airblast equivalent weight and yield determinations …€¦ · each scaled parameter of interest...
TRANSCRIPT
A-P-T Research, Inc. | 4950 Research Drive, Huntsville, AL 35805 | 256.327.3373 | www.apt-research.com
ISO 9001:2015 CertifiedT-18-00915 | 1
AIRBLAST EQUIVALENT WEIGHT AND YIELD DETERMINATIONS BASED ON MEASUREMENT OF ENERGY AND OTHER BLAST WAVE PARAMETERS
Michael M. Swisdak, Jr. (A-P-T Research, Inc.)
Lippe D. Sadwin (Sadwin Consultancy)
A-P-T Research, Inc. | 4950 Research Drive, Huntsville, AL 35805 | 256.327.3373 | www.apt-research.com
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OVERVIEW
Classic Equivalent Weight Defined
New Methodology Description
Sample Problem
Shockwave Energy Definition
Shockwave Energy Application to Pressure-Time Waveform
Shockwave Energy Closed Form Solution for Modified Friedlander
Waveform
Summary
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EQUIVALENT WEIGHT ANALYSIS FOR PRESSURE
Pre
ssu
re (
psi)
Scaled Distance (ft/lb1/3
)
Test
Standard
s
T
P
𝐸𝑊𝑝 = 𝜆𝑇 𝜆𝑆3
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EQUIVALENT WEIGHT ANALYSIS FOR SCALED PARAMETERS, X (TIME OF ARRIVAL, DURATION, IMPULSE)
Scale
d P
ara
mete
r (x
/lb
1/3
)
Scaled Distance (ft/lb1/3
)
Test
Standard
EW Slope Line
S
T
EW= 𝜆𝑇 𝜆𝑆3
Values of scaled range
(λ) are taken from the
test and standard curves
at the intersections of a
sloped line
corresponding to the
slope of the logarithmic
cycles of the graph.
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AN ALTERNATIVE CALCULATIONAL METHODOLOGY
Assume that the “Standard” Explosive is a hemispherical TNT surface burst
as defined by Kingery and Bulmash (ARBRL-TR-02555)
For each scaled parameter, X (time of arrival, duration, impulse), consider the
ratio of the scaled parameter to the scaled distance
(X/W1/3)/ (R/W1/3) = X/R(note: relation works in both Imperial and SI units)
Next consider the scaled distance as a function of this parameter ratio for
each scaled parameter of interest
To calculate a yield based on a given scaled parameter (X/W1/3) at the
measurement range R, perform the following steps:
Calculate the ratio of the parameter to the range (X/R)
Enter the appropriate graph and determine the hemispherical TNT scaled distance
corresponding to that parameter ratio
Effective weight of TNT = (actual range R/effective TNT scaled distance)3
Equivalent weight = Actual weight/Effective Weight
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SCALED TIME OF ARRIVAL/SCALED DISTANCE RATIO
0.1
1
10
100
0.1 1
Sca
led
Dis
tan
ce (
ft/l
b1/3)
Scaled Time of Arrival-Scaled Range Ratio (ms/ft)
500
0.03
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SCALED DURATION/SCALED DISTANCE RATIO
0.1
1
10
100
0.01 0.1 1
Sca
led
Dis
tan
ce (
ft/l
b1
/3)
Scaled Duration-Scaled Range Ratio (ms/ft)
500
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SCALED POSITIVE IMPULSE/SCALED DISTANCE RATIO
0.1
1
10
100
0.0001 0.001 0.01 0.1 1 10 100
Sca
led
Dis
tan
ce (
ft/l
b1/3)
Scaled Positive Impulse-Scaled Range Ratio (psi-ms/ft)
500
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SCALED REFLECTED IMPULSE/SCALED DISTANCE RATIO
0.1
1
10
100
0.001 0.01 0.1 1 10 100 1000
Sca
led
Dis
tan
ce (
ft/l
b1/3)
Scaled Reflected Impulse-Scaled Range Ratio (psi-ms/ft)
500
A-P-T Research, Inc. | 4950 Research Drive, Huntsville, AL 35805 | 256.327.3373 | www.apt-research.com
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SAMPLE CALCULATION
An unknown material weighing 500 lb detonates. At a range of 90 ft,
the following parameters are measured:
Time of arrival = 40.0 ms
Positive duration = 21.0 ms
Positive impulse = 60.0 psi-ms
Based on these values, what is the effective TNT hemispherical
weight and the effective hemispherical TNT equivalence?
