Tutorial Exercises

Answers to se/ected even-numbered exercises fol/ow.

1-1. An automobile with mass of 1250 kg travelling at the legal speed Iimit of90 km/h {55 mph) collides head on with an unyielding stone wall. a) What is the energy of the impact? b) What is its TNT equivalent?

1-2. The energy release per fission of a uranium nucleus is approximately 195 million electron volts (one electron volt equals 1.602 x 10-19 J). Of this, about 89% is released promptly and the balance of 11% appears in the course of time during radioactive decay of fission products. a) Compute the number of atoms of uranium which must undergo fission in order to provide an energy release of twenty kilotonnes TNT. b) How many moles of uranium is this? {The Avogadro number is 6.022 x 10 23 per mole). c) How many kilograms of pure uranium-235?

1-3. The standard 30-06 militaryrille fires a buHet with mass 150 g at a muzzle velocity of 884 m/s (2900 ft/s). a) What is the kinetic energy? b) What is its TNT equivalent?

1-4. The energy released in a lightning flash has been found tobe about 105 Jjm. What is the TNT equivalent of the energy release in a lightning fiash that extends 1.6 km?

1-5. A propellant "powder" based on cellulose nitrate shows an energy of explo• sion of about 3 kJ/g.

195 196 Tutorial Exercises a) Characterize this material with regard to brisance and whether it is a deflagrating or a detonating explosive. b) Specify its explosive strength relative to TNT.

1-6. A munitions factory plans a storage facility for 7.5 tonnes explosive. a) What minimum distance should this facility be away from a public highway? b) The quality controllaboratory should be at least how far away? c) How close could sentries and guards be stationed?

1-7. A small hand-carried satchel is suspected of containing a terrorist bomb. a) What quantity of explosive might such a satchel contain? b) Out to what distance could missiles from its possible explosion be thrown? c) What distance should be corded off? d) Fire fighting foam can reduce missiledarnage distances by about one half. To what distance would missiles be expected if the area were foam protected?

1-8. Two standard igloo magazines are located twenty metresapart in an open area. a) What is the maximum amount of chemical explosivestobe stored in each if neither is earth covered? b) If both are earth covered? c) If one of these earth covered magazines exploded accidently when containing its maximum permissible contents about how far would missiles and fragments be thrown? d) What diameter crater would such an explosion create? e) Estimate the probability that there is a near simultaneaus sympathetic detonation of the second magazine.

1-9. A tank er has off-loaded 4200 steres of crude oil cargo so that the nominally empty tank contains an explosive mixture ofhydrocarbon fumes and air. The explosive strength of such fumes for surface explosions is estimated to be about 0.6 g TNT per litre. a) What would be the TNT equivalent of the explosion of this cargo tank? b) How far from explosion center would debris from deck piping, deck pumps, etc., be expected to be thrown?

1-10. Two structures used for assembly oftest munitions might house as much as 75 kg of high explosive each. a) How close to each other may these structures be ifthere is no protecting barricade between them? b) To what distance would this be reduced if a protecting barricade were erected between them? c) What are the odds against an accidental explosion in one structure being propa• gated into the other if there is no barricade?

1-11. Assurne a one-tonne PETN "block buster" bomb hits the ground and explodes at a distance of only ten metres away from a store of explosive ammunition. What is the probability that this store of ammunition would also explode? Tutorial Exercises 197

1-12. A crater near Winslow, Arizona, has a diameter of about 1250 m and a parapet of about 40 m. Estimate the energy required to produce such a crater in terms of the TNT equivalent.

1-13. A meteor with a mass of 300 kg strikes the earth at a speed of 16,000 m/s. a) What is the TNT equivalent of its kinetic energy? b) What diameter crater would this probably produce if impact were normal to the earth's surface?

1-14. What minimum amount of demolition explosive C-4 placed in direct contact is required in order to puncture a bunker wall of concrete 350 cm thick?

1-15. What minimum thickness of reinforced concrete is needed in order to defeat a projectile from a !arge Naval rifle with a mass of210 kg and an impact velocity of 415 m/s?

2-1. The high explosive 2,4,6-trinitroaniline has the chemical formula

C6 H 2 (N02}JNH 2 • a) What is its oxygen balance to carbon dioxide and to carbon monoxide? b) Characterize this explosive as oxygen rich, oxygen balanced, or oxygen deficient. c) Write chemical equations depicting its explosive d~composition into nominal prod• ucts at the very high pressures comparable to detonation conditions, to fireball conditions, and for fully expanded products.

2-2.

a) For each explosion requested in part b), compute its mass percentage oxygen balance, and then characterizc its relative oxygen content. b) Write a material balance in form of a chemical equation for explosion to nominal products for the following conventional chemical explosives: HMX, PETN, Tetryl, Nitromannite, and Cyclonite.

2-3. Amatol 80/20 is a mixture 80% by mass ammonium nitrate (AN) and 20% TNT.

a) Assign this mixture an apparent chemical formula and a corresponding formula mass. b) What is the oxygen balance for Amatol 80/20 to carbon monoxide; to carbon dioxide? c) Express in form of a chemical equation the explosive decomposition of Amatol 80/20 to nominal lireball products.

2-4. Torpex is an aluminized explosive containing 42% RDX, 40% TNT, and 18% finely powdered aluminum. a) Convert these mass percentages into male percentages; find an apparent chemical formula and an apparent formula mass for Torpex. b) Write a chemical equation for explosion of Torpex into the nominal products. c) What is the mass percentagc oxygen balance for Torpcx to carbon monoxide? 198 Tutorial Exercises

2-5. The organic compound bis(2,2-dinitropropyl) fumarate has the formula

C 10 H 10 N 4 0 12 . It is a relatively dense explosive developed in about 1951. a) Classify this explosive as oxygen deficient, oxygen balanced, or oxygen rieb with respect to carbon monoxide formation. b) Write balanced chemical equations that describe the combustion, the formation, and the explosion of this explosive. c) The "heat of combustion" forthismaterial is reported as 3070 calfg. Take it that this reputed value is for constant pressure conditions with water formedas a liquid, and report the corresponding thermodynamic item "enthalpy of combustion" in kilo• joules per mole. d) What is the corresponding "internal energy of combustion" in kilojoules per mole? e) What is the corresponding "internal energy of formation"? f) Compute a theoretical value for the "heat of explosion" of bis(2,2-dinitropropyl) fumarate. g) A "heat of explosion" describes the thermal energy release as a material explodes and so could be measured in a conventional but sturdy calorimeter. What ad• ditional information is required for augmentation so that the total "energy of explosion", and also the relative strength of this material, can be computed?

2-6. Butanetrial trinitrate (BTTN), C4 H 7 N 3 0 9 , is an explosive plasticizer for cellulose nitrate. Its formula mass is 241 g/mol and its heat of combustion (Reference 3 of Chapter 2) is 2168 cal/g. a) Convert this heat of combustion into a molar enthalpy of combustion in metric units and also into an internal energy of combustion. b) What is its internal energy of formation? c) Write a material balance in form of a chemical equation for its explosion into nominal products. Then compute the molar internal energy of explosion and the corresponding heat of explosion as might bc measurcd in a sturdy calorimeter.

2-7. Butanetrial trinitrate, C4 H 7 N 3 0 9 , the BTTN of Exercise 2-6, could be obtained on paper through a transmutation of butane by substituting three nitrate

(ON02) groups for three hydrogen atoms. a) On this basis, obtain an estimated internal energy of formation for butanetriol trinitrate. b) Compare this estimated value for the internal energy of formation of BTTN with that obtained by calorimetric methods in the laboratory, -365 kJjmol. c) Estimate the entropy for solid BTTN by the transmutation method of Table V. Compare with that indicated by the approximation of equation (2-9).

2-8. a) Write a chemical equation that describes the explosion of picric acid into nominal products. b) From values for the internal energy of formation for each component of this equation find the corresponding internal energy of explosion. c) Similarly, find the entropy of explosion. d) Compute a corresponding theoretical value for the Helmholtz free energy of explo• sion of picric acid. e) What explosive strength does this thermodynamic calculation indicate? What Tutorial Exercises 199

explosive strength is indicated by the Berthelot approximation? Campare these calculated values with measured values reported in Table I. 2-9. a) Estimate the internal energy of formation of tetranitrotoluene using the group Substitution method. What is the corresponding "heat of explosion" (nominal products)? b) Estimate the entropy of solid tetranitrotoluene and also its entropy of explosion. c) What is the corresponding Helmholtz free energy of explosion, and also the explo• sive strength for this material?

2-10. Dinitroaniline, formula C6 H 3 (N02hNH2 , is to be considered as a pos• sible useful explosive. Make an informed estimate based solely on its assigned chemical formula of the following items for dinitroaniline. a) Interna! energy offormation. b) Interna! energy of explosion into nominal products. c) Heat of explosion. d) Third law entropy. e) Entropy of explosion. f) Helmholtz free energy of explosion. g) Explosive strength based on the Helmholtz free energy. h) Explosive strength by the Berthelot approximation. i) Gurney constant for fragment velocity. 2-11. a) What is the explosive strength of trinitrobenzaldehyde as given by the Berthelot approximation? Its chemical formula can be written as C6 H 2 (N02}JCHO, and its heat of explosion is given as 2630 Jjg. b) What is its Gurney constant?

2-12. Using the internal energy of formation of Tetryl given in Table I, and assuming water formed as a gas, compute a) Interna! energy of explosion b) Explosive strength using the Berthelot approximation. c) The Gurney constant. d) Campare computed values of parts b) and c) with experimental values reported in TableI or Table 2-2.

2-13. A cylindrical warhead contains 14 kg TNT in a steel case with mass 9.5 kg. a) What is the initial velocity of the steel fragments? b) What proportion of explosion energy goes into the kinetic energy of these fragments?

2-14. A cylindrical antiaircraft warhead with mass of 70 kg contains 40 kg of composition B. a) What is the initial velocity of the casing fragments? b) What is their total momentum? c) What is their total kinetic energy? 200 Tutorial Exercises

2-15. A spherical grenade, diameter 6.0 cm, is tobe filled with a spherical charge ofHMX at a loading density of 1.88 g/cm 3 and with a Gurney constant of3120m/s. Its casing is to be of steel which, after allowing for fragmentation control indentations, shows an average density of6.3 gjcm 3 • a) Select several casing thicknesses and compute for each the corresponding charge mass, meta! mass, and fragment velocity. Plot total fragment velocity, energy, and momentum versus casing thickness. b) Find the thickness that corresponds to the maximum fragment momentum and the associated fragment velocity. c) Similarly, find the casing thickness for maximum fragment kinetic energy. d) For some purposes, mean ofthe two thicknesses is taken as a design value. What is the corresponding casing thickness? What are the associated masses of charge and of meta!, and total mass of the grenade?

2-16. A television tube with volume 161 fails catastrophically. a) What is the energy of this implosion in joules? b) Such an explosion resembles a deflagration rather than a detonation. In this circumstance the deflagrating explosive black powder with an energy of explosion of about 700 Jjg is a preferred standard. What is the corresponding implosion yield? 2-17. A tank of 325 I of compressed oxygen at 21 oc and 220 bars fails catastrophically. a) What is the energy release in the failure and what is its TNT equivalent? (The heat capacity ratio for oxygen is 1.4). b) It is desired to compare this explosive energy release with that for the nonexplosive failure of a similar tank undergoing a hydrostatic test with water. For this, it may be taken that water is compressed about one percent for each two hundred bars of imposed pressure. Then for ordinary expansions the Helmholtz free energy integral of equation (2-5) can be evaluated using a mean pressure P and a volume change

(V2 - V1 ). What is the energy or tank failure during a hydrostatic test and what is its TNT equivalent?

3-1. The space shuttle, Columbia, reentered the earth's atmosphere at an altitude ofabout 120 km. At this altitude atmospheric pressure is about 2.54 x 10- 5 mbars and the temperature is about 87 oc. Takeair composition at this altitude the sameasthat at the earth's surface. a) Compute its density in grams per litre. b) What is its specific gravity? (Density relative to air at some reference condition). c) What is the speed of so und in the rarefied atmosphere? 3-2. A shock front in air at 10°C and 1000 mbars momentarily increases the pressure to 1390 mbars and the temperature to 38.4 oc. The specific gas constant for air is 287 Jjkg-K and the heat capacity at constant pressure is 1.006 Jjg-K. a) What is the enthalpy increase and what is the entropy growth? b) Consider air being compressed adiabatically and reversibly (that is, isentropically) through this same pressure increase. What temperature would result? c) What is the temperature increment resulting from the irreversible nature of the shock front? Tutorial Exercises 201

3-3. A shock wave at a Mach nurober of 1.47 moves through an atmosphere at 1013.25 mbars and 15 oc. The corresponding pressure jump factor is 1.35 and the temperature jump factor is 1.30. a) Compute the speed of so und in the air before the shock using the conventional form a = (kRT) 1i 2 . Compare with the value in the tables for air properties. b) Compute, using this value and the temperature ratio, the speed of so und in the air immediately after the shock. Compare with Table VII. c) What enthalpy increase injoules pergram of air is caused by this shock? What is the corresponding internal energy increase? What is the entropy growth in joules per gram-kelvin?

3-4. The blast wind from an explosion shows a Mach nurober 0.55 in air which has been shocked to 107 oc and 2.280 bars. a) What is the blast wind velocity? b) What temperature and pressure would develop if this wind were suddenly halted? c) Compute the reference critical temperature for this blast wind and the reference Mach nurober M*.

3-5. A missile from an explosion has advanced before the shock front and is moving at a Mach nurober of 1.50 through the air at 20 oc and one bar. a) What is the missile velocity? b) What temperature and pressure exist momentarily on the blunt front face of this missile? c) What is the TNT equivalent ofthe kinetic energy ofthis missile ifits mass is 1.37 kg?

3-6. A warehouse 20m wide, 10m high, and 40 m long, isstruck by a hurricane forcewind with a velocity of 42 m/s. Ambient air is at 20 oc and 1000 millibars. a) What is the stream stagnation pressure for this wind? b) Estimate the drag coefficient and find the corresponding drag pressure drop. c) What is the (absolute) pressure on the rear face oftbis structure assuming that its front face is subjected to the stream Stagnation pressure? d) Compute the net lateral force in kilonewtons that this wind exerts across the structure assuming uniform pressure and that the structure remains intact.

3-7. A meteorite from outer space plunges into our atmosphere and shows a speed of 7.2 km/s at an altitude of 100 km. (Table XIV lists characteristics of the U.S. Standard Atmosphere). a) What is its Mach number? b) What is the temperature at its Iead point? c) Assurne that the meteorite is approximately spherical with a diameter of two centimeters and a mass of thirty grams. What drag pressure is developed? d) What is the corresponding retarding force?

3-8. The following structures were exposed to a blast wind with Mach nurober 0.130 in an atmosphere at 320 K and 1.52 bars. Estimate for each its drag coefficient, the drag pressure drop, and the total wind Ioad. a) A reetangular structure 3 m high, 10m wide, and 30m long. 202 Tutorial Exercises b) A billboard 3m high and 10m wide mounted on the ground. c) A cylindrical standpipe 11 m in diameter and 38 m tall. d) A spherical water tank 15 m in diameter.

4-1. An air stream moving at a Mach number of 1.215 undergoes normal shock. a) What is the ratio of pressures across this shock? What is the downstream pressure if the upstream pressure is 1013.25 mbars? What is the pressure jump? b) What is the ratio of temperatures across this shock? What is the downstream temperature if the upstream temperature is 15 oc? What is the temperature jump? c) What is the ratio of the speeds of sound across this shock? What are the actual speeds? d) What is the Mach number for the stream after the shock? e) What is the ratio of stream velocities across this shock? What are the actual velocities? f) Compare values computed above with those in the two shock tables.

4-2. An air stream at Mach 1.54, pressure 820 mbars, and temperature 0 oc undergoes normal shock. a) What is the Mach number for the departing stream? b) What pressure and temperature exist in the departing stream? c) What is the velocity of the initial stream, as given by its Mach number and temperature? What is the velocity ofthe stream after the shock, as given by its Mach number and temperature? What is the ratio of these two velocities? Compare with the value of this ratio as given by an analytical expression. 4-3. A normal shock in a steady-flow stream shows a pressure jump from 820 mbars to 1450 mbars. a) What is the initial stream Mach number and what is the velocity if the local temperature is 20 °C? b) What is the Mach number for stream departing the shock and what is the departing stream velocity? c) Compute the reference critical values for stream functions Yx_*, Ty*, a:, aj, M:, and Mi. Show that the product of (M:) x (Mi) equals unity. d) What is the thickness ofthisshock in millimetersandalso in terms ofthe mean free path for a gas molecule in the initial stream?

4-4. The shock front for the blast wa ve from a !arge explosion moves through air at 15 oc and one bar with a Mach number of 1.185. a) What is the shock front overpressure? b) What blast wind immediately follows this shock front? What is the ratio ofthiswind speed to the speed of so und in the air oftheblast wind? To the speed of so und in the air before the shock? c) What is the blast stagnation pressure and the blast stagnation overpressure? d) What is the temperature of the air in the blast wind? What is the temperaturein the shocked air after the original pressure of one bar has been restored?

4-5. An explosiveshock in air at 15 oc and 920 mbars shows an overpressure of 275 mbars. Tuterial Exercises 203 a) What is the velocity of this shock front? b) What istheblast wind? c) What istheblast wind drag pressure drop across an ungainly reetangular structure with a drag coefficient of 2.0? Across a cylindrical water tank with a drag coefficient of 1.2?

4-6. Air at 15 oc and one bar suffers an explosiveshock with an overpressure of 350 mbars. a) This shock is moving at what velocity? b) What blast wind is generated by this shock? c) Presume that this shock, one with an overpressure of 350 mbars, moves through a quite different atmosphere, as on the Antarctic plateau where the temperature is -40°C and the pressure only 370 mbars. Make the calculations ofparts a) and b) above for this different situation.

4-7. An explosiveshock in air at 850 mbars and 10oc develops ablast wind of 296 m/s. a) What is the pressure jump across this shock and what is the temperature jump? b) What Mach number is to be assigned to this shock?

4-8. Air at 15°C and 1013.25 mbars streaming in steady flow at Mach 1.85 undergoes oblique shock at an angle of 45" relative to the direction of the stream. a) What is the stream velocity u1 ? Resolve this velocity into a component ux normal to the plane ofthe shock and a component u' parallel with the plane. What is the Mach number Mx for normal shock? b) What is the normal component uy of the downstream velocity as given by the Mach number for normal shock? c) From computed values for the normalandparallel components for the downstream velocity, compute the angle through which the stream is deflected by the oblique shock. d) Combine the normal and parallel components for the downstream velocity to obtain the velocity u2 • e) What is the speed of sound downstream as given by the Mach number for normal shock? What is the Mach number M2 for the departing shock? f) What is the downstream pressure Py as given by the Mach number for normal shock?

4-9. An air stream at 15 °C, 1013.25 mbars, and Mach 1.85 undergoes oblique shock at an angle of 45", as in the tutorial exercise above where the oblique shock problern was solved by resolving the oncoming stream velocity into components and utilizing the normal shock equations. a) Using the analytical expressions developed for oblique shock, compute the down• stream Mach number, velocity, and pressure. Also compute the angle through which the stream is deflected. Campare with results obtained in Exercise 4-8. b) Use the oblique shock diagram and find the downstream Mach number and deflection angle for this shock. Then compute the downstream velocity and pressure. Campare the results of the graphical computation with those of the analytical computations with regard to both convenience and the precision method. 204 Tutorial Exercises

4-10. A stream of air at 15 oc and Mach 3.0 is deflected 33° by an oblique shock. a) What is the angle of this oblique shock relative to the stream? (Use graphical methods and find the "weak shock" solution.) What is the downstream Mach number? b) What is the angle ofthe oblique shock, relative to the stream, for the "strong shock" solution? What is the corresponding downstream Mach number? c) Correlate the computed changes in stream Mach number with the terms "weak" and "strong."

4-11. A supersonic air stream at Mach 2.033 undergoes oblique shock at an angle of 50°. By how much is the stream deflected and in what direction? Verify analytical answer by a graphical answer.

4-12. a) What angle of incident shock gives the maximum deflection of a stream at Mach 2.5 as indicated by the oblique shock chart of Figure 4-4? b) Write out the equations that provide more precise answers than those obtained from the chart.

4-13. The oblique shock chart ofFigure 4-4 is useful as a basis for organizing the varied aspects of oblique shock in a steady-flow stream. It also is very useful in connection with the study of shock reflections. a) For review purposes, make a schematic outline of the oblique shock chart that shows contours for representative upstream and downstream Mach numbers. b) Indicate regions on this chart for weak oblique shock and strong oblique shock. Where does normal shock appear in this diagram? c) Indicate regions on the schematic oblique shock chart where the downstream velocity is supersonic and where subsonic. d) Select a typical upstream Mach numbcr and indicate (1) an oblique shock at an angle that produces sonic velocity; (2) the oblique shock that produces maximum deflection; and (3) a conjugate pair of weak and strong oblique shock angles and Mach numbers.

5-1. A shock at Mach 1.170 moves through air at 960 mbars and 7 oc. a) What is the shock overpressure? b) What is the speed of so und in the air, both before and after the shock? c) What particle velocity is generated by this shock? d) This shock impinges head-on onto an unyielding surface and so generates a reflected shock with particle velocity magnitude equal tothat of the incident shock. What is the associated Mach number for this reflected shock? e) What is the pressure ratio across the reflected shock, and what pressure jump is generated across this shock? f) What overpressure on the surface results from this shock reflection? What is the reflection coefficient?

5-2. A shock front with overpressure 275 mbars moves through air at the meteorological standard condition of 15 oc and 1013.25 mbars and impinges head-on onto an unyielding surface. Tutorial Exercises 205 a) What is the Mach nurober for this incident shock and for the reflected shock? b) What is the pressure jump across the incident shock front, across the reflected shock front, and for the two shocks combined? c) What is the reflected overpressure and what is the reflection coefficient?

5-3. An explosiveshock at Mach 1.245 in an atmosphere at 15 oc and 1.01325 bars impinges onto an unyielding surface at 30° thereby undergoing oblique reflection. a) Make a schematic diagram for this shock reflection system. Indicate shock Mach numbers Mx and M" the angle of incidence ß and the angle of reflection o. b) Make a second schematic diagram for the steady-flow counterpart ofthe reflection system of part a). Indicate stream Mach numbers M1 , M2 , and M3 , shock angles relative to a stream ß1 and ß2 , and the deflection angle e.

