measurements of muzzle brake effectiveness

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19th International Symposium of Ballistics, 711 May 2001, Interlaken, Switzerland

MEASUREMENTS OF MUZZLE BRAKE EFFECTIVENESS

E. Schmidt

U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005-5066, USA

INTRODUCTION

Muzzle brakes, Fig. 1, are devices that act to recover momentum from the exhaustinggun propellant gases. Interest in optimizing the performance of brakes has come and goneover the years. During World War II, considerable research was undertaken. As weaponcalibers increased to counter more powerful tanks with heavier armor, recoil became a de-sign problem. Germany1,2 demonstrated an understanding of the muzzle gasdynamicsand developed an amazing array of different brake variants, some of which were placedinto production. In the United States, a major concern3 centered on brake-like devicesapplied as blast deflectors. The goal was to reduce obscuration caused by debris lofted inthe muzzle exhaust. After the war interest waned until in the seventies, when attack heli-copters were fielded with muzzle brake equipped cannon. Interest centered4,5 on blastoverpressure on the aircraft surface particularly sections housing electronic components.In the eighties, blast68 in the crew stations of towed howitzers became a concern. Pre-sently, there is interest in lightweight fighting vehicles mounting high performance can-non. Recoil mitigation is a major consideration and provides a need to revisit previousefforts. This paper will give an overview of work to define the properties of open muzzlebrakes, Fig.1, and their impact on the overall functionality of the weapon system.

The paper examines the analytic and theoretical work done on muzzle brakesover the past twenty years. The nature of the flow over the devices is consid-ered and its implications on brake performance discussed. Correlations are pre-sented between brake efficiency, blast overpressure, muzzle flash, and accuracy.

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Figure 1. Open baffle muzzle brake.

The flow from guns has been studied extensively9. The high pressure propellant gasesdrive into the atmosphere displacing the surrounding air to form a strong blast wavewhich decays as it propagates away from the weapon. The propellant gas flow has thestructure of a highly underexpanded supersonic jet. A property of the jet structure is thatwithin the supersonic core, i.e., the region internal to the lateral shocks and Mach disc, theflow is quasi-steady. This means that the highly transient events occurring in the blastlayer do not propagate beyond the jet shocks and property variations within the core aregoverned by the slower process of gun tube blow down. Since the muzzle brake functionslargely within this core region, its treatment is simplified.

Oswatitsch1 and Smith10 both took advantage of the quasi-steady nature of the coreflow to perform experiments on muzzle brake simulators immersed in steady jet flow.They define a brake efficiency factor

= (Two Tw)/Two (1)where Tw is the thrust with the brake installed and Two is the thrust without the brakeinstalled. Since these were steady flow experiments, no projectile was launched.

Using what is in essence a ballistic pendulum, Pater11 measured muzzle brake perfor-mance on an actual cannon. For this transient event, the brake efficiency factor was defi-ned as

= (Iwo Iw)/(Iwo mpvp) (2)where Iw is the impulse imparted to the free recoil device with the brake installed, Iwo isthe impulse without the brake, and mpvp is the muzzle momentum of the projectile. Thus,the term in the denominator is the total momentum available from the propellant gases. Ifthe highly transient initial phase and the low momentum late time collapse of the core areneglected, Eq. (1) and (2) are essentially the same. This is the definition of brakeefficiency used for the remainder of this paper. Subsequent sections will examine the vari-ation of efficiency with brake geometry and consider the impact of efficiency on otherbrake properties, such as blast.

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Launch Dynamic & Propulsion

RECOIL ATTENUATION

Baur and Schmidt6 used a free recoil device of Paters design to measure the recoil at-tenuation characteristics of a variety of brake designs mounted on a 20 mm cannon. Topermit rapid changes in geometry, axially symmetric configurations were employedwhere baffles were connected to the muzzle by a set of threaded rods. It was assumed thatinterference of the rods with the flow was small. Flat and angled baffles were examined,both singly and in pairs. To test the applicability of the axisymmetric data to an actualmuzzle brakes, three-dimensional models were built for two of the designs (simulatingthe brakes on the M109 and M198 howitzers). Data were taken of the brake efficiencyand blast overpressure. In addition, the muzzle flow field was observed using spark sha-dowgraphs.

