ABSTRACT 
 
 
 
 
Title of Document: VEHICLE SHAPING FOR MINE 
BLAST DAMAGE REDUCTION 
  
 Kevin Genson,  
Master?s of Science, 2006 
  
Directed By: Dr. William Fourney, Chairman,  
Aerospace Engineering Department 
 
 
When a buried explosive is detonated beneath a target (such as a vehicle), the 
target is rapidly loaded by flying ejecta, high pressure gas, and shock waves.  This 
paper explores how changes in the shape of the underside of a target affect the total 
impulse captured from the detonation of a buried charge.  The effects of changes in 
target height and charge burial depth are also examined.  Testing was conducted on 
dihedral target plates using 0.636 gram charges.  These were buried in saturated sand 
at three depths, and shaped targets were placed at four heights above the surface.  The 
impulse applied to the plate by the exploding charge was determined through analysis 
of high speed digital video recordings.  Changing the geometry of the target reduced 
the impulse by up to 45%.  Increasing standoff distance reduced impulse by up to 
70%.  
  
  
 
 
 
 
 
 
 
VEHICLE SHAPING FOR MINE BLAST DAMAGE REDUCTION    
 
 
 
By 
 
 
Kevin William Genson 
 
 
 
 
 
 
Thesis submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Master?s of Science 
2006 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Dr. William Fourney, Chair 
Dr. Jim Duncan 
Dr. Henry Haslach 
Mr. Leslie Taylor 
  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
? Copyright by 
Kevin William Genson 
2006 
 
 
 
 
 
 
 
 
 
 
 
 
 ii  
Acknowledgements 
I would like to thank the following individuals for their assistance in 
completing this research.  Without them my research would have not been possible. 
Dr. William Fourney, for your leadership, guidance, and patience.  Meeting 
your expectations was a rewarding and educational challenge.  I could not have asked 
for a better advisor. 
Dr. Robert Bonenberger, Uli Leiste, Chi-Ming Wang, Alexander Tsarev, and 
all of the German students who worked at the Dynamic Effects Lab.  Thank you for 
your support, your advice, and countless hours of entertainment. 
Mr. Leslie C. Taylor, for sharing your experience and mentorship.  Your 
insight into explosive effects, as well as your advice regarding my research, was 
invaluable. 
Mr. Brian Beechener, my undergraduate assistant, for your dauntless work in 
completing many tests with the utmost in precision and efficiency.   
Mr. Timothy Hennessey and the Office of Naval Research (Contract ONR 
N000140610335), for making this research possible and for providing me with the 
opportunity to make even larger explosions. 
And lastly, my family for their love and support.  Thank you Mom for your 
kind words and care, and the little bits of advice that always seem to fit right.  Thank 
you Dad for your wisdom and insight, and for always having the right perspective on 
things.  Mom, Dad, Laura; I love all of you.
 
 iii  
Table of Contents 
Acknowledgements ..................................................................................................... ii 
Table of Contents .......................................................................................................iii 
List of Figures.............................................................................................................. v 
List of Tables ............................................................................................................. vii 
Chapter 1: Introduction & Background................................................................... 1 
Overview................................................................................................................... 1 
1.1 Antivehicular (AV) Mines ............................................................................ 2 
1.2 Casualty Mechanisms ................................................................................... 4 
1.3 Physics of Mine Blasts.................................................................................. 5 
1.3.1 Early Interaction & Shock .................................................................... 6 
1.3.2 Gas Expansion ...................................................................................... 6 
1.3.3 Soil Ejecta ............................................................................................. 7 
1.4 Load Mechanism Components ..................................................................... 8 
1.4.1 Shock Load ........................................................................................... 9 
1.4.2 Impact Load .......................................................................................... 9 
1.4.3 Distributed Load ................................................................................. 11 
1.5 Parameter Investigaton................................................................................ 12 
1.5.1 Standoff Distance................................................................................ 12 
1.5.2 Depth of Burial ................................................................................... 12 
1.5.3 Soil Condition ..................................................................................... 15 
1.5.4 Target Shape ....................................................................................... 15 
1.6 Blast Scaling ............................................................................................... 16 
Chapter 2: Research Equipment ............................................................................. 18 
Overview................................................................................................................. 18 
2.1 Explosive Charge........................................................................................ 18 
2.2 Phantom Digital Camera System................................................................ 19 
2.3 Phantom Software....................................................................................... 21 
2.4 Firing System.............................................................................................. 22 
2.5 Dummy Charge........................................................................................... 23 
2.6 Trigger Mechanism..................................................................................... 24 
2.7 Test Bed Area ............................................................................................. 25 
2.8 Target Plates................................................................................................ 26 
Chapter 3:  Research Methodology......................................................................... 28 
Overview................................................................................................................. 28 
3.1 Dihedral Plate Fabrication .......................................................................... 28 
3.1.1 Dihedral Plate Machining Procedure .................................................. 30 
3.2 636 mg Charge Fabrication......................................................................... 34 
3.3 Initial Setup and Testing ............................................................................. 35 
3.3.1 Test Bed Setup .................................................................................... 35 
3.2.2 Camera Setup...................................................................................... 41 
3.2.3 Testing................................................................................................. 42 
3.4 Data Collection and Analysis...................................................................... 43 
3.4.1 Collection of Data............................................................................... 43 
3.4.2 Analysis of Data.................................................................................. 45 
 
 iv  
Chapter 4: Results..................................................................................................... 48 
Overview................................................................................................................. 48 
4.1 Presentation of Target Shape Findings ....................................................... 49 
4.1.1 Results at Constant Depth of Burial.................................................... 50 
4.1.2 Results at Constant Plate Angle.......................................................... 56 
4.1.3 Results at Constant Standoff Distance................................................ 65 
4.1.4 Pyramid v. Dihedral Shaped Plates..................................................... 72 
4.2 Discussion of Target Shape Findings ......................................................... 74 
4.2.1 Standoff Distance................................................................................ 74 
4.2.2 Depth of Burial ................................................................................... 79 
4.2.3 Dihedral Plate Angle........................................................................... 83 
4.3 Scaling and Expected Values...................................................................... 88 
4.4 Blast Damage Effects: Erosion and Impact ................................................ 98 
4.4.1 Impact Region................................................................................... 101 
4.4.2 Erosion Region.................................................................................. 104 
Chapter 5: Summary & Conclusions .................................................................... 105 
5.1 Summary................................................................................................... 105 
5.2 Conclusions............................................................................................... 107 
5.3 Future Work.............................................................................................. 109 
Appendix A:  Deformable Plate Shapes................................................................ 110 
Appendix B:  Additional Target Shapes ............................................................... 116 
B.1 Pyramid and Dihedral Shapes................................................................... 117 
B.2 Pyramid Grid Target Shapes..................................................................... 120 
Appendix C:  Standoff Distance Measured from Centroid ................................ 124 
Glossary ................................................................................................................... 128 
References................................................................................................................ 130 
 