5-4. The oblique shock chart for steady-flow streams is conveniently utilized in the study of oblique reflection but it provides only stream Mach numbers and shock angles relative to a stream. Using graphical methods, find the following for the steady• flow counterpart of part b) of Exercise 5-3 immediately above. a) What is the Mach nurober M1 for the initialentering stream, and what is the angle of

orientation ß1 of the first shock relative to this stream? b) What is the Mach nurober M 2 for the stream departing the initial shock, and through what angle e has it been deflected? c) The stream at Mach nurober M 2 enters a second shock and is re-deflected by the angle e so that its direction of flow parallels that of the initial stream. What is the angle of orientation ß2 of this second shock relative to its entering stream? d) What is the departing stream Mach nurober M3 ?

5-5. It is desired to characterize the shock reflection system ofExercise 5-3, using graphical values for its steady-flow counterpart where necessary. a) What is the pressure, temperature, and speed of sound in the unshocked atmosphere? b) What is the pressure, temperature, and speed of so und in the atmosphere immedi• ately after the initial explosive shock? c) What is the Mach nurober for the reflected shock? What is the angle of reflection? What is the pressure, temperature, and speed of so und immediately after reflection? What is the reflection coefficient for this system? What is the blast wind? d) Campare the pressure after reflection, the reflection coefficient, the angle of reflec• tion, and the blast wind as computed for an oblique reflection by the detailed analysis above with those for a shock with the sameMach nurober but undergoing normal reflection.

5-6. Outline an analytic method with inherent high precision for solving the various parts of the oblique reflection problern of Exercise 5-5 (the graphical methods there have limited precision).

5-7. What is the angle of reflection and what is the reflection coefficient for a shock at Mach 1.350 impinging onto an unyielding surface at an angle of 22.SO?

5-8. A shock at Mach 1.115 impinges onto an unyielding surface at an angle of 75°. Assurne a standard atmosphere. 206 Tutorial Exercises

What is the Mach number for the shock over the surface? What is the apparent reflection ratio? What is the blast wind?

5-9. a) Compute the overpressure and the blast wind created by a shock with an overpres• sure of210 mbars in the standard atmosphere after it has impinged on an unyielding surface at an angle of 62.5°. What is the apparent reflection coefficient? b) Make the calculations for an impingement angle of 57.5".

5-10. a) A shock with overpressure of 600 millibars in the standard atmosphere impinges onto an unyielding surface. Find the angle for the transition from oblique reflection to Mach stem formation. b) What is the Mach number for the Mach stem formed at an angle only differentially greater than the transitionangle of part a)? What is the overpressure on the surface and what is the reflection coefficient? What is the blast wind? c) Consider the oblique reflection ofthe above incident shock at an angle differentially less than the transition angle. Referring to the steady-flow counterpart of this

reflection, find (graphically) the stream Mach numbers M1 , M2 , and M3 ; the entering angles ß1 and ß2 , and the angle of deflection e. d) What is the Mach number for the reflected shock and what is its angle of reflection? What is the overpressure on the surface and what is the reflection coefficient? What is the blast wind?

5-11. Consider the Mach stems that might be formed by a shock with an overpressure of 195 mbars in an atmosphere at 810 mbars and 20°C. a) Verify that an explosiveshock with an overpressure of 790 mbars in the ordinary atmosphere would undergo oblique reflection at all angles of incidence less than about 45° and show Mach stem formation at incident angles greater than 45° b) For the Mach stems that could be generated by this explosive shock, find the overpressures for angles ofincidence of 45°, 60°, and 75°. What are the correspond• ing apparent reflection coefficients? c) What are the blast winds for these three Mach stems? d) Generalize the items of parts b) and c) with regard to the effect of angle of incidence on intensity of the shock in a Mach stem.

6-1. Consider a chemical explosion with yield of one kilogram TNT in the standard atmosphere at 1.01325 bars and 15 oc as described in Table XI. a) At what distance does its direct blast show a peak overpressure of 210 mbars? b) How long does it take for the blast wave to travel out to this distance from the explosion? c) What is its average travel speed as given by their ratio and also as reported in the table? d) How long does the positive phase overpressure last? e) What is the wave form parameter for the quasi-exponential decay relation? f) What is the positive blast wave im pulse per unit area as found by the overpressure• time integral (equation (6-14)), and as indicated by the factors ofTable XIII? Tutorial Exercises 207

6-2.

a) At what distance from a nuclear explosion with energy release of one kilotonne TNT in the standard atmosphere is there a shock front with Mach number 1.300? b) At this distance, what is the peak overpressure, the positive phase duration of the blast wave and what is its impulse per unit area? c) Determine the wave form parameter forthisblast wave and show that it describes, at least approximately, the blast wave impulse per unit area.

6-3. a) What is the peak overpressure in millibarsinan atmosphere at 15 oc and 1.01325 bars developed at a distance of 3.5 m away from a chemical explosion with an energy release of one kilogram TNT? b) What are the Mach number and the velocity of the shock front? c) What is the velocity oftheblast wind immediately after the shock front passes?

6-4. Blast wave overpressures in the far field decrease linearly with distance. This corresponds to a hyperbolic relation of the form (overpressure) x (distance) = a constant a) Evaluate this constant for a one kilotonne nuclear explosion in the standard atmosphere using data for the reference explosion at 5000 m, the maximum distance listed. b) Check the propriety ofthe far-field assumption here by computing an overpressure at a lesser distance of 4000 m. c) What overpressure is to be expected at a distance of 6000 m, some twenty percent greater than the greatest distance of the tables?

6-5. a) At what distance does the reference chemical explosion of one kilogram TNT generate a shock front with Mach number 1.250? b) What is the corresponding overpressure in millibars? c) What is the temperature rise for this shock front? d) What is the temperature of the air after the blast has subsided?

6-6. The following data apply totheblast wave from a spherical charge of 50-50 pentolite in an atmosphere at 1034 mbars and 8 °C:

Distance (m) 0.768 0.981 1.253 1.558 2.021 2.960 Peak overpressure (millibars) 12,760 7150 4220 2290 1300 630 a) What do these data show for the arrival time of the blast wave at a distance of one metre? At two metres? b) What is the average speed of advance from the explosionout to one metre? To two metres? c) What is the average speed of advance between one metre and two metres? 208 Tutorial Exercises

6-7. Arrival time data as determined in a laboratory at sea Ievel as listed below. Under the conditions of measurement, the speed of so und was found tobe 348 m/s.

Time (microseconds) 40 60 80 100 120 Distance (centimetres) 9.92 11.60 13.5 14.64 15.90 Time 160 200 240 280 320 Distance 17.98 19.74 21.48 23.17 24.87

Compute the corresponding (distance)/(travel time) ratios in metres per second and plot versus distance on log-log coordinates. Determine the slope of the plot at various distances. Using smoothed values for the slopes, compute peak overpressures for the various distances.

6-8. At unmanned observation station 3.31 km from a one kilotonne nuclear explosion registered the time difference between the initial flash and shock front arrival at 4.70 s (c!osely). What peak overpressure is indicated? Assurne the standard atmosphere.

6-9. a) What time is required for the shock front to travel from the reference chemical explosion of one kilogram TNT to a distance of 10m? b) How much later does the zero-overpressure condition arrive at this point? c) To what additional distance will the shock front have advanced by the time the zero• overpressure condition has reached 10m? (This additional distance corresponds to a half wave length forthisblast wave.) d) Recall the propagation relation that speed ofa pressure wave advance is given as the product of wave length and frequency, and assign an apparent frequency to this pressure pulse. e) Make similar computations for a point four times as far away, or 40 m. Then observe the effect of distance on the audible pitch oftheblast wave from typical explosions.

6-10. a) At what distance from the reference one kilotonne nuclear explosion is there ablast wind of 100 knots? b) What additional distance is required for reducing the blast wind to half this? c) What are the Stagnation overpressures for these winds?

6-11. What is the blast impulse per unit area 5 m away from the reference chemical explosion? Compare the listed value with that computed using the listed peak overpressure, duration, and wave form parameter.

6-12. Ablast wave from an explosion in air at 15 oc and one bar shows a peak overpressure of 670 mbars, a positive pressure phase duration of 1.58 ms, and an im pulse per unit area for the positive phase of 0.375 bar-ms. Select the corresponding wave form parameter and construct (schematically) a curve depicting the pressure• time history for this blast wave. Tutorial Exercises 209

7-1. A "block-buster" chemical explosion in a sea Ievel atmosphere shows a yield of 800 kg TNT.

a) What is the scaled distance to a target at an actual distance of 50 m (transmission factor is unity)? b) What peak overpressure is feit by the target? c) What is the scaled arrivaltime and what is the actual arrivaltime fortheblast wave? d) What is the scaled duration and what is the actual duration for the positive pressure phase of the blast wa ve? e) What is the wave form parameter and what is the corresponding value oftheblast impulse per unit area? f) What is the blast wind?

7-2. Consider a possible nuclear explosion in a sea Ievel atmosphere with an energy release of 20 kt TNT. a) At what distance from this explosion does the blast wave show a peak overpressure of 1140 mbars? b) How long does it take the blast wave to travel from the explosion to this distance? c) What is the duration oftheblast wave? d) What is its wave form parameter and what is the corresponding blast impulse per unit area?

7-3.

a) What is the peak overpressure at a point 5.4 m away from the explosion of 10 kg ofa conventional chemical explosive in a sea Ievel atmosphere? b) What is the overpressure twice this distance away? c) Express the indicated overpressure-distance relation in an equation of the form where overpressure is proportional to distance raised to some power. d) Comparc the exponent ofthe deduced equation with the slope ofthe overpressure• distance curve for thc referencc cxplosion (Figurc 6-4) at the average scaled distance.

7-4. a) How long does it take the blast wave from the explosion of75 kg of TNT in a sea Ievel atmosphere to travel 21.0 m? b) What is the shock front Mach number forthisblast wave? c) What is its peak overpressure? d) How long does the positive pressure phasc last? e) What is its wave form parameter? f) What is the positivephaseblast impulse per unit area?

7-5. Asounding balloon indicates a temperature of -46 oc and a pressure of 303 mbars at an altitude of 11,300 m. a) Compute corresponding atmospheric transmission factors at altitude. b) What is the scaled distance to a point at this altitude that is 600 m away horizontally from a nuclear explosion with a yield of 40 kt TNT? c) What is the peak overpressure at this distance? d) What is the scaled duration and what is the actual duration oftheblast wave at this point? 210 Tutorial Exercises e) What istheblast impulse per unit area? f) What is the blast wind?

7-6. What are the atmospheric Iransmission factors for the path oftheblast wave from an explosion at an elevation of 1800 m to a target 1500 m away at an elevation of 1000 m? Assurne the U.S. Standard Atmosphere.

7-7. Consider a one megaton nuclear explosion at an altitude of 4000 m. a) What are the atmospheric Iransmission factors at this altitude? b) What are the average Iransmission factors for the path to the ground? c) What are the average transmission factors for the path straight up to 8000 m altitude? d) Compute Mach numbers and peak overpressures for three different blast waves from this explosion each ofwhich has travelled a distance of 4000 m but by different paths, one horizontally, one straight down, and one straight up.

7-8. A blast gage 28.0 m away from a test chemical explosion in a sea Ievel atmosphere measured a peak overpressure of 660 mbars. What explosion yield is indicated?

7-9. A chemical explosion at sea Ievel produced a peak overpressure of 3.75 bars on a gage 8 m away. What blast impulse is indicated by scaling law calculations?

7-10. A time of 23.5 ms elapsed after an explosion's flash before its blast wave arrived at a sensor18m away. The test atmosphere was at 15 oc and 938 mbars. The corresponding transmission factors were 0.98 which for purposes here may be taken as unity. What is the indicated scaling law yield for this chemical explosion?

7-11. A conventional blast warhead with 48 kg TNT is to be exploded at an altitude of 4500 m. a) What atmospheric conditions are to be expected at this altitude, and what are the associated atmospheric transmission factors? b) How long would it take fortheblast wave to travel from the explosion to a target 100m away? c) What peak overpressure, duration, impulse, and blast wind would the blast wave show at this target distance?

7-12. A rocket-borneblast gage indicates a peak overpressure of 169 millibars for a blast wave that arrives 74 ms after a chemical explosion. Altitudes of both explosion and gage are 1800 m, closely. What is the scaling law yield for this explosion?

7-13. A chemical explosion at an altitude of 3650 m was monitared by a gage at about this altitude. Its records indicated that ablast wave with a peak overpressure of 212 millibars arrived 14.7 ms after the explosion. What is the corresponding Scaling Law Yield?

8-1. A bomb with chemical explosion yield of 1000 kg TNT explodes at the high altitude of 8000 m. Tutorial Exercises 211

a) What is the atmospheric pressure? What is the transmission factor for distance at this altitude? b) What is the scaled distance and what is the overpressure ratio fortheblast wave at a target at the same altitude that is 1000 m away? What is the overpressure? c) Consider a target 1000 m (the same distance as in part b) but above the explosion. What is the atmospheric pressure at this elevation? What is the mean transmission factor for the distance from explosion to target? What is the scaled distance from explosion to target? What is the overpressure ratio at the target and what is the actual overpressure? d) Make the computations of part c) but for a target 1000 m below the explosion.

8-2. A nuclear explosion with the high yield of 20 Mt TNT occurs in the upper atmosphere at an altitude of 8 km. a) Find the atmospheric transmission factor for distance to each of the following targets: 1) the earth's surface immediately below the explosion. 2) the same distance away from the explosion but alongside. 3) the same distance away but directly above the explosion. b) What are the scaled distances of these points which are each the same actual distance away? c) What is the peak overpressure at each target point?

8-3. Consider a 20 Mt TNT nuclear explosion at an altitude of 8 km. a) How far out from ground zero does a Mach stem begirr to form? b) This explosion is at an altitude so high that it might not show surface burst effects. But if so, what is the minimum distance from ground zero for these effects to occur?

8-4. Consider a point on the ground 12 km from the ground zero under a nuclear explosion with 20 Mt TNT yield at an altitude of 8 km. a) What time interval between initial explosion flash and arrival oftheblast wave is available for evasive maneuvers? b) Verify by Figure 8-6 that the blast wave over the surface at this point has the form of a Mach stem. What is the height of this stem? c) What is the peak overpressure in this Mach stem? d) What is the corresponding blast wind? e) How lang does the positive overpressure phase oftheblast wave last and what is its im pulse per unit area?

8-5. Surface tests are to be made with charges of 100 kg of a new chemical explosive with an explosive strength estimated as 180% TNT. One is tobe conducted for a hard surface where the effective explosive yield is doubled, another on a float which is expected to absorb all downward directed blast energy. Plots of expected peak side-on blast overpressure, blast wave duration, and total blast wave im pulse per unit area are desired. For present purposes only these values for a point10m distant are needed. Compute these.

8-6. Test of a nuclear explosive with an estimated yield of 18 megatonnes TNT is to be conducted on an atoll in the West Pacific. 212 Tutorial Exercises a) Out to what distance is a peak (side-on) overpressure of 500 millibars to be expected? b) How long does it takesuchablast to travel this distance? How long does the blast wave last? What is its total impulse per unit area? c) A small warehouse at this distance has an estimated responsetime of210 ms, which is very short compared with blast duration. Assurne that during this short time there is negligible blast wave decay. Estimate that portion of the total blast wave impulse per unit area (the pressure-time product) which occurs during the ware• house response time.

8-7. lt is desired to make wind tunnel-type tests on models ofvarious structures at a scaled distance of 500 m/kt 113 from a large explosion. It was suggested that it might be preferred to magnify the yield from a small explosion rather than use a !arge explosion in the unconfined atmosphere. For this, a yield magnification of about one hundred across a test area 0.5 x 0.5 m is needed. What are the corresponding dimen• sions of the magnifier for test charges with 12.6 kg TNT yield?

8-8. Draw the curve of peak overpressure on the ground versus distance from explosion center for a chemical explosion at the surface with a yield of 8.00 t TNT. Assurne negligible energy Iosses by crater formation, but estimate the probable diame• ter of the crater.

8-9. a) A nuclear explosion at 600 m altitude shows a yield of 20 kt TNT. Find the scaled height ofburst, the scaled horizontal distance, and the actual distance from ground zero to the point on the ground at sea Ievel where a Mach stem is first formed. Also find both scaled and actual distances to where surface hurst behavior would be observed. b) Select several distances on the ground within the range from zerotothat for Mach stem formation and compute for each its slant range from the explosion. Then find the incident peak overpressure at each point, and the corresponding peak reflected overpressure, assuming the reflection coefficient for normal reflection. c) Select several distances on the ground for the range from Mach stem formationout to a scaled distance of 700 m from ground zero. Determine for each whether Mach stem formation or surface hurst behavior is tobe observed. Then for each compute the peak overpressure in the blast wave at that point. d) Plot the peak overpressure at each point, then smooth out the overpressures in any transition region and obtain a curve ofpeak overpressure versus horizontal distance from ground zero as computed for this 20 kt hurst.

8-10. A paper study of nuclear explosions all at a scaled height of hurst of 600 m/kt1i 3 is tobe made. a) As part of this study, find the actual heights of hurst for explosions with yields as follows: 1) two kilotonnes TNT 2) twenty kilotonnnes TNT 3) two hundred kilotonnes TNT 4) one megatonne TNT 5) fifty megatonnes TNT Tutorial Exercises 213

b) What is the overpressure on the ground immediately below each of these bursts? c) What is the duration ofthe positive pressure phase oftheblast wave on the surface for each of these bursts? d) What is the positive impulse per unit area on the surface for each of these bursts?

8-11. Tutorial Exercise 8-7 called for the computation ofthe overpressure over the ground for a 20 kt explosion at a height of 600 m above ground zero. It is desired to extend these computations so that the optimum height of burst for an overpressure of 300 mbars can be determined.

a) Forthis purpose add to the plot of Exercise 8-7(d) for the distance-overpressure relation the corresponding values for heights of burst of 400 and 800 m. b) Determine the height ofburst at which a 20 kt explosion generates an overpressure of 300 mbars on the ground. c) Determine for a surface burst at sea Ievel with a yield of20 kt TNT the distance out to an overpressure of 300 mbars on the ground. d) Make a plot (similar to that of Figure 8-7) for the 20 kt burst of this exercise of horizontal distance from ground zero out to 300 mbars overpressure versus height of burst (burst heights are 0, 400, 600, 800 m plus maximum). e) At what height of burst would the 20 kt explosion inflict 300 mbars overpressure over a maximum area? What is this area?

9-1.

a) Maximum internal blast overpressures for various fuel-air explosions, plus corre• sponding volume percentages and stoichiometric fuel fractions, are listed in Table 9-1. Identify these for methane, formula CH4 , a major component of natural gas. Then compare these values with those indicated for maximum overpressure by the approximation of generalized chart 9-3. b) What are the corresponding values at maximum overpressure for propane gas, formula C 3 H 8 , that often is a major component in commercially distributed liqui• fied petroleum gases? c) Note similarity (or dissimilarity) of these two hydrocarbons.

9-2. a) What volume percentage ofmethyl ethyl ketone vapor, formula CH3 -CO-C2 H 5 , in air corresponds to a stoichiometric fuel percentage of 100%? (This also corre•

sponds to the idealized combustion to the C02 -H2 0 point.) b) What is thc volume percentage of methyl ethyl ketone vapor in air that corresponds to the stoichiometric fuel fraction of 1.25 indicated in Figure 9-3 as giving maximum internal blast overpressure? c) Campare volume percentages and blast overpressures for the two explosive mix• tures of parts a) and b ).

9-3. a) Write a chemical equation for the idealized combustion of ethanol, formula C2 H 5 0H, to the C02 -H2 0 point. Then write a corresponding equation for its combustion to the CO-H2 0 point. b) What are the stoichiometric fuel fractions for each of these combustions, and what are the corresponding volume percentages of ethanol vapor? 214 Tutorial Exercises c) Estimate, using the generalized chart of Figure 9-3, internal blast overpressure for each of these two combustions. d) Campare the above volume percentage and overpressure values with those for maximum internalblast overpressure quoted in Table 9-1.

9-4. Maximum blast overpressure in internal explosions of methane in air is about 8 bars and occurs at about 10% by volume of methane. The rate of the internal pressure rise depends on circumstances, but a useful index for this rate is the pressure rise rate coefficient defined by equation (9-4). Here, this is about 0.4 mfbar-s. a) The flammability range formethanein air is from about 5% to about 15% methane by volume. Convert these volume percentages to stoichiometric fuel fractions. Then from the approximation of Figure 9-4 estimate the corresponding overpressures. b) What are the corresponding pressure rise rate coefficients for these mixtures, as estimated by equation (9-6)? c) The violence of internal explosions increases with both the blast overpressure and the rate of rise of this overpressure. Accordingly, estimate the comparative violence of internal explosions of methane at its flammability Iimits relative to that for maximum internal blast overpressure.

9-5. The TNT equivalent for internal explosions offuel-air gaseaus mixtures can be estimated by basic equation (2-5) by noting that negligible entropy change occurs in these gas phase reactions. Thus here only the internal energy of explosion appears, and for these purposes this can be taken as the heat of combustion (without distinction between "lower" and "higher" values). a) Compute the total number ofmoles of gas in one cubic metre of any gaseaus mixture at the ordinary temperature and pressure of 15 oc and one bar. Then compute the number of moles of methane in such a mixture that contains 10% methane by volume. b) The heat of combustion of methane is listed in conventional handbooks as 210.8 kcaljmol. Convert this to metric and compute the energy release in the combustion reaction of one cubic metre of the methane mixture of part a). What is the corre• sponding TNT equivalent? (The energy of explosion of TNT is 4680 Jjg). c) The cargo tank of a petroleuro tankship has a volume of 2000 m 3. If this volume were filled with a 10% methane-air mixture that somehow became ignited, what would be the TNT equivalent ofthis internal explosion?

9-6. A material containing a volatile solvent is processed in a room with dimen• sions 8 x 10 x 3 m. lt is possible that an accumulation of this solvent vapor could occur, and if so, this could Iead to a damaging internal explosion unless the room were properly vented. a) What is the critical vent area for this processing room? b) lt is desired to instaU a vent to Iimit overpressures from a possible internal explosion to about 150 mbars. What minimum vent area should be provided?