For a single baffle moved along the line of fire, the brake efficiency first grows andthen decays, Fig. 2. This behavior was observed and explained by Smith10. Near themuzzle, the lateral extent of the core flow is small and much of the momentum flux sim-ply passes through the projectile hole in the baffle. As the device moves away from themuzzle, the lateral extent of the jet grows and more of the baffle is effective in turning theflow, thus recovering momentum. Eventually, the efficiency decays as the lateral extent ofthe jet becomes sufficiently large for momentum flux to pass around the outer edge of thebaffle. The location of the peak6 changes with brake geometry. For larger baffle geome-tries, the maxima is reached further from the muzzle. However, for all cases observed thegrowth and decay of efficiency was seen.

Figure 2. Variation in efficiency of single, axisymmetric baffle as it is moved away fromthe muzzle.

When a second baffle is added, some interesting behavior is observed, Fig. 3. The fa-mily of curves represents the variation of efficiency as the second baffle is moved awayfrom the first. The changes are overlaid on data from Fig. 2. For example with the firstbaffle at z/D = 0.5, the total efficiency (for the two baffles) grows as the second baffle mo-ves downstream. A maximum is reached when the second baffle is at z/D = 2.5. It is notedthat the maximum double baffle efficiency does not follow from the optimal location forthe single baffle; rather, it is attained when the first baffle z/D = 1.0 and the second baffle

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Measurements of Muzzle Brake Effectiveness

z/D = 3.5. The gain in performance for the second baffle is typically lower than that of thefirst (except for z/D = 0.5 where flow through the projectile hole is largely undisturbed)and occurs at a greater offset for the second baffle relative to the first than for the first re-lative to the muzzle. This behavior was noted by Oswatitsch1 and ascribed to the loss ofstagnation pressure as the flow is processed through the strong shocks developed by thefirst baffle.

Figure 3. Variation of efficiency of two axisymmetric baffles as second baffle is movedrelative to the first.

A related behavior can be observed as the weapon exit conditions change. A typical ar-tillery piece is fired over a set of muzzle velocities (zones of fire) in order to provide accu-rate coverage of desired ranges. In firing the model M109 and M198 brakes, it was obser-ved that as muzzle velocity changed, so did the brake efficiency, Fig. 4.

Figure 4. Variation of efficiency of model scale three-dimensional brakes with muzzlevelocity.

The muzzle conditions at shot exit are presented in Table 1. The pressure is that afterin-bore expansion to sonic conditions following projectile exit. As the muzzle velocity(and pressure) increase, the efficiency of both brakes change. However, the efficiency of

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the M109 model brake increases while that of the M198 decreases. The cause of this be-havior is related to the geometry of the brakes relative to the flowfield. As muzzle pres-sure increases, the longitudinal and lateral extent of the supersonic core grow. Photo-graphs4 show the M198 baffle to be fully immersed in the supersonic core before the 460 m/s case. At higher velocities, the core grows past the baffle. When this occurs,momentum flux passes beyond the outer edge of the baffle and efficiency drops. For theM109 baffle, a different behavior is observed. This is a relatively large baffle and is sweptback toward the muzzle. As velocity increases, the baffle becomes more fully immersedin the supersonic core, interdicting more of the momentum flux. By 615 m/s, the coremoves to the edge of the baffle and it would be expected that the efficiency would beginto decrease. This was not observed in the data and is thought to be associated with theprocesses occurring on the second baffle of the double baffle brake. Obviously, the flow isnot as simple as described in this paragraph; however, it is felt that the explanationsreflect the basic phenomenology of the process.