 v  
List of Figures 
Figure 1.1:  Unprotected 5/4 Ton Truck Against a 6.5kg TNT Antitank Mine [1]...... 3 
Figure 1.2:  Unprotected 5/4 Truck After Mine Test [1] .............................................. 3 
Figure 1.3:  Fragments and Ejecta Created After Mine Blast [1] ................................. 4 
Figure 1.4:  Time Sequence of Mine Explosion [1]...................................................... 5 
Figure 1.5:  Detonation Products and Soil Ejecta [1] ................................................... 7 
Figure 1.6:  Small-Scale Mine Blast Test (Top) and Simulation (Bottom) [10] .......... 8 
Figure 1.7:  Initial Blast from 0.5g Charge at 0.69? Depth of Burial ......................... 10 
Figure 1.8: Elapsed Time (40?s/frame) of Buried Charge Explosion for 3 DOBs .... 14 
Figure 1.9:  Casspir APC ............................................................................................ 15 
Figure 2.1:  636 mg Charge ........................................................................................ 18 
Figure 2.2:  Phantom v7.1 High Speed Digital Camera [12]...................................... 19 
Figure 2.3:  Phantom v7, Camera Stand, Protective Skirt, and Cover........................ 20 
Figure 2.4:  Phantom Camera Control Software......................................................... 21 
Figure 2.5:  FS-10 EBW Firing System...................................................................... 22 
Figure 2.6:  Dummy Charge ....................................................................................... 23 
Figure 2.7:  Trigger Mechanism ................................................................................. 24 
Figure 2.8:  Test Bed Setup and Saturation System.................................................... 25 
Figure 2.9:  Plate Angle .............................................................................................. 26 
Figure 2.10:  0? plate, 13? Bent Plate, 13? Single Pyramid ........................................ 27 
Figure 3.1:  Fixture Plate, Bolts, and Aluminum Plate............................................... 28 
Figure 3.2:  Target dimensions ................................................................................... 29 
Figure 3.3:  Underside of 20? Plate (note removed material)..................................... 29 
Figure 3.4:  Clamping Aluminum Plate to Mill Table................................................ 30 
Figure 3.5:  Milling the Edges of the Target Plate...................................................... 30 
Figure 3.6:  Tapping the Drilled Hole Pattern ............................................................ 31 
Figure 3.7:  Mounting Aluminum Plate to Fixture Plate ............................................ 31 
Figure 3.8:  Angled Mill Table ................................................................................... 32 
Figure 3.9:  Clamping Fixture Plate to Angled Mill Table......................................... 32 
Figure 3.10:  Facing the Target Plate.......................................................................... 33 
Figure 3.11:  Finished 13? Target Plate ...................................................................... 33 
Figure 3.12:  636 mg Charge Fabrication Components.............................................. 34 
Figure 3.13:  636 mg Charge ...................................................................................... 34 
Figure 3.14:  Compacted Sand Bed ............................................................................ 35 
Figure 3.15:  Test Bed and Sand Plane....................................................................... 36 
Figure 3.16:  Wired 636 mg Charge ........................................................................... 36 
Figure 3.17:  Placement Grid for Charge and Plate.................................................... 37 
Figure 3.18:  Confirming Depth of Burial .................................................................. 37 
Figure 3.19:  Standoff Posts and Buried Charge......................................................... 38 
Figure 3.20:  Measuring Standoff Distance ................................................................ 38 
Figure 3.21:  Leveled Target Plate.............................................................................. 39 
Figure 3.22:  Oversaturated Sand (Left) and Properly Saturated Sand (Right) .......... 39 
Figure 3.23:  Completed Test Setup ........................................................................... 40 
Figure 3.24:  Camera Configuration and Plate Display.............................................. 41 
Figure 3.25:  Typical Buried Charge Test .................................................................. 42 
 
 vi  
Figure 3.26:  Oversaturated Sand (Left) and Properly Saturated Sand (Right) .......... 44 
Figure 3.27:  Initial Displacement Curve Graph......................................................... 45 
Figure 3.28:  Total Displacement Curve Graph.......................................................... 47 
Figure 4.1: Total Impulse Tests at Constant 0.04? Depth of Burial ........................... 51 
Figure 4.2: Total Impulse Tests at 0.25? Depth of Burial .......................................... 53 
Figure 4.3:  Total Impulse Tests at 0.5? Depth of Burial ........................................... 55 
Figure 4.4:  Total Impulse Tests with 0 Degree Angled Plate.................................... 57 
Figure 4.5:  Total Impulse Tests with 7 Degree Angled Plate.................................... 59 
Figure 4.6:  Total Impulse Tests with 13 Degree Angled Plate.................................. 61 
Figure 4.7:  Total Impulse Tests with 20 Degree Angled Plate.................................. 63 
Figure 4.8:  Total Impulse Tests at 0.0? Standoff Distance........................................ 65 
Figure 4.9:  Total Impulse Tests at 0.5? Standoff Distance........................................ 67 
Figure 4.10:  Total Impulse Tests at 1.0? Standoff Distance...................................... 69 
Figure 4.11:  Total Impulse Tests at 1.5? Standoff Distance...................................... 71 
Figure 4.12:  Pyramid and Dihedral Shaped Plate Impulse Tests............................... 73 
Figure 4.13:  Percent Total Impulse Change from 0? to 0.5? Standoff Distance ....... 76 
Figure 4.14:  Percent Total Impulse Change from 0.5? to 1.0? Standoff Distance .... 77 
Figure 4.15:  Percent Total Impulse Change from 1.0? to 1.5? Standoff Distance .... 78 
Figure 4.16:  Percent Total Impulse Change from 0.04? to 0.25? Burial Depth ........ 80 
Figure 4.17:  180? Rotation of Figure 4.16................................................................. 81 
Figure 4.18:  Percent Total Impulse Change from 0.25? to 0.5? Burial Depth .......... 82 
Figure 4.19:  Percent Total Impulse Change from 0? to 7? Dihedral Plate ................ 85 
Figure 4.20:  Percent Total Impulse Change from 0? to 13? Dihedral Plate .............. 86 
Figure 4.21:  Percent Total Impulse Change from 0? to 20? Dihedral Plate .............. 87 
Figure 4.22:  Surface Graph of Reduced Small and Full Scale Tests Values [15]..... 89 
Figure 4.23:  4.467 3 lbin  Reduced Impulse: Expected vs. Actual Values [15]...... 90 
Figure 4.24:  8.93 SOD Reduced Impulse: Expected vs. Actual Values [15] ............ 91 
Figure 4.25:  13.4 SOD Reduced Impulse: Expected vs. Actual Values [15] ............ 91 
Figure 4.26:  Measured vs Expected Total Impulse for Constant Reduced DoB....... 93 
Figure 4.27:  4.98 3 lbin  Reduced Impulse Values for 460mg Charge Size ........... 95 
Figure 4.28:  9.95 SOD Reduced Impulse Values for 460mg Charge Size................ 95 
Figure 4.29:  14.93 SOD Reduced Impulse Values for 460mg Charge Size.............. 96 
Figure 4.30:  New and Worn 13? Dihedral Target Plates........................................... 98 
Figure 4.31: Worn 13? Plate ....................................................................................... 99 
Figure 4.32:  Erosion and Impact Damage Regions ................................................. 100 
Figure 4.33:  Spray Pattern on the Underside of the 13? Plate ................................. 101 
Figure 4.34:  Impact Crater Close-Up....................................................................... 102 
Figure 4.35:  Impact Region as Compared to 636 mg Charge.................................. 103 
Figure A.1:  13? Deformable ?Bent? Plate ............................................................... 110 
Figure A.2:  609mg Charge Consisting of 3 RP-80 Detonators ............................... 111 
Figure A.3:  Time Elapse (1 ms/frame) of Bent Plate Starting at 0ms ..................... 112 
Figure A.4:  Rigid and Deformable 13 Degree Plates at 0.04? Burial Depth........... 114 
Figure B.1:  13? Dihedral & Pyramid (Top) and Pyramid Grids (Bottom) .............. 116 
Figure B.2:  7? Pyramid and Dihedral Plate Tests.................................................... 118 
Figure B.3:  13?Pyramid and Dihedral Plate Tests................................................... 118 
Figure B.4:  0.25? and 0.5? Pyramid Grid Plate Tests.............................................. 120 
 