9-7. A railroad tank car with 14 tonnes (14,000 kg) of acetone, a volatile solvent with formula CH3 -CO-CH3 and a standard heat of combustion of 426.8 kcaljmol, is derailed. lts cargo is so released and forms a !arge cloud of combustible vapor. a) If this vapor were ignited how much thermal energy, in kilojoules, would be released? Tutorial Exercises 215 b) There is the possibility that this vapor could become mixed with air and then ignited so that the vapor cloud would detonate. This is an unlikely circumstance. Were it to happen what would be the TNT equivalent of the detonation of the entire cloud? c) Out to what distance from this cloud would its explosion cause minor darnage such as window breakage?

10-1. Consider a nuclear explosion with yield of 20 kt TNT in the standard atmosphere at a height of hurst of 814 m, and a point on the ground at 1790 m from ground zero. a) Verify that this point on the ground lies within the Mach stem region. b) What is the peak side-on overpressure on the ground, the blast wave duration, and the wave form parameter in this Mach stem? c) Find the side-on overpressure at several timesintermediate between zerotime (time ofimpact) and duration time. Then draw the curve for this overpressure (millibars) versus time (milliseconds) for this explosion situation. d) Add curves for reflected overpressure, Stagnation overpressure, drag pressure drop for a drag coefficient of two, and for the difference (stagnation overpressure minus drag pressure drop).

10-2. The 20 kt TNT yield of Exercise 10-1 was at one time the "standard" for nuclear explosions. Other explosions may show darnage effects different from that of the standard explosion. For study of this, yields of 5, 10, 20, and 50 kt are to be considered, each at a scaled height of hurst of 300 m/kt1' 3 in a standard atmosphere with transmission factors of unity and for a drag coefficient of two, and for each a point on the ground each at a scaled distance of 660 mjkt1' 3• a) Select a particular explosion situation. Find for this the actual distance from the explosion corresponding to the specified scaled distance. How long does it take for the blast wave to travel to this distance? What is its positive pressure phase duration? What is the peak side-on overpressure, the peak reflected overpressure, the peak stagnation overpressure, and the peak drag pressure drop? What is the wave form parameter? b) Compute and plot overpressure versus time curves for the explosion situation selected in part a) and for its (stagnation minus drag) pressure difference. Note: The curves prepared in this exercise aretobe used in subsequent analyses ofthe dynamic Ioads imposed in various structures, and for estimation of their overall responses.

10-3. A reetangular structure of reinforced concrete is 140 m long, 21 m wide, and 30m high. The blast wave selected for Exercise 10-2 strikes this structure sidewise on its 140 x 30 m face. Draw dynamic blast Ioad curves for the following situations using previously prepared curves and the overlay technique with semitransparent paper. In each case the zero of time is to be taken as the instaut at which the shock front strikes the specified front face. a) A small panel on the front face that is 10m off the ground and 8 m from a side edge. b) Average for the entire front face of the structure. c) A small panel on its back face 10m off the ground and 8 m from the nearest edge. d) Average for the entire back face. e) Panels on the side very near the front edge, very near the back edge, and one intermediate between these. 216 Tutorial Exercises

f) Average cornpression Ioad on the sides and top. g) Cornbine the (average) Ioads for the front face and the for the back face to obtain the Iateralload developed on the frarne of this structure. h) Find the equivalent triangular pulse Ioad on the frarne of this structure. Specify its peak value, its duration, and the irnpulse per unit area.

10-4. Consider that the blast wave of Exercise 10-2 strikes the !arge structure of Exercise 10-3 on the end with the 30 x 21 rn face. a) Make the cornputations suggested in Exercise 10-3 for this sidewise (rather than endwise) situation. b) Cornpare the equivalent triangular pulse Ioads developed by the sarne blast wave but striking different faces.

10-5. A srnall stucco building 20 x 8 rn in frontal area and 7.5 rn long isstruck on the 20 x 8 rn face by the blast wave of Exercise 10-2. Draw dynarnic Ioad curves for the following: a) The average for the front face. b) The average for the back face. c) The totallateral Ioad on the frarne of the structure. d) Find the equivalent triangular pulse for the laternal Ioad on the frarne of this building. What is the peak value, its duration, and what is the irnpulse per unit area?

10-6. A cylindrical standpipe of structural steel is 10.6 rn in diarneter and 46 rn tall. a) Assurne the explosion situation of Exercise 10-2 and draw a curve for the dynarnic blast Ioad irnposed on this standpipe. b) Find the triangular pulse equivalent for this Ioad and deterrnine its peak overpres• sure, its total duration, and the irnpulse per unit area. c) Cornpare the triangular pulse here with that for the frarne of the !arge structure of Exercise 10-3 and 10-4. Classify these structures as diffraction type or drag type structures.

10-7. A spherical water tank of structural steel has a diarneter of 15.4 rn. It is supported by ten peripheral steel colurnns so that its center is 36 rn above the ground. Assurne the explosion situation of Exercise 10-2 and find the equivalent triangular pulse for this sphere. Then deterrnine its peak overpressure, its duration, and the irnpulse per unit area. Cornpare this blast Ioad with that for the standpipe of Exercise 10-6 in the sarne explosion situation.

10-8. A warehouse, substantially windowless, is 32 rn long, 27 rn wide, and 24 rn high. It is built tobe both earthquake and fire resistant with a lateral resistance of 8120 kN for the 27 x 24 rn face. Its natural period of vibration is about 250 rns. Find the triangular equivalent of the blast Ioad irnposed on this structure by the explosion situation ofExercise 10-2 and report the corresponding ratio of(peak dynarnic Ioad) to (static resistance) and that of (pulse duration) to (natural period).

10-9. A highway bridge and overpass of reinforced concrete is designed toresist wind Ioads of at least 16 kN/rn2 (kilopascals). Its period of natural free vibration is about 1.1 s. Tutorial Exercises 217

a) Assurne the explosion situation of Exercise 10-2 and draw a curve that represents the dynamic blast Ioad imposed on the bridge by this explosion. b) Determine the characteristics of the triangular pulse equivalent for this blast loading. c Report the ratio of(peak dynamic Ioad) to (design resistance), and the ratio of(pulse duration) to (natural period). d) Campare these indices of blast interaction effects with those for the warehause of Exercise 10-8 when exposed to the same nuclear explosion.

11-1. A small structure is designed with a lateral resistance of 25 kN/m2 (kilopascals). Its fundamental natural period for free vibration is 180 ms. a) Campare the time required for excursion from zero displacementout to the elastic Iimit in free vibration with that required when forced by ablast wave with a peak (reflected) overpressure of 600 mbars. b) Estimate the dynamic lateral resistance per unit area and compare with the design (static) value. c) Compute the displacement greater than which plastic deformation is presumed to occur, and draw the two-part formalized dynamic resistance-displacement curve. d) Draw the corresponding two-part formalized resistance-time curve, taking it that in the elastic displacement region the displacement is proportional to the time raised to the second power.

11-2. A building of reinforced concrete construction is 20m tall, 30m lang, and 25m wide. It is built tobe earthquake resistant with an averagedesignlateral resistance of 9000 kN. Mass of the structure is estimated as 1900 t, and the natural period of free vibration as about 0.25 s. It isstruck on its 20 x 25m face by an explosive blast wave of lang duration and a peak side-on overpressure of 680 mbars and with the correspond• ing reflected overpressurc. a) Estimate the time rcquired forthisblast wave to push this structurc out to its elastic Iimit. b) Estimatc the dynamic lateral resistance of this structurc forthisblast situation. c) What is the limiting elastic displacement for the cerlter of mass of this structure? What displacement ofthe peak ofthis structure corresponds to initiation ofperma• nent structural damage? What displaccment ofthe pcak would represent significant structural damage, assuming a ductility ratio of 30? d) Draw the formalized resistance-displacement diagram, and indicate the displace• ments corresponding to the maximum completely rccoverable one and to the displacement that rcpresents significant structural damage. e) Indicate schematically the resistance-time relation for this structure.

11-3. A reetangular structure of reinforced concrete with floor dimensions of 140 x 21m is 30m high (as in Exercise 10-3). It is built with steel reinforcing bars so that it can withstand a static side Ioad of 90,000 kN on the 140 x 30m face. Mass of the structure is 25,000 t. a) Estimate the fundamental natural period for its vibrationnormal to the 140 x 30m face. Then compute the corresponding limiting elastic displacement for the center of mass of this structure. b) Refer to Tutorial Exercise 10-1 (or 10-2) and for the explosion yield selected there, compute the time req uircd for its blast wave to producc the limiting elastic displace- 218 Tutorial Exercises

ment. Compare with the time required for the same movement in undamped free vibration. c) Estimate the dynamic yield strength per unit area for this structure in pascals (newtons per square metre) andin millibars. Then draw the formalized resistance• displacement curve, and indicate the displacement estimated as corresponding to darnage Class D (some reparis required) and to darnage Class C (structure only partially usable). d) Construct the formalized resistance-time curve, then combine with the dynamic Ioad curve for the frame ofthe building as obtained in Tutorial Exercise 10-3. Solve graphically for the veolcity and the displacement of the center of mass of this structure in this selected explosion situation. Present results in the form of graphs and characterize the extent of the darnage to be expected in this situation.

11-4. A steel standpipe 10.6 m in diameter stands 46 m tall (as in Exercise 10-6). Its water capacity is 3.8 x 10 3 steres (cubic metres) with mass of3.8 x 103 t, and mass of the empty standpipe is 220 t. The center ofmass can be displaced elastically as much as 3.4 cm with a spring constant of 1.02 x 106 kN/m. The explosion situation is that selected for study in Tutorial Exercise 10-1 (or 10-2). a) Find the acceleration, the velocity, and displacement ofthe center ofmass ofthe full tank when hit by the specified blast wave. b) Find the corresponding acceleration, velocity, and displacement for the empty tank, and compare with values for the full tank.

11-5. A spherical water tank ofblast resistant design is 15.4 m in diameter with its center36m above the ground (as in Tutorial Exercise 10-7). Mass of the tank itself is 150 t and mass of its water is 1900 t iffull.lts horizontal resistance at yield is 4300 kN.It is tobe assumed that this is maintained throughout any plastic deformation, the onset of which is at the limiting elastic displacement of its center by 13.5 cm. The explosion situation to be studied is that of Tutorial Exercise 10-1 (or 10-2). a) What is the natural fundamental period ofvibration forthistank ifit is full, and ifit is empty? b) Estimate the times required for the specified blast wave to force this tank out to its elastic Iimit if full, and if empty. c) Determine the dynamic resistance of this tank to the lateral displacements that correspond to plastic deformation. d) The blast Ioad imposed by the specified explosion is described by the equivalent triangular pulse of Exercise 10-7, and its resistance to this blast was determined above. Combine graphs for the forcing function and for the resistance-time function and determine graphically the acceleration, the velocity, and the displacement ofthe center of mass for the full tank and for the empty tank.

11-6. An office building with a structural steel framework is to occupy a 70 x 70 m plot and be 33 m high. a) From blast wave curves for the explosion selected for study (Tutorial Exercise 10-1 or 10-2) determine the corresponding dynamic blast Ioad on a front ofthe face ofthis building, on its rear face, and the overall Ioad on its frame. Then determine the equivalent triangular pulse for the Ioad on the frame. b) Estimate the undamped natural period for this structure, and a ductility ratio which Tutorial Exercises 219

would permit its frame to withstand the postulated explosion with no more than moderate (repairable) structural damage. c) What lateral resistance must be built into its frame for this structure to be consi• dered blast resistant? 11-7. The explosion situationtobe studied isthat described for the small stucco building of Exercise 10-5. a) Estimate the natural period of vibration for this structure. b) Estimate a displacement that corresponds todefinite but limited structural darnage for this building. c) Estimate the lateral resistance that built-in bracing should provide in order for this building to resist the specified blast wave with only a limited amount of damage.

11-8. A !arge warehouse constructed of reinforced concrete has the dimensions of80 x 80 m and is 17m high. a) What dynamic Ioad does the explosion selected for study in Tutorial Exercise 10-1 or 10-2 exert in its front face? On its rear face? On its reinforced concrete frame? b) Determine the characteristics ofthe equivalent triangular pressurepulse Ioad on the frame of this warehouse. c) The frameoftbis structure is designed toresist explosionblast Ioads (or correspond• ing earthquake Ioads) so that it would suffer no more than very moderate structural damage. Estimate the required ductility ratio. d) What is the estimated natural period of vibration for this structure? e) The reinforcing steel bars in the concrete frame of this structure are essential for providing adequate resistance to lateral deformations. What is the resistance per unit area expressedas a ratio to the peak postulated blast Ioad per unit area? What overall totallateral resistance should be provided?

11-9. The equivalent static Ioad diagram of Figure 11-10 can be used in an inverted sense, but it should be recognized that such computations must be regarded as rough approximations only. For illustrative purposes Iet us select for study the blast wave of Tutorial Exercise 10-1 (or 10-2) and the reinforced concrete structure of Tutorial Exercise 10-3 and 11-3. a) Identify the peak dynamic Ioad on the frame of this structure and duration of the equivalent triangular pressure pulse. b) Estimate the period for undamped vibration for this structure. Also identify its design (static) resistance to lateral Ioads and its maximum elastic lateral deformation. c) From the ratio of peak pulse Ioad to the lateral resistance per unit frontal area and the ratio of blast duration to natural period, estimate by aid of Figure 11-10 the corresponding ratio of the projected deformation to the limiting elastic deformation. d) Characterize the type of blast darnage that this structure would sustain. 11-10. a) Characterize situations in which the impulse-time criterion for blast darnage is to be preferred to the simpler peak overpressure criterion of Table XV. b) In what respects do the "square-wave" overpressures ofTable 11-2 differ from the peak overpressures for darnage of Table XI? 220 Tutorial Exercises

11-11. A !arge store of explosives in a sparsely built-up district accidently exploded. A small farm instrument storage building 720 m from the explosion was damagt:d beyond repair, and a residence 9 km from the explosion had some windows broken. a) Estimate the overpressure at each location. b) What are corresponding values for the magnitude ofthe explosion in tonnes TNT? c) Comment on the uncertainty attached to such yield computations, recalling that at !arge distances sonic ducts may occur, and that such yield computation can magnify ordinary uncertainties by a factor of about three.

11-12. A warehouse stores about 50 t of ammonium nitrate "fertilizer." If this were tobe detonated accidently, a) What diameter crater would be produced? b) Out to what distance would most surrounding buildings be destroyed? c) Out to what distance would personnel injuries such as ruptured eardrums, damaged lungs, or being knocked down by the blast wave be expected? d) At what distance from the explosion could one expect minor and repairable struc• tural darnage such as cracked plaster, torn away shingles, doors dismantled, chim• neys destroyed, broken dishes, and shattered windows?

11-13. Consider an accidental explosion of a magazine with 145 t of military explosive. a) What diameter crater is to be expected? b) At what distance is there a probability of only one in a thousand of causing a sympathetic secondary explosion? c) Approximately how far would such an explosion throw fragments (flying missiles) arising from the demolished magazine? d) Personnel injury can result not only from flying missiles, but also by the direct blast wave. How far out would this blast wave probably knock a persondown and how far out might eardrum rupture be caused? e) Out to what distance would darnage such as cracked plaster, destroyed awnings, and broken windows be expected? Answers to Tutorial Exercises

Answers to selected even-numbered exercises.

1-2. a) Nurober of atoms is 3.47 x 1024 b) Moles ofuranium = 5.77 c) Mass of uranium is 1.36 kg

1-4. TNT equivalent ofthe lightning is 34 tonnes TNT.

1-6. a) Distance away from public traflic ways, at least 240m. b) Distance away from an inhabited building, at least 400 m. c) Regular patrol should be at least 400 m away.

1-8. a) Maximum amount of explosives if magazines are not earth covered is 400 kg TNT in each. b) If earth covered, maximum amount is increased to 60,000 kg TNT. c) Missile distance from fully loaded earth covered magazines is about 1800 m. d) Crater diameter would be about 30 m. e) Probability ofpropagation ofthe explosion about 0.046 (about one in twenty).

1-10. a) Separation ofunbarricaded buildings is 18m. b) If barricaded, separation reduced to 9 m. c) Odds against propagation of the explosion are about 2000 to 1.

1-12. Energy of crater formation is equivalent to about 4 megatonnes TNT.

1-14. Amount of explosive required for breaching is about the equivalent of 460kgTNT.

221 222 Answers to Tutorial Exercises

2-2. HMX a) Oxygen balance, -22% to C02, 0% to CO. Oxygen delicient to C02, oxygen balanced to CO. b) C4H8N80 8 -+4CO + 4H20 + 4N2 PETN a) Oxygen balance, -10% to C02, + 15% to CO. Slightly oxygen delicient to C02, slightly oxygen rich to CO. b) For products assignment as in Table 2-1 for lireball conditions: C5H8N40 12 -> 3C02 + 2CO + 4H20 + 2N2. TETRYL

a) Oxygen balance, -47% to C02 , -8% to CO. Somewhat oxygen delicient, particularly with respect to co2. b) For products assignment as in Table 2-1 for lireball conditions: C7H 5N50 8 -> 7CO + H20 + l!H2 + 2!N2. NITROMANNITE a) Oxygen balance, + 7% to C02, + 28% to CO. An oxygen rich explosive.

b} C6 H8N 6 0 18 -> 6C02 + 4H20 + 0 2 + 3 N 2 . CYCLONITE a) Oxygen balanced as for HMX.

b) C3H6N 6 0 6 ->3CO + 3H2 0 + 3N2.

2-4. a) By methods of Example 2-2, mole percentage RDX = 18.3%, TNT = 17.1%, and Al= 64.6%. The apparent formula mass is 75 g/mol and the apparent formula is as written in subsequent part b). b} The chemical equation for the explosion ofTorpex, with oxygen assignment as described in Table 2-1,

C~. 75 Ht. 95 Al 0 . 65 Nl.6 1 0 2.12 -> 0.32Al20 3 + 1.15 CO+ 0.6 C + 0.98 H2 + 0.80N2 . c) Oxygen balance to CO is -26%, which indicates a markedly oxygen delicient explosive.

2-6. a) /J.Hc = 2186 kJ/mol, !J.Ec = 2168 kJ/mol. b} By methods of Example 2-3, t1EJ = -365 kJ/mol. c) Equation for the explosion is C4H7N309-+ 2tco + 1tc02 + 3tH20(1} + 1tN2. Interna! energy of explosion = -1490 kJ/mol, and Heat of explosion = 6.2 kJ/g.

2-8. a) Chemical equation written in accord with the oxygen assignment of Table 2-1,

C6 H3N30 7 -> 6CO + H 2 0 + !H2 + l!N2 • b) !J.Ej (Tables I and V, rounded} are, respectively, 224, 112, 282, 0 and 0 kJ/mol. (Water is a liquid for these purposes.) Indicated energy of explosion = 953 + 224 = 0.729 kJ/mol. Answers to Tutorial Exercises 223

c) Entropies, respectively (equations (2-8), (2-9), and Table V), are 245, 198, 70, 131, and 192 Jjmol-K. Entropy ofexplosion is (1611 + 81)- 245 = 1447 Jjmol-K. d) Helmholtz free energy of explosion = -729 - 298 x 1447/1000 = -1160 kJjmol. e) Explosive strength estimated from the change in the Helmholtz free energy is

100 X (1160/229)/4.680 = 108%. Explosive strength estimated by the Berthelot approximation, taking water vapor as a gas, is

840 X 9 X 769/(229)2 = 110%. Each of these is in good agreement with the measured value.

2-10. a) By group substitution approximation, ßEJ = 47- 85 + 0 + 0 = -38 kJjmol. b) Interna! energy ofexplosion = -671 + 38 = -633 kJjmol. c) Heat of explosion = (633/215) x 1000 = 2944 Jjg. d) By group substitution, entropy = 145 + 35 + 30 + 0 = 210 kJjmol-K. e) Entropy of explosion -1680 Jjmol-K. f) t..A = -1134 Jjmo!. g) Explosive strength = 100 x (1134/215)/4.68 = 113% (Helmholtz). h) Explosive strength = (840 x 10 x 633)/215)2 = 115% (Berthelot). i) Gurney constant = (2 x 2944) 1' 2 = 2425 mjs.

2-12. a) Interna! energy of explosion is ( -1023- 39) = -1062 kJjmol. b) Formula mass is 289 gjmol, and 12 moles of gases are produced by explosion of one mole of Tetryl. Explosive strength computed by equation (2-10) is 840 x 12 x 1062/289 2 = 130%. c) The Gurney constant of equation (2-11) is (2 x (1062 x 1000)/287 x 1000) 1' 2 = 2710 mjs. d) Computed explosive strength of 130% TNT compares weil with the 131% measured in a Trauzl block. Computed Gurney constant of2710 compares reasonably weil with the experimental value of Table 2-2 of 2500 mjs.

2-14. a) Gurney constant for Composition Bin Table 2-2 is 2680 mjs and the charge to meta! ratio for this warhead is 40/30 = 1.33. Then by equation (2-11 ), fragment velocity = 2680 x [1.33/(1 + 0.67)] 1' 2 = 2400 mjs. b) Total fragment momentum = 30 x 2400 = 7.2 x 104 kg-m/s. c) Total fragment kinetic energy = 86.4 mJ.

2-16. In SI units, energy of implosion = 0.016 x 100,000 = 16,000 J. Yield = 16,000/700 ~ 20 g black powder.

3-2. a) By equation (3-8) or (3-18), ßH = 28.5 Jjg. By equation (3-12) and (3-14), or (3-19), t..E = 20.4 Jjg. By equation (3-21) or (3-20), ßS = 0.0017 Jjg-K. 224 Answers to Tutorial Exercises

b) By equation (3-23), isentropic temperature = 310.9 K, or 37.9 •c. c) lrreversibility accounts for the temperature increment 38.4 - 37.9 = 0.5 •c.

3-4. a) Blast wind velocity = 0.550 x 390.5 = 215 mjs. b) Stream stagnation temperature, equation (3-38), 50 T. = (107 + 273) X [ 1 + e~ rJ = 403 K, or 130 ·c.