Table 1. Muzzle exit conditions (20 mm cannon)

BLAST OVERPRESSURE AND FLASH

In diverting the propellant gases to recover momentum, the muzzle brake alters the di-rectional nature of energy deposition and through this the blast overpressure field. The va-riation in blast strength with angle away along a constant radius arc6 is shown in Fig. 5.For the bare muzzle, the blast is quite strong ahead of the gun, i.e., the axis along whichthe gases exhaust. With each of the brakes, the peak pressure moves toward the rear of thegun reflecting both the brake efficiency and the baffle sweep angles. This property ofmuzzle brakes is well known by gun crews stationed behind the weapon.

Figure 5. Variation in peak blast overpressure with angle relative to the line of fire for thebare muzzle and M198 and M109 three-dimensional brakes.

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Vp (m/s) 280 463 615 775 1050T* (K) 875 933 1052 1320 1705P* /P 14 45 101 189 287

From the 20 mm data for the set of muzzle brakes tested, Baur and Schmidt define acorrelation between overpressure with and without a brake in place

(3)

where is the angle from the line of fire (zero is forward), pw, pwo are the peak pressuresbehind the blast wave, and p is the ambient pressure. This expression is reasonablyaccurate for directions fore and aft of the line of fire; however, laterally, it does not accu-rately predict the blast field. In part this is due to a failure to account for the details of baf-fle geometry, both in terms of baffle sweep angle and the three-dimensional nature of realbrakes (i.e., with upper and lower attachment plates). Fortuitously, in the vicinity of thecrew both the axially symmetric and three-dimensional overpressures converge.

There are some techniques that can be used to reduce the blast overpressure while stillmaintaining brake efficiency. For multi-baffle brakes, it has been observed6 that magni-tude of blast is dominated by the characteristics of the first baffle; thus, it is of interest toexamine the blast overpressure variation with position of the first baffle, Fig. 6. The plotshows the variation of efficiency and overpressure, both normalized to their respectivepeak values, as the baffle position is changed. The overpressure data is taken on the 150ray at a radial separation of r/D = 30 from the muzzle. It is seen that the overpressure in-creases along with the brake efficiency, but peaks at z/D = 1 while efficiency peaks at z/D= 1.5. At the location of maximum brake efficiency, the overpressure has dropped by 20%relative to its peak value. This behavior was also observed for other brake designs. Thebaffle tested was the same as that used in Fig. 3 and 4. Since the blast overpressure withtwo baffles was only slightly greater than with the single baffle case, it can be hypothesi-zed that the best configuration would be one where the first baffle is located close to themuzzle (e.g., z/D = 0.5, Fig. 4) and the second baffle placed near the peak efficiency point(e.g., z/D = 2.5). This provides a smaller blast overpressure in the crew area, a high levelof efficiency, and a relatively compact device.

Figure 6. Variation of efficiency and peak overpressure (both normalized to local ma-xima) along 150 ray with location for a single axisymmetric baffle.

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(pw - p)/ p = [pwo- p)/ p][1 + (0.8 1.5cos ]

In addition to increasing overpressure behind the weapon, the presence of a muzzlebrake can act to increase the probability of flash. It is well known12 if there is a propermixture between propellant gas and air with sufficiently high temperature over a reason-able induction period, ignition may take place. The luminous region produced by suchcombustion has significant brightness and extent. It is called secondary flash. For highperformance tank guns, secondary flash almost always occurs. Flash suppressants such aspotassium sulfate are employed to reduce the probability of flash in artillery. However,the use of muzzle brakes can have the opposite effect. The baffle surfaces of muzzle bra-kes cause strong shock waves to form in the exhaust flow. Passage through a series ofinternal shocks followed by a final Mach disc can significantly heat the propellant gases.A highly idealized approximation of this flow shows8 the influence of the shock heating,Fig. 9. The plot shows the mixture temperature versus the mixture ratio where r = 0 ispure propellant gas and r = 1 is pure air. The double baffle brake significantly raises themixture temperature when compared to the bare muzzle case. The dashed lines show em-pirical ignition criteria13 for different percentages of flash suppressant. In fact, tests sho-wed that the howitzer in question did flash. While bare muzzle tests were not conductedto show an absence of flash, the model was applied to each zone of fire with the brake inplace and produced reasonable agreement with data.