 vii  
Figure B.5:  Wear on 0.5? Pyramid Grid Plate After Testing................................... 122 
Figure B.6:  0.5? Pyramid Grid Plate, 0.04? DOB, 0.58? SOD, 5ms Elapsed Time 123 
Figure C.1:  Impulse Test and Centroid Standoff Distances, Constant 0.04? DOB. 125 
Figure C.2:  Impulse Test and Centroid Standoff Distances, Constant 0.25? DOB. 126 
Figure C.3:  Impulse Test and Centroid Standoff Distances, Constant 0.5? DOB... 127 
List of Tables 
Table 2.1:  Plate Shapes and Properties...................................................................... 26 
Table 3.1:  Target Dimension Values ......................................................................... 29 
Table 3.2:  Camera Settings........................................................................................ 41 
Table 4.1: Average Total Impulse Values (lb-s) at 0.04? Depth of Burial................. 51 
Table 4.2: Average Total Impulse Values (lb-s) at 0.25? Depth of Burial................. 53 
Table 4.3: Average Total Impulse Values (lb-s) at 0.5? Depth of Burial................... 55 
Table 4.4:  Average Total Impulse Values (lb-s) with 0 Degree Angled Plate .......... 57 
Table 4.5:  Average Total Impulse Values (lb-s) with 7 Degree Angled Plate .......... 59 
Table 4.6:  Average Total Impulse Values (lb-s) with 13 Degree Angled Plate ........ 61 
Table 4.7:  Average Total Impulse Values (lb-s) with 20 Degree Angled Plate ........ 63 
Table 4.8:  Average Total Impulse Values (lb-s) at 0.0? Standoff Distance .............. 65 
Table 4.9:  Average Total Impulse Values (lb-s) at 0.5? Standoff Distance .............. 67 
Table 4.10:  Average Total Impulse Values (lb-s) at 1.0? Standoff Distance ............ 69 
Table 4.11:  Average Total Impulse Values (lb-s) at 1.5? Standoff Distance ............ 71 
Table 4.12:  Pyramid and Dihedral Shaped Plate Impulse Values (lb-s).................... 73 
Table 4.13:  Percent Total Impulse Change Values, 0? to 0.5? SOD......................... 76 
Table 4.14:  Percent Total Impulse Change Values, 0.5? to 1.0? SOD...................... 77 
Table 4.15:  Percent Total Impulse Change Values, 1.0? to 1.5? SOD...................... 78 
Table 4.16:  Percent Total Impulse Change Values, 0.04? to 0.25? DOB.................. 80 
Table 4.18:  Percent Total Impulse Change Values, 0.25? to 0.5? DOB.................... 82 
Table 4.19:  Percent Total Impulse Change Values, 0? to 7? Dihedral Plate ............. 85 
Table 4.20:  Percent Total Impulse Change Values, 0? to 13? Dihedral Plate ........... 86 
Table 4.21:  Percent Total Impulse Change Values, 0? to 20? Dihedral Plate ........... 87 
Table 4.22:  0? Plate Small Scale Test Results ........................................................... 90 
Table 4.23:  0? Plate Small Scale Test Results for 460mg Effective Charge Size ..... 94 
Table A.1:  Rigid and Deformable Plate Impulse Test Values................................. 114 
Table B.1:  Dihedral and Pyramid Plate Test Values ............................................... 117 
Table B.2:  0.25? and 0.5? Pyramid Grid Plate Test Values .................................... 121 
Table C.1:  Centroid Distances ................................................................................. 124 
Table C.2:  Impulse Values for Figure C.1............................................................... 125 
Table C.3:  Impulse Values for Figure C.2............................................................... 126 
Table C.4:  Impulse Values for Figure C.3............................................................... 127 
 
 1  
Chapter 1: Introduction & Background 
Overview 
This paper describes research conducted at the University of Maryland, 
College Park in the Dynamic Effects Lab of the A. James Clark School of 
Engineering.  This was accomplished through the use of small-scale explosive testing 
and high speed digital photography. 
The primary research goal was to examine the effect of variations in plate 
angle, standoff distance, and depth of burial on the impulse transmitted by a buried 
charge to a suspended target plate.   The independent variables were target geometry 
(dihedral angle), depth of burial and standoff distance.  The measured dependent 
variable was captured impulse. 
Buried explosives in the form of mines or improvised explosive devices are a 
constant threat to vehicles.  Light armored vehicles (LAV) are particularly susceptible 
to this form of attack due to their reduced protection when compared to heavier 
vehicles such as main battle tanks.  Adding armor to a LAV is not always an option 
due to weight constraints, so alternate protection schemes must be explored.   
This research involved small scale explosive testing.  Full scale testing is 
extremely expensive, and requires the use of specialized facilities and technicians.  
Small scale testing is cheaper, simpler, and is easily repeated.  The explosive charges 
used in this research consisted of 0.636 g charges, or 0.01% of the 10lb of explosive 
in a typical anti-vehicular mine. 
 
 2  
1.1 Antivehicular (AV) Mines 
Since World War II, more vehicles have been lost to land mines than all other 
threats combined [1].  Antivehicular (AV) mines are capable of disabling a heavy 
vehicle, or completely destroying a lighter vehicle.  Mine survivability is one of the 
least understood aspects of vehicle survivability, and is typically defended against 
through the use of extra armor.  The physics surrounding a buried landmine blast and 
the loading mechanisms that damage a vehicle are not well understood. 
The most common form of antivehicular landmine is the blast mine, which 
uses a large amount of explosive to directly damage the target.  Light or unprotected 
vehicles are particularly susceptible to blast mines.  Figures 1.1 and 1.2 show the 
detonation and aftereffects of a 6.5kg TNT blast mine against an unprotected 5/4 ton 
truck.  Heavily armored vehicles are less threatened by most blast mines, but can be 
damaged by shaped charges and penetrator mines.  Shaped charges consist of an 
inverted hollow cone of ductile metal (typically copper) surrounded by a jacket of 
high explosive.  The explosive is detonated in such a manner that it compresses the 
cone, forcing a hot jet of molten metal to spurt forward.  This jet is capable of cutting 
through several inches of steel.  Penetrator mines defeat armor by shooting a 
projectile into the target.  Both shaped charges and penetrator mines are beyond the 
scope of this study.   
 
 3  
 
Figure 1.1:  Unprotected 5/4 Ton Truck Against a 6.5kg TNT Antitank Mine [1] 
 
Figure 1.2:  Unprotected 5/4 Truck After Mine Test [1] 
 
 4  
1.2 Casualty Mechanisms 
Vehicles must be designed to protect the crew from several casualty 
mechanisms.  The greatest threat comes from blast overpressure, which causes severe 
damage to the lungs and as well as burns and secondary fires from the fireball.  A 
floor rupture in the event of an explosion is considered a crew kill [1].  Fragments 
from the casing and secondary projectiles (Figure 1.3) have varying levels of 
lethality.  Small fragments from antipersonnel mines are a moderate threat to crews, 
and can be defended against through light armor.  Large, heavy fragments are very 
energetic and pose a severe threat.  Shock loads transmitted through the floor can 
break bones, while deformation of the crew compartment can cause crushing injuries.  
Finally, gross vehicle movement in the form of a crash has also been found to be a 
source of injury. 
 
Figure 1.3:  Fragments and Ejecta Created After Mine Blast [1] 
 
 5  
1.3 Physics of Mine Blasts 
Detonation is the process of a pressure wave propagating through an explosive 
medium, causing a chemical reaction to initiate behind it.  This reaction rapidly 
releases energy in the form of a shock wave and, more slowly, in the form of an 
expanding gas bubble.  Initial pressures near the detonation products can be as high as 
200,000 atmospheres and temperatures can be as high as 6000?C [1].  When the 
explosive is confined in soil, the result is three distinct phases as the explosive 
interacts with the soil, gas expands to the surface, and soil interacts with the vehicle.  
Figure 1.4 shows a time sequence of a full-scale mine explosion, with the detonation 
products expanding upward surrounded by a ring of ejected soil. 
 