Stream stagnation pressure, equation (3-39) or (3-23), P0 = 2.800 bars. c) Reference critical temperature, equation (3-41), T* = 336 K. Reference Mach number, equation (3-44), M* = 0.585.

3-6. a) Stagnation pressure, equation (3-39), P. = 1011.5 millibars. b) From Table VIII, drag coefficient is estimated tobe about 2.0. Drag pressure drop, equation (3-47), = 20.9 millibars. c) Rear face pressure = 1011.5 - 20.9 = 990.6 millibars. d) Lateralforce = 20 x 10 x 20.9 = 4180 millibars per square metre, or 418 kN.

3-8. Drag coefficients as estimated from Table VIII, drag pressure drops found from equation (3-47), and computed wind Ioads are as follows: a) 2, 36 mbars, 1160 kN. b) 1.25, 22 mbars, 700 kN. c) 1.2, 22 mbars, 1515 kN. d) 0.1, 2 mbars, 17 kN.

4-2. a) MY = 0.687. b) PY = 2.13 bars; T.; = 95•c. c) ux = 510 mjs, uy = 264 m/s, uy/ux = 0.518 (equation (4-17)).

4-4. a) p = PY - Px = 0.472 bars. b) uP = 97 mjs, up/ay = 0.269, up/ax = 0.284. c) Pstag = 1.547 bars, Pstag = 0.547 bars. d) T.; = 49 ·c, 1;,. = 15.5 ·c.

4-6. a) ux = 388 mjs. b) uP = 74 m/s. c) ux = 412 mjs, uP = 155 mjs.

4-8. a) u1 = 629 m/s, ux = u' = 445 mjs, Mx= 1.31. b) By equation (4-11) or (4-17), uy = 291 m/s. c) By equation (4-35), () = 11.8°.

d) u2 = 532 mjs. e) By Table IX, aY = 372 mjs, M2 = 1.43. f) By equation (4-20) or Table IX, PY = 1850 mbars. Answers to Tutorial Exercises 225

4-10. a) ß = 59°, closely; M2 = 1.8.

b) ß = 71o; M2 = 0.80.

4-12. a) At M1 = 2.5, shock plane angle for maximum dellection is 65°; deflec• tion angle is 30° (closely). b) Use equation (4-43) for ß, and equation (4-41) for fJ.

5-2. a) By equation (4-26) (or Table X), Mx= 1.110; by equation (5-7), M, = 1.106. b) P,- Px (specified) = 275 mbars; by equation (4-25), P,- P, = 337 mbars; P, - Px = 612 mbars. c) Reflected overpressure = 612 mbars; rellection coefficient = 2.22.

5-4. a) M1 = 2.490; ß1 = 30°.

b) M2 = 2.17; (} = 8° (closely, by chart) analytical solution gives M2 = 2.1649; (} =7.87".

c) ß2 = 34° (analytical solution ß2 = 34.24°).

d) M3 = 1.9 (analytical solution M3 = 1.871).

5-6. By equation (4-20), pressure P, = 1650 mbars; temperature 7;, = 60 oc; speed ofsound a, = 366 m/s. Reflected shock Mach number M, = 1.218, by equation (5-15).

d) Found first by equation (4-14) (requires iteration), stream angle ß2 = 34.24°, then by equation (5-16), reflection angle 1J = 26°. e) By equation (5-17), pressure P, = 2600 mbars, and by equation (4-14), speed of sound a, = 106 oc and 390 m/s. f) By equation (5-18), reflection coefficient = 2.49. g) By eq uation (5-14), blast wind = 117 mjs.

5-8. a) By Figure 5-7 (or by equation (5-23) for more precision) shock incidence is in the Mach stem regime. Then, by equation (5-22), M. = 1.154. b) Reflection coefficient (from Table X) = 0.393/0.287 = 1.36. c) By Table X, blast wind = 80 mjs.

5-10. a) Mach number ofthe incident shock (Table X) is 1.228. By Figure 5-7 (or equation (5-23)) transitionangle ß = 47° (c!osely). b) M. = 1.707, corresponding overpressure = 2260 millibars (Table X). Reflec• tion coefficient = 2260/600 = 3.8. Blast wind= 318 m/s.

c) M1 = 1.707 (as forM.), M2 = 1.38, and M3 = 0.97. ß1 = 46°, ß2 = 70°, fJ = 9°. d) By equation (5-15), M, = 1.30, and by equation (5-16), 1J = 61°. By equation ( 5-17), reflected overpressure = 1900 millibars; by equation (5-18), reflection coefficient = 3.16. T, 7;, found through Mach numbers M, and Mx as 583 K, then by equation (5-19), blast wind is 122 m/s. Note: In the circumstance here, the Mach stem develops the greater overpressure and the greater blast wind.

6-2. a) From Table XI, Part A, r = 250 m. 226 Answers to Tutorial Exercises

b) p• = 818 mbars, td = 245 ms, and 1/A = 45.2 bar-ms. c) Wave form parameter a = 3.2, and by Table XIV, 1/A = 0.220 x 0.818 x 245 = 44.1 bar-ms, in substantial agreement with a directly obtained value.

6-4. a) Hyperbolic constant = p0 x r = 0.011 x 5000 = 55 bar-m. b) At 4000 m, p0 = 55/4000 = 0.014 bars, as listed in the table. c) At 6000 m, p• = (55/6000) x 1000 = 9.2 mbars.

6-6. a) Peak overpressures are converted into overpressure ratios, then into Mach numbers, as by equation (4-26), and reciprocal Mach numbers plotted versus distance.

Distance: 0.758 0.981 1.253 1.558 2.021 2.960 1/Mx: 0.294 0.390 0.471 0.587 0.694 0.811

Area under the curve from acharge radius of 0.05 m to one metreis found as 0.190 m, and to two metres as 0.710 m. Dividing by the speed of sound, 336 mjs, given the respective arrival times as 0.565 and 2.11 ms. b) Averagespeed to one metreis 1/0.565 = 1.77 mfms, to two metres is 2/2.11 = 0.95 mfms. From one to two metres, average speed is 1/(2.11 - 0.565) = 0.65 mfms.

6-8. Averagespeed = 3310/4.70 = 704 mjs. By Table XI, this corresponds to a peak overpressure of 700 mbars, closely.

6-10. a) A wind of 100 knots, by Table XVI, is 51.4 m/s. This corresponds, by Table X, to a shock front Mach number of 1.095. For the nuclear explosion ofTable XI, this occurs at a distance of 510 m. b) Fora blast wind of 51.4/2 = 25.7 mfs, the shock Mach number, by Table X, is 1.046, and for the explosion this occurs at a distance of 825 m (Table XI) or at an additional distance of 315m. c) Blast wind Stagnation overpressures for these shock front Mach numbers are (Table X) 254 mbars and 115 millibars, respectively.

6-12. Impulse fraction = 0.375/(0.670 x 1.58) = 0.345. Wave form parameter (equation (6-13) or Table XIII) is about 1.2. The corresponding overpressure-time curve is constructed through equation (6-12), and resembles that of Figure 6-8.

7-2. a) Scaled distance (Table XI)= 210m. Actual distance = 210 x (20) 113 = 570m. b) Scaled arrivaltime = 247 ms, actual arrivaltime = 247 x (20) 113 = 670 ms. c) Scaled duration = 0.216 s, actual duration = 0.216 x (20) 113 = 0.586 s. d) Wave form parameter is 3.7. Scaled 1/A = 49.2 bar-ms. Actual 1/A = 49.2 x (20) 113 = 133 bar-ms.

7-4. a) Scaled distance = 21/(75)113 = 4.98 m. Scaled arrival time = 8.85 ms, actual arrival time = 8.55 x (75) 113 = 37.3 ms. Answers to Tutorial Exercises 227

b) Mx= 1.115. c) p• = 0.290 bars.

d) Scaled duration = 2.46 ms. Actual duration = 2.46 x (75) 1' 3 = 10.4 ms. e) a = 0.50.

f) Scaled 1/A = 0.302. Actual 1/A = 0.302 x (75) 1' 3 = 1.28 bar-ms.

7-6. From the ground to 1800 m, i:J = 0.971, J, = 0.962. From the ground to 1000 m,i:J = 0.984,!, = 0.979. For the path 1000-1800 m,

jd = (0.971 X 1800- 0.984 X 1000)/(1800- 1000) = 0.955

f.= (0.962 X 1800- 0.979 X 1000)/800 = 0.941

7-8. Scaled distance, from Table X, is 3.30 m. Yield computed by equation (7-19) is (28.0/3.30) 3 = 610 kg TNT.

7-10. Average shock front speed of 15 oc is 18.0/23.5 = 766 mjs. Corresponding scaled distance, by Table XI, Z = 2.99 m. Yield (equation (7-19)) is computed as (18.0/2.99) 3 = 218 kg TNT.

7-12. Atmospheric pressure at altitude is 815 mbars (Table XIV). Transmission factor for time at this altitude is listed as 0.923. Reference overpressure is 169 x (1013/815) = 210 mbars. Scaled arrivaltime is given in the tables as 11.57 ms. Yield, by equation (7-19), is [(74/11.57) x 0.923] 3 = 200 kg TNT.

8-2. a) From Table XIV,fd = 0.875; by equation (7-18),Jd = 0.645. b) 258m, 223m, 190m. c) From Table XI or equation (6-2), p• = 760, 358, 192 mbars.

8-4. a) Actual slant range is 14400 m and the scaled slant range is 14400 x 0.875/(20000) 1' 3 = 470 m/kt1' 3, where the transmission factor for distance, 0.875, pertains to all paths from point of hurst to the earth's surface. The scaled arrival time (Table XI) is 886 ms/kt113, and the transmission factor for time (Table XIV) is 0.837. Actual arrival time = 25.6 s.

b) Scaled horizontal distance from ground zero is 12,000 x 0.875(20,000) 1' 3 = 387 mjkt1' 3, and a point on the surface at this distance away from ground zero under a hurst at a scaled height of 258 m/kt 113 is within the Mach stem regime according to Figure 8-6. This regime begins, by equation (8-4), at 312 m/kt1i 3• Figure 8-5 (or equation (8-7)) indicates that at a distance ratio of387/340, the stem height is about one percent of the hurst height, or approximately 80 m. c) Mach nurober for the incident shock (Table XI) is 1.107, and for the stem, by equation (8-2), is 1.328. Peak overpressure for ordinary air (Table X) is 900 mbars, closely. d) The peakblast wind is 163 mjs. e) Scaled duration (Table XI) is 0.235 s and the wave form parameter is 3.4 with an im pulse fraction of0.211 (Table XIII). The actual duration is 0.235 x (20,000) 1' 3 /0.837 = 7.6 s, and the positive impulse per unit area is 900 x 7.6 x 0.211 = 1450 bar-ms.

8-6. a) 10.7 km. 228 Answers to Tutorial Exercises

b) Travel time 17 s, duration 9.3 s, side-on impulse 1240 bar-ms. c) 105 bar-ms.

8-8. The desired curve decreases monotonically from a maximum of about 500 bars at the charge radius distance. The very !arge range to be plotted suggests a logarithmic scale. Fora log-log plot, the ordinates (overpressures) are identical with those of Figure 6-4 for a chemical explosion and the abscissas (distances) are numeri• cally greatet by the factor (8000) 1' 3 = 20.

8-10. a) Using the transmission factors of Table XIV and iteration as needed, rounded heights of hurst are found as: 1) 765 m, 2) 1670 m, 3) 3.5 km, 4) 6.7 km, and 5) 75 km. b) Overpressures are identical for explosions of the same scaled distance; or 180 mbars. c) Durations computed from scaled duration, explosion yield, and transmission factor for time. d) 1) 420 ms, 2) 925 ms, 3) 3.2 s, 4) 3.8 s, and 5) 27.4 s. e) Wave form factor is 1.7 and impulse fraction is 0.30. Positiveimpulseper unit area in bar-milliseconds is found as: 1) 50, 2) 110, 3) 245, 4) 450, and 5) 3250

9-2. a) 3. 7%. b) 4.6%. c) Different volume percentages but not greatly different overpressures.

9-4. a) SFF = 0.5 and 1.7; overpressure = 5.8 and 7.0 bars. b) C, = 0.07 and 0.07 mjbar-s. c) Violence ratios are 0.13 and 0.09, each tobe rounded to 0.1.

9-6. a) A * = 2.4 m2 •

b) A' =18m2 •

10-2. a) Actual distances from ground zero = 1130, 1420, 1790,2430 m.

Scaled slant range = 725 mjkg1i3 ; Scaled travel time = 1.59 s; Actual travel time = 2.72, 3.43, 4.32, 5.86 s. Actual duration = 580, 730,925, 1250 ms

M, = 1.159, peak side-on p• = 405 mbars, P,.r = 940 mbars, P.,. 8 = 110 mbars, IX = 1.5. b) Overpressure-time curves are.similar to those of Figure 10-2.

10-4. This exercise concerns a diffraction type situation. The initial peak reflected overpressure is 940 mbars. The blast duration depends on the explosion selected for study. The various Ioad curves resemble those ofFigures 10-4, 10-5, 10-6, and 10-7. The equivalent triangular pulse resembles that of Figure 10-10 (a). Answers to Tutorial Exercises 229

10-6. This exercise concerns a drag type Ioad situation. The Ioad curve resembles that of Figure 10-9 (b). Equivalent triangular pulse resembles that of Figure 10-10 (b).

11-10. a) The peak overpressure criterion for blast darnage is applicable to situations in which blast duration is appreciably Ionger than the critical time for inflicting target damage. In general, this occurs with !arge explosions such as nuclear explosions or ones of a !arge store of chemical explosives. b) The "square wave" overpressure of Table 11-1 corresponds to the minimum overpressure for inflicting darnage by !arge explosions with their long durations. Smaller explosions in general must show overpressures considerably greater than this in order for the inflicted impulse to exceed the minimum darnage impulse within a relatively short duration time.

11-12. a) Diameter ofthe crater, by equation (1-4), would be about 30m. b) Indicated darnage overpressure would be about 500 mbars and correspond to a scaled distance (Table XI) of about 3.8 mfkg 1' 3 . Actual distance would probably extend to about 3.8 x (50,000) 1' 3 = 140m. c) Darnage overpressures extend over a very wide range, from about 100 mbars for personnel being knocked down to about 2000 mbars for Jung damage. Correspond• ing scaled distances (Table XI-A) are 9.7 and 1.5 mfkg 1' 3 . The actual distances extend to about 55 m for Jung darnage and to about 350m for knocking down personnel. d) The indicated damages could probably be inflicted by an overpressure of about 100 mbars. Corresponding scaled distance is 9.7 mfkg 1' 3. The actual distance is about 350m from the explosion. Tables

I. Properties of Explosive Materials A. Pure Materials B. Mixtures II. Safety Distances III. Probability of Occurrence of Deviations IV. Thermodynamic Properties of Products of Explosions V. Group Substitution Approximations A. Hypothetical Transmutations B. Basic Compounds VI. Entropy of Mixing VII. Properties of Dry Air at Atmospheric Pressure VIII. Drag Coefficients IX. Air Shock Characteristics as Dimensionless Parameters X. Shock in Dry Air at 15 oc and 1.01325 mbars XI. Reference Explosions A. Chemical B. Nuclear XII. Blast Wave Decay Characteristics A. Overpressure versus Time B. Impulse versus Time XIII. Impulse Fraction versus Wave Form Parameter XIV. The U.S. Standard Atmosphere (1976) XV. Blast Damage-Side-On Overpressure Correlation XVI. Conversion Factors

230 w er' <> >-l N Pl

1

3 1 1 1 1 2 1 1 3 1 1 1 1

1 4 2 2 4 2 2 4

(#) Ref.

3)

(m/s)

Gurney

1761

1727

1924 1394

1850 3410 3692 2838 2676 2306 2314 2675 (Note 3001 2796 2173 2734 2408 2234 2978 2308

2590

Constant

95p 60p

159b

136b

192b 168b 190b 139m, 102b 185b, 108b, 167b

108b

131b 58b 158b

77b 92b

(%TNT)

Strength

Explosive

109s,

150b lOlt, 104s, 180t, 112t, 160t, 148b 125t, 88s lOSt, 125t, 60t, 102t, 137t,

84b 6lb 55t, 55b 80t, 95t, 90t, 97b

(J/g) 2512

8398 5227 7104 7890 8437 2285 7810 4921 7300 4602

12013 11942(n) 10844 17391 10582 12457 17915 10179 12004 14876

(-L'lsn

199.67

(L'lEJ)

+89.54 +69.27

-81.76 -66.94

-75.31

(kJ/mol)

+ +287.44

-359.55 -144.35(n) -527.18 +435.14 -233.14 -262.34 -100.42 -368.19 -148.11 -723.83 -136.82 -166.94 -447.69 -242.67 -234.30

)

3

1.73

1.35 1.00 1.60 1.64 5.1 1.71 1.72 1.052 1.58 1.128 1.69 1.105 1.53 1.22 1.48 1.626 1.42 1.70

-

(g/cm

Density

d)

d)

d)

T,,

14.2

75.4 50 70.7 82(ex)

('C)

103 160 152( 111 155 175 140(d) 188

255( (d) 217

232

-50 -29 - -20

-102

60 89(n) 75 80 75 77 96 61 91 90 94

F.M.

123 169 150 150 104 186

196 105 152 188 122

(g/mol)

azide

1) 1) (GDN)

(NQ)

materials dinitrate

(NM)

+ +

nilrate

azide

nilrate

dinitramine

Name

nilrate

dinitrate

azide

nitrate nitramine

nilrate

explosive

ver

nitrate dinitrate

{AN) (EDNA)

{TNM)

of

Ethanolamine Ammoniumnitrate Ethylene Si! Ethylenediamine Guanidinenitrate Ammonium Urea Polyvinyl Ethyl Hydrazinium( Methyl Nitroethane Ethyl Tetranitromethane Nitroguanidine Methylamine Hydrazinium( Nitromethane Glycol Tetracene

Nitrourea

materials

Pure

6

2 6

4

0 0 3

3 2 3

3 2 4

Properties

A.

4

0 0 0 2 3

3

10

2 2 4 0 0 0 0 0

I

N

3 8 3

2

4 4

Formula

0

N0 N0 N N N N

3

3

5

10 8 5

6 6

N N 0 N0 N N0 N N 4

5 3 3 6 3 6 4

4

N

H H H H H H H

5

2 2 2 2 2 2 2

H4N203 C Table AgN H4N4 HsNs C C2H7N306 H CN CH C C CH C CH C CH (C2H3N03). C CH CH CH N w N

P' >-l cr' ~

4 4 2 3

2

(#) Ref.

(m/s)

Gurney

3205 3575 3017 3062 3478 2495 3337 3038 2768 3198

3425

Constant

88s,

173b,

176b, 173b

176b

150m, 140m, 113b

115b

176b,

145m,

90m,

(%TNT)

Strength

Explosive

135p

130s, 136s,

149b 150m

129p,

lOls,

160t, 186t, 126!, 145t, 144b 161b 163b

77t, 145t,

180t,

(J/g)

-L'iH,o)

7568 9452 6396 6783 9049

9429

8122

(

10326 11723 10267 11635

83.82

(!iE})

+

-66.67

(kJ(mol)

+928.85 +104.77 -333.66 -370.28 -284.51 -301.25

-472.79 -415.89

-514.63

)

3

1.59 1.82 1.54 1.835

1.52 1.52 1.38 1.60

1.90

1.77

(g/cm

Density

2.2

2

7;,.

94 (OC) 62

204

141 273

-27

F.M.

196 227 222 206 204 220

302 241

296 204 316

(g/mol)

7-

(RDX)

(PETN)

{DEGN)

(Cyanuric

(Nitrogly-

Name

(NG)

Butanetrioltri-

Triazido-1,3,5-

trinitro-1,3,5-triazine nilrate trinitroimidazole triazide) nitrate (BTTN) tetrazine) triazine (Cyclotrimethylene- oxamide cerin) trinitramine) dinitrate tetranitro-1,2,5,

dinitrate (Cyclotetramethylene- tetranitramine) tetranitrate

(beta-HMX)

1,2,3-Propanetrioltri- Hexahydro-1,3,5-

1,2,4- Ammonium-2,4,5- 2,4,6-

Dinitrodimethyl

Erythritol tetranilrate Diethyleneglycol Octahydro-1,3,5,7- Diethanolnitramine Pentaerythritol

6 9

6 12 7 8 9 6 12 8

(Contd.)