Figure 7. Effect of a muzzle brake on air/propellant gas mixture temperature (horizontallines show ignition threshold for different percentages of flash suppressant).

CONCLUSIONS

The use of muzzle brakes may be necessary to reduce recoil of high performance can-non on future lightweight fighting vehicles. There is a significant body of experimentaldata describing the muzzle brake gasdynamics which points out some of the pitfalls asso-ciated attempts to optimization of brake performance. While not discussed in this paper,there have been a number of numerical studies of muzzle flow both axially symmetric14and fully three-dimensional15. The work of Carofano uses the most advanced numericalscheme and produces impressive results. Given the advances in these techniques, it would

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be worth applying modern computational fluid dynamics to predict the complete proper-ties associated with any new family of muzzle brakes being considered. Such an approachwould greatly improve the understanding of the flow internal and external to the devicesand would aid in optimizing their performance.

REFERENCES1. K. Ostwatisch, Flow Research to Improve the Efficiency of Muzzle Brakes, R1001, Army Ordnance,

Goettingen, GE, Oct 1944.2. E. Hammer, Muzzle Brakes, Volume 1, History and Design, TR1-1000L, The Franklin Institute, Phila-

delphia, PA, Jun 1949 (AD111481). 3. E. Hammer, Anti-Obscuration Devices and Muzzle Brakes, PN 1750-3, The Franklin Institute, Philadel-

phia, PA, Apr 1948 (AD71819).4. E. Gion and E. Schmidt, Measurements on a Circular Plate Immersed in Muzzle Flow, MR2762, Ballistic

Research Laboratory, APG, MD, Jun 1977.5. E. Schmidt, E. Baur and W. Thompson, Comparison of the Performance of Candidate Muzzle Devices for

30 mm Cannon, MR03337, Ballistic Research Laboratory, APG, MD, Feb 1984.6. E. Baur and E. Schmidt, Relationship Between Efficiency and Blast from Gasdynamic Recoil Brakes, Pa-

per 85-1718, AIAA, Jul 1985.7. R. Dillon, A Parametric Study of Perforated Muzzle Brakes, ARLCB-TR-84015, Benet Weapons Labora-

tory, Watervliet, NY, May 1984.8. E. Schmidt, Secondary Combustion in Gun Exhaust Flows, ARO R82-1, Transactions of the 27th Con-

ference of Army Mathematicians, 1982.9. Gun Muzzle Blast and Flash, AIAA Progress in Astronautics and Aeronautics, Vol. 139, 1992.

10. F. Smith, Model Experiments on Muzzle Brakes, R2/66, RARDE, FT Halstead, UK, Jun 1966(AD487121).

11. L. Pater, Scaling of Muzzle Brake Performance and Blast Field, TR3049, Naval Weapons Laboratory,Dahlgren, VA, Oct. 1974.

12. G. Klingenberg and H. Mach, Investigation of Combustion Phenomena Associated with the Flow of HotPropellant Gases, Combustion and Flame, Vol. 27, 163176, 1976.

13. G. Carfagno, Handbook on Gun Flash, Franklin Institute, Philadelphia, PA, 1961.14. G. Carofano, A Note on the Blast Signature of a Cannon, ARCCB-TR-92014, Benet Weapons Labora-

tory, Watervliet, NY, Mar 1992.15. J. Buell and G. Widhopf, Three-Dimensional Simulation of Muzzle Brake Flowfields, Paper 841641,

AIAA, 1984.

