Lethality to Humans Due to Blast Effects Morris

ScientificResearchCorporation

Lethality to Humans - 2002 Mines, Demolition andNon-Lethal Conference June 4, 2002

Lethality to Humans Due to Blast Effects

from Buried Landmines

Introduction

Sponsored byU. S. Army

Project Manager Instrumentation, Targets andThreat Simulators (PM ITTS)

Presented byScientific Research CorporationNorman Morris, Sr. Engineer



Coordinates of sensor head and soldier feetlocation (x, y, z) are transmitted andplotted in real time within TMS.

TMS

OkToo fastUncovered

Foot

Legend

Motivation: Threat Minefield System (TMS)

TMS supports countermine testing and training withreal time position and sensor data collection and analysis.



Threat Minefield System Overview

OperatorInstrumentation

SurveyorInstrumentation

TMS will Enable:

DIS/HLATHREATS

NODE

Phase 1 Requirements / Capabilities

Mass StorageMine Properties

DatabasePost-ExerciseAnalysis

Graphics & Display Evaluator

WorkstationReal-TimeAnalysis

2-Way RemoteCommunications

Event Output

• Actual and Virtual Minefield Environments• Real-time Operator Analysis Capability for Training • Testbed for De-mining Instrumentation Development

Pre-ExerciseSetup

Sensor Input

Post Phase 1 Enhancements

VirtualInterface

Enhanced MineSimulations

Flexible SiteSelection

Site SpecificRequirements

Detector SpecificRequirements

User SpecificRequirements

VehicularInstrumentation



VIRTUAL MINE

MODELS

ANALYSIS,STATISTICS,& GRAPHICS

REAL

• (X,Y,Z)• ALARMS

• Detector sweeps• PD• PFA• Evaluations• Blasts & effects

VIRTUALMINE

MODELS

ANAL., STATS & GRAPHICS

• (X,Y,Z)• ALARMS

VIRTUAL

ACOUSTICFEEDBACK

(x,y,z), shape, EM responses oftargets, soil & clutter, ...

INO

UT

DIS /HLA

(x,y,z), shape, ...

TMS PROCESSOR

TMS PROCESSOR

• Sweeps• PD• PFA• Eval.• Blasts

TMS Real and Virtual Processing

• ALERTS

• ALERTS



I

LETHALITIES DUE TO SHOCK WAVES



Mine shock parms

R

ComputeBlast

Overpressure

ComputeBlast

Duration

LovelaceFoundation

LethalityAnalysis

plethalCompute

Range to kth

BattlefieldEntity

TMS/MISP Blast Effects System - Shock Wave

Threat Minefield System (TMS)

When a mine detonation occurs:

Mine loc.Entityloc.

MISP* Shock Wave Analysis Component

*Mine Interaction Simulation Program



0.11

10100

100010000

1000001000000

10000000100000000

100000000010000000000

0.01 0.1 1 10 100

Peak

Ove

rpre

ssur

e (p

sig)

Distance (ft)

Peak Overpressure vs. Distance (Mahn)

Pover ~ 29/Z + 552/Z2 + 1106/Z3 where: Z = (dist. from explosive) ÷ (wt. of TNT to match explosive effect)1/3



0.01

0.1

1

10

0.01 0.1 1 10 100 1000

Scal

ed D

urat

ion

I II III

Scaled Distance

Shock Wave Duration vs. Distance (Baker)

Rscaled=[R(p0)1/3]/E 1/3

Tscaled=[Tsa0(p0)1/3]/E 1/3

where: a0= ambient sound speed (ft/s) E = explosive energy (in-lb) p0 = ambient pressure (psi) R = dist. from explosive Ts = side-on duration (s)



10

100

1000

0.1 1 10 100 1000 10000

Ove

rpre

ssur

e (p

si)

Duration (msec)

99%90%

50%10%

1%

Lethality Due to Shock Waves (Lovelace)

Graphs and equations also availablefor parallel blast winds. All formulaslisted in Appendix B of paper