0

0 0

0 0 0 0 0 0

0

6 3

6

8 3

4 2

4 4

4

Formula

N

N N

N N N N N N

N

6 5

6 7 4 6 8

8 8

8

H H H

H H H H H H H

3

3 3

4 4 5 4 4 4

4

TableI

C

C C C,N12

C C C C C C C l;.l l;.l

N

<>

~ >-3 0"

2 4

3 2 4

3

4

2321 2591 2250 2477 3626 2954 2293 2879 3190 2439 3266 2400 2708 2028 2232 2192 2398 2961 2196

!lOb

99b,

120b 110m, 129b 16lb 112m, 118b

160b 82b

90b

90m,

llOs, 107p 115s,

89b

lOSt, 137t, llOt, 125t, 144b lOSt, 116b 120t, 115t, 180t, 106b

95b

154b 86t, 8lb 140t, 88b 82b

92b

6510 7100 9128

11135 17445 13576 17283 12983 11868 12244 10016 10325 12291

11764 17244 15737 11083 28646

10.46

51.88 13271

-9.62

217.57

619.46

+ + -16.74 -78.91 -35.56

-72.74 -23.43 -37.13

-523.00 +343.09 + -112.97 -132.60 + -366.08 -223.84

-401.66

+1129.68

1.70 1.83 1.81 1.87 1.76 1.56 1.76 1.63 1.73 1.57 1.97 1.69 1.90 1.86 1.57 1.79 1.68

1.47

61 89

·- -

-3

180

118 !57 121 173 131 122 216 188

286 111

450(d)

168

348 119 168

168 318 273 229 184 336 213 213 245 252 243

228 210 258

255

(PA)

(TNA)

(MIN)

,2,5-

Hexanitro-

(HNB)

1

Acid)

azide

Tetranitroaniline

Trinitroresorcinol

Trinitrobenzene Trinitrobenzene

Triazido-2,4,6- Trinitrophenol Trinitroaniline

Dinitrobenzene

Dinitrobenzene Diamino-2,4,6-

trinitrobenzene

trinitrobenzene

benzerre Pentanitroaniline oxadiazole-1-oxide) (TATB) trinilrate (BTF) (Picric (DATB) (Picramide) trinitrobenzene (TNB)

Trimethylolethane-

1,1-

,3,5-

I

1,2- 1,2,4- 1,3-Dinitrobenzene 1,2,3,4,5,6- 1,3,5-triamino-2,4,6- 1,4- 1,3- 1,3,5- 1, Phenyl

Diazodinitrophenol 2,3,4,5,6- 2,4,6- Benzotris( 2,3,4,6- 2,4,6- 2,4-Dinitrophenol 2,4,6-

6 7 8

6 6

6

0• 0 0• 0s 0 6 0 0o 0 06 0s 0 0 0• 0s

12 3 2 3 3 3 5 5 3 3 2 6 2 6 2 4

4

0

0 2 N

N N N 0 N N N N N N N N N N N

3 3 3 3 3

2 3 6 6 5 6 4 9 4

4

4 4

N H H H N H N, H H H H H H H H H H H

5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

C C C C C6H2N60to C C C C C C C C C C C C C C N -1:>. w >-l 0" "' ö "'

3

3

3

2 2

4

2

3 Ref. (#)

(m/s)

Gurney

964

2137

2189

2473 1478 2966 Constant 2170

3451 2952 2307

2315

2131 2350 2202

2710

2098

2200

84s,

lOOb,

130b,

148b

140t

99m,

156b

94b 100m,

131m,

93b

138b

(%TNT)

Strength

87b

82b

Explosive

94b

87b,91p,85a

100s,

100p

116p 123s,

100t,

102b,

82b

95s, 50b 170t, 87b 115m, 125t,

lOOt,

103b

112t,

131t, 98t,

70t,

23b

93t,

(J/g)

9358(n)

9210(n)

9188(n)

6258

(-ßH,o)

11603

14912

10658(n) 10130

12593

14967

15039 13287 13442 12146

19537

17639

16802

38.91

(MJ)

(kJ/mol)

-54.39

-35.98 +

-41.42

-79.50 -343.09

-880.50(n) -812.63(n)

-627.6(n)

-440.41 -795(n)

-635.97 -589.94 -132.21

+221.75 -184.10

-560.97

)

3

1.72

1.67

1.66

1.47

- 1.66 1.73 1.47

1.65

1.447 - 1.68 1.41 1.73

1.52 (g/cm

1.28

Density 1.60

Tm

(Oe)

-

- 81

81 68

71

265(d)

160(d)

112

119

106 130 -6

181

F.M.

246

263(n)

274(n)

(g/mol) 297(n)

204 252(n)

452 299 241

227 227 243 243 182 287

220

241

N

N

D)

(EDNP)

pierate

(GLTN)

(Ne)

(DNPA)

hexanitrate

TNT) trinitrate-

Name dinitrate-

monolactate N(NC)

N

Trinitro-

Trinitrotoluene Trinitrotoluene Trinitro-m-cresol Trinitroanisole

Trinitro-m-xylene

(EXPLOSIVE

14.1% (Ne)

(NC) acrylate 11.1%

trinitrate

benzaldehyde

(TNT)

(Liquid tetranitroaniline

(TETRYL) (DNT)

pentanoate

Ammonium

Nitrocellulose-12% Nitrocellulose-13.35%

Cellulose 2,2-Dinitropropyl-

Cellulose Mannitol Glycerol 2,4,6-

2,4,6- 2,4,6-

2,4,6- 2,4,6- N-Methyl-N,2,4,6-

2,4-Dinitrotoluene

Ethyl-4,4-dinitro-

2,4,6-

).

11

7

18 6 11

7

6 7 7 8

4

6

(Contd.)

0

0

0

0 0

0

0 3 0 0 0

0

4 0

2

6 3

3

3 3 5 3

2

3

Formula

N

N

N N N

N 7

N

N N N

N

6 N

8

8 9 3

5

5 5 5

6

7

H7Nz.zsÜ9.s)n

H

H

H H H

H 6

6 H H H H

H

6 H

6

7 6 6

7 7 7 7

7

8

TableI

C

(C

(C6H7Nz.s010)n

(C C C (C6HsN409)n C C

C7HSN306 C C C C

C

C7H,zNz06

C u.> N

Ul cr" "' 0 .....j 1>0

2

4

4 3 4 4

4 3 4 4

2197 3268 2588 2401 2655

2656 26Il

2693 2431 2738 2352 2524

182b

116t

142m,

95b

78b

123s,

128!, 108b 114b, 106t, 88t, 108b IlOb

122b 105b 122b 108b

92b

17507 12638 14574 10779 14818

14822 13310 12335

12248 12390 14034 14314

16.14

+4.18

107.99 313.84

+94.47 -28.03

+

-89.53

+483.52

+485.20 +326.40 -523.00 +

+657.93 +

1.63 1.74

1.81 1.85

1.74 1.78 1.79 1.86 1.86 1.74

-

74

-

-

-

263 203 378

263 221 318{d) 303

524 308 263 218 424 388

388

647 452

420 450 454 407

benzo-

-3,

(T-

Hexanitro-

Hexanitro- te

{HNBP)

(HNAB)

{HNS~

{Z-TACOT)

tra

AM) ,6,6'-

Tetranitro-

Tetranitro

Trinitro-

,4,4',6,6'- 7,9- ,4,4'

DIP

naphthaJene biphenyJ naphthaJene hexani Tetranitrobenzo- triazolo-(1,2-a) benzotriazole triazoJo-(2,1-a)benzo- benzophenone 5-dinitro-pyridine TACOT) triazoJe stilbene (PADP) {DPEHN) picrylbenzotriazole Hexanitroazo- biphenyl benzene {PENCO) ~Dipicrarnide)

{BTX)

,3,

1,3,8,10- 1,3,8- 1,3,6,8-

2,2' 1 Dipentaerythritol- 2,2',4,4',6-Pentanitro- 5,7-Dinitro-1- 2,6-Bis(picrylazo 2,2'

2,2',4,4',6,6'- Diarninohexanitro-

6

12 8

0

0 0

3

8

8

N

N N

5

4 4

H

H H

10

12

12

CIOHI6N6019 C CI2H4N60,2 CIOH4N408 C,2H4Ns0s

C C,2H4NsO,o C

C,4H6N6012 C,2H6Ns0,2 C,7HsN,3016 C,3HsNsO" "'

w

~

r:::r

N >-l 0\

(;"

4

4

4

4

4

4

4

4 2

4

4

4

(#)

Ref.

(m/s)

Gurney

2210

2400

2537

2427

2267

2608

2625

2699

2242

2212

2785

Constant

(%TNT)

Strength

Explosive

101b

106b

113b 86b

82b

98b

120b

127b

114b

69b 8lb

40t

)

0

(J/g)

-f1H,

2365

12451

11999

12140

( 13610

12036

12480

12329

14738

12421

12291

73.73

+7.77

130.38

170.35

(!iEJ)

263.01

-42.56

-30.95

+

(kJ/mol)

+

+ -248.73

+ +447.69

+532.88

+846.64

-201.21

)

3

1.79

1.75

1.80

1.80

1.88

1.78

1.30

1.78 1.81

1.67

1.81

4.8

(g/cm

Density

Tm

(Oe)

(d)

-163.64

30

F.M.

847

590

665 759

803 635

291

874

711

846

902

(g/mol)

)-

)-

)-

)-

'

111

,6"-

)-

,4",4

,6,6',6"-

,6,6'

(BisHNAB)

-Dodeca-

,4"

Name

oxide

,4,4'

Tris(picrylamino

Tris(picrylamino

Tris(picrylamino

Tripicrylbenzene

Bis(picrylamino

,2"

,2",2"',4,4'

1

3,5-dinitropyridine

Octanitroterphenyl

s-nitropyrimidine

2,4,6-trinitrobenzene

Nonanitroterphenyl

s-triazine

(TPB)

(NONA) hexanitrobiphenyl 6,6',6",6"' bis(phenylazo (ONT) biphenyl

(ABH)

nitro-m,m'-

quatraphenyl

1,3-

2,4,6-

2,4,6-

2,2',2",4,4',4"

2,4,6-

1,3,5-

2,2'

Leadazide

Nitric

Azobis(2,2',4,4',6,6')- 2,2

Dodecanitro-3,3-

18

0

(Contd.)

15Ü2o

15Ü22

14Ü24

16024

12024 9

N

Formula

5

H7Nll01s

H

H6Ns016

Pb

8

6

18

18

C23H9N

C

C21H9N1s01s C22H9N

C1

TableI NO N

C24H9N901B C

C24H6N

C24H6N

C24H5N >-) w N ö -.1 "' cr' "'

3 2 3 4 4 3 2 4

I

4 3 4 4 4

(#) Ref.

-

-

--

2769 2843 2979 2908 2727 2801

(m/s) 3033 2815 2965 2342 2970

Gurney

(Note3)

Constant

lOt

149b 109a

116a,

130t,

158b, 122t,

130m, 135m,

130m,

140p

122m

50m,

Strength (%TNT)

Explosive

133p 123t 126p, 115p 132p,

156b, 108p !60p

105s, 142b 133m, 159b, 112u, 143b, 157b, 17s, 160b,

153b, 115m, 117b 167b 126m,

93s

- -

-

5197 5080

(J/g)

11432 !2823 10717 12361

12335 10217 12161 11176 10735

(-öH;)

81.31

-

-

(t.E[)

+22.62

+52.88 +67.38

+24.48

+16.40 -3Ll4 + -24.54 -65.71

-357.86

-362.66 (kJfmol)

)

3

1.63 1.743 1.60 1.65 1.66 1.713

1.65 1.83 1.65 1.767 1.809

(gjcm

Density

85

-

100 100 100

288

347 275 100 100 100

329 388

F.M.

(gjmol)

Assigned

oil

sebacate/

RDX/Di-

Diesel

/Plasticizers

2

fPETN

#

Potassium

HMXjTNT

HMX/ESTANE

RDXfTNT RDXfTNT Composition

Ammonium

HMXjESTANE RDXfBINDER TNT

Ammonium

RDXfWAX

Nitrocellulose/

nitrate/Carbon/Sulfur nitrate/ nitrate/TNT Polyisobutylene/Motor Oil (2-ethylhexyl)

5702-FI

Diphenylamine

RDXfTNT

75/15/10 91/5.3/2.1/1.6 75/15/10 94/6 64/36 77/23 80/20 91/9

99/1

86/14 50/50 90/10 76.3/23.7 95.5/4.5

sJ

1

so.31

o.4o

t

14.1

mixtures

o2.s1

.6so09.3oo

1.29303.219

Formula

.••

N6.s760,.

2

N5.3.o

713N2.ooo03.ooo

1soN,

.461

7

o.ooN9.2oO

>.s•N

t

Ha.

explosive

Apparent

Co.J6sH4. Co.62H<.<.s> C1.s1H>. ci.2,KI..2 C1.s2H C6.sst Cs.o4sH, -

Ct.96aH3.746N2.3S602.474 C2.332H2.366N c.H1N2.s01o Cs.696Hto.476Ns.o620s.ss9 C6.aoH C1.s2H2.92N2.soÜ2.66

Name

Mixtures

Nonaluminized

POWDER

POWDER

1.

BLACK COMP.A-3 ANFO AMATOL COMP.B-3 B. CYCLOTOL COMP.C-4 DYNAMITE (MVD)

PBXC-116 LX-14 PENTOLITE PBX-9011 SMOKELESS OCTOL "'

...., cr' Pl

N 00 (b

VJ

by

4

4 4 4 4 4 4 4 4

4

name.

(#) Ref.

by

alphabetical

3}

is

-

1984

2500

2213

(m/s)

order

Gurney

(Note

alphabetical

Constant

is

the

Briefly,

107a

123a

102p

111m,

95p

120p,

arrangement

here.

93p,

11}.

Strength

the

(%TNT)

Explosive

124m,

116a,l59u 138m,

used

121b*,

127b* 125b*, !!Ob*, 128b* 136b*

138b* 93b* 89b*, 118b*,

is

reference

mixtures,

2,

Office

(J/g)

18947

19749 16973

17265 15600 17337

15508

18131 15691

20431

Patent

(~t..H~)

Chapter

explosive

U.S.

(see

For

the

~0.07

~2.95 ~0.48

~4.33

~7.90 +2.89

136.84

(t..E/} ~27.91

~56.77

~23.22

present.

LaRocca

~

(kJ/mol)

is

of

)

Abstractsand

3

method

hydrogen

1.88

1.68 1.80 1.81 1.71 1.75 1.72 1.72 1.77

1.81

if

the

(g/cm

Density

by

Chemical

"H"

by

1979

by

used

are:

100

100 100 100 100 100 100 100

100

327

F.M.

as

calculated

(gjmol}

Assigned

follows:

are

California,

as

immediately

is

references

others

key

compounds

AX

Berkeley, All

These

followed

The

Al(W

used.

first,

AX/

Press,

/

chemical

for

da.ta

explosives.

RDX/TNT/Al

1977

Al/BINDER

comes

1981

for

Composition

(1949)

determination.

RDX/TNT GRAPHITE RDX/TNT/Al(WAX RDX/ TNT/Al/W RDX/TNT/Al(WAX RDX/TNT/Al(WAX

RDXjTNT/Al(WAX RDX/Al/NYLON

ofCalifornia

of

always

March

January,

37.4/27.8/30.8/4

74.8/18.7/4.7/1.8

31/29/35/5

71/17/12 44/32.2/19.8/4 80/20TNT/Al 68/20/12 45/30/20/5

40/38/17/5

42/40/18

aluminized

419·45

reference

"C"

22,478 (1900))

for

44.

s

mcthod

o

706-177.

University

the

1.975

t.6oJ

z.os

6.431 (JACS

primary

symbol

01.744

Üz.oJ9

Üz.o4s to

0

Üz.ooo Oz.t91

reported

6

Reviews,

UCRL-52997.

the

tbe

AMCP

are

refer

system

t.J6s

t.6t3

t.946

t.zzoÜ

t.sa Lo6o0z.tt 1.663

I.6tt

6.4310

No.9asÜ

N N

N N N

N N N

data

conditions)

Formula

Chemical

sJo 341

76oN

designate

ofDetonations,

t.

2.

Handbook.

constant

indexing Pamphlet

compounds,

conditions)

Hz.JI2

H H9.

Hz.ss9

H

row

mixtures

7Hz.o93

Hill

791

Strength

AMC

each

Gurney

carbon

Handrick,

Cl.64

Apparent CI.s7JH2.469 Cz.

Modelling Cz.o6s C2.46s C4.s9z

C1.sss

(fireball (detonation

of

Explosives

R.

for

tbe

734

741

modified

G.

end

of

Explosive

that

explosive

Alo.693 Alo.

A1t.t4z

A11.29sCt.669Hz.ts9 the Alo.6JoCI.6soHJ.tJs test

Alo.6Jo Alo. Alz.4zz

Alo.74z Alo.667ct.sooHz.ots

the

LLNL

blast

Command,

and

test

the

test

at

Numerical

calculation

calculation

values

mortar

except

block

dent

crush

cited

Lothrop Material

materials,

Dobratz,

Mader,

following

C.

Bertbelot

Airblast Underwater Bertbelot Sand Ballistic Plate

Trauzl

L.

M.

measured

symbol,

pure

=

= = = =

= =

=

W. Anny

B. C.

Name

Aluminized

I.

a

2.

3.

4.

Letters b u b* References m p Only For

PBXC-117 DESTEX HBX-1 ALEX-20 PBXN-1 HBX-3 ALEX-32 H-6 2.

1.

TORPEX

TRITONAL

element

NOTES: 2. 3.

4. Tables 239

Table II (Part I) Safety distances for inhabited buildings and public traffic ways*

Safety Distance, metres Mass of Explosives, kg Inhabited Buildings Public Traffic Ways

Not Frag. Chem. Frag. Chem. Over Over Mun. Explo. Mun. Explo.

0 20 380 21 230 13 20 25 380 24 230 14 25 30 380 26 230 16 30 35 380 28 230 17 35 40 380 30 230 19 40 50 380 34 230 21 50 60 380 38 230 23 60 70 380 41 230 25 70 80 380 45 230 27 80 90 380 48 230 29 90 100 380 50 230 30 100 120 380 56 230 33 120 140 380 60 230 36 140 160 380 66 230 39 160 180 380 70 230 42 180 200 380 74 230 44 200 250 380 84 230 50 250 300 380 92 230 56 300 350 380 100 230 60 350 400 380 110 230 64 400 500 380 120 230 74 500 600 380 135 230 80 600 700 380 145 230 88 700 800 380 160 230 94 800 900 380 170 230 100 900 1000 380 180 230 105 1000 1200 380 200 230 120 1200 1400 380 215 230 130 1400 1600 380 230 230 140 1600 1800 380 245 230 145 1800 2000 380 250 230 150 2000 2500 380 270 230 165 2500 3000 380 290 230 175 3000 3500 380 300 230 180 3500 4000 380 320 230 190 4000 5000 380 340 230 205 5000 6000 380 360 230 220 6000 7000 380 380 230 230 7000 8000 400 400 240 240 8000 9000 420 420 250 250 9,000 10,000 430 430 260 260 10,000 12,000 460 460 270 270 12,000 14,000 480 480 290 290 240 Tables

Table II, Part I (Contd.)

Safety Distance, metres Mass of Explosives, kg Inhabited Buildings Public Traffic Ways

Not Frag. Chem. Frag. Chem. Over Over Mun. Explo. Mun. Explo.

14,000 16,000 500 500 300 300 16,000 18,000 520 520 310 310 18,000 20,000 540 540 330 330 20,000 25,000 580 580 350 350 25,000 30,000 620 620 370 370 30,000 35,000 660 660 390 390 35,000 40,000 680 680 410 410 40,000 50,000 740 740 440 440 50,000 60,000 780 780 470 470 60,000 70,000 820 820 490 490 70,000 80,000 860 860 520 520 80,000 90,000 900 900 540 540 90,000 100,000 920 920 560 560 100,000 120,000 980 980 600 600 120,000 140,000 1050 1050 620 620 140,000 160,000 1100 1100 660 660 160,000 180,000 1150 1150 680 680 180,000 200,000 1150 1150 700 700 200,000 250,000 1250 1250 760 760 250,000 300,000 1350 1350 800 800 300,000 350,000 1400 1400 840 840 350,000 400,000 1450 1450 880 880 400,000 500,000 1600 1600 960 960 500,000 600,000 1700 1700 1000 1000 600,000 700,000 1800 1800 1050 1050 700,000 800,000 1850 1850 1100 1100 800,000 900,000 1950 1950 1150 1150 900,000 1,000,000 2000 2000 1200 1200 1,000,000 1,200,000 2150 2150 1300 1300 1,200,000 1,400,000 2250 2250 1350 1350 1,400,000 1,600,000 2350 2350 1400 1400 1,600,000 1,800,000 2450 2450 1450 1450 1,800,000 2,000,000 2500 2500 1500 1500 2,000,000 2,500,000 2700 2700 1650 1650 2,500,000 3,000,000 2900 2900 1750 1750 3,000,000 3,500,000 3000 3000 1800 1800 3,500,000 4,000,000 3200 3200 1900 1900 4,000,000 5,000,000 3400 3400 2050 2050 5,000,000 6,000,000 3600 3600 2200 2200 6,000,000 7,000,000 3800 3800 2300 2300

*Taken frorn tentative and abbreviated rnetric tables of NWC Technical Report TP 6277, Naval Weapons Center, China Lake, California (1981). Tables 241

Table II (Part II) Safety distances; intraline and magazine separation*

Safety Distance, metres Mass of Explosives, kg Intraline Magazine Separation

Not Earth Not Earth Over Over Bar. Unbar. Covered Covered

0 50 6 13 1 6 50 60 7 14 1 6 60 70 7 15 1 6 70 80 8 16 1 6 80 100 9 18 1 6 100 125 10 21 1 7 125 150 12 23 2 8 150 175 13 25 2 8 175 200 14 27 2 9 200 250 15 30 2 10 250 300 17 33 2 11 300 350 18 36 3 12 350 400 20 39 3 13 400 500 22 44 3 15 500 600 25 49 3 16 600 700 26 52 4 18 700 800 28 56 4 19 800 1,000 32 64 5 22 1,000 1,250 36 72 5 24 1,250 1,500 40 80 6 27 1,500 1,750 43 86 6 29 1,750 2,000 45 90 6 30 2,000 2,500 49 98 7 33 2,500 3,000 52 105 7 35 3,000 3,500 54 110 8 36 3,500 4,000 58 115 8 38 4,000 5,000 62 125 9 41 5,000 6,000 66 130 9 44 6,000 7,000 68 140 10 46 7,000 8,000 72 145 10 48 8,000 10,000 78 155 11 52 10,000 12,500 84 165 12 56 12,500 15,000 88 180 13 60 15,000 17,500 94 185 13 62 17,500 20,000 98 195 14 66 20,000 25,000 105 210 15 70 25,000 30,000 110 225 16 74 30,000 35,000 120 235 17 78 35,000 40,000 125 245 17 82 40,000 50,000 135 270 19 88 50,000 60,000 140 280 20 94 60,000 70,000 150 300 21 98 70,000 80,000 155 310 22 105 80,000 100,000 165 330 23 110 100,000 125,000 180 360 25 120 242 Tables

Table II, Part II (Contd.)