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1_IBS01.pdfIBS 2001 19 th International Symposium on BallisticsTable of ContentsINVITED SPEECHESIS01 The Ballistics of HornussenIS02 The History of Explosives in Switzerland

INTERIOR BALLISTICSIB01 Insensitive High Energy PropellantsIB02 Advanced Cartridge Design for the Term-KE RoundIB03 High Performance Propulsion Design forIB04 Ballistic Shelf Life of Propellants for MediumIB05 Development and Validation of a Comprehensive ModelIB06 Comparison of 0D and 1D Interior Ballistics ModellingIB07 Two-phase Flow Model of Gun InteriorIB08 Interior Ballistic Principle of High/Low PressureIB09 Factors Effecting the Accuracy of Internal Ballistics,IB10 ATwo-Dimensional Internal Ballistics Model for ModularIB11 Investigations for Modeling Consolidated PropellantsIB12 Burning Characteristics of Foamed PolymerIB13 The Analysis of Gun Pressure InstabilityIB14 Influence of Different Ignition Systems on the Interior BallisticsIB15 ALeading-Detonation-Tube Ignitor and Its Firing ResultsIB16 Functional Lifetime of Gun PropellantsIB17 Spheroidal Propellant Stabilizer StudiesIB18 Applicability of the Hydrogen Gas Erosion Theory toIB19 Experimental Investigation of Heat Transfer in a 120 mm GunIB20 Analysis of ETC or Classical Manometric Closed Vessel TestsIB21 Variation in Enhanced Gas Generation RatesIB22 Plasma Ignition of Consolidated PropellantsIB23 Plasma Ignition and CombustionIB24 Discussion on Emission Spectroscopy Measurements

LAUNCH DYNAMICSLD01 Sabot Discard Model for Conventional andLD02 Experimental and Simulation Analysis of SetbackLD03 Measurements of Muzzle Break EffectivenessLD04 Transitional Motion of KE Projectile and GoverningLD05 Numerical Simulation of Intermediate BallisticsLD06 Multistage Method for Acceleration ofLD07 Computation of Muzzle Flow Fields Using UnstructuredLD08 Modelling of Fume ExtractorsLD09 Modeling and Simulation of the Gas ChargingLD10 Numerical Analysis of the Propagating BlastLD11 Intermediate Ballistics Unsteady Sabot Separation:LD12 Temperature and Heat Transfer at the CommencementLD13 Gun Barrel Erosion: Study of ThermallyLD14 AStudy on the Erosion Characteristics of the MicropulsedLD15 Friction and Wear Mechanism at High Sliding SpeedsLD16 Increasing the In-Bore Velocity MeasurementsLD17 The Development of Composite Sabots for KineticLD18 Structural Analysis of a Kinetic Energy ProjectileLD19 Joining Jacket and Core in Jacketed Steel/Tungsten PenetratorsLD20 Soft Recovery of Large Calibre Flying ProcessorsLD21 New Materials for Large-Caliber RotatingLD22 Methodology for Hardening Electronic ComponentsLD23 Adiabatic Depressurisation of Vented VesselsLD24 Solid Fuel Ramjet (SFRJ) Propulsion for Artillery

EXTERIOR BALLISTICSEB01 Transonic Aerodynamic and Scaling Issues forEB02 Flight Dynamics of a Projectile with High DragEB03 Flight Test Results of the Swedish-Dutch Solid FuelEB04 Aeroelasticity of Very High L/D Bodies in Supersonic Flight:EB05 ASimulation Technique for Analyzing EffectEB06 The Transition Ballistic Simulation FacilityEB07 Acceptance Criteria for Fire Prediction AccuracyEB08 On the Influence of Yaw and Yaw RateEB09 Diagnostic of the Behaviour of a Course-correctionEB10 The Influence of a Projectile Stability SubjectedEB11 Aerodynamic Aspects of a Grid Finned ProjectileEB12 Magnus Instabilites and Modeling for a 12.7 mm ProjectileEB13 Wind Tunnel Investigation of a High L/D ProjectileEB14 Roll Producing Moment Prediction for Finned ProjectilesEB15 Aerodynamic Wind-tunnel Test of a Ramjet ProjectileEB16 Numerical Model for Analysis and SpecificationEB17 Numerical Ricochet Calculations of Field Artillery Rounds

