)might result in significantly enhanced casualty rates. Other flammable dust producers, such assawmills, coal mines, and cotton gins, may also make viable targets for terrorist attack. Table 11-15lists a number of potentially hazardous flammable dusts.[23],[24] Studies of dust explosions haveindicated that explosions are likely when a critical set of initial conditions exists.[25] The conditionsare summarized in Table 11-16.

As we shall see shortly, dust explosions may have more significance than their potential inindustrial safety, terrorism, or special warfare. One could envision a “fuel-air explosive” thatconsisted entirely of fine aluminum powder or magnesium powder mixed with air. An advantagewould accrue here because the solid metals are much denser than typical fuels, allowing them to bepackaged in smaller weapons. It is also likely that the intense light and heat radiated by the metaloxide residues will cause significant radiant heating effects (charring or ignition of flammablematerials) on targets in addition to blast effects.

153

Table 11-15. Explosive hazard severity of various dusts in air. [23], [24]

IGNITION MIN. EXPLOSIVE EXPLOSION TYPE OF DUST TEMPERATURE (K) CONC. (kg/m3) HAZARDAlfalfa ModerateAluminum 923 0.045 SevereAl-Mg Alloy 0.020 SevereChromium 0.23 StrongCoal (low volatile) ModerateCoal (high volatile) 883 0.055 StrongCocoa ModerateCoffee WeakCopper 1173 ----- Fire OnlyCork SevereCornstarch SevereCottonseed Hulls WeakCotton Fiber Dust Severe?Crude Rubber StrongEpoxy Resin 803 0.020 SevereFlour SevereIron 693 0.100 StrongKelp WeakMagnesium 793 0.020 SevereMoss WeakOnions WeakPea Flour SeverePeanut Hulls StrongPhenol Formaldehyde StrongPitch SeverePolyethylene StrongPolyvinyl Chloride WeakRice ModerateSilicon 0.11 StrongSkimmed Milk ModerateSoy Protein StrongStearic Acid SevereSugar SevereTantalum ModerateTin 903 0.190 ModerateTitanium 733 0.045 SevereTrioxane WeakUranium 293 0.060 SevereUrea Formaldehyde WeakWalnut Shell StrongWheat Severe?Zinc 873 0.480 ModerateZirconium Severe

SEVERITY: Weak << Moderate << Strong << SevereDusts with concentration data are dried samples passing 200 mesh sieve.

154

Table 11-16. Critical parameters for flammable dust explosions.[25]

INITIAL CONDITION VALUE

Particle size < 0.1 mmDust concentration 40-4000 g/m2

Moisture content < 11% moistureOxygen level > 12%Ignition energy > 10 mJ - 100 mJIgnition temperature 410 - 600 C

The extension of air-mixed explosives beyond simple fuel vapor-air mixtures leads into thewhole topic of thermobaric weapons. The word “thermobaric” is derived from the Greek wordsfor heat and pressure. Ostensibly, thermobaric weapons produce damage and casualties by hightemperatures and high pressures rather than through blast (shock waves) or fragmentation. They are“a class of fuel-rich compositions that release energy over a longer period of time than standardexplosives, thereby creating a long-duration pressure pulse when detonated in confined spaces.[26]

Fuel-air explosives are often considered thermobaric weapons because the extended natureof the explosive cloud (cloud dimensions often exceed the cloud-to-target separation distance)causes an extended period of overpressure relative to conventional explosive shocks (shock wavesfrom different parts of the cloud arrive at slightly different times) and because frequent incompletecombustion of the fuel during the detonation phase results in a short period of afterburning. In anideal vapor explosion at a distance from the target, heating would be produced only by the effect ofthe passing shock wave and the shock wave would be of short duration. Unfortunately, this isseldom the case and the term thermobaric is appropriate.

In the same light, dust-air explosions and explosions in which a significant fraction of thefuel is in aerosol form are more likely to produce radiation heating as the larger dust particles andaerosols will continue to burn for short durations after the detonation wave has passed them by. They too are thermobaric in nature.