Safety Distance, metres Mass of Explosives, kg Intraline Magazine Separation

Not Earth Not Earth Over Over Bar. Unbar. Covered Covered

125,000 150,000 190 380 27 130 150,000 175,000 200 400 28 135 175,000 200,000 210 420 29 140 200,000 250,000 225 450 31 150 250,000 300,000 240 480 33 160 300,000 350,000 250 500 35 170 350,000 400,000 270 540 37 175 400,000 500,000 290 580 40 190 500,000 600,000 300 600 42 200 600,000 700,000 320 640 44 215 700,000 800,000 330 660 46 225 800,000 1,000,000 360 720 50 240 1,000,000 1,250,000 390 780 54 260 1,250,000 1,500,000 410 820 58 270 1,500,000 1,750,000 430 860 60 290 1,750,000 2,000,000 450 900 62 300 2,000,000 2,500,000 490 980 68 330 2,500,000 3,000,000 72 350 3,000,000 3,500,000 76 360 3,500,000 4,000,000 80 380 4,000,000 5,000,000 86 410 5,000,000 6,000,000 90 440 6,000,000 7,000,000 96 460

*Taken from tentative and abbreviated metric tables of NWC Technical Report TP 6277, Naval Weapons Center, China Lake, California (1981). Tables 243

Table 111 Probability of occurrence of deviations

Ratio of Actual Deviation to Standard Probability of Odds Against, Deviation Occurrence to One

0.675 0.500 1 0.8 0.424 1.36 1.0 0.317 2.15 1.2 0.230 3.35 1.4 0.162 5.19 1.6 0.110 8.12 1.8 0.072 12.9 2.0 0.0455 21.0 2.5 0.0124 80 3.0 0.0027 370 3.5 0.00046 2150 4.0 0.000063 15,770 5.0 0.00000057 1,744,000 6.0 2 x w- 9 5 X 108 7.0 2.6 x w-12 3.9 X 10 11

Table IV Thermodynamic properties of products of explosions (25 °C, 1.01325 bars)

Species State• t..Ej so t..H}

AlF3 c -1506.7 66.5 -1510.4 Al 2 0 3 c -1672.0 50.9 -1675.7 Bz03 c -1266.7 53.9 -1270.4 BaO c -546.9 72.1 -548.1 C (graphite) 0 5.7 0 K 2 C03 c -1146.5 155.5 -1150.2 Na2 C03 c -1127.1 138.8 -1130.8 CO -111.8 197.5 -110.5 C02 -393.5 213.7 -393.5 CaO ~; -633.9 38.2 -635.1 HCl g -92.3 186.8 -92.3 KCl c -435.4 82.6 -436.7 HF c -272.5 173.7 -272.5 Hz g 0 130.6 0 H 2 0 g -240.6 188.7 -241.8 H20 -282.1 69.9 -285.8 K20 -361.9 94.1 -363.2 Nz 0 191.5 0 02 0 205.0 0 S02 i! -296.8 248.1 -296.8 •(g), gaseous; (1), liquid; (s), solid; (c), crystalline; ö.E[ standard internal energy of forrnation, kilojoules per mole; so standard (absolute) entropy, joules per rnole-kelvin; ö.HJ standard enthalpy of forrnation, kilojoules per rnole. Based on values frorn Stull, D. R., and Prophet, H., (eds), JANAF Thermochemical Tab/es, Second Edition, National Bureau ofStandards Report NSRDS-NBS 37, U.S. Dept ofCornrnerce, Washington, D.C., June 1971. 244 Tables

Table V Group substitution approximations

Change in Interna! Energy Change in of Formation Entropy Part A: Hypothetical Transmutations kifmal Jjmoi-K

Substitute -CH3 for -H, aliphatic 20 20 Substitute -CH3 for -H, aromatic 10 25 Remave 2 - H to form double band 80 0 Remave 4 - H to form triple band 300 -30 Substitute -C6 H 5 for -H 190 70 Substitute -OH for -H to form an alcohol -150 0 Substitute -OH for -H to form a phenol -170 4 Insertion of -0- linkage to form an ether -85 0 Insertion of -C0-0- to form an ester -300 20 Substitute-CHO for -H to form an aldehyde -85 25 Substitute -0 for 2 -H to form a ketone -125 4 Substitute -COOH for -H to form an acid -350 25 Substitute -NH2 for -H to form an amine 0 0 Substitute -CN for -CH3 to form nitrile 150 50 Substitute -Cl for -H 0 25 Substitute-S- for -0- to form thioether 150 8 Substitute -N02 for -H, aliphatic -40 30 Substitute -N02 for -H, aromatic, first -85 35 Substitute -N02 for -H, aromatic, other than 1st 0 30 Substitute -N02 for -Hof amine to form nitramine 60 20 Substitute -ON02 for -H, to form nitrate ester -85 25 Substitute -ON02 for -OH to form nitrite ester 100 20 Add HN0 3 to formnitratesalt of an amine -300 30 Substitute -NH-N02 for -H to form nitramine 60 20

Interna! Energy of Formation Entropy Part B: Basic Compounds kifmal I/mol-K

Normalparaffin hydrocarbons, CnHzn+z (liquid) -38- 23(n) 105 + 32(n) (solid) -25- 28(n) 75 + 23(n) Benzene, C 6 H 6 (liquid) 56 180 (solid, hypothetical) 47 145 Tables 245

Table VI Entropy of mixing*

Mole Entropy of Mixing, Jjmol-K Fraction y per Mole of Component per Mole of Mixture

0.05 24.908 1.245 0.10 19.144 1.914 0.15 15.773 2.366 0.20 13.381 2.676 0.25 11.526 2.882 0.30 10.010 3.003 0.35 8.729 3.055 0.40 7.618 3.047 0.45 6.639 2.988 0.50 5.763 2.882 0.55 4.971 2.734 0.60 4.247 2.548 0.65 3.582 2.328 0.70 2.966 2.076 0.75 2.392 1.794 0.80 1.855 1.484 0.85 1.351 1.149 0.90 0.876 0.788 0.95 0.426 0.405 1.00 0.000 0.000

*Per mole of component gas: Smix = - Rm In y; per mole of mixture: Sm,, = - yRm In y, where y is the mole fraction of the component gas and Rm the molar gas constant, 8.31434 joules per mole-kelvin. 246 Tables

Table VII Properties of dry air at atmospheric pressure*

Speed of Sound at Constant Temperature Pressure Heat Capacity

Rate of oc Change Molar Specific Ratio K (rounded) mjs mj(s-K) Jjmol-K. Jjg-K cp/cv = k

200 -73 283.4 0.7 29.14 1.006 1.406 210 -63 290.5 0.7 29.14 1.006 1.405 220 -53 297.4 0.7 29.14 1.006 1.405 230 -43 304.1 0.7 29.14 1.006 1.404 240 -33 310.6 0.7 29.11 1.005 1.404 250 -23 317.1 0.7 29.11 1.005 1.404 260 -13 323.4 0.6 29.12 1.005 1.403 270 -3 329.6 0.6 29.13 1.006 1.403 280 +7 335.6 0.6 29.14 1.006 1.402 288.15 15 340.4 0.6 29.14 1.006 1.402 290 17 341.5 0.6 29.14 1.006 1.402 300 27 347.3 0.6 29.15 1.006 1.402 310 37 353.1 0.6 29.17 1.007 1.401 320 47 358.7 0.6 29.19 1.007 1.401 330 57 364.2 0.6 29.20 1.008 1.400 340 67 369.6 0.5 29.21 1.008 1.400 350 77 375.0 0.5 29.23 1.009 1.399 360 87 380.2 0.5 29.26 1.010 1.399 370 97 385.4 0.5 29.28 1.011 1.398 380 107 390.5 0.5 29.31 1.012 1.398 390 117 395.5 0.5 29.34 1.013 1.397 400 127 400.4 0.5 29.37 1.014 1.396

* Apparent formula mass: 28.966 gjmol. Gas law constant 8.31434/28.966 = 0.2870 Jjg-K. { nitrogen 78.09% Composition, mole oxygen 20.95% (volume) percent argon 0.93% carbon dioxide 0.03%. Note: Basedon heat capacity ratios given in Handbook ofTablesjor Applied Engineering Science, CRC Press, Inc., Cleveland, Ohio (1977) and credited to "Tables ofThermal Properties ofGases", National Bureau of Standards Circular 564 (1955). Tables 247

Table VIII Drag Coefficients•

BOOtES OF REVOLUTION

Cd Cd

SPHERE 0.10 CIRCULAR PLATE 1.17

HALF SPHERE •t 0.42 60° CONE ~ 0.5 HALF SPHERE t 1.42

STRUCTURAL SHAPES (LONG MEMBERS WITHOUT END EFFECTSI

Cd Cd Cd I 2.0 _j 1.8 ~ 1.55 r- 2.0 < 1 .45 ~ 2.0 --1 1.65 > 2.2 II 2.0 I 2.05 c 1.2 1.55 L 2.0 ) 2.3 • 1.05 1.2 -I 1.54

PROTUBERANGES (WITHOUT END EFFECTS)• • 0.80 1.03 1.20 • 1.00 1.25 1.28

• Flow direction from left to right. For high Reynolds numbers. 248 Tables

Table IX Air shock characteristics as dimensionless parameters

TP,- T" pdrag M" Py/P" ay/a" T.,/T" uP/a" P,/P" Pstag/Px T" CdPx

1.000 1.000 1.000 1.000 0.0000 0.000 1.00 1.000 0.000 1.005 1.012 1.002 1.003 0.0000 0.008 1.02 1.012 0.000 1.010 1.023 1.003 1.007 0.0000 0.017 1.05 1.024 0.000 1.015 1.035 1.005 1.010 0.0000 0.025 1.07 1.036 0.000 1.020 1.047 1.007 1.013 0.0000 0.033 1.10 1.048 0.001 1.025 1.059 1.008 1.017 0.0000 0.041 1.12 1.060 0.001 1.030 1.071 1.010 1.020 0.0000 0.049 1.15 1.073 0.002 1.035 1.083 1.011 1.023 0.0000 0.057 1.17 1.086 0.002 1.040 1.095 1.013 1.026 0.0000 0.065 1.20 1.098 0.003 1.045 1.107 1.015 1.030 0.0000 0.073 1.22 1.111 0.004 1.050 1.120 1.016 1.033 0.0000 0.081 1.25 1.125 0.005 1.055 1.132 1.018 1.036 0.0001 0.089 1.28 1.138 0.006 1.060 1.144 1.019 1.039 0.0001 0.097 1.31 1.151 0.007 1.065 1.157 1.021 1.043 0.0001 0.105 1.33 1.165 0.009 1.070 1.169 1.023 1.046 0.0001 0.113 1.36 1.179 0.010 1.075 1.182 1.024 1.049 0.0001 0.121 1.39 1.193 0.011 1.080 1.194 1.026 1.052 0.0002 0.128 1.42 1.207 0.013 1.085 1.207 1.027 1.055 0.0002 0.136 1.45 1.222 0.015 1.090 1.219 1.029 1.059 0.0002 0.144 1.48 1.236 0.017 1.095 1.232 1.030 1.062 0.0003 0.151 1.51 1.251 0.019 1.100 1.245 1.032 1.065 0.0003 0.159 1.54 1.266 0.021 1.105 1.258 1.033 1.068 0.0004 0.167 1.57 1.281 0.023 1.110 1.271 1.035 1.071 0.0004 0.174 1.60 1.296 0.025 1.115 1.284 1.037 1.074 0.0005 0.182 1.63 1.312 0.028 1.120 1.297 1.038 1.078 0.0005 0.189 1.67 1.327 0.030 1.125 1.310 1.040 1.081 0.0006 0.197 1.70 1.343 0.033 1.130 1.323 1.041 1.084 0.0006 0.204 1.73 1.359 0.036 1.135 1.336 1.043 1.087 0.0007 0.212 1.77 1.375 0.039 1.140 1.350 1.044 1.090 0.0008 0.219 1.80 1.392 0.042 1.145 1.363 1.046 1.093 0.0009 0.226 1.83 1.408 0.045 1.150 1.376 1.047 1.097 0.0009 0.234 1.87 1.425 0.048 1.155 1.390 1.049 1.100 0.0010 0.241 1.90 1.442 0.051 1.160 1.403 1.050 1.103 0.0011 0.248 1.94 1.459 0.055 1.165 1.417 1.052 1.106 0.0012 0.256 1.97 1.476 0.059 1.170 1.430 1.053 1.109 0.0013 0.263 2.01 1.494 0.062 1.175 1.444 1.055 1.112 0.0014 0.270 2.05 1.511 0.066 1.180 1.458 1.056 1.115 0.0016 0.277 2.08 1.529 0.070 1.185 1.472 1.058 1.119 0.0017 0.284 2.12 1.547 0.074 1.190 1.485 1.059 1.122 0.0018 0.291 2.16 1.566 0.079 1.195 1.499 1.061 1.125 0.0019 0.298 2.20 1.584 0.083 1.200 1.513 1.062 1.128 0.0021 0.306 2.24 1.603 0.088 1.205 1.527 1.064 1.131 0.0022 0.313 2.28 1.622 0.092 1.210 1.541 1.065 1.134 0.0024 0.320 2.32 1.641 0.097 1.215 1.556 1.066 1.137 0.0025 0.327 2.36 1.660 0.102 1.220 1.570 1.068 1.141 0.0027 0.334 2.40 1.680 0.107 1.225 1.584 1.069 1.144 0.002!! 0.341 2.44 1.699 0.112 1.230 1.598 1.071 1.147 0.0030 0.347 2.48 1.719 0.118 1.235 1.613 1.072 1.150 0.0032 0.354 2.52 1.739 0.123 1.240 1.627 1.074 1.153 0.0034 0.361 2.56 1.760 0.129 7;., = post-shock ternperature. Tables 249

Table IX (Contd.)

~s- Tx pdrag Mx Py/Px ayfax Ty/Tx uPfax P,/Px Pstag/Px Tx CdPx

1.245 1.642 1.075 1.156 0.0035 0.368 2.61 1.780 0.135 1.250 1.656 1.077 1.159 0.0037 0.375 2.65 1.801 0.141 1.255 1.671 1.078 1.163 0.0039 0.382 2.69 1.822 0.147 1.260 1.686 1.080 1.166 0.0041 0.389 2.74 1.843 0.153 1.265 1.700 1.081 1.169 0.0043 0.395 2.78 1.865 0.159 1.270 1.715 1.083 1.172 0.0046 0.402 2.83 1.887 0.166 1.275 1.730 1.084 1.175 0.0048 0.409 2.87 1.908 0.172 1.280 1.745 1.085 1.178 0.0050 0.416 2.92 1.931 0.179 1.285 1.760 1.087 1.181 0.0052 0.422 2.97 1.953 0.186 1.290 1.775 1.088 1.185 0.0055 0.429 3.01 1.975 0.193 1.295 1.790 1.090 1.188 0.0057 0.436 3.06 1.998 0.200 1.300 1.805 1.091 1.191 0.0060 0.442 3.11 2.021 0.208 1.310 1.835 1.094 1.197 0.0065 0.456 3.21 2.068 0.223 1.320 1.866 1.097 1.204 0.0070 0.469 3.30 2.116 0.238 1.330 1.897 1.100 1.210 0.0076 0.482 3.41 2.164 0.255 1.340 1.928 1.103 1.216 0.0082 0.495 3.51 2.214 0.272 1.350 1.960 1.106 1.223 0.0088 0.508 3.61 2.264 0.289 1.360 1.991 1.109 1.229 0.0095 0.521 3.72 2.316 0.307 1.370 2.023 1.111 1.235 0.0101 0.533 3.83 2.368 0.326 1.380 2.055 1.114 1.242 0.0108 0.546 3.94 2.422 0.346 1.390 2.087 1.117 1.248 0.0115 0.559 4.05 2.476 0.366 1.400 2.120 1.120 1.255 0.0123 0.571 4.17 2.532 0.386 1.410 2.153 1.123 1.261 0.0130 0.584 4.28 2.589 0.408 1.420 2.186 1.126 1.268 0.0138 0.596 4.40 2.646 0.429 1.430 2.219 1.129 1.274 0.0146 0.609 4.52 2.705 0.452 1.440 2.253 1.132 1.281 0.0155 0.621 4.65 2.765 0.475 1.45 2.2S6 1.135 1.287 0.016 0.634 4.77 2.83 0.50 1.46 2.320 1.137 1.294 0.017 0.646 4.90 2.89 0.52 1.47 2.354 1.140 1.300 0.018 0.658 5.03 2.95 0.55 1.48 2.389 1.143 1.307 0.019 0.670 5.16 3.01 0.57 1.49 2.423 1.146 1.314 0.020 0.682 5.29 3.08 0.60 1.50 2.458 1.149 1.320 0.021 0.694 5.43 3.15 0.63 1.51 2.493 1.152 1.327 0.022 0.706 5.56 3.21 0.66 1.52 2.529 1.155 1.334 0.023 0.718 5.70 3.28 0.69 1.53 2.564 1.158 1.340 0.024 0.730 5.84 3.35 0.71 1.54 2.600 1.161 1.347 0.025 0.742 5.99 3.42 0.74 1.55 2.636 1.164 1.354 0.026 0.754 6.13 3.50 0.78 1.56 2.673 1.166 1.361 0.027 0.766 6.28 3.57 0.81 1.57 2.709 1.169 1.367 0.029 0.778 6.43 3.64 0.84 1.58 2.746 1.172 1.374 0.030 0.789 6.58 3.72 0.87 1.59 2.783 1.175 1.381 0.031 0.801 6.74 3.80 0.90 1.60 2.820 1.178 1.388 0.032 0.813 6.89 3.88 0.94 1.61 2.857 1.181 1.395 0.033 0.824 7.05 3.96 0.97 1.62 2.895 1.184 1.402 0.035 0.836 7.21 4.04 1.01 1.63 2.933 1.187 1.409 0.036 0.847 7.38 4.12 1.05 1.64 2.971 1.190 1.416 0.037 0.859 7.54 4.20 1.08 1.65 3.010 1.193 1.423 0.039 0.870 7.71 4.29 1.12 1.66 3.048 1.196 1.430 0.040 0.881 7.88 4.37 1.16 1.67 3.087 1.199 1.437 0.041 0.893 8.05 4.46 1.20 1.68 3.126 1.202 1.444 0.043 0.904 8.22 4.55 1.24 Table IX (Contd.)

7;,.- T" Pdrag Mx P,/P" a,fax T,/Tx up/ax P,/Px pstag/Px T" CdPx

1.69 3.165 1.205 1.451 0.044 0.915 8.40 4.64 1.28 1.70 3.205 1.208 1.458 0.046 0.926 8.58 4.73 1.32 1.72 3.285 1.214 1.473 0.048 0.949 8.94 4.92 1.41 1.74 3.366 1.220 1.487 0.051 0.971 9.32 5.11 1.49 1.76 3.447 1.226 1.502 0.055 0.993 9.70 5.31 1.58 1.78 3.530 1.232 1.517 0.058 1.015 10.09 5.51 1.68 1.80 3.613 1.238 1.532 0.061 1.037 10.49 5.72 1.78 1.82 3.698 1.244 1.547 0.064 1.059 10.90 5.94 1.88 1.84 3.783 1.250 1.562 0.068 1.080 11.32 6.16 1.98 1.86 3.870 1.256 1.577 0.071 1.102 11.74 6.39 2.09 1.88 3.957 1.262 1.592 0.075 1.123 12.18 6.62 2.20 1.90 4.045 1.268 1.608 0.079 1.145 12.63 6.86 2.31 1.92 4.134 1.274 1.624 0.082 1.166 13.08 7.11 2.42 1.94 4.224 1.280 1.639 0.086 1.187 13.55 7.36 2.54 1.96 4.315 1.287 1.655 0.090 1.208 14.02 7.62 2.66 1.98 4.407 1.293 1.671 0.094 1.229 14.51 7.88 2.79 2.0 4.50 1.30 1.69 0.098 1.25 15.0 8.2 2.92 2.1 4.98 1.33 1.77 0.119 1.35 17.6 9.6 3.60 2.2 5.48 1.36 1.86 0.142 1.45 20.4 11.2 4.37 2.3 6.01 1.40 1.95 0.167 1.55 23.5 13.0 5.22 2.4 6.55 1.43 2.04 0.192 1.65 26.8 15.0 6.14 2.5 7.13 1.46 2.14 0.220 1.75 30.4 17.2 7.15 2.6 7.72 1.50 2.24 0.248 1.85 34.2 19.6 8.23 2.7 8.34 1.53 2.34 0.278 1.94 38.2 22.1 9.39 2.8 8.98 1.57 2.45 0.309 2.04 42.5 24.9 10.63 2.9 9.65 1.60 2.56 0.341 2.13 47.0 27.8 11.94 3.0 10.33 1.64 2.68 0.375 2.22 51.7 31.0 13.33 3.1 11.05 1.67 2.80 0.409 2.31 56.6 34.3 14.80 3.2 11.78 1.71 2.92 0.444 2.41 61.8 37.9 16.34 3.3 12.54 1.75 3.05 0.480 2.50 67.2 41.6 17.95 3.4 13.32 1.78 3.18 0.518 2.59 72.8 45.6 19.64 3.5 14.13 1.82 3.32 0.556 2.68 78.6 49.7 21.40 3.6 14.95 1.86 3.45 0.595 2.77 84.7 54.1 23.23 3.7 15.81 1.90 3.60 0.634 2.86 90.9 58.6 25.13 3.8 16.68 1.93 3.74 0.675 2.95 97.4 63.4 27.10 3.9 17.58 1.97 3.89 0.716 3.04 104.1 68.3 29.14 4.0 18.50 2.01 4.05 0.758 3.13 111.0 73.4 31.25 4.1 19.45 2.05 4.20 0.801 3.21 118.1 78.7 33.43 4.2 20.41 2.09 4.37 0.845 3.30 125.4 84.2 35.67 4.3 21.41 2.13 4.53 0.889 3.39 133.0 89.9 37.98 4.4 22.42 2.17 4.70 0.934 3.48 140.7 95.8 40.36 4.5 23.46 2.21 4.88 0.979 3.56 148.6 101.9 42.80 4.6 24.52 2.25 5.05 1.025 3.65 156.8 108.1 45.31 4.7 25.61 2.29 5.23 1.072 3.74 165.1 114.6 47.89 4.8 26.71 2.33 5.42 1.120 3.83 173.7 121.2 50.53 4.9 27.85 2.37 5.61 1.168 3.91 182.4 128.0 53.23 5.0 29.00 2.41 5.80 1.216 4.00 191.4 135.0 56.00 5.1 30.18 2.45 6.00 1.265 4.09 200.6 142.1 58.83 5.2 31.38 2.49 6.20 1.315 4.17 209.9 149.5 61.73 5.3 32.61 2.53 6.40 1.365 4.26 219.5 157.0 64.69 5.4 33.85 2.57 6.61 1.416 4.35 229.2 164.7 67.71 TableX Shock in dry air at 15 oc and 1.01325 bars