Figure 1.4:  Time Sequence of Mine Explosion [1] 
 
 6  
1.3.1 Early Interaction & Shock 
When the detonation wave emerges from the explosive product in the form of 
a shock wave, it interacts with the surrounding soil [1].  The strength of the shock 
wave depends on the acoustic impedance match between the materials the wave 
travels through; if a shockwave travels from a high impedance material (such as soil 
or metal) to a low impedance material (such as gas), then most of the shock wave is 
reflected.  When the shockwave from an explosive reaches the surface, a thin layer of 
soil is ejected upward as the shockwave transitions between the soil and air.  The 
large impedance mismatch between soil and air generally means the explosive shock 
wave has little direct effect on the target unless the target is directly touching the soil 
[2].  If the target touches the soil, energy is transmitted into the target in the form of a 
stress wave [9].   
1.3.2 Gas Expansion 
The detonation products also produce mechanical work in the form of 
expanding gas.  The mass of the explosive determines the amount of gas produced.  
Confinement by the soil causes the gas to expand primarily in the vertical direction 
[9].  As the detonation products expand they eject the soil plug at supersonic speeds 
and create a bow shock wave in the air.  Figure 1.5 shows the distribution of 
detonation products as they begin to expand upward.  It is theorized that the gas may 
have a high dynamic pressure which can cause localized deformation if flows are 
trapped by the geometry of the target.  The expanding gas may be confined by the soil 
and target to create a ?bubble? with a high pressure that acts on a large area of the 
target.  It is theorized that the gas expansion phase produces significant global and 
 
 7  
localized effects on the target.  The direction and amount of the gas expansion is 
heavily dependent on the soil properties.  Deeper burial depths, increased soil density, 
and higher moisture content will cause the gas flow to expand in a more vertical 
direction [1].   
1.3.3 Soil Ejecta 
The initial expansion of the detonation products causes the soil directly above 
the charge (the ?plug? or soil plug) to rapidly move upward ahead of the expanding 
gas.  The expanding gas also imparts energy into the surrounding soil, causing it to 
flow as an annulus of ejecta surrounding the expanding detonation products [9].  The 
properties of the soil, particularly saturation level and porosity, determine the amount 
of soil and the direction of soil flow [1].  Figure 1.5 shows the distribution of the 
detonation products and soil ejecta for a typical blast.  Notice how the soil ejecta (the 
blue shaded region) rings the detonation products.  This effect is more pronounced in 
the final frames of Figure 1.4.  During testing, the portion of the ejecta ringing the gas 
will be referred to as the ?soil annulus.? 
 
Figure 1.5:  Detonation Products and Soil Ejecta [1] 
 
 8  
1.4 Load Mechanism Components 
The data seems to indicate that the interaction of the gas expansion and soil 
ejecta on the target plate results in a loading mechanism that can be divided into two 
components.  The first is a concentrated, short duration load referred to as the impact 
load.  This component is composed of the soil plug ejected ahead of the detonation 
products and overpressure effects from the high pressure of the gas pushing it.  The 
second component is a dispersed, longer duration load referred to as the distributed 
load.  This component appears to be a product of extended pressure from the 
expanding gas bubble and momentum transfer from the crater ejecta.  The effects of a 
mine blast over time can be seen in Figure 1.6, which compares digital imagery taken 
from a small-scale buried mine test featuring a transparent target to a computer 
simulation of that test.  It is postulated that the target is first impacted by the soil plug 
above the charge propelled by the initial expansion of the detonation products, and 
then subject to extended loading by the impact of ejecta and the gas bubble. 
 
Figure 1.6:  Small-Scale Mine Blast Test (Top) and Simulation (Bottom) [10]  
 
 9  
1.4.1 Shock Load 
One loading component comes from the shock wave emitted from the 
detonation products.  The poor impedance match between the soil and air means this 
component is only present when the target is touching or extremely close to the 
surface.  At further standoff distances the shock load has a minimal effect [3].  The 
relative magnitude of this component is unknown, but the duration is extremely short.   
1.4.2 Impact Load 
The data seems to indicate that the initial loading comes in the form of a high-
speed ?plug? of soil.  The soil plug can have an initial velocity of up to 1.5 km/s for a 
full-size charge [2], and the initial impact of these products against a vehicle has the 
capacity to induce large loads in a very short period of time.  It is suggested that 
changes in the flow field resulting from target geometry can create localized pressure 
spikes, particularly if the field stagnates inside reentrant corners [1].  The effects of 
dynamic pressure changes and impact of the soil plug can cause localized material 
failure and breach the vehicle, exposing the crew directly to the blast effects. 
Figure 1.7 is a series of images from a small-scale test captured by a high 
speed camera.  A 0.5g charge of Detasheet was buried to a depth of 0.69? and 
detonated, and the resulting explosion was recorded.  The camera captured an image 
once every 44?s.  Figure 1.7 shows the first frame before the explosion and then the 3 
frames afterward.
 
 10  
 0?s  44?S
 88?s  132?s
Figure 1.7:  Initial Blast from 0.5g Charge at 0.69? Depth of Burial 
The frames in Figure 1.7 show the soil directly above the charge (the soil 
plug) being projected upward a velocity of over 400 m/s.  The soil directly over the 
charge has a supersonic vertical velocity, and in the presence of an air gap (meaning 
the shock load is mitigated) the soil plug is the first thing to strike against the target.  
The impact of the soil plug, acting as a concentrated load over a short period of time 
is called the impact load in this paper.
 
 11  
1.4.3 Distributed Load 
The second loading component involves a load acting over a longer period of 
time and a greater area.  If the detonation products are confined by the target plate 
and ejecta, they form an expanding gas bubble that places an extended pressure load 
on the target.  As long as the bubble is confined it will continue to load the target, and 
may even ?suck back? the target if the expanding bubble pressure falls below 
ambient.  The ejecta from the crater impacts against the target, producing a direct 
momentum transfer.  These effects act for a longer period of time after the detonation.  
Small-scale tests involving rigid flat plates suggest that loading by the soil annulus 
imparts 2/3 of the impulse transmitted to a target plate from a buried charge [3].  As 
seen in Figure 1.6 the soil and gas bubble act on the target for at least 5 ms; this is a 
significant period of time when dealing with small-scale explosive events.  The 
distributed load acts over a much larger area than the impact load. 
 
 12  
1.5 Parameter Investigaton 
Target response is heavily dependent on several factors, including the standoff 
distance, depth of burial, conditions of the soil, and shape of the target.  All four 
factors have a significant effect on the total impulse captured by a target from a 
buried charge. 
1.5.1 Standoff Distance 
The distance between the target and the surface is one of the primary factors 
in determining blast damage.  If the target is in contact with the soil, the shock wave 
will be directly transmitted into the target as the impedance match between the soil 
and a solid (such as a steel tank track) is much closer than that between soil and air.  
Increasing the distance between the target and the soil causes direct shock wave 
effects to be negligible.  Higher standoff distances allow for greater expansion of the 
gas bubble and soil annulus diameter [2].  While this increases the area over which 
the forces act, it decreases their intensity.  
1.5.2 Depth of Burial 
The depth of burial of an exploding charge has a significant influence on the 
nature of the loading mechanism against the target.  At shallow burial depths, the 
loading mechanism is primarily from the detonation products rather than the soil.  As 
the depth of burial increases, the detonation products are forced to move more soil out 
of the way.  The deeper burial increases the mass and reduces the velocity of the soil 
plug.  The impact of the soil plug against the target plate is also dispersed over a 
larger area.
 
 13  
 Figure 1.8 contains pictures comparing the initial blast from a 0.5g Detasheet 
charge buried at three depths of burial.  These tests were conducted at the University 
of Maryland Dynamic Effects Lab.  The first column is a charge buried at 0.19?, the 
middle column is a charge buried to 0.69?, and in the third column the charge is 
buried to a depth of 1.19?.  Each frame is a picture taken by a high speed camera at a 
40?s interval, starting with the first frame immediately after the explosion.  
Comparing the images between the different tests can provide insight into the effect 
of burial depth on the loading of a target above an exploding charge. 
  The most apparent difference between the tests is the difference in velocity of 
the ejecta and detonation products as the depth of burial changes.  The ejecta from the 
charge buried to 0.19? travels significantly faster than the ejecta from the charges 
buried at deeper depths.  By the last frame, the ejecta from the 0.19? charge has 
traveled approximately twice the distance of the 0.69? charge, and over four times the 
distance of the 1.19? charge.  This difference in velocity may be a result of the 
additional mass of soil from the deeper burial depths. 
The flow is also more horizontal for shallower depths of burial.  At the 0.19? 
burial depth the plume expands upward and outward, whereas at the 0.69? and 1.19? 
burial depths the plume is primarily dome-shaped for the region tested.  The 
additional soil surrounding the deeper buried charges restricts the radial flow of the 
detonation products.  Constrained by the crater walls, the expanding gas is forced to 
flow upward in a more vertical direction compared to the shallower charges.
 