WARHEAD MECHANICSWM01 Active Protection Against KE-Rounds andWM02 Multiple Explosively Formed PenetratorWM03 Barnie: A Unitary Demolition WarheadWM04 Experimental and Numerical Studies of AnnularWM05 Shaped Charge Warheads Containing Low MeltWM06 Comparing Alternate Approaches in the ScalingWM07 Effect of Fragment Impact on ShapedWM08 Breakup of Shaped-Charge Jets: ComparisonWM09 Application of Overdriven Detonation of HighWM10 Relative Performance of Anti-air Missile WarheadsWM11 ARetrospective of the Past 50 Years of Warhead ResearchWM12 Time-Reversed, Flow-Reversed Ballistics Simulations:WM13 TNT Blast Scaling for Small ChargesWM14 ANovel Approach to the Multidimensional NatureWM15 Fragmentation Properties of AerMet 100 Steel inWM16 Using a Numerical Fragmentation Model to UnderstandWM17 Dual Mode Warhead Technology for FutureWM18 Steerable Hitiles Against TBM WarheadsWM19 The Design of Small-Calibre Tandem Warhead against TankWM20 Application of Loose Powder Liner Shaped ChargesWM21 Lasers for AP-Mine NeutralisationWM22 AReactive Mine Clearing Device: REMICWM23 The Measure of Jet Goodness M.E. MAJERUS, R.M. COLBERTWM24 Some Improvements into Analytical Models of ShapedWM25 Role of Texture in Spin Formed CuWM26 Predicted and Experimental Results of ShapedWM27 The Design and Performance of Annular EFPsWM28 Explosively Formed PenetratorsWM29 Analytical Code and Hydrocode ModellingWM30 The Contribution to the Optimization of DetonationWM31 Variational Principle for Shaped Charge Jet FormationWM32 The Effects of Finite Liner Acceleration on Shaped-ChargeWM33 Investigation of Several Possibilities to DisturbWM34 Further Analytical Modelling of Shaped ChargeWM35 Shaped Charge Jet Break-up Time Formula ConfirmedWM36 Computer Simulation of Shaped ChargeWM37 Determination of Dynamic Tensile Strength of MetalsWM38 Coupled Map Lattice Model of Jet BreakupWM39 The Indeterminacy of the Outgoing Flow of TwoWM40 Electromagnetic Control of the Shaped-charge EffectWM41 Aero Stripping from a Water JetWM42 Photoinstrumentation for Warhead CharacterisationWM43 APractical Method to Determine Poisson's Ratio

VULNERABILITY MODELING AND WOUND BALLISTICSVM01 The Development of a Physical Model of Non-PenetratingVM02 Advanced Multiple Impact Endgame Model Against BallisticVM03 Assessment of Shaped Charge Jet Mitigation,VM04 Analysis of Active Protection Systems: When ATHENAMeetsVM05 Numerical Modeling of a Simplified Surrogate LegVM06 Numerical Head and Composite Helmet ModelsVM07 The Testing of the Tank Fire Control Systems AccuracyVM08 Methodology for Predicting Ballistic Shock ResponseVM09 Major Issues Affecting Characterisation and ModelingVM10 Digitization of Witness Pack PlatesVM11 Lightweight Passive Armour for Infantry Carrier VehicleVM12 Lightweight Transparent Armour SystemsVM13 Non-KKV End Game Kinematic Plan of Anti Tactical BallisticVM14 Defeating Active Defense Systems by Double-VM15 AComparative Evaluation of Personnel Incapacitation MethodologiesVM16 Behind Armour Blunt Trauma for Ballistic Impacts on Rigid Body ArmourVM17 Soap and Gelatine for Simulating Human Body Tissue:VM18 Sphere Penetration into Gelatine and BoardVM19 AComputer Program to Assess the Effectiveness of ShotgunVM20 Creams for Protection Against Skin Burns in Explosions