Po ux uP T, ay Pref Pstag Pdrag/Cd bar Mx m/s m/s oc m/s bar bar bar

0.000 1.000 340 0 15 340 0.000 0.000 0.000 0.010 1.004 342 2 16 341 0.020 0.010 0.000 0.020 1.008 343 5 17 341 0.040 0.020 0.000 0.030 1.013 345 7 17 342 0.061 0.030 0.000 0.040 1.017 346 9 18 342 0.081 0.041 0.001 0.050 1.021 348 12 19 343 0.102 0.051 0.001 0.060 1.025 349 14 20 343 0.123 0.061 0.001 0.070 1.029 350 16 21 344 0.144 0.072 0.002 0.080 1.033 352 19 21 344 0.165 0.082 0.002 0.090 1.037 353 21 22 345 0.187 0.093 0.003 0.100 1.041 355 23 23 345 0.208 0.103 0.003 0.110 1.045 356 25 24 345 0.230 0.114 0.004 0.120 1.050 357 27 24 346 0.252 0.125 0.005 0.130 1.054 359 30 25 346 0.274 0.136 0.006 0.140 1.058 360 32 26 347 0.296 0.147 0.007 0.150 1.062 361 34 27 347 0.319 0.158 0.008 0.160 1.066 363 36 27 348 0.341 0.169 0.009 0.170 1.069 364 38 28 348 0.364 0.180 0.010 0.180 1.073 365 40 29 348 0.387 0.191 0.011 0.190 1.077 367 42 30 349 0.410 0.202 0.012 0.200 1.081 368 44 30 349 0.433 0.214 0.014 0.210 1.085 369 46 31 350 0.456 0.225 0.015 0.220 1.089 371 48 32 350 0.480 0.237 0.017 0.230 1.093 372 50 32 351 0.503 0.248 0.018 0.240 1.097 373 53 33 351 0.527 0.260 0.020 0.250 1.101 375 55 34 351 0.551 0.271 0.021 0.260 1.105 376 56 35 352 0.575 0.283 0.023 0.270 1.108 377 58 35 352 0.599 0.295 0.025 0.280 1.112 379 60 36 353 0.624 0.307 0.027 0.290 1.116 380 62 37 353 0.648 0.319 0.028 0.300 1.120 381 64 37 353 0.673 0.331 0.030 0.310 1.123 382 66 38 354 0.698 0.343 0.032 0.320 1.127 384 68 39 354 0.723 0.355 0.035 0.330 1.131 385 70 39 355 0.748 0.367 0.037 0.340 1.135 386 72 40 355 0.773 0.379 0.039 0.350 1.138 388 74 41 355 0.799 0.392 0.041 0.360 1.142 389 76 41 356 0.824 0.404 0.043 0.370 1.146 390 77 42 356 0.850 0.416 0.046 0.380 1.150 391 79 43 356 0.876 0.429 0.048 0.390 1.153 393 81 43 357 0.902 0.441 0.051 0.400 1.157 394 83 44 357 0.928 0.454 0.053 0.410 1.161 395 85 45 358 0.954 0.467 0.056 0.420 1.164 396 87 45 358 0.981 0.480 0.059 0.430 1.168 398 88 46 358 1.007 0.492 0.061 0.440 1.171 399 90 47 359 1.034 0.505 0.064 0.450 1.175 400 92 47 359 1.061 0.518 0.067 0.460 1.179 401 94 48 359 1.088 0.531 0.070 0.470 1.182 402 95 49 360 1.115 0.544 0.073 0.480 1.186 404 97 49 360 1.143 0.557 0.076 0.490 1.189 405 99 50 360 1.170 0.571 0.079 TableX (Contd.)

p• ux uP Yy aY Pref Pstag Pdrag/Cd bar Mx mfs mfs oc mfs bar bar bar

0.500 1.193 406 101 51 361 1.198 0.584 0.082 0.520 1.200 408 104 52 362 1.253 0.611 0.089 0.540 1.207 411 107 53 362 1.309 0.638 0.096 0.560 1.214 413 111 54 363 1.366 0.665 0.102 0.580 1.221 416 114 56 364 1.423 0.692 0.110 0.600 1.228 418 117 57 364 1.481 0.720 0.117 0.620 1.235 420 120 58 365 1.539 0.748 0.125 0.640 1.242 423 124 59 366 1.598 0.776 0.132 0.660 1.248 425 127 61 366 1.657 0.805 0.140 0.680 1.255 427 130 62 367 1.717 0.833 0.149 0.700 1.262 430 133 63 368 1.777 0.862 0.157 0.720 1.268 432 136 64 368 1.838 0.892 0.166 0.740 1.275 434 139 65 369 1.899 0.921 0.175 0.760 1.282 436 142 67 370 1.961 0.951 0.184 0.780 1.288 439 145 68 370 2.024 0.981 0.193 0.800 1.295 441 148 69 371 2.087 1.011 0.203 0.820 1.301 443 151 70 372 2.150 1.041 0.212 0.840 1.308 445 154 71 372 2.214 1.072 0.222 0.860 1.314 447 157 73 373 2.278 1.103 0.232 0.880 1.321 450 160 74 374 2.343 1.134 0.243 0.900 1.327 452 163 75 374 2.408 1.166 0.253 0.920 1.334 454 166 76 375 2.474 1.197 0.264 0.940 1.340 456 168 77 375 2.540 1.229 0.275 0.960 1.346 458 171 78 376 2.607 1.261 0.286 0.980 1.352 460 174 80 377 2.674 1.294 0.297 1.000 1.36 462 177 81 377 2.74 1.33 0.309 1.050 1.37 468 183 84 379 2.91 1.41 0.338 1.100 1.39 473 190 86 380 3.09 1.49 0.369 1.150 1.40 478 196 89 382 3.26 1.58 0.401 1.200 1.42 483 203 92 383 3.44 1.67 0.434 1.250 1.43 488 209 95 385 3.62 1.75 0.468 1.300 1.45 493 215 98 386 3.81 1.84 0.503 1.350 1.46 498 221 100 388 4.00 1.94 0.540 1.400 1.48 503 227 103 389 4.18 2.03 0.577 1.450 1.49 508 233 106 390 4.38 2.12 0.615 1.500 1.51 513 239 108 392 4.57 2.22 0.655 1.550 1.52 517 245 111 393 4.77 2.31 0.695 1.600 1.53 522 250 114 394 4.97 2.41 0.736 1.650 1.55 527 256 117 396 5.17 2.51 0.779 1.700 1.56 532 261 119 397 5.37 2.61 0.822 1.750 1.57 536 267 122 399 5.58 2.72 0.866 1.800 1.59 541 272 124 400 5.79 2.82 0.911 1.850 1.60 545 277 127 401 6.00 2.93 0.957 1.900 1.61 550 282 130 402 6.21 3.03 1.004 1.950 1.63 554 287 132 404 6.42 3.14 1.051 2.000 1.64 558 293 135 405 6.64 3.25 1.100 2.100 1.67 567 302 140 408 7.08 3.47 1.199 2.200 1.69 576 312 145 410 7.53 3.70 1.302 2.300 1.72 584 322 150 413 7.98 3.93 1.408 2.400 1.74 593 331 156 415 8.44 4.17 1.517 TableX (Contd.)

p• Ux uP r;, ay Pref Pstag Pdrag/Cd bar Mx m/s m/s oc m/s bar bar bar

2.500 1.76 601 340 161 418 8.91 4.42 1.629 2.600 1.79 609 349 166 420 9.38 4.67 1.744 2.700 1.81 617 358 171 423 9.87 4.92 1.861 2.800 1.84 625 366 176 425 10.35 5.18 1.981 2.900 1.86 633 374 181 427 10.85 5.44 2.104 3.000 1.88 640 383 186 430 11.35 5.71 2.229 3.100 1.90 648 391 191 432 11.86 5.98 2.357 3.200 1.93 655 399 196 434 12.37 6.26 2.487 3.300 1.95 663 407 201 437 12.89 6.54 2.620 3.400 1.97 670 414 206 439 13.41 6.82 2.754 3.500 1.99 677 422 211 441 13.94 7.11 2.891 3.600 2.01 685 430 216 443 14.47 7.41 3.030 3.700 2.03 692 437 221 446 15.01 7.71 3.171 3.800 2.05 699 444 226 448 15.55 8.01 3.314 3.900 2.07 706 451 231 450 16.10 8.32 3.459 4.000 2.09 713 458 235 452 16.65 8.63 3.61 4.100 2.11 720 465 240 454 17.21 8.95 3.75 4.200 2.13 726 472 245 457 17.77 9.26 3.91 4.300 2.15 733 479 250 459 18.34 9.59 4.06 4.400 2.17 740 486 255 461 18.91 9.92 4.21 4.500 2.19 746 493 260 463 19.48 10.25 4.37 4.600 2.21 753 499 265 465 20.06 10.58 4.52 4.700 2.23 759 506 270 467 20.64 10.92 4.68 4.800 2.25 766 512 275 469 21.22 11.26 4.84 4.900 2.27 772 518 279 471 21.81 11.61 5.01 5.000 2.29 778 525 284 473 22.40 11.96 5.17 5.200 2.32 791 537 294 478 23.60 12.66 5.50 5.400 2.36 803 549 304 482 24.80 13.39 5.84 5.600 2.40 815 561 313 486 26.02 14.12 6.18 5.800 2.43 827 573 323 490 27.26 14.87 6.52 6.000 2.46 839 584 333 494 28.50 15.63 6.87 6.200 2.50 851 595 342 498 29.75 16.40 7.23 6.400 2.53 862 606 352 501 31.01 17.18 7.59 6.600 2.57 873 617 362 505 32.29 17.98 7.95 6.800 2.60 885 628 371 509 33.57 18.78 8.32 7.000 2.63 896 638 381 513 34.86 19.60 8.69 7.200 2.66 906 649 391 517 36.16 20.43 9.07 7.400 2.69 917 659 400 520 37.47 21.27 9.45 7.600 2.73 928 669 410 524 38.79 22.11 9.83 7.800 2.76 938 679 419 528 40.11 22.97 10.21 8.000 2.79 949 689 429 531 41.44 23.83 10.60 8.200 2.82 959 698 439 535 42.78 24.71 10.99 8.400 2.85 969 708 448 539 44.13 25.59 11.39 8.600 2.88 979 717 458 542 45.48 26.48 11.78 8.800 2.91 989 727 467 546 46.84 27.38 12.18 9.000 2.93 999 736 477 549 48.20 28.29 12.58 9.200 2.96 1009 745 487 553 49.57 29.20 12.99 9.400 2.99 1018 754 496 556 50.95 30.13 13.39 9.600 3.02 1028 763 506 560 52.33 31.06 13.80 9.800 3.05 1038 772 515 563 53.71 32.00 14.21 254 Tables

Table XI Reference explosions, chemical and nuclear Part A: Chemical (one kilogram TNT in air at 15 oc and 1.01325 bars)

z ta

0.053 21.16 528.3 0.000 0.10 16.70 328.6 0.007 13500 7.777 5.72 0.15 13.65 219.0 0.017 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 0.290 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 0.118 3830 0.095 1.09 0.50 5.83 39.0 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 4.60 23.9 0.227 2870 0.144 1.05 0.70 4.29 20.6 0.260 2700 0.191 1.04 0.75 4.02 18.0 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 1.00 0.95 3.21 11.0 0.459 2070 0.471 0.99 0.952 3.200 10.924 0.461 2067 0.473 0.993 4.0 1.00 3.05 9.83 0.506 1980 0.520 1.015 3.71 1.05 2.91 8.84 0.555 1890 0.565 1.039 3.46 1.10 2.78 7.98 0.606 1820 0.608 1.053 3.24 1.15 2.67 7.23 0.660 1740 0.647 1.058 3.03 1.20 2.56 6.57 0.716 1680 0.685 1.057 2.85 1.25 2.46 6.00 0.774 1620 0.720 1.051 2.68 1.30 2.38 5.49 0.834 1560 0.755 1.041 2.53 1.35 2.29 5.04 0.897 1510 0.788 1.028 2.40 1.40 2.22 4.64 0.962 1460 0.820 1.013 2.27 1.50 2.08 3.96 1.098 1370 0.882 0.980 2.05 1.60 1.97 3.41 1.242 1290 0.943 0.943 1.86 1.70 1.87 2.96 1.395 1220 1.001 0.905 1.70 1.75 1.83 2.77 1.474 1190 1.030 0.886 1.63 1.80 1.786 2.590 1.555 1157 1.058 0.867 1.56 1.85 1.748 2.429 1.638 1129 1.087 0.849 1.50 1.90 1.712 2.283 1.723 1103 1.115 0.830 1.44 1.95 1.679 2.148 1.809 1078 1.142 0.812 1.39 2.00 1.647 2.025 1.897 1054 1.170 0.794 1.34 2.05 1.618 1.912 1.987 1032 1.197 0.777 1.29 2.10 1.590 1.808 2.078 1011 1.224 0.760 1.25 2.15 1.565 1.711 2.171 990 1.251 0.743 1.21 2.20 1.540 1.622 2.265 971 1.278 0.727 1.17 2.25 1.518 1.540 2.361 953 1.305 0.712 1.14 2.30 1.496 1.464 2.458 936 1.331 0.696 1.10 2.35 1.476 1.393 2.557 919 1.357 0.682 1.07 Tables 255

Table XI (Contd.)

z t. (J td I jA (m) Mx po/Pa (ms) (m/s) (ms) (bar-ms) (J.

2.40 1.457 1.327 2.656 903 1.383 0.667 1.04 2.50 1.422 1.209 2.860 874 1.434 0.640 0.99 2.60 1.391 1.105 3.069 847 1.485 0.614 0.94 2.70 1.363 1.015 3.281 823 1.535 0.590 0.90 2.80 1.338 0.935 3.498 800 1.584 0.567 0.86 2.90 1.316 0.865 3.72 780 1.63 0.546 0.82 3.00 1.296 0.802 3.94 761 1.68 0.526 0.79 3.10 1.277 0.746 4.17 743 1.73 0.507 0.76 3.20 1.261 0.697 4.40 727 1.77 0.490 0.74 3.30 1.246 0.652 4.64 712 1.82 0.473 0.72 3.50 1.219 0.575 5.11 685 1.91 0.443 0.67 3.75 1.192 0.498 5.72 655 2.01 0.410 0.63 4.00 1.170 0.437 6.34 631 2.11 0.382 0.60 4.25 1.152 0.387 6.98 609 2.21 0.357 0.57 4.50 1.137 0.347 7.62 591 2.30 0.336 0.54 4.75 1.125 0.313 8.27 575 2.39 0.317 0.52 5.00 1.114 0.285 8.92 560 2.47 0.300 0.50 5.50 1.097 0.240 10.25 537 2.63 0.271 0.47 5.75 1.090 0.223 10.92 526 2.70 0.259 0.46 6.00 1.084 0.207 11.60 517 2.76 0.248 0.45 6.25 1.079 0.194 12.28 509 2.83 0.238 0.44 6.50 1.074 0.182 12.96 502 2.89 0.229 0.43 6.75 1.070 0.171 13.64 495 2.95 0.220 0.42 7.00 1.066 0.162 14.33 488 3.00 0.213 0.41 7.50 1.060 0.146 15.71 477 3.10 0.199 0.39 8.0 1.055 0.132 17.1 468 3.19 0.187 0.38 8.5 1.050 0.121 18.5 459 3.27 0.176 0.37 9.0 1.046 0.112 19.9 452 3.34 0.167 0.36 9.5 1.043 0.104 21.3 446 3.41 0.158 0.35 10.0 1.040 0.097 22.7 440 3.47 0.151 0.34 11.0 1.036 0.086 25.5 431 3.57 0.138 0.33 12.0 1.032 0.077 28.4 423 3.65 0.127 0.31 13.0 1.029 0.070 31.2 416 3.72 0.118 0.30 14.0 1.027 0.064 34.1 411 3.78 0.110 0.29 15.0 1.025 0.059 37.0 406 3.83 0.103 0.28 16.0 1.023 0.055 39.8 402 3.87 0.097 0.28 18.0 1.020 0.048 45.6 395 3.93 0.087 0.26 20.0 1.018 0.043 51.4 389 3.98 0.078 0.25 22.5 1.016 0.038 58.6 384 4.03 0.070 0.24 25.0 1 014 0.034 65.8 380 4.06 0.063 0.23 27.5 1.013 0.030 73.1 376 4.09 0.058 0.22 30.0 1.012 0.028 40.3 374 4.11 0.053 0.22 32.5 1.011 0.026 87.6 371 4.12 0.049 0.21 35.0 1.010 0.024 94.9 369 4.13 0.046 0.20 37.5 1.009 0.022 102.1 367 4.14 0.043 0.20 40.0 1.009 0.021 109 366 4.15 0.040 0.20 45.0 1.008 0.018 124 363 4.16 0.036 0.19 50.0 1.007 0.016 139 361 4.17 0.032 0.18 256 Tables

Table XI (Contd.)

z t. (J td 1/A (m) Mx p•;p. (ms) (m/s) (ms) (bar-ms) IX

55.0 1.006 0.015 153 359 4.18 0.029 0.18 60.0 1.006 0.014 168 358 4.19 0.027 0.17 70.0 1.005 0.012 197 355 4.19 0.023 0.17 80.0 1.004 0.010 226 354 4.20 0.020 0.16 100.0 1.003 0.008 285 351 4.20 0.016 0.15 125.0 1.003 0.007 358 349 4.21 0.013 0.14 150.0 1.002 0.005 431 348 4.21 0.011 0.14 200.0 1.002 0.004 578 346 4.21 0.008 0.13 250.0 1.001 0.003 725 345 4.21 0.007 0.13 300.0 1.001 0.003 871 344 4.21 0.005 0.13 400.0 1.001 0.002 1165 343 4.21 0.004 0.12 500.0 1.001 0.002 1459 343 4.21 0.003 0.12

Part B: Nuclear (one kilotonne TNT in air at 15 oc and 1.01325 bars)

z t. (J td 1/A (m) Mx p•;p. (s) (m/s) (s) (bar-ms) IX

10 52.0 3200 0.2 0.16 15 28.7 970 0.6 0.15 20 18.9 420 1.3 0.15 25 13.7 220 2.2 0.14 30 10.5 128 3.4 0.14 35 8.43 82.9 5.0 6970 0.13 322 33 40 7.02 57.0 6.9 5770 0.13 268 27 45 5.99 41.2 9.2 4890 0.13 228 22 50 5.21 31.0 11.8 4230 0.13 197 19 55 4.62 24.0 14.8 3710 0.13 172 16 60 4.14 19.1 18.2 3300 0.12 153 14 65 3.76 15.5 21.9 2970 0.12 137 13 70 3.45 12.9 26.0 2690 0.12 125 12 75 3.19 10.8 30.4 2470 0.13 114 11 80 2.966 9.22 35.2 2270 0.126 105.8 9.9 90 2.620 6.93 45.7 1970 0.129 92.5 8.6 100 2.362 5.41 57.5 1740 0.134 82.9 7.6 110 2.163 4.35 70.5 1560 0.139 75.7 6.8 120 2.007 3.58 84.6 1420 0.146 70.3 6.2 130 1.882 3.00 99.7 1300 0.152 66.0 5.7 140 1.780 2.562 116 1210 0.160 62.5 5.3 150 1.695 2.215 133 1130 0.168 59.7 5.0 160 1.624 1.937 150 1070 0.176 57.4 4.7 170 1.564 1.711 169 1010 0.184 55.3 4.4 180 1.513 1.524 188 959 0.192 53.6 4.2 190 1.469 1.369 207 917 0.200 52.0 4.0 200 1.431 1.237 228 879 0.208 50.5 3.9 Tables 257

Table XI (Contd.)

z t. (J td 1/A (m) Mx po/P. (s) (m/s) (s) (bar- ms) a.