 14  
DOB: 0.19? 
 
  
 
  
 
  
 
  
 
 
 
 
 
 
DOB: 0.69? 
 
 
 
 
 DOB: 1.19? 
Figure 1.8: Elapsed Time (40?s/frame) of Buried Charge Explosion for 3 DOBs 
 
 15  
1.5.3 Soil Condition 
The condition of the soil, particularly the saturation level, has a significant 
effect on the loading mechanism.  High levels of water saturation reduce the shear 
strength of the soil, which decreases the amount of energy required to displace it [1].  
The rate of soil movement during the gas bubble phase is dependent on the porosity 
and bulk density of the soil, which in turn is mainly dependent on the water content.  
Wet or saturated soils contain pores filled with water and are more resistant to 
crushing [4].  This constrains the gas bubble and prevents the gas from being 
dispersed throughout the soil, which results in more energy directed to the target. 
1.5.4 Target Shape 
Vehicle geometry can have a channeling effect that either diverts the blast 
effects away from the target, or traps them and causes damaging overpressures.  
South African vehicle designers began incorporating angles into the underside of 
vehicles in the late 1970?s [13].   The Casspir armored personnel carrier (Figure 1.9) 
is one such example.  Testing on angled plates angled between 0? and 30? using air 
blasts revealed that loading decreased significantly as the plate angle increased within 
the range tested [4].  Similar results should be expected in soil. 
 
Figure 1.9:  Casspir APC 
 
 16  
1.6 Blast Scaling 
Scaled testing is one of the most common forms of explosive testing.  A full 
scale test can cost many thousands of dollars, require specialized equipment and 
training, and take months to set up and run.  Smaller scale tests on the order of a few 
pounds are less expensive and take far less time to set up, but still require specialized 
blast chambers or testing sites.  Very small scale testing, on the order of a few grams 
or less, is far less expensive and can be conducted indoors.  The University of 
Maryland Dynamic Effects Lab specializes in small scale testing, with charge sizes 
up to 8 grams.  The Dynamic Effects Lab primarily uses Hopkinson-Cranz scaling to 
scale between small-scale and full-scale test results. 
Hopkinson-Cranz scaling, or cube-root scaling, is based on the theory that 
similar blast waves are produced at the same scaled distance when the scaled charge 
geometry, explosive, and atmospheric conditions are the same [5].  For small time 
scales, air is assumed to be a perfect gas and gravity is assumed to have a negligible 
effect.  Hopkinson scaling is used to scale air blast (shock) and underwater shock, and 
has also been used for scaling other effects from buried charges.  Hopkinson scaling 
is so prevalent that almost all data is presented in terms of the parameters Z (reduced 
distance), ? (reduced time), and ? (specific reduced impulse).  R, t, i, W are the 
unscaled distance, time, specific impulse, and charge weight.  
3
1
W
RZ =  
3
1
W
t  =?    
W
i=?
 
 17  
Although charge weight is the primary term used for Hopkinson scaling, total 
energy is an alternative scaling term.  Hopkinson scaling is designed for use with 
ideal explosives, and fails to scale non-ideal explosive compositions.  Chock [6] 
suggests that energy is a much more ?physically realistic? parameter, and Fu [7] was 
able to properly scale non-ideal explosives through a correlation factor based on 
detonation energy.  Weight is a sufficient parameter for the majority of scaling 
research.  Scaling between full-scale and small scale tests on the order of a few 
pounds has been confirmed down to research scale weights below 100 grams [7].  
The region between 100g and 1g (the scale used in the Dynamic Effects Lab) has also 
shown good behavior, but requires more study [3].   
 
 
 18  
Chapter 2: Research Equipment 
Overview 
 The specific demands of plate impulse testing required specialized pieces of 
equipment to be custom fabricated for the Dynamic Effects Lab.  Other components 
had to be modified or specially protected in order to withstand the rigors of blast 
testing.  The choice of sensor equipment and test bed allowed for repeated tests once 
setup was completed.  
2.1 Explosive Charge 
The charge (Figure 2.1) consisted of 0.9g of 
Detasheet (63% PETN by weight, or 567 mg 
PETN) detonated by an RISI RP-87 EBW 
(exploding bridge wire) detonator (26mg PETN 
initiating explosive, 43 mg RDX output explosive).  
PETN is Pentaerythritol Tetranitrate, a very stable  Figure 2.1:  636 mg Charge 
explosive commonly used in commercial applications.  RDX is cyclonite, a common 
military explosive component.  The total explosive mass of this charge was 636 mg.  
 
 19  
2.2 Phantom Digital Camera System 
The displacement of the plate was measured visually using high speed digital 
cameras.  The original camera used was the Vision Research Phantom v4.1, a 
monochrome high speed digital camera which was operated at 1000 pictures per 
second at pixel resolutions of 512x512.  A Nikon 28-80mm f/3.5-5.6D lens was 
mounted to the camera to focus the image.  Later on in the testing, the lab obtained a 
new Phantom v7.1 digital camera (Figure 2.2), which was operated at 8000 pictures 
per second at 512x512 resolution.  Focus was achieved through the use of a Tamron 
(IF) 28-75mm 1:2.8 MACRO ?67 lens.  The selection of frame rate and resolution 
was largely dependent on the memory capacity and performance capability of the 
cameras.  The Phantom v4 contains 256 megabytes of memory and could take 1000 
pictures at full resolution.  The Phantom v7 contained 2 gigabytes of memory and 
could capture over 8000 pictures at full resolution.  The sharper image and faster 
frame rate of the v7.1 made it a superior platform compared to the v4.1. 
 
Figure 2.2:  Phantom v7.1 High Speed Digital Camera [12] 
  
 
 20  
Data was collected by the camera and then transmitted to a personal computer.  
The camera was either connected by a FireWire cable (Phantom v4) or CAT5 cable 
(Phantom v7).  The FireWire cable was more susceptible to outside electrical 
interference and repeatedly caused signal loss.  This could cause the camera to lose 
connection with the PC or fail to trigger the camera during a test.   The connection 
could be restored by resetting and reconnecting the camera and PC. 
 The digital camera was mounted on a standard duty, fluid head tripod mount 
sold by Vision Research (Figure 2.3).  A foam skirt protected the stand from flying 
soil and water.  The camera itself was protected by a translucent plastic case.  The 
front of the container was removed and replaced with a clear pane of acrylic plastic, 
while the rear was cut out to allow the wiring to connect to the camera.    
 
Figure 2.3:  Phantom v7, Camera Stand, Protective Skirt, and Cover 
 
 21  
2.3 Phantom Software 
 Phantom cameras utilize proprietary software to analyze the recording (Figure 
2.4).  The control software allows the user to control resolution, frame rate, exposure 
time, zoom, picture quality, and other options.  The control software also contains 
integrated filtering imagery that can sharpen a picture.  The view window shows 
exactly what the camera sees in real time, allowing the researcher to determine 
precisely how the recording should look.  The controller can either trigger the camera 
from the software, or place the camera in ?Capture? mode and trigger using an 
external device.  The Phantom software also allows the user to record movement, 
scale distances from a reference, and determine angular and linear acceleration and 
velocity.   
 