The detonation velocity of explosives is related to its density. If a relatively sensitiveexplosive is dispersed in the form of a collection of particles or droplets and initiated, the detonationwithin each particle may proceed normally but the entire cloud will detonate slowly. The releaseof energy from such dispersed explosive agents over a longer time will produce a thermobariceffect. These differ from fuel-air or dust-air explosions because the explosive itself provides all theoxygen needed. Atmospheric oxygen is not necessary.

Perhaps the classical or prototypical thermobaric agent is a liquid monopropellant (a lowexplosive that produces large gas volumes when it exothermically decomposes) mixed withenergetic particles such as high explosives or powdered metals.[27] Ethylene oxide plus powderedaluminum or hydrazine plus powdered aluminum would fall into this category of thermobaricmaterials.

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Another category of explosives that are almost the opposite of thermobaric explosives areenhanced blast materials. These materials are usually made by adding powdered metals toconventional high explosives, especially those with a positive oxygen balance (perchlorates, heavilynitrated materials, ammonium nitrate, etc.). The metal will react with the excess oxygen releasingconsiderably extra energy. The purpose here is to increase the detonation velocity and the strengthof the shock waves produced. However, if such enhanced blast materials were dispersed as powdersor aerosols, effective thermobaric agents would result. Two formulations pursued by Soviet/Russianresearchers include “reactive-surround” materials (aluminum powder and nitrocellulose mixtures)and “slurry explosive” mixtures in which powdered explosive solids are mixed with combustibleliquids.[28] In both cases, the materials are dispersed before ignition.

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Incendiary Devices

There are times when fire is a more effective weapon than blast. Small fires often grow toconsume entire buildings (or an entire forest or grassland). Fire magnifies the area over which aweapon can produce damage. Complete destruction of a petroleum storage complex or an oilrefinery by blast alone would require hundreds of weapons. However, a single incendiary devicestarting a fire could ultimately consume the whole complex. Fires are long-lasting (typicallyminutes) while blast is gone instantly. Thus, fires make better blocking or isolation weapons thanexplosives. Fire may also have a stronger psychological effect on the survivors than blast. Almosteveryone is capable of visualizing being horribly burned. Few can imagine being atomized by amassive explosive. Mankind has had a “love-hate” relationship with fire ever since its discovery.For these and other reasons, many militaries maintain stockpiles of incendiary weapons. Incendiaryweapons are weapons intended to produce damage or casualties through fire rather than blast,fragment penetration, or other physical effect.

Many different incendiary combinations are described in the literature.[29]-[31] The moresignificant ones are listed in Table 11-17. Most are easily manufactured in large quantities giventhe raw ingredients. A few (such as gasoline + styrofoam and paraffin + sawdust) have ingredientswhich can be easily obtained in large quantities by anyone. All produce hot, persistent flamescapable of igniting most flammable materials.

White phosphorus [32] is a form of phosphorus metal that burns spontaneously in air.When ignited it produces intense heat and light output. The combustion products are phosphorusoxides that immediately extract water vapor from the air forming phosphoric acid aerosols. Theaerosols scatter light in the visible and form an effective smoke. Phosphorus is used in artilleryshells and rockets both for its incendiary and obscuration effects as desired. If phosphorus metalis mixed with phosphorus pentasulfide (55% to 45% by weight), the resulting eutectic mixtureexhibits an extremely low melting point of -40C. The eutectic retains its flammability but beingliquid can be dispensed more effectively than solid phosphorus. Burning phosphorus can beextinguished with water. To prevent this, phosphorus is often coarsely mixed with sodium. Whenliquified by heat from the burning phosphorus, the sodium will also burn in air. However, sodiumreacts violently with water (liberating hydrogen gas), so any attempt to extinguish the phosphorus-sodium mixture with water will result in a disastrous secondary explosion.

Triethylaluminum (TEA) is a liquid organometallic compound that burns spontaneouslyin air, that is, it is pyrophoric. When mixed with polyisobutylene (rubber) it forms a thickened agentthat retains its pyrophoricity. The mixture is called TPA (for thickened pyrophoric agent). It isexpected that other trialkylaluminum compounds (e.g., trimethylaluminum or triisopropylaluminum)will have similar incendiary properties.