1-34 TERMINAL BALLISTICSTB01 Whipple Shields Against Shaped Charge JetsTB02 General Overview of Capability in the SimulationTB03 Analytical Model to Optimize the Passive ReactiveTB04 Approximating the Ballistic PenetrationTB05 Sensitivity of ERA-boxes Initiated by ShapedTB06 ANumerical Investigation of Top-Attack SubmunitionTB07 Protective Power of Thick Composite LayersTB08 The effect of matrix type on the ballistic andTB09 Size Scaling in Ballistic Limit Velocities for SmallTB10 Reference Correlations for Tungsten Long RodsTB11 Oblique Plate Perforation by Slender Rod ProjectilesTB12 Tungsten into Steel Penetration IncludingTB13 On the Behaviour of Long-Rod Penetrators UndergoingTB14 Penetration Comparison of L/D=20 and 30 Mono-blocTB15 Definition and Uses of Rha Equivalences for MediumTB16 Analytical Model of Long Rod InteractionTB17 Penetration of APProjectiles into Spaced Ceramic TargetsTB18 Behavior and Performance of Amorphous and NanocrystallineTB19 Kinetic Energy Projectiles: Development History,TB20 Kinetic Energy KE Ammunition for Medium CalibreTB21 Multirole APFSDS-T Expanding the TraditionalTB22 Penetration Mechanics of Extending Hemicylindrical RodsTB23 Evaluation of Replica Scale Jacketed PenetratorsTB24 Replica Scale Modelling of Long Rod Tank PenetratorsTB25 High Velocity Jacketed Long Rod Projectiles HittingTB26 The Penetration Process of Long Rods into ThinTB27 Oblique Penetration in Ceramic TargetsTB28 The Influence of Penetrator Geometry and ImpactTB29 Observations on the Ratio of Impact Energy to Crater VolumeTB30 Cavity Shape Evolution During PenetrationTB31 Instrumented Small Scale Rod Penetration Studies:TB32 AParameter that Combines the Effects of BendTB33 The Effects of Stress Pulse Characteristics on the DefeatTB34 Penetration Efficiency of Tungsten Penetrators

35-68 TERMINAL BALLISTICSTB35 Shock Reduction Power of DifferentTB36 Cavity Expansion Theory Applied to Penetration of TargetsTB37 Development and Validation of a Dwell ModelTB38 Glass Ceramic Armour Systems for LightTB39 Ballistic Resistance and Impact BehaviourTB40 Dynamic Fragmentation of Alumina with AdditionsTB41 Influence of Liners on the Debris Cloud ExpansionTB42 Mass Efficiency of Aramid Composites DependingTB43 Numerical Fragmentation Modeling and ComparisonsTB44 Fragment Impact on Bi-Layered Light ArmoursTB45 Penetration Analysis of Ceramic Armor with CompositeTB46 Ballistic Limit of Fabrics with ResinTB47 Finite Element Design Model for Ballistic ResponseTB48 Numerical Simulations of Dynamic X-Ray ImagingTB49 Perforation of Spaced Glass Systems by the 7.62 mmTB50 The Development of the Glass LaminatesTB51 Model of the Wood Response to the High Velocity of LoadingTB52 Terminal Ballistics of EFPs ANumerical ComparativeTB53 An Experimental Investigation of Interface DefeatTB54 Cutoff Velocity in Precision Shaped Charge JetsTB55 Performances and Behaviour of WCu-pseudo-alloyTB56 AComputational Method of Fast Simulating Full-physicsTB57 Numerical Simulation of the PerformanceTB58 Study of Spin-compensated Shaped ChargesTB59 Jet Perturbation by HE TargetTB60 Evaluation of High Explosive ParametersTB61 Combination of Inert and Energetic MaterialsTB62 Interaction Between a Metallic Reactive ArmorTB63 Numerical Simulation of Shape Charge Jet InteractionTB64 A3D Modelling Study of the Influence of SideTB65 Effect of Multiple and Delayed Jet Impact and PenetrationTB66 Hydrocode Modelling of High-velocityTB67 The Effect of Obliquity and Conductivity on the CurrentTB68 Taylor Impact Experiments of Electrified Copper

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