Figure 2.4:  Phantom Camera Control Software 
 
 22  
2.4 Firing System 
The charge is detonated with a Reynolds Industries Inc FS-10 EBW firing 
system [11] (Figure 2.5).  This battery-operated firing system is charged from an 
110V power source, and uses coaxial cable to connect to the charge leads.  A trigger 
system is connected from the firing module to the camera via coaxial cable.  The FS-
10 is designed specifically to fire exploding bridge wire detonators. 
The firing system consists of a control unit and firing module; in Figure 2.5 
the firing module is the metal box in the upper-right corner.  The control unit provides 
between 32 and 40 volts to the firing module, which charges a 1?F capacitor to 
3000V.  When a 30V pulse is applied to the red terminal on the module, the capacitor 
discharges 3000V into the lead (upper right) terminals.  The detonator will fire 10?s 
after the 30V pulse is applied to the module.  A safety interlock key ensures the 
control unit will not fire until the key is inserted in the proper location. 
 
Figure 2.5:  FS-10 EBW Firing System 
 
 23  
2.5 Dummy Charge 
The camera is tested three times before each test to ensure the data will be 
collected.  Testing the firing and data collection system requires the use of a bridge 
wire gap ?dummy charge? that does not contain explosive powder (Figure 2.6).  A 
dummy charge consisting of two leads inserted into a block of graphite inside an 
aluminum tube is used to ensure the firing system is functioning.  The gap between 
the two wires is approximately 1/8?.  When the firing system is initiated a 3000V 
pulse runs across the leads.  This pulse causes a visible spark that is recorded by the 
camera. 
Figure 2.6:  Dummy Charge 
 
 24  
2.6 Trigger Mechanism 
 The camera can be remotely triggered by sending an electrical pulse to the 
trigger (red) coaxial lead on the camera.  The trigger lead is kept at +5V when the 
camera is powered and running properly.  If a -5V pulse is sent along the trigger lead, 
it causes the voltage to drop and triggers the camera.  When the 30V activation pulse 
is transmitted, the trigger mechanism converts this into a -5V pulse that triggers the 
camera.  Figure 2.7 shows the trigger mechanism, with the coaxial cable on the left 
leading to the camera and the red and white wires on the right connecting to the firing 
module.    
 
Figure 2.7:  Trigger Mechanism 
 
 
 25  
2.7 Test Bed Area 
The test bed is a 1.5 meter by 1.5 meter steel tank measuring 0.6 meters deep 
(Figure 2.8, left).  The bottom of the tank is filled with coarse gravel covered by a 
geotextile mesh blanket.  A 25cm layer of HD-2 uniformly graded medium quartz 
sand lies on top of the mesh.  Piping to the underside of the tank allows the test bed to 
be evenly saturated with water (Figure 2.8, right).  The saturation system uses a stand 
column to move water into the underside of the tank and upwards into the sand bed.  
Equilibrium is established when the water level inside the water column equals that of 
the test bed.  A drainage valve on the lowest part on the system allows the tank to 
drain completely.  It takes approximately fifteen minutes to saturate the tank. 
Six 500W halogen work lights on three stands provide illumination for the test 
setup.  Lights are located in each of the three corners opposite the target plate.  The 
work lights must be capable of withstanding repeated sprays of sand and water. 
 
Figure 2.8:  Test Bed Setup and Saturation System 
 
 26  
2.8 Target Plates 
 A wide variety of shapes were tested to examine the effect of shape on total 
captured impulse from the detonation of a buried charge.  These shapes included a 
grid of pyramids (similar to some forms of acoustic paneling), plates bent into 
dihedral shapes, and plates machined into pyramid and dihedral shapes.  The plates 
were machined from 6061-T6 free machining aluminum to be 8? x 8? in the plane 
parallel to the soil, and to have a mass of approximately 1500 grams.  The dimensions 
and mass of the plates are the standard size used at the Dynamic Effects Lab for the 
given charge size, and were shown to provide good results in previous tests [14].  
Table 2.1 lists the various plate shapes tested and their respective masses. 
Plate Shape Mass (g) 
0? Plate 1525 
7? Dihedral Plate (1) 1458 
7? Dihedral Plate (2) 1556 
7? Pyramid Plate 1500 
13? Dihedral Plate (1) 1506 
13? Dihedral Plate (2) 1523 
20? Dihedral Plate 1519 
Table 2.1:  Plate Shapes and Properties 
 
 
Figure 2.9:  Plate Angle
Figure 2.9 shows the angle referenced in Table 2.1; it is the angle between the 
front face of the plate and a line parallel to the ground.  The 0? plate shape refers to a 
flat plate of material (Figure 2.10, Top).  This geometry served as a baseline to 
compare the performance of other target shapes.  Dihedral shapes (Figure 2.11, 
Bottom Left) are solid plates machined into an angled form with a triangular cross-
section.  The single pyramid shapes (Figure 2.10, Bottom Right) are solid plates 
machined into a pyramid form. 
 
 27  
 
 
Figure 2.10:  0? plate, 13? Bent Plate, 13? Single Pyramid   
The most extensive testing was done on the dihedral test plates, and in fact so 
much testing was conducted that two of the plates (the 7? and 13? plates) had to be 
replaced midway during the test.  The decision to replace the plates was based on 
observations made over time.  Although erosion was initially felt to be a significant 
factor, repeated tests revealed that plate wear had a minor effect on the total impulse 
captured by a dihedral target plate.  The 7? pyramid plate was compared to the 7? 
dihedral plate at the 0.04? standoff distance to further examine the effects of target 
geometry on total impulse.  Additional testing was conducted with alternate plate 
shapes; the results of these tests are in Appendix B.   
 
 
 28  
Chapter 3:  Research Methodology 
Overview 
In order to determine the impulse transmitted to a plate by explosive loading, 
the initial velocity imparted to the plate is required.  High speed digital imaging 
captured the movement of the plate in response to the blast.  Specialized software was 
used to analyze the video to determine displacement, and the data points were then 
fitted to a curve to find the initial velocity.  Common problems encountered during 
testing included spray obscuring the video, camera failure, and dud charges. 
3.1 Dihedral Plate Fabrication 
The unusual geometry of the angled plates requires specialized fixturing and 
machining techniques to fabricate.  Figure 3.1 shows the fixture and aluminum plate 
before machining.  All parts have a nominal tolerance of 0.05?. 
 
Figure 3.1:  Fixture Plate, Bolts, and Aluminum Plate 
 
 29  
The fixture plate is a 1? thick steel plate measuring 8? x 10?.  Four 3/8? holes 
in a square pattern were drilled and countersunk into the center of the plate.  The 
coordinates of the four holes with the center of the plate as the origin are (1?, 0?), (-
1?, 0?), (0?, 1?), and (0?,-1?).  1? long 3/8?-16 socket cap bolts were used to hold the 
aluminum block to the fixture plate. 
The initial dimensions of the aluminum plate depended on the angle of the 
target to be fabricated.  All aluminum plates required an 8? x 8? billet.  All targets 
were fabricated to a nominal mass of 1.5 kg (3.306 lbs), which requires a total of 33.9 
in3 (55.6 cm3) of aluminum.  Figure 3.2 and Table 3.1 show the dimensions of each 
target plate.  The 20? target plate required the removal of 9.86 in3 of material from the 
back of the plate to meet the specified mass, as can be seen in Figure 3.3.
 
Figure 3.2:  Target dimensions 
?? h (in.) ? (in.) 
0 0.500 0.500 
7 0.487 0.286 
13 0.900 0.080 
20 1.368 0 
Table 3.1:  Target Dimension Values
 
Figure 3.3:  Underside of 20? Plate (note removed material) 
 
 30  
3.1.1 Dihedral Plate Machining Procedure 
The aluminum plate was clamped to the mill bed, with a machined edge 
placed against the reference posts (Figure 3.4).  A piece of stock between the plate 
and the table allowed the edges of the plate to be milled in a single pass.  The corners 
of the plate were then indexed using an edge finder. 
 
Figure 3.4:  Clamping Aluminum Plate to Mill Table 
The plate was milled until it was square and dimensioned as close to 8? x 8? 
as possible (Figure 3.5).  Tolerances were less than 0.05?, and surface finishes were 
not important at this stage. 
 