Ordinary fuels such as alcohol, naphtha, kerosene, or gasoline will burn quite strongly andrapidly. However, they are low-viscosity liquids and quickly run off of vertical surfaces.Furthermore, they tend to vaporize quickly, tending to cool the materials on which they rest. Thefuel vapor burns but the underlying materials may not ignite. Thickened fuels are designed toovercome these limitations. The thickener converts the liquid into a material the consistency of thin

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Table 11-17. Common Incendiary Mixtures.[29]-[31]

THERMITE Aluminum Powder 25% (by weight)Ferric Oxide (Fe2O3) 75%

orAluminum Powder 13.5% (by weight)Ferrosoferric Oxide (Fe3O4) 86.5%

THERMATE Thermite 68.7% (by weight)Barium Nitrate 29.0%Sulfur 2.0%Oil (binder) 0.3%

SUGAR- Granulated Sugar 50% (by volume)CHLORATE Sodium or Potassium Chlorate 50%

PARAFFIN- Paraffin 50% (by volume)SAWDUST Sawdust 50%

FLARE Powdered Magnesium 33% (by weight)COMPOSITION Polytetrafluoroethylene (Teflon) 67%

NAPALM Gasoline (or other fuel) 96%-88% (by weight)M1 Thickener 4% -12%M1 = Aluminum Naphthenate 25% (by weight)Thickener Aluminum Laurate 50%

Aluminum Oleate 25%

NAPALM B Gasoline 33% (by weight)Benzene 21%Polystyrene 46%

THICKENED Any Fuel + Thickener Mixtures (all % measures by volume)FUELS 1 gal + Alkyl amine 50-60g + Aryl isocyanate 25-30g Gasoline 80% + Wax 19.5% + Lye 0.5% Diesel Oil 78% + Rosin 19.5% + Lye 2.5% Kerosene 75.5% + Ethanol 4% + Lye 2.5% + Tallow 18% Naphtha 82.5% + Balsam 14.5% + Lye 3% Turpentine 63% + Ethanol 2% + Soap 35% Benzene 92% + Acid 1% + Latex 7% Toluene 50% + Styrofoam 50%

TRIETHYL- Triethylaluminum 99% or 94% (by weight) = Thickened PyrophoricALUMINUM Polyisobutylene 1% 6% Agent (TPA)

WHITE PHOSPHORUS

EUTECTIC WHITE Phosphorus 55% (by wt.)PHOSPHORUS Phosphorus pentasulfide 45%(m.p. -40C)

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syrup. When thickened fuel lands on a vertical surface, it sticks and does not run off. Second, thethickener reduces the rate of fuel evaporation. This causes the fuel to burn slower, but at the sametime to transfer more heat to the underlying materials, enhancing the probability of ignition. As isevident in the table, many materials can act as thickeners for almost any standard flammable liquid(fuel). Some are field expedient and useful for improvised devices.

Napalm is the prototypical thickened fuel. Originally it was a mixture of gasoline and athickener made from the soaps aluminum naphthenate and aluminum palmitate. Napalm is acontraction of the first few letters of the words naphthenate and palmitate. Later, the aluminumpalmitate was replaced with aluminum laurate and aluminum oleate, but the original name stuck.Napalm was usually prepared in the field by adding roughly 5-10% of M1 thickener (the soapmixture) to canisters containing whatever fuel was readily available. Napalm B is an incendiaryagent based on a mixture of gasoline and benzene thickened by polystyrene (the material from whichstyrofoam is made).

Flare composition is a mixture of finely powdered magnesium and teflon flakes pressed intoa solid mass. When ignited, the magnesium reacts with fluorine from the teflon forming MgF2particles and carbon soot. The reaction heats both kinds of particles to white heat (2000 K). Flarecomposition is normally used only in illumination and countermeasure flares.