Use of Lovelace Foundation Analyses

PLethal

Overpressure

Duration

10

102

103

104

0.1 1 10 102 103 104



II

LETHALITIES DUE TO CASE(PRIMARY) FRAGMENTATION



Battlefield Entity parms

TMS/MISP Blast Effects System - Fragmentation

GurneyInitial

Velocity

Trajectory Analyses: • Torso impact tests • Impact velocities

ExtractRandom

Fragments

Detonated mine parms

Ahlers &FeinsteinLethalityAnalysis

plethal



Fragment FlightAngles

Impacting FragmentMass & VelocityMISP Fragment Analysis Component



Mott’s Distribution of Fragments

m (mass)

(No.

of f

ragm

ents

)

0

200

400

600

800

1000

0 0.25 0.5 0.75 1

N(m)=Aexp(-Bm½), Mott

N(m)=Aexp(-Bm), Exponential

N

E{Total number of hurled fragments} = AA = M0 /(2B) where:M0 = total casing massB = f{casing thickness, diameter and explosive}

∑=

=N

ii Mm

10



Illustrative Example for Mott’s Usage

m (mass)

0

200

400

600

800

1000

0 0.5 1.0 1.5 2

(No.

of f

ragm

ents

)

N

0.50 0.5250.49

535251

53 Fragments of mass > 0.49

52 Fragments of mass > 0.50

••

•

••

•

0.5080.493Nearest integerrepresentation

Inverse map

∑=

=N

ii Mm

10



Fragment EjectaObstruct Angle

Projected patch(incremental area)

Assume:• Fragments eject at right angles to the surface.• Fragment density is uniform on casing.

θ

Ground

θ

Ejected Fragment Flight Angles and Densities



Initial Fragment Velocity Formula (Gurney)

M / C

6000

7000

8000

9000

10000

11000

12000

0 0.2 0.4 0.6 0.8 1

Cylinder

Sphere

( )CME

V/20/11

20 +

=In

itial

Vel

ocity

charge ofor weight mass C

casing ofor weight mass MVelocity) sGurney’ TNT,(for fps 8000 2

:

=

==E

where



SRC trajectory algos: • Runge-Kutta • Closed-form approx.

Battlefield Entity parms

TMS/MISP Blast Effects System - Fragmentation

GurneyInitial

Velocity

Trajectory Analyses: • Torso impact tests • Impact velocities

ExtractRandom

Fragments

Detonated mine parms

Ahlers &FeinsteinLethalityAnalysis

plethal



Fragment FlightAngles

Impacting FragmentMass & VelocityMISP Fragment Analysis Component



Trajectories & Velocities

Formulas and algorithms for aboveapproaches listed in Appendix A of paper.

Vz

(m/s

ec)

time (sec)

X (m)Z

(m) Closed form

approximation

Runge-Kutta 4th Order simulationtime (sec)

Vx

(m/s

ec)

Runge-Kutta 4th Order simulation

Closed formapproximation

Runge-Kutta 4th Order simulation

Runge-Kutta vs. Closed-Form

Component Velocities TrajectoryCase: θ0 = 10°, v0 = 677 m/sec

Formulas and algorithms for above approaches listed in Appendix A of paper.



10

100

1000

0.001 0.01 0.1 1 10

10%

90%50%

Kill Rate:

Injury Threshold

Ter

min

al V

eloc

ity

(fps

)

Fragment Weight (lbs)

Abdomen and Limbs

Lethality Due to Fragment Impact (Ahlers)

Graphs and equations also available forhead and thorax impacts; all formulaslisted in Appendix B of paper



Use of Ahlers & Feinstein Analyses

P(Lethal|Hit)

10

100

1000

0.001 0.01 0.1 1 10

Velocity, v

Weight, w

Ahlers & Feinstein Analyses Algorithm

Injury Threshold



• Motivation...The Threat Minefield System (TMS)

• Shock wave lethality - Shock wave duration (Baker) - Shock wave overpressure (Mahn) - Lethality computations (Lovelace Foundation)

• Fragmentation lethality - Mass distribution (Mott) - Ejection angle of flight (geometry) - Fragment initial velocity (Gurney) - Fragment trajectories & impact velocities (SRC) - Lethality computations (Ahlers & Feinstein)

Summary



Backup

Backup (Support) Slides



DIS/HLAComms CSCICSCI

Op Data (Reduced)TSMO

THREATSNode

Op Data (Raw)•Position{x,y,z(t)}•alarm/event (binary)•Sensor I/Q/Video•Audio / Video

MassStorage(Cumulative)

•RAID•Internal HD•R/W CD•Firewire HD

Op

Dat

a(R

aw)

TMS Master CSCICSCI

Mine InteractionSimulationProgram CSCI CSCI

Inst

rum

enta

tion

CSC

IC

SCI RS-232 IDDIDD

CT

MS

IDD

IDD

CTMS CSCICSCI

•Evaluation/User Interface

•Mine Image JPG Files CSCICSCI

•MS Access Reports

•Ground Truth File (Survey)

Data Comms/DSP CSCICSCI

•Pre-Exercise•Exercise•Post-Exercise

States

Wand Survey CSCICSCI(Ground Truth)• Site Data (Pos., Envir.)• Target Data (Pos., Envir.)

SharedMemoryResource

• Mode Data

(Static)•VMM Data•Ground Truth

(Dynamic)•Op Data•MISP Results•Interface Flags

•Position File (Cumulative)

•Alarm File (Cumulative)

VMM Database CSCI CSCI(Static)

•Political•Physical

•Statistical - Research - Ops

N

Ethernet IDDIDDM

IEEE 1394 IDDIDDL

TMS ARCHITECTURE ELEMENTSTMS ARCHITECTURE ELEMENTS



ri=|{Poper}i - Pmine|ri

EstimateShock

DurationAnd

Over-pressure

LovelaceFoundation

Analysis {PLethal}i

i++

Mineshockparams

Next OperatorData/Comms

RGM

Y

PositionSensor

MISPDetonation

Yes/No?

Foot/Wheel

N

No Action

i=1

Mineposition, Pmine

VMM/RGM

{Poper}i=1,2,...,N

MISP System for Lethal Probabilities



10

100

1000

10000

0.1 1 10 100 1000 10000

99%

90%50%

10%1%

Ove

rpre

ssur

e (p

si)

Duration (msec)

Lethality Due to Shock Wave (Lovelace)



10

100

1000

0.001 0.01 0.1 1 10Fragment Weight (lbs)

Ter

min

al V

eloc

ity

(fps

) Injury Threshold

90%

10%50%

Kill Rate: Head

Lethality Due to Fragment Impact (Feinstein)



1

10

100

1000

10000

0.001 0.01 0.1 1 10

Injury Threshold

90%

10%50%

Kill Rate:

Ter

min

al V

eloc

ity

(fps

)


Thorax

Lethality Due to Fragment Impact (Feinstein)



Determination of the Weight-Velocity Curve

10

100

1000

10000

0.001 0.01 0.1 1 10

V(w)=min {f1(w), f2(w)}, usedfor injury assessment


Vel

ocity

(fps

)

f2(w), linear curve based on MV4 hits

f1(w), linear curve based on MV2 hits



EXPLOSIVE

Baratol - 33 TNT, 67 BA(NO3)2 5200

Tritonal - 20 Aluminum, 80 TNT 7200TNT 8000

HBX-1 - 11 TNT, 67 Comp B,17 Aluminum, 5 D-2 8100

Comp B - 40 TNT, 60 RDX 8800Cyclotol - 30 TNT, 70 RDX 8860Cyclotol - 25 TNT, 75 RDX 8900Comp A3 - 9 wax, 91 RDX 9000RDX - 3 wax, 97 RDX 9200RDX - 100% 9300

Black powder - 10 S, 16 C, 74 KNO3 3100

Smokeless powder - double base 5500

fpsE ,2

Some Gurney Energy Constants (Henry)



vkvF rr

−=mdrag

y2dragdrag

)sin()sin(mm

y kvvkvFF

−=−== θθ

gkvvv −−= yy Thus &

(mach)C m,/k Where)cos(

ddd21

x2

x

=≡−=−=

CACkvvkvv

ρθ&

θ

∫=t

yxyxyx dtvvvvyxvv0

},,,{},,,{ &&

Which integration is performed by 4th-order Runge-Kutta*

*Note: Closed form exact solutions do not exist. Runge-Kutta numerical integration issuperior to closed-form approximate solutions for accuracy/speed/data-access.