210 1.397 1.125 248 846 0.216 49.2 3.7 215 1.382 1.075 259 831 0.220 48.6 3.6 220 1.367 1.028 269 816 0.224 48.0 3.6 225 1.354 0.985 280 803 0.228 47.4 3.5 230 1.341 0.945 291 790 0.231 46.8 3.4 235 1.329 0.907 302 778 0.235 46.2 3.4 240 1.318 0.871 313 766 0.238 45.7 3.3 245 1.307 0.838 324 755 0.242 45.2 3.3 250 1.297 0.807 336 745 0.245 44.6 3.2 255 1.288 0.778 347 735 0.248 44.1 3.1 260 1.279 0.750 358 726 0.251 43.6 3.1 270 1.262 0.700 381 708 0.257 42.6 3.0 280 1.246 0.655 405 692 0.263 41.6 2.9 290 1.233 0.614 429 677 0.268 40.7 2.8 300 1.220 0.577 452 663 0.272 39.7 2.8 325 1.193 0.500 513 633 0.283 37.6 2.6 350 1.171 0.439 575 608 0.291 35.6 2.5 375 1.153 0.389 638 587 0.298 33.8 2.3 400 1.138 0.348 703 569 0.303 32.2 2.2 425 1.125 0.314 767 554 0.308 30.7 2.1 450 1.114 0.285 833 540 0.312 29.5 2.1 475 1.105 0.261 899 528 0.316 28.3 2.0 500 1.097 0.239 966 518 0.319 27.3 1.9 525 1.090 0.221 1033 508 0.321 26.4 1.9 550 1.083 0.205 1101 500 0.324 25.6 1.8 575 1.078 0.191 1168 492 0.326 24.9 1.7 600 1.073 0.178 1240 485 0.328 24.3 1.7 625 1.068 0.167 1310 478 0.330 23.7 1.7 650 1.064 0.157 1380 471 0.332 23.2 1.6 675 1.061 0.148 1450 466 0.334 22.7 1.6 700 1.058 0.140 1520 461 0.335 22.3 1.5 725 1.055 0.133 1590 456 0.340 21.9 1.5 750 1.052 0.126 1660 452 0.340 21.6 1.5 800 1.047 0.114 1800 444 0.340 20.9 1.4 850 1.043 0.104 1940 438 0.340 20.4 1.4 900 1.040 0.096 2080 432 0.350 20.0 1.3 950 1.037 0.088 2220 428 0.350 19.7 1.3 1000 1.034 0.082 2360 423 0.350 19.3 1.2 1500 1.019 0.046 3790 396 0.360 14.0 1.1 2000 1.013 0.032 5240 382 0.400 11.8 1.0 3000 1.008 0.019 8150 368 0.400 7.3 1.0 4000 1.006 0.014 11100 361 0.400 6.5 0.9 5000 1.004 0.011 14000 357 0.400 5.1 0.9 258 Tables

Table XII Blast wave decay characteristics (overpressure ratios p/po at time fractions t/td for selected values of wave form parameter 11. (as given by equation 6-12))

Wave Form t/td Param- eter 11. 0.05 0.10 0.15 0.25 0.50 0.75

0.00 0.950 0.900 0.850 0.750 0.500 0.250 0.16 0.942 0.886 0.830 0.721 0.462 0.222 0.20 0.941 0.882 0.825 0.713 0.452 0.215 0.25 0.938 0.878 0.819 0.705 0.441 0.207 0.30 0.936 0.873 0.813 0.696 0.430 0.200 0.35 0.934 0.869 0.807 0.687 0.420 0.192 0.40 0.931 0.865 0.800 0.679 0.409 0.185 0.45 0.929 0.860 0.795 0.670 0.399 0.178 0.50 0.927 0.856 0.789 0.662 0.389 0.172 0.60 0.922 0.848 0.777 0.646 0.370 0.159 0.70 0.917 0.839 0.765 0.630 0.352 0.148 0.80 0.913 0.831 0.754 0.614 0.335 0.137 0.90 0.908 0.823 0.743 0.599 0.319 0.127 1.00 0.904 0.814 0.732 0.584 0.303 0.118 1.10 0.899 0.806 0.721 0.570 0.288 0.110 1.20 0.895 0.798 0.710 0.556 0.274 0.102 1.50 0.881 0.775 0.679 0.515 0.236 0.081 2.00 0.860 0.737 0.630 0.455 0.184 0.056 3.00 0.818 0.667 0.542 0.354 0.112 0.026 4.00 0.778 0.603 0.466 0.276 0.068 0.012

Table XIII Impulse fraction versus wave form parameter

0 pot 0 p•t IJ. r· IJ. r· potd potd

6.00 0.139 1.40 0.330 5.00 0.160 1.30 0.339 4.00 0.189 1.20 0.348 3.50 0.207 1.10 0.358 3.00 0.228 1.00 0.368 2.80 0.237 0.90 0.378 2.60 0.248 0.80 0.390 2.40 0.259 0.70 0.401 2.20 0.271 0.60 0.413 2.00 0.284 0.50 0.426 1.90 0.291 0.40 0.440 1.80 0.298 0.30 0.454 1.70 0.305 0.20 0.468 1.60 0.313 0.10 0.484 1.50 0.321 0.00 0.500 Tables 259

Table XIV The U.S. Standard Atmosphere (1976) Transmission Factors

Mean to Earth's At Altitude Surface

Altitude Pressure Temperature fd !. h !. metres mbar K oc (Distance) (Time) (Distance) (Time)

-400 1056 291 17.6 1.011 1.016 1.006 1.008 -200 1038 289 16.3 1.007 1.009 1.004 1.004 0 1013.25 288 15.0 1.000 1.000 1.000 1.000 200 989 287 13.7 0.993 0.991 0.997 0.996 400 966 286 12.4 0.987 0.983 0.993 0.991 600 943 284 11.1 0.981 0.974 0.990 0.987 800 921 283 9.8 0.975 0.966 0.987 0.983 1,000 899 282 8.5 0.968 0.958 0.984 0.979 1,200 877 280 7.2 0.962 0.948 0.981 0.974 1,400 856 279 5.9 0.956 0.940 0.978 0.970 1,600 835 278 4.6 0.945 0.932 0.974 0.966 1,800 815 276 3.3 0.943 0.923 0.971 0.962 2,000 795 275 2.0 0.937 0.915 0.968 0.957 2,200 775 274 0.7 0.930 0.907 0.965 0.953 2,400 756 273 -0.6 0.924 0.899 0.961 0.949 2,600 738 271 -1.9 0.918 0.891 0.957 0.945 2,800 719 270 -3.2 0.912 0.882 0.954 0.941 3,000 701 269 -4.5 0.904 0.874 0.951 0.936 3,200 684 267 -5.8 0.900 0.866 0.948 0.932 3,400 666 266 -7.1 0.893 0.858 0.945 0.928 3,600 649 265 -8.4 0.886 0.850 0.942 0.924 3,800 633 263 -9.7 0.881 0.842 0.939 0.920 4,000 617 262 -11.0 0.875 0.834 0.936 0.916 5,000 541 257 -17.5 0.843 0.796 0.920 0.896 6,000 472 249 -24.0 0.814 0.757 0.905 0.876 7,000 411 243 -30.5 0.784 0.720 0.890 0.856 8,000 357 236 -36.9 0.755 0.683 0.875 0.837 9,000 308 230 -43.4 0.725 0.648 0.860 0.818 10,000 265 223 -49.9 0.698 0.613 0.845 0.799 20,000 55.3 217 -56.5 0.417 0.362 0.701 0.643 30,000 12.0 227 -46.6 0.247 0.219 0.578 0.526 40,000 2.87 250 -23 0.148 0.138 0.483 0.439 50,000 0.80 271 -3 0.094 0.092 0.411 0.374 60,000 0.22 247 -26 0.0633 0.0586 0.355 0.324 70,000 0.052 220 -54 0.0407 0.0356 0.312 0.285 80,000 0.011 199 -75 0.0250 0.0208 0.277 0.253 90,000 0.0018 187 -86 0.0140 0.0113 0.248 0.226 100,000 0.0003 195 -78 0.0076 0.0062 0.225 0.205 110,000 7 X 10-5 240 -33 0.0044 0.0040 0.205 0.186 120,000 3 X 10-5 360 86 0.0029 0.0032 0.188 0.171 130,000 1 X 10-5 470 196 0.0018 0.0023 0.174 0.158 140,000 7 x w- 6 560 286 0.0015 0.0021 0.161 0.147

Notes: fd '=blast transmission factor for distance (equation 7-16 or 7-18). J, = blast transmission factor for time (equation 7-17 or 7-18). 260 Tables

Table XV Blast damage-side-on overpressure correlation (!arge explosions)

Type of Darnage Millibars

Minimum darnage to glass panels 1-3 Typical window glass breakage 10-15 Overpressure at Iimit for debris and missile darnage 15-25 Windows shattered, plaster cracked; minor darnage to some buildings 35-75 Personnel knocked down 70-100 Panels of sheet meta! buckled 75-125 Failure of wooden or asbestos siding for conventional homes 75-150 Failure of walls constructed of concrete blocks or einder blocks 125-200 Self-framing paneled buildings collapse 200-300 Oil storage tanks ruptured 200-300 Utility poles broken off 300-500 Serious darnage to buildings with structural steel framework 300-500 Eardrum rupture 350-1000 Reinforced concrete structures severely damaged 400-600 Railroad cars overturned 400-600 Probable total destruction of most buildings 700-800 Lung darnage 2000-5000 Lethality 7000-15000 Crater formation in average soil 20000-30000

Table XVI Conversion factors

The Systeme International d'Unites (designated SI in all Ianguages) is a coherent system based on seven defined units from which all other units are derived. Basic SI units are:

Unit Name Symbol length metre m mass kilogram kg time second s current flow ampere A temperature kelvin K Iurtlinous intensity candela cd amount of substance mole mol

Derived SI units include: volume stere (m 3) m3 velocity metres per second m/s acceleration metres per second per second m/s2 force newton (kg-m/s 2) N energy joule (kg-m 2/s2) J power watt (J/s) w pressure pascal (N/m2) Pa Tables 261

Table XVI (Contd.) Both SI metric units and working metric units are used here. Conversion factors for working metric units to SI metric units are:

To Convert from Working Metric Unit SI Metric Unit Working to SI Units litre stere divide by 1000 bar pascal multiply by 100,000 gramsfcubic centimetre kg/m3 multiply by 1,000 grams/litre kg/m3 multiply by 1 degrees Celsius kelvin add 273 bar-litre joule multiply by 100

English units such as the foot and the pound as used in older Iiterature can be converted to metric units as follows:

To Convert from English Unit Metric Unit English to SI Units foot metre multiply by 0.3048 foot metre divide by 3.281 cubic foot stere divide by 35.315 gallon (U.S.) litre multiply by 3.785 degree Fahrenheit kelvin add 460 and divide by 1.8 miles per hour metres per second multiply by 0.477 knots metres per second multiply by 0.5144 atmosphere bars multiply by 1.01325 psi bars divide by 14.5 psi millibars multiply by 6.895 foot-pound joule multiply by 1.356 calorie joule multiply by 4.184 pound (mass) kilogram multiply by 0.436 pound (mass) kilogram divide by 2.205 pounds per cubic foot grams per litre multiply by 16.018

Computations usually proceed most easily by first converting individual quantities into SI metric units. Reference: Mechtly, E. M., The International Sy$tem ofUnits, Physical Constants and Gonversion Factors, National Aeronautics and Space Administration, Washington, D.C. (1969). Index

Aceeieration equation, 176, 178 standard, 113, 259 Acoustic speed (see Sound, speed of) transmission factors, 259 Air, 35-49, 246 blast, 88-106 characteristics, 248-253 Bar, definition, 35, 261 composition, 246 Berthelot dry, 246 approximation for explosion energy, enthalpy, 36-38 26, 32 entropy, 37-38 Blast, 88-106 equation of state, 35-36 darnage formula, apparent, 246 analogue computer solution, 177 gas law constant, 36, 246 criteria, 187-190, 260 heat capacity, 36-37, 246 decay parameter, 100, 254-258 ratio, 37-38, 246 intemal, 157, 160 intemal energy, 37-38 reftected, 69-87 isentropic relation 38-39 resistance design, 150 sonic speed, 39-40 scaling, 111 specific heat capacity 36, 246 space, 122 thermodynamic properties, 36-38, 246 Stagnation characteristics, 58, 248-253 Analogue computer solution, blast dam• wave form parameter, 100, 254-258 age, 177 winds, 4, 57-58, 82-83, 248-253 Apparent formula Blast waves, 4, 57-58, 82-83, 88-106 air, 246 arrival times, 95-97, 254-259 mixtures of explosives, 20, 29-30 configuration, 90-91, 98-100, 104, Arrival time, 95-97, 104-105, 115-117, 254-258 254-257 decay characteristics, 98-100, 103, Atmosphere 254-258 263 264 Index

Blast waves (cont.) Deilagrating explosives, 3 durations, 97-98, 254--258 Deflection angles forcing function, 175 in supersonic streams, 60-63, 66-67, Breaching concrete, 10-11 86 Brittle materials, 180-186 Denmark, Lake, explosion, ll-12 Burst height, 125-131 Density Optimum, 132 of explosives, 231-238 relations, 36-39 Detonations, 3-4 Chemical Diffraction type structures, 170-171 equilibrium, 18, 138 Dimensionless formulas, 20, 29-30, 231-238, 246 shock pararneters, 248-250 Clouds and rain, effect of, 120 speed, 40 Coefficients of Discharge coefficient, 151 discharge, 151 Distance Iimits, Mach stem formation, drag, 43, 247 127 reflection, 72, 129 Distances, Combustion intraline, 6, 241-242 enthalpy of, 22 safety, 6-8, 239-242 heat of, 21, 30 Drag idealized, 140 coefficients, 43, 24 7 intemal energy of, 22 Ioads on structures, 169-170 Compressed gas explosions, 28, 33 pressures, 43, 47-48, 162 Computer solutions for blast effects, 177 type structures, 170 Confined explosions, 137-160 Dry air, 246 Conservation equations Ductile versus brittle materials, 185 energy, 51 Ductility ratio, 185-186 mass, 50 Duration of blast waves, 97-98, 116, momentum, 52 133, 254--258 Contours, overpressure, 119-120, 123, Dust explosions, 140, 142 131-132 Dynamic Conversion factors, 260-261 blast Ioads, 161-187 Cooling by confining wall, 148-149 pressure, 44-45 Craters, 9, 135 yield values, 180 Criteria for blast damage, 187-190, 260 Critical values darnage time, 187-190 Earthquake resistance, 179 overpressure, 154 Elastic deformation constant, 179-181 pressure, 151 Energy of explosion vent area, 152-154 Berthelot approximation, 26 Cylindrical structures, 170, 247 calculation of, 23-27, 31 description, 23 equations of, 23 Darnage Enthalpy, 22, 36-37 classes, 184-185 Entropy overpressure table, 260 estimates for solids, 25 Darnaging aspects of explosions, 4 of explosion, 24, 31 Decay characteristics, blast waves, 100, of ideal gas, 37-38 103, 254-258 mixing, 24, 31, 245 Defense against explosions, 191 shock front growth, 52 Index 265

Equation Formation internal energy, 22, 30, 231- of acceleration, 17 6-17 8 238, 243 of motion Formula mass, apparent, 20, 29, 246 computer solution, 177 Fragment graphical solution, 175-178, 183 distances, 7-8 of State, ideal gas, 35 Gurney analysis, 27-28 Equilibrium explosion products, 18, 138- Frame Ioads, 168-169 139 Free energy of explosion, 23 Equivalent Frontface Ioads, 162-167 static Ioads, 186 triangular pulse, 171-1 72 Exercises, tutorial, 195-220 Gas law Explosions constant, molar, 35 chemical, 254-256 specific, 36 confined, 137-156 equations, 35-48 defense against, 191 limitations, 46 dust, 140-142 Gibbs free energy, 23 energy of, 23 Graphical solution, equation of motion, entropy of, 24 183-184 equilibrium products, 18, 138-139 Group substitution methods, 22, 25, 32, free energy of, 23 244 heat of, 21 Gurney internal, 137-160 analysis, 27-28 internal energy of, 21 constant, 28 Lake Denmark, 11-12 equation, 27-28 nominal products of, 19, 29 nuclear, 256-257 overpressures, 119-136 Heat products of, 18-20, 139 of combustion, 22, 30 sympathetic, 8-9, 16 of explosion, 21, 31 Texas City, 12-15 capacity vapor cloud, 156 molar values for air, 246 yield, 2 ratio, ideal gases, 37-38 Explosives, 2-4, 231-238 specific, 36, 246 detlagrating, 3 Iosses, internal explosions, 148-149 high, 3 Height low, 4 of hurst relations, 126--135 mixtures of, 20, 237-238 of the Mach stem, 126 oxygen balanced, 19 Helmholtz free energy of explosion, 23- power, 2 24 shock, 55 High explosives standard, 2 definition, 3 strength, 2-3, 25-27, 231-238 table of, 231-238 yield, 2

Ideal gas Fireball products, 19-20 equation of state, 35 Forcing function for blast waves, 175 isentropic relations, 38 Formalized resistance-displacement curve, law, 35-36 179 limitations, 46 266 Index

Implosions, 29 Iimits, 80-81, 86 Induction times, intemal explosions, 145 overpressures, 124-125, 134 Impulse regime, 128, 133 blast wave, 98-100, 187 Magazine separation, 6-7, 240-241 darnage criteria, 187 Magnification, yield, 121 , 129 per unit area, 98-100, 254-258 Mean free paths, 55 scaling, 11 0-111 Metric units, 35, 260-261 time criterion Missiles, trajectories, 7-9 blast damage, 187 Mitigation of intemal blast effects, 155- Intraline distances, 6, 241-242 156 Interna] Mixing, entropy of, 24, 31, 245 blast, 137-160 Mixtures of explosives, 20, 237-238 duration, 137, 154 Molar heat transfer effects, 148-149 gas law constant, 35 rnitigation of, 155-156 heat capacity for air, 246 overpressures, 138-144, 149-154 Multistory structures, 174-175 pressure rise rates, 141, 144--147 products compositions, 139 stoichiometric fuel fractions, 140- Natural periods, 180-182, 192-193 144 Negative overpressures, 4, 5, 90, 169 temperatures, 140-141 , 146-148 Nominalexplosion products, 19, 29 violence, 154-155 Normal energy reftection, 69-71, 83 ideal gases, 36-37 shock, 50-55, 64, 248-253 of explosion, 21, 30 of formation, 22, 32, 231-238, 243, 244 Oblique explosions, see also intemal blast reftection, 69, 72-78 Isentropic relations, ideal gases, 38 overpressures, 129-133 regime, 128 shock, 59-63, 65-67 Lake Denmark explosion, 11-12 chart, 62, 75 Lateral resistance, structural, 176, 192- One-mass representation, 174-177 193 Open structures, 169 Lirnitations, ideal gas law, 46 Optimum burst height, 132 Limits for the Mach stem, 127-128 Overpressures Loads altitude, 119-120 dynarnic, 174-184 contours, 119-120, 123, 131-132 equivalent static, 186 critical discharge, 149-154 Local properties, thermodynamic, 40, 47 darnage criterion, 188-189, 260 Low explosives, 4 equations, 56-57 intemal blast, 137-156 Mach stem, 124-126 Mach negative, 4, 5 number, 39, 47 oblique reftection, 129-130 stem on the ground, 130-133 description, 69, 78-81, 124-128, peak values, 91-97, 101, 105, 254- 134-135 257 distance Iimits, 127-128, 133 reftected, 71-83, 248-253 height, 126 scaling, 109, 116 Index 267

side-on, 161 angles, 72-78, 84-86 Oxygen balance, 19-20, 29 characteristics, 81-84 deficient explosives, 19-20 coefficients, 72, 7 4 rich explosives, 19-21 normal, 69-71, 83 transitions, 127-129 Relief afforded by Parameter, wave form, 98-100, 254-258 heat transfer, 148-149 Partide velocity, 57-58, 82-83 venting, 149-154 tables, 248-253 Resistance Pascal displacement relations, 178-180 conversion factors for, 260-261 earthquake, 179 definition, 35 function, 17 5-177 Peak overpressure (see Overpressures) time relations, 182-184 Plastic deformations, 178-182 resistance, 179 Safety distances, 6-8, 239-242 Post-shock temperatures, 59, 248-249 Scaled Power, explosive, 2 blast wind, 111 Prandtl's relation, 53 distance, ii, 7-10, 108-109 Pressure impulse, 11 0-111 relief overpressure, 109 of dynamic Ioad, 164 time, 109-110 internal explosions, 149-154 Scaling law, 107-118 rise rates, 144-146 yield, 114-115 versus altitude, 259 Separation, magazine, 6-9, 240-241 Probability factors, 243 Shock, 50-87 Products of explosion, 18-20, 139 characteristics, 248-253 lireball, 19-20 explosive, 56-57 nominal, 19-29 fronts, 50-8 7, 248-25 3 Pulse, equivalent triangular, 171-172 normal, 50-55 oblique, 59-63 reflected, 69-87 Quantity-Distance standards, 6-7, 239- spherical, 63 242 thickness, 55 Side Ioads, 167 SI units, 2, 35, 260-261 Rain, effects of, 120 Side-on overpressure, 161 Rankine-Hugoniot relations, 52-55 Slant range, 125, 134 Rear face Ioads, 166-167 Smoothed overpressure-time records, Reference 100-103 critical So nie ducts, 121 Mach number, 42 multiplication factors, 121 relations, 42-43 Sound, speed of, 39-40, 46, 168, 246 explosions, 2, 15 Space blast, 122 chemical, 254-256 Specific nuclear, 256-258 gas constants, 36 Reflected heat capacity, 36, 246 overpressures, 69-87, 162-166 Spherical shock, 69-87, 162-165 shock, 63 Reflection structures, 170 268 Index

Spring constant, 181 conversion factors, 260-261 Stagnation darnage classes, 185 pressure, 40-41, 45, 162-173 drag coefficient, 247 properties, 40-45 Gumey constants, 28 temperature, 40-41 intemal blast characteristics, 141-142 Standard oxygen assignment, 20 atmosphere, 113-259 properties of air, 246, 259 deviation, 9, 16, 243 safety distances, 239-242 explosions, 2, 92 thermodynamic properties, 243-245 chemical, 254, 256 Temperature nuclear, 256-257 blast stagnation, 58, 248-253 transmission factors, 113, 259 conversion factors, 260-261 Static intemal blast, 139-142, 146-150 Ioad, equivalent, 186 isentropic, 38-39 properties of a stream, 40 local, 40 yield resistance, 180 post-shock, 59 Stere, definition, 1 I, 35, 260 shock front jump, 53-54, 61, 248-253 Stoichiometric fuel ratios, 20, 139-144 static, 40 Stream functions, 40-45 stream Stagnation, 40-41 Stream Stagnation characteristics, 40-41 total, 40 (see also Blast stagnation Texas City explosion, 12-15 characteristics) Thermodynamic properties, 40-47, 231- Strong shock solution, 63, 77 238, 243-246 Structural darnage Thermodynamics of explosions, 18-34, classification, 184 243-246 Structures Thickness of the shock front, 55 cylindrical, 170 Time of arrival (see Arrival time) diffraction type, 170-171 TNT equivalent, 2, 15 drag type, 170-171 Top Ioads on a structure, 167-168 dynamic 1oads, 161-173 Trajectory front face Ioads, 162-166 missile, 7-8 open, 169 triple point, 126 rear face Ioads, 166-167 Transition angles, reflected shock, 80-81 response, 174-194 Transmission factors, 108-113, 116, 133, side Ioads, 167 259 spherical, 170 Trave1 time (see Arrival time) top Ioads, 167 Triangular pressure pulse, 171-172, 187 Substitution approximations, 22, 244 Tripie Point, Mach stem, 126 Surface Tutoria1 bursts, 9-10, 128-129 exercises, 195-220 interactions with blast waves, 122-123 answers (se!ected), 221-229 Sympathetic explosions, 8-9, 16 Systeme International d'Unites, 2, 35, 260-261 Unconfined vapor cloud explosions, 156 Units Tables conversion factors, 260--261 blast darnage capability, 187 metric, 2, 35, 260--261 blast wave characteristics, 248-258 U. S. Standard atmosphere, 259 Index 269

Vapor cloud explosions, 156 Ioads, 43, 47-48 Vent area, critical, 152, 158 Venting intemal explosions, 149-154, 158 Yield Violence, intemal explosions, 154-155 displacement relations, 181 explosive definition, 2 Wave form parameter, 98-100, 254-258 magnification, 121, 129 Weak shock solution, 63, 77 relative values, 231-238 Wedge angle, 60 standard TNT value, 2 Wind resistance, structural, 178-186 blast, 47, 57-58, 83 scaling law, 114-115, 117