Figure 3.5:  Milling the Edges of the Target Plate 
 
 31  
Figure 3.6 shows the drilling and tapping of the machined and dimensioned 
stock plate.  With the center of the plate as the origin, the coordinates of the hole 
pattern were (1?, 0?), (-1?, 0?), (0?, 1?), and (0?,-1?).  The holes diameters were 
5/16? and approximately 0.5? deep.  The tap size was 3/8?-16.   
 
Figure 3.6:  Tapping the Drilled Hole Pattern 
The plate was then removed from the table, cleaned, and then tightly bolted to 
the fixture plate as seen in Figure 3.7.  The bolt heads needed to be flush with the 
surface of the fixture plate. 
 
Figure 3.7:  Mounting Aluminum Plate to Fixture Plate 
 
 
 
 32  
Figure 3.8 shows the installed and adjusted angled mill table. 
 
Figure 3.8:  Angled Mill Table 
The fixture plate was clamped to the angled mill table as shown in Figure 3.9.   
 
Figure 3.9:  Clamping Fixture Plate to Angled Mill Table 
 
 33  
A facing cutter was run across the plate (Figure 3.10) until the reference 
dimensions reach the values specified in Table 3.1. 
 
Figure 3.10:  Facing the Target Plate 
The fixture was then unclamped, rotated 180?, and then clamped to the 
milling table again.  The facing operation was then repeated on the other side of the 
target.  Figure 3.11 shows a completed target plate. 
 
Figure 3.11:  Finished 13? Target Plate 
 
 34  
3.2 636 mg Charge Fabrication 
Fabricating the 636 mg charge required 0.9g of Detasheet, an RP-87 
detonator, a delrin ring, and 5-minute epoxy (Figure 3.12).  The delrin ring has an 
inner diameter of 33/64", an outer diameter of 9/16", and a nominal height of 0.3".  
The inner diameter is the most critical dimension.  Wax paper prevents the Detasheet 
from sticking to any surfaces, and a ?? brass rod is useful for tamping the explosive. 
 
Figure 3.12:  636 mg Charge Fabrication Components 
 The charge is fabricated by first 
firmly tamping the explosive into the 
delrin ring.  A RP-87 is then pushed into 
the center of the detasheet approximately 
1/8?deep.  The back of the charge and the 
detonator wire leads are then sealed with 
epoxy and allowed to dry (Figure 3.13).  
Figure 3.13:  636 mg Charge
 
 35  
3.3 Initial Setup and Testing 
3.3.1 Test Bed Setup 
 Setting up the test bed properly is crucial for consistent results.  The process 
involves disturbing and compressing the sand, burying the charge, setting the target 
plate, and finally saturating the soil.  The sand in the bed had to be reasonably dry 
before beginning; it took approximately an hour after draining the tank from 
saturation for the soil to be dry enough.  Disturbing the soil a few minutes after all the 
water had drained accelerated the drying process. 
 First, the sand needed to be completely turned over using a scoop.  
Once the soil was disturbed a cinder block was used to pound the sand down into a 
compacted form (Figure 3.14).  If the sand bed was not dry enough, compacting the 
sand forced water up through the sand bed.   If this happened, the sand bed was given 
another 30 minutes to dry. 
 
Figure 3.14:  Compacted Sand Bed 
 
 36  
The sand bed was then planed to a level shape, as seen in Figure 3.15.   Once 
planed, a small trench was dug around the edge of the sand to help distribute the 
water. 
 
Figure 3.15:  Test Bed and Sand Plane 
Figure 3.16 shows how the charge was wired to the firing system leads.  The 
firing system was disconnected before the charge was wired, and the leads were 
sealed with electrical tape.   
 
Figure 3.16:  Wired 636 mg Charge 
 
 37  
 The charge was placed by first marking two very long, perpendicular lines in 
the soil using a ruler, and then creating a 7? x 7? square with the intersection of the 
two lines in the center (Figure 3.17).  For tests using a 636mg charge and 8? by 8? 
plate the edges of the square were at least a foot from any wall of the tank.   
 
Figure 3.17:  Placement Grid for Charge and Plate 
The charge was then buried in the center of the square, and a caliper was used 
to measure the depth of burial as seen in Figure 3.18. 
 
Figure 3.18:  Confirming Depth of Burial 
 
 38  
Once the charge was buried to the correct depth, the top was covered with 
sand and gently compacted with a small block of wood.  A standoff post was placed 
at each corner of the previously marked square (Figure 3.19), and their height 
adjusted so that the bottom of the plate was at the required standoff distance. 
 
Figure 3.19:  Standoff Posts and Buried Charge 
The standoff distance was measured by first finding the distance from the top 
of the plate to the ground (Figure 3.20), and then subtracting the plate thickness. 
 
Figure 3.20:  Measuring Standoff Distance 
 
 39  
The plate was then leveled and centered over the charge using the centerlines 
marked in the soil (Figure 3.21).  The standoff distance was then checked again. 
 
Figure 3.21:  Leveled Target Plate 
Once the plate was accurately positioned the tank was filled with water until 
the sand was saturated.  When properly saturated the sand developed a light sheen 
(Figure 3.22, Right).  If the sand was oversaturated (Figure 3.22, Left) then the tank 
was drained until the water level reached an acceptable height.  Figure 3.23 shows a 
completed test bed setup with properly saturated sand around the target plate. 
 
Figure 3.22:  Oversaturated Sand (Left) and Properly Saturated Sand (Right) 
 
 40  
 
Figure 3.23:  Completed Test Setup 
 
 41  
3.2.2 Camera Setup 
 The camera was set up facing one of the corners of the plate, raised high 
enough that all four plate corners can be seen.  The precise height was not important 
because the variation caused from the change in perspective is insignificant.  The 
camera was zoomed and tilted so that the plate filled the view window horizontally 
(Figure 3.24).  The software settings depended on the camera model, as seen in Table 
3.2.  The image quality settings (brightness and contrast) were adjusted during each 
test depending on the light conditions. 
  Phantom v4 Phantom v7 
Frame rate: 1000 pps 8213 pps 
Exposure Time: 594 ?s 120 ?s 
Post Trigger: 1000 p 10802 p 
Resolution: 512x512 512x512 
Zoom: Fit Fit 
Exposure: Auto Auto 
Table 3.2:  Camera Settings 
 
Figure 3.24:  Camera Configuration and Plate Display 
 
 42  
3.2.3 Testing 
 The next step was to ensure the camera and trigger system were functioning 
properly.  The dummy charge was connected to the detonator leads and placed on top 
of the plate.  The camera was set to receive the trigger signal, and the dummy charge 
was detonated.  If the system was working properly, the video showed the dummy 
charge flashing at the same time the timer indicated the charge had detonated.  The 
test was repeated twice for a total of three successful trial runs.  The dummy charge 
was then removed, the leads were connected to the live charge, the camera was reset, 
and then the live test was conducted (Figure 3.25). 
 
Figure 3.25:  Typical Buried Charge Test 
 
 43  
3.4 Data Collection and Analysis 
3.4.1 Collection of Data 
 The Phantom camera recorded the movement of the plate in .cin files which 
can only be read by the Phantom camera software.  The movies were truncated to 
reduce their size; a full size movie using the Phantom 7 takes up two gigabytes of 
hard drive space.  The movie was cut to only show a few frames before the trigger 
event, and then every frame until the target plate was no longer on screen.  Any video 
of the descent of the plate was considered unusable because the target plates typically 
hit the ceiling.   
 The four corners of every target plate were marked with black electrical tape 
in order to make recording plate displacement easier.  Each corner was designated by 
its position relative to the camera.  The left and right corners were located to the 
camera?s left and right respectively, the front corner was closest to the camera, and 
the back corner was furthest.   
The displacement of selected points on the plate was manually measured 
using tools contained within the software suite.  The software was set to read inches, 
and the distance between the left and right corners of the plate was used to calibrate 
the scale.  The position of the four corners in each frame were captured and measured 
independently.  Data points were gathered from the first 50 to 100 frames, and then 
every 10th frame afterwards until the plate was out of view.  The first 50 to 100 points 
were needed to fully characterize the initial displacement.  Once the data was 
collected, Microsoft Excel was used to translate the raw text files produced by the 
 
 44  
Phantom software into readable spreadsheets.  The Y position and time after trigger 
were the only columns needed. 
The most common hindrance to recording the displacement of the target plates 
was spray obscuring one or more corners.  This was partially overcome by zooming 
in to observe the movement of a specific point, or by using the image processing 
filters to sharpen the image.  The location of a corner could also be extrapolated by 
intersecting the lines of each edge.  If the data point was too obscured, then it was not 
recorded. 
If the sand was found to be oversaturated, then the test was thrown out and 
repeated.  Over saturation was detected by observing the condition of the sand during 
a test.  If the sand was oversaturated it appeared ?soupy? in consistency, similar to the 
sand in Figure 3.26 (Left).  Properly saturated sand flew in chunks as seen in Figure 
3.26 (Right).   
 