A-P-T Research, Inc. | 4950 Research Drive, Huntsville, AL 35805 | 256.327.3373 | www.apt-research.com
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SAMPLE CALCULATION (CONTINUED)
Time of Arrival
TOA ratio = 40.0/90.0 = 0.44 ms/ft
Effective hemispherical scaled distance = 10.05 ft/lb1/3
Effective TNT yield = (90/10.05)3 = 718 lb
Effective TNT Equivalence = (718/500) = 1.44
Duration
Duration ratio = 21.0/90.0 = 0.23 ms/ft
Effective hemispherical scaled distance = indeterminate
Effective TNT yield = (90/???)3 = indeterminate
Effective TNT Equivalence = (718/500) = indeterminate
Positive Impulse
Impulse ratio = 60.0/90.0 = 0.67 psi-ms/ft
Effective hemispherical scaled distance = 11.10 ft/lb1/3
Effective TNT yield = (90/11.10)3 = 533 lb
Effective TNT Equivalence = (533/500) = 1.07
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HEMISPHERICAL EQUIVALENCE CALCULATOR
23 May 2018
Hemispherical
Calculator
Developed
by
Lippe D. Sadwin
Michael M. Swisdak, Jr.
Version 2.0
and
Equivalence
(HEC)
Tool developed to automate
calculation process
Tool available from author
A-P-T Research, Inc. | 4950 Research Drive, Huntsville, AL 35805 | 256.327.3373 | www.apt-research.com
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SHOCKWAVE ENERGY
The shockwave energy flux is defined as:
𝐸 =1
𝜌𝑈 𝑃𝑠
2 𝑑𝑡
ρ = Air density
U = Wave velocity
U = Characteristic Impedance
Ps = Overpressure
t = Time
For underwater explosions, the characteristic impedance, ρU, is
nearly constant except very close to the explosion point. However,
this is not the case in air. The product ρU in real air is a strong
function of γ, the ratio of the specific heats.
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CHARACTERISTIC IMPEDANCE (U) OF AIR
100
1000
104
105
106
0.001 0.01 0.1 1 10 100 1000
*
U (
kg
/(m
2-s
)
P (bars)
Ps < = 0.6 bars: ρU = 421.43 e0.918 Ps
0.6 < Ps <1.2 bars: ρU = 504.47e0.6Ps
Ps >= 1.2 bars: ρU = 868.86 Ps0.763
A-P-T Research, Inc. | 4950 Research Drive, Huntsville, AL 35805 | 256.327.3373 | www.apt-research.com
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APPLICATION
For digitized pressure-time wave-forms, application can be
accomplished in the same manner as the positive impulse—by
numerically integrating the wave form
Impulse—numerically integrate p(t) dt from 0 to the , the positive phase
duration
Energy—numerically integrate [P(t)]2 dt from 0 to the , the positive phase
duration
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SAMPLE WAVEFORM
0.5 kg TNT
Detonated 1m
above ground
Range = 7m
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AIRBLAST WAVEFORMS
Assume that a blast wave can be described by a Modified Friedlander
Wave Form:
P(t) = Ps*(1-t/)*e-at
Ps = Measured peak overpressure
= Positive phase duration
t = Time (in same units as )
“a” = Modified Friedlander parameter
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MODIFIED FRIEDLANDER IMPULSE AND ENERGY
Impulse
If the Modified Friedlander wave form is integrated between 0 and , a
value for the Positive Phase Impulse, I, is obtained
Energy
If the integral of [P(t)]2 between 0 and is taken, a value for E(U) will be
obtained:
I = Ps*(aτ + e-aτ -1)/(τ*a2) (1)
E*(U) = {[(2*a*τ*(a*τ-1)-e-(2*a*τ) + 1]/(4*τ2*a3)}*Ps2 (2)
Measured values of Ps, I, and can be used with Equation 1 to
calculate a for each (Ps, I, ) combination
Each combination of (Ps, I, , a ) can be used with Equation 2 to
calculate E*(U)
A-P-T Research, Inc. | 4950 Research Drive, Huntsville, AL 35805 | 256.327.3373 | www.apt-research.com
ISO 9001:2015 CertifiedT-18-00915 | 19
MISTY PICTURE EXAMPLE
4,684.7 ton hemisphere of Ammonium Nitrate/Fuel Oil
Use airblast data compiled on the event to estimate the hemispherical
TNT equivalent weight based on incident pressure, positive phase
impulse, and energy flux
A-P-T Research, Inc. | 4950 Research Drive, Huntsville, AL 35805 | 256.327.3373 | www.apt-research.com
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MISTY PICTURE
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 10 100
PressureImpulseEnergy
Eq
uiv
ale
nt
Wei
gh
t
(Rel
ati
ve
to H
em
isph
eric
al T
NT
)
Scaled Distance (ft/lb1/3
)
A-P-T Research, Inc. | 4950 Research Drive, Huntsville, AL 35805 | 256.327.3373 | www.apt-research.com
ISO 9001:2015 CertifiedT-18-00915 | 21
SUMMARY
Conventional methodologies for calculating equivalent weight have
been reviewed
A new calculation methodology was described and its use explained
through the solution of a sample problem
A new tool implementing the procedure was introduced
The concept of shockwave energy as a metric for explosions in air
was presented and implementation methodologies discussed
The use of a Modified Friedlander waveform description for the
observed pressure-time wave form was described and a closed form
solution of the shockwave energy derived