Sugar/chlorate and paraffin/sawdust are favorites of school-age pyromaniacs. Paraffin/sawdust also has significant commercial application. When tightly compressed, a mixture ofsawdust with minimal paraffin will form a decent “fireplace log” or wood substitute. When brokenup, such logs burn so fiercely they are fire hazards. Artificial fireplace logs carry warnings thatshould be heeded about not burning multiple logs, not adding new logs onto older burning logs, andnot poking at a log that is burning down to break it up and make it burn faster. Often it will burnmuch faster than ever anticipated.

Thermite is a stoichiometric mixture of powdered iron oxide (any iron oxide can be used)and powdered aluminum. Thermate is thermite modified by the addition of barium nitrate andsulfur. The author is unsure of the advantages of thermate over thermite, if any. However, thermateis likely to burn more slowly and will release significant quantities of hot gas (thermite does notproduce any gaseous products). It may be easier to ignite than thermite. Thermite is difficult toignite, but once ignited, it burns at extremely high temperatures. The products are molten iron andalumina (Al2O3). The reaction does not require external oxygen and is thus almost impossible toextinguish. Because thermite burns at such high temperature and will burn under water, it is oftenused for cutting steel structural members. The high temperature also ensures that thermite will igniteany flammable material it contacts.

Conventional thermite is one example of a class of reactions known as “thermite reactions”.Almost any metal oxide will react exothermically with powdered aluminum.[33] It is also possibleto substitute powdered zirconium or titanium for powdered aluminum, although these are harder toobtain and yield less heat. Note that thermite compounds will be hard to detect by traditionalexplosives detection systems, as they contain no nitrogen, leave no unique particulate residues, andemit no vapors. They will strongly attenuate xrays, but no more so than any metallic object..

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References

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[4] Davis, Tenney L., The Chemistry of Powder & Explosives (Angriff Press, Hollywood CA,1943).

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[10] Meyer, Rudolf, Explosives, 3rd Edition (VCH Verlagsgesellschaft mbH, Weinheim FRG,1977).

[11] Dobratz, Brigitta M., “Properties of Chemical Explosives and Explosive Simulants”,Lawrence Livermore National Laboratory Report UCRL-51319 (15 December 1972).

[12] Gibbs, Terry R. and Alphonse Popolato, LASL Explosive Property Data (University ofCalifornia Press, Berkeley CA, 1980)

[13] Department of Defense, “Fuze Explosive Component Terminology, Dimensions &Materials”, MIL-STD-320A (30 June 1975).

[14] Reif, F., Fundamentals of Statistical and Thermal Physics (McGraw-Hill Book Co., NewYork NY, 1965).

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[16] Anonymous, “Gas Properties”, BOC Gases (undated). Available on the Internet at http://www.boc.com/gases/products/special/America/support/gasprop.htm .

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[18] Anonymous, “A Brief History of U.S. LNG Incidents”, CH-IV Corporation (30 May 1997).Available on the Internet at http://www.ch-iv.com/lng/incid1.htm .

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[22] Associated Press, “Search for Grain Worker Turns Grim”, Las Vegas Sun (13 June 1998).Available on the Internet athttp://www.lasvegassun.com/sunbin/stories/archives/1998/jun/13/061300185.html .

[23] Anonymous, “Flammable Solids”, University of Nebraska Lincoln (undated). Available onthe Internet at http://www.unl.edu/environ/hazard/flamsol.htm .

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[26] Anonymous, “Thermobaric Warheads”, Defense Threat Reduction Agency (28 January2002). Available on the Internet at http://www.dtra.mil/td/thermo/td_thermo.html .

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[30] Stockholm International Peace Research Institute, Incendiary weapons (M.I.T. Press,Cambridge MA, 1975).

[31] Department of the Army, “Military Chemistry and Chemical Compounds”, Field Manual FM3-9 (October 1975), pp. 3-30 - 3-33.

[32] Anonymous, “White Phosphorus (P4) Chemical Backgrounder”, National Safety Council(1 July 1997). Available on the Internet at http://nsc.org/ehc/ew/chems/phosphor.htm .

[33] Weast, Robert C. (Ed.), Handbook of Chemistry and Physics 49th Ed. (Chemical RubberCompany, Cleveland OH, 1968), pp. D38-D49.

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Problems