Figure 3.26:  Oversaturated Sand (Left) and Properly Saturated Sand (Right) 
 
 45  
3.4.2 Analysis of Data 
The data was analyzed using curve fitting through Microsoft Excel.  The 
vertical displacement was graphed with respect to time, and a curve was fit to 
determine the initial velocity.  Different curve fit methods were used to determine the 
initial velocity from the displacement data.  The effectiveness of each method 
depended on the number of the points captured and the time interval between them. 
Initial Displacement, Test K-68
Impulse: 0.61 lb-s
y = 54.136x + 0.0124
R2 = 0.9912
y = 63.157x - 0.0036
R2 = 0.9899
y = 91.268x - 0.0226
R2 = 0.9887
y = 74.1x + 0.0057
R2 = 0.9922
0
0.2
0.4
0.6
0.8
1
1.2
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
Time (s)
Di
sta
nc
e (
in)
Front Back
Left Right
 
Figure 3.27:  Initial Displacement Curve Graph 
The first method fit the first ten frames to a linear fit (Figure 3.27).  The slope 
of the fit line was taken as the initial velocity.  This method was mostly used with the 
Phantom v4 camera with its relatively low frame rate.  The higher frame rate of the 
Phantom v7 had too much scatter within the first ten frames to produce viable results 
with this method.  This method was also ineffective if the initial data points were 
 
 46  
obscured by water spray or flying soil.  Another method involved fitting a linear 
curve to the data points within the first two inches of travel.  This method was more 
effective with the Phantom v7 camera and was less affected by flying debris and soil.   
The entire recorded displacement was also fit to a parabolic curve to obtain 
another equation of motion.  This method had the advantage of not being significantly 
affected by obscuring spray and ejecta, but was less useful if the plate rotated or 
flipped.  The parabolic curve fit produced a quadratic equation (Ax2 + Bx + C) that 
could be compared to the displacement equation 
OO XtVgttx ++=
2)
2
1()(  
where t is time, g is acceleration due to gravity, Vo is the initial velocity, and Xo is the 
initial position.  If the A term (acceleration term) of the fitted curve equation was 
close to -198 (half the acceleration due to gravity in in/s2) then the B term was 
considered a good value for the initial velocity.  Deceleration due to air drag was 
considered negligible for this analysis, but deceleration of the plate from the collapse 
of the bubble was considered a potential factor if the parabola was imperfect.  Figure 
3.28 shows a typical displacement plot, in this case for a 20? dihedral plate with a 
0.04? DOB and 0.5? SOD. 
 
 47  
Plate Displacement, Test K-68
Impulse: 0.65 lb-s
y = -166.15x2 + 61.259x - 0.0312
R2 = 0.9997
y = -178.84x2 + 67.128x - 0.0332
R2 = 0.9998
y = -189.96x2 + 88.366x - 0.0018
R2 = 0.9999
y = -185.21x2 + 81.889x - 0.0611
R2 = 0.9998
0
2
4
6
8
10
12
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Time (s)
Di
sta
nc
e (
in)
Front Back
Left Right
 
Figure 3.28:  Total Displacement Curve Graph 
For each method, the velocities for each corner were averaged and the result 
was multiplied by the plate mass to obtain the impulse.  The impulse reading and R2 
value for each method was compared and each curve was examined visually for 
anomalies and degree of scatter.  The linear fit to the initial displacement was 
generally used as the impulse result for the test.  The parabolic fit to the total 
displacement was used when the initial displacement was obscured by flying sand or 
water.  The difference between impulse values was typically 10%. 
 
 48  
Chapter 4: Results 
Overview 
 This chapter presents the findings on testing of the effect of variations in plate 
angle, standoff distance, and depth of burial on the impulse transmitted by a buried 
charge to a suspended target plate.  
Section 4.1 presents the primary results from the impulse testing in the form 
of eleven surface graphs.  In each graph one of the four standoff distances, the three 
depths of burials, or the four plate angles is held constant.  Any specific trends within 
the graph are examined and discussed. 
Section 4.2 discusses these findings and analyzes the effect of variations in 
target shape, standoff distance, and depth of burial on impulse.  Trends between the 
individual graphs are linked to establish conclusions regarding the interaction of the 
variables.  This section will also present potential explanations for the trends found in 
the data.   
Section 4.3 discusses inconsistencies found between the results of 0? plate 
testing and expected values derived from previous experiments.  It also explains how 
the small size Detasheet charge may be responsible for these inconsistencies. 
Section 4.4 discusses the effects of repeated tests on the target plates, and how 
the wear pattern supports the presence of the impact load and a dispersed load 
components. 
 
 49  
4.1 Presentation of Target Shape Findings 
Sections 4.1.1 through 4.1.3 contain surface graphs depicting impulse as a 
function of depth of burial, standoff distance, and dihedral plate angle.  For each 
graph one of the variables is held constant, and the other two are plotted in the X and 
Y directions.  The Z direction is always impulse in lb-s.  The color of the surface 
graph corresponds to the height.  Each of the blue dots represents a single data point; 
multiple points at the same location indicate repeated tests. 
Section 4.1.4 contains a line graph comparing impulse as a function of 
standoff distance for two different plate shapes (pyramid and dihedral) at a constant 
depth of burial.  The X axis is standoff distance, while the Y axis is total impulse.  
The different color lines represent different target shapes (either the pyramid or 
dihedral shape).
 
 50  
4.1.1 Results at Constant Depth of Burial 
Figure 4.1 and Table 4.1 show total impulse as a function of standoff distance 
and plate angle for a constant depth of burial of 0.04?.  At this shallow depth of burial 
there is little soil to impact against the target, which means most of the load comes 
from the expanding gas.  The impulse falls quickly as the standoff distance increases 
to 0.5? and then levels off as the standoff distance increases further. The decrease in 
impulse with standoff distance becomes less pronounced as the plate angle increases.  
The difference in total impulse with constant 0.0? standoff distance is peculiar; there 
is a large change in impulse between the 7? and 13? angles, but at smaller and larger 
angles the effect of plate angle is negligible .  A similar phenomena occurs at the 0.5? 
standoff distance. 
 
 
 51  
0
0.5
1
1.5
0
5
10
15
20
0
1
2
3
4
Standoff Distance (in)
Plate Total Impulse Test, 0.04" Depth of Burial
Plate Angle (Degrees)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure 4.1: Total Impulse Tests at Constant 0.04? Depth of Burial 
0" 0.5" 1" 1.5"
0? 3.42 0.98 0.75 0.96
7? 3.39 0.88 0.57 0.71
13? 1.93 0.52 0.65 0.63
20? 2.23 0.61 0.56 0.60A
ng
le
Standoff Distance
 
Table 4.1: Average Total Impulse Values (lb-s) at 0.04? Depth of Burial
 
 52  
Figure 4.2 and Table 4.2 show the total impulse as function of standoff and 
plate angle when the depth of burial is 0.25?.  This deeper depth of burial means there 
is more soil above the charge.  This added soil may change the loading mechanism by 
dispersing the gas bubble and increasing the amount of momentum transfer through 
soil impact.  At the smaller standoff distