Supporting Munitions Safety Probabilistic Modeling of Initiation due to Fragment Impact IMEMTS 2019 Dr. Ernie Baker Christiaan Leibbrandt Martijn van der Voort Warheads Technology TSO Transport and Storage TSO e.baker@msiac.nato.int m.vanderVoort@msiac.nato.int
Overview Supporting Munitions Safety • Fragment Impact Testing • Jacobs-Roslund Initiation Model • Deterministic initiation response model • Augmenting deterministic initiation response model – Algebraic model: Geometrical aspects of fragment impact – Validation – Implementation in deterministic model • Probabilistic initiation response model • Conclusions and recommendations
Fragment Impact Gun Testing Supporting Munitions Safety ➢ NATO STANAG 4496, Ed. 1 ➢ Standard test: 2530 90 m/s Alternate test of 1830 60 m/s • ➢ Standard fragment (projectile) geometry ➢ Several loosely defined and undefined characteristics that can affect the test item response • Velocity variation • Aim point variation • Projectile tilt upon impact • Fragment material characteristics ➢ Develop a probabilistic model that accounts for these variations and conduct an associated case study
Typical FI Test Setup Supporting Munitions Safety Test Item NSWC Dahlgren Support Table Sabot Stripper Plate TOA Gun Screens 3 meters 4.5 meters Redstone Test Center ➢ The test item is as close to gun as possible without causing damage to the gun in order to reduce aim point variability. ➢ Fragment velocities are measured using either make/break screens or photographic techniques. ➢ Majority of testing is completed using single stage powder guns
FI Testing Variation Supporting Munitions Safety Velocity, projectile tilt and impact point variation are common ➢ Gun barrel wear GD-OTS ➢ Gun powder variation ➢ Ignition anomalies ➢ Sabot release ➢ Measurement error AFRL Eglin AFB DGA/EM France GD-OTS USA Sabots High Speed Framing Images
J ACOBS -R OSLUND M ODEL Supporting Munitions Safety Supporting Munitions Safety Deterministic initiation response model V Impact < V Critical : No detonation 𝐷𝑠𝑗𝑢𝑗𝑑𝑏𝑚 = 𝐵 𝑒 0.5 ∗ 1 + 𝐶 ∗ 1 + 𝐷 𝑢 V Impact > V Critical : Detonation 𝑊 𝑒 Symbol Definition Unit Critical impact velocity [m/s] V Critical for warhead detonation Fragment critical [m] d dimension or diameter Fragment Projectile shape [-] B coefficient Warhead cover [m] t thickness [m 3/2 s -1 ] Explosive sensitivity Warhead A coefficient Cover plate protection [-] C coefficient
R ESEARCH Q UESTION Supporting Munitions Safety Supporting Munitions Safety • How can tilted and off-centre fragment impact variation be implemented in a response model for probabilistic prediction of munitions initiation response? Bron: MSIAC, NATO
I NITIATION M ODEL D EVELOPMENT Supporting Munitions Safety Supporting Munitions Safety Augment the Jacobs-Roslund model • Velocity variation: can already account for it • Aim point variation: match pressure histories with a reduced velocity based on oblique impact • Projectile tilt upon impact: match pressure histories with a reduced velocity based on oblique impact Use previous 3D hydrocode modeling as data set • 1-D GODLAG hydrocode within Temper for impact velocity and impactor thickness studies • Use 1-D results to infer new velocity relationships for impact point offset and projectile tilt Baker et al., “Insensitive Munitions Fragment Impact Gun Testing Technology Challenges” Propellants, Explosives, Pyrotechnics 10.1002/prep.201600045, 2016.
A PPARENT V ELOCITY C ONCEPT M ODEL Supporting Munitions Safety Supporting Munitions Safety G EOMETRICAL A SPECTS OF F RAGMENT I MPACT 𝑊 1 = 𝑊 0 ∗ cos 𝜄 + 𝛾 𝑌 𝜄 = tan −1 (− 𝑆 2 − 𝑌 2 ) Θ + β ( β clockwise is negative)
M ODEL V ALIDATION USING H YDROCODE C ALCULATIONS Supporting Munitions Safety Supporting Munitions Safety 𝑊 1 = 𝑊 0 ∗ cos 𝜄 + 𝛾 • Reproduce 3-D pressure histories in 1-D • Use resulting 1-D impact velocities for apparent velocity quantification and validation
M ODEL VALIDATION Supporting Munitions Safety Supporting Munitions Safety 3-D and 1-D model pressure histories for -10° tilted impact 12,00 10,00 Pressure [GPa] 8,00 6,00 4,00 2,00 0,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 10,00 Time [ μ s] 1-D model with v=2342 m/s 1-D model with v=2074 m/s 1-D model with v=1699 m/s 3-D model -10° tilt and 0mm off-centre 3-D model -10° tilt and 12.5mm off-centre 3-D model -10° tilt and 25mm off-centre
M ODEL VALIDATION Supporting Munitions Safety Supporting Munitions Safety Average 1-D hydrocode velocities for different fragment impact orientation 2700 2500 Velocity [m/s] 2300 2100 1900 1700 1500 Fragment orientation
M ODEL VALIDATION Supporting Munitions Safety Supporting Munitions Safety Model velocities (V 1 ) and hydrocode velocities 2600 Impact Velocity (m/s) 2400 2200 2000 1800 1600 1400 V,hydrocode,avg Model 𝑊 1 = 𝑊 0 ∗ cos 𝜄 + 𝛾
M ODEL VALIDATION Supporting Munitions Safety Supporting Munitions Safety Model velocities (V 1 ) and hydrocode velocities 2600 Impact Velocity (m/s) 2400 2200 2000 1800 1600 1400 Model λ=3,832 (SSD first 8 data points) V,hydrocode,avg 0 ∗ (cos 𝜄 + 𝛾 ) λ 0 ∗ (cos 𝜄 + 𝛾 ) 3.832 𝑊 1 = 𝑊 0 ∗ cos 𝜄 + 𝛾 𝑊 1 = 𝑊 𝑊 1 = 𝑊
M ODEL I MPLEMENTATION Supporting Munitions Safety Supporting Munitions Safety ( JR Leibbrandt Model) O FFSET & T ILT M ODIFIED J ACOBS -R OSLUND (co s( 𝜄 + 𝛾) 𝜇 ∗ 1 + 𝐶 ∗ 1 + 𝐷 𝑢 𝐵 𝑊 𝐷𝑠𝑗𝑢𝑗𝑑𝑏𝑚 = 𝑒 0.5 ∗ ) 𝑒 Symbol Definition Unit V Critical Critical impact velocity for warhead [m/s] detonation d Fragment critical dimension or diameter [m] θ Angle of tangent at impact point [°] β Fragment’s angle of tilt [°] Fragment λ Leibbrandt-coefficient [-] B Projectile shape coefficient [-] t Warhead cover thickness [mm] [m 3/2 s -1 ] A Explosive sensitivity coefficient Warhead C Cover plate protection coefficient [-]
P ROBABILISTIC ANALYSIS Supporting Munitions Safety Supporting Munitions Safety
FI Case Study Supporting Munitions Safety • Input parameters: o Target explosive: PBXN-9 o Target cover thickness ( t ): 8.6mm o Fragment shape (NATO standard cone) o Fragment critical dimension (d) • Variables o Fragment impact velocity ( V ) o Fragment tilt o Fragment aimpoint • Output o Critical impact velocity for detonation ( Vc ) o Detonation likely or not? Example: 155 mm projectile
P ROBABILISTIC I NITIATION C ASE S TUDY Supporting Munitions Safety Supporting Munitions Safety - V Critical = 1859 m/s ( Deterministic ) - V Impact = 1900 m/s , σ = 30 m/s, no tilt or offset - Deterministic prediction: 100% Detonation - Probabalistic prediction: 91% of time detonation - Now add tilt (β = 0 ° , σ = 4 ° ) and offset impact position X (off-centre) [mm] Detonation [%] σ = 2,5 Center Aimpoint 73.3 σ = 12,5 Center Aimpoint 41.6 σ = 25 Center Aimpoint 25.9
P ROBABILISTIC I NITIATION C ASE S TUDY Supporting Munitions Safety Supporting Munitions Safety - V Critical = 1859 m/s ( Deterministic ) - V Impact = 1830 m/s, σ = 30 m/s, no tilt or offset - Deterministic prediction: 0% Detonation - Probabalistic prediction: 16.6% of time detonation - Now add tilt (β = 0 ° , σ = 4 ° ) and offset impact position Off-center Impact [mm] Detonation [%] σ = 2.5 Center Aimpoint 8.9 σ = 12.5 Center Aimpoint 4.2 σ = 25 Center Amipoint 2.1
C ONCLUSIONS AND R ECOMMENDATIONS Supporting Munitions Safety Supporting Munitions Safety • Tilt and off-centre have influence on munitions response to fragment impact – Commonly observed angle of tilt during FI testing has some influence – Commonly observed off-centre distance during FI testing has a large influence • It is possible that munitions “pass” fragment impact tests unjustly due to testing variation and a small number of tests – Perhaps tilt and off-center impact should be accounted for when reviewing test results • STANAG 4496 updated March 2019 (STANAG 4496 Ed. 2, AOP-4496 Ed. A) – Tilt: ± 10 ° tilt recommendation – Off-center distance: Aimpoint accuracy diameter to be defined before testing
Supporting Munitions Safety Supporting Munitions Safety QUESTIONS?
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