X

Y

vr

Trajectory Equations of Motion



(1)TableFactor )Mach(dC

1/CRMach d MdC≡

0 .915.6 .9151 11.2 1.121.6 1.182 1.142.5 1.093 1.0810 1.08

Run Numerical IntegrationUser Inputs

.2sec)t( (mass)

1

0

0

≤∆

≡

hm

ACj

v

Md

θ

Initialization

θθ

ρθθ

sin

cos225.1

0

0

vv

vv

vv

y

x

=====

n. touchdowuntil topfromRepeat

},,,,{},,,,{nIntegratio Kutta-Rungeorder -4

/)/( equation- from Calculate

table)mach(C from R Calculate

21

21

(2)

(1)d

22

−−−−−−−−−−−−−−−−−−−−−−−

+⇒

−−−−−−−−−−−−−−−−−−−−−−−

−−=−=

=

+=

yxvvhtvvvvt

gvkvvvkvv

mjRmACk =

vvv

yxyxyx

th

yyxx

d

yx

&&

&&

ρρρρ

))))000102895.00134459(. 0152585(.07757(..1/(225.1

.1000/)2(

hthththt

yht

−−++=

=ρ

Trajectory Generation (Runge-Kutta)



0

0.6

1.0

1.2

1.6

2.0

2.5

3.0

10.0

0.915

0.915

1.0

1.12

1.18

1.14

1.09

1.08

1.08

Velocity (Mach) CD/CD,Mach1

Drag Coefficient CD vs. Velocity



Data/Comms

RGM

Y

PositionSensor

{Poper}i=1,2,...,N

ri

Ahlers3

& Feinstein4

Analysis( Update

max PLethal )

{PLethal}i

Mine Position, Pmine

Obtain Gurney1

Fragment InitialVelocity Estimates

Obtain Mott2

Fragment WeightDistribution

Fragmentation Parameters(AMSAA)

ObtainFragmentTrajectoryEstimates(∩ Oper.)

Init

iali-

zati

ons

Next Operator(i++)

i=1

Calculate: • Distance, ri

• Oper. area, Ai Ai=A0cos[θ(ri)],

ri=|{Poper}i - Pmine|

VMM/RGM

V,W

MISPDetonation

Yes/No?

Foot/Wheel

N

NoAction

Ai

OperatorInformation,Size, Weight,

etc.

MISP System for Fragmentation Lethalities



Fragment Density, ρ

PH

it

( ) ( ) ( )!

exp,

KAA

AKP operK

operoper

ρρ −= ( ) ( )operoperHit AAPP ρ−−=−=⇒ exp1,01

Using the Poisson Distribution* (with Aoper=2 ft2),

*See Wilbur B. Davenport, Jr.., William L. Root, “An Introduction to the Theory of Random Signals and Noise”McGraw-Hill, 1958, §7-2 (pp. 115-117)...Note that here we replace shot noise electron-emission times withfragment spatial locations and time intervals with spatial areas.

00.20.40.60.8

1

0 0.5 1 1.5 2 2.5 3

Prob. of at Least One Hit vs. Density



Probability of Hit Calculations

r

VMM/RGM LUT’s

A(r)Operator SizeInformation, A0

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6

Calculate:

• Oper. area, A A=A0cos[θ(r)]

Retrieve formine m:

• Fragment density at range r

ρ(r)

ρA

PHit

θ(ri), ρ(ri)

Poisson Distribution



1Joseph Petes, “Part IV. Explosive Effects: Blast and Fragmentation Characteristics” Annals of theNew York Academy of Sciences, Vol. 152, 1968, pp. 283-316

MATERIALPeak Pressure

(PM)TNT

Comp B/TiH2 70/30 1.13

Tritonal - 20 Aluminum, 80 TNT 1.07

TNT 1.00

HBX-1 - 11 TNT, 67 Comp B,17 Aluminum, 5 D-2

1.21

Comp B - 40 TNT, 60 RDX 1.13

Cyclotol - 30 TNT, 70 RDX 1.14

RDX - 5 wax, 95 RDX 1.19

Impulse(I)TNT

1.13

1.11

1.00

1.21

1.06

1.09

1.16

Explosive D 0.85 0.81

Comp A-3 1.09 1.07

Picratol 0.90 0.93

Minol II 1.24 1.22Torpex II 1.23 1.28

H-6 1.27 1.38

Pentolite 1.16 1.15HBX-3 1.16 1.25

TNETB 1.13 0.96

RDX - 2 wax, 98 RDX 1.19 1.16

Equivalent Weights for Free Air Effects1

Lethality to Humans Due to Blast Effects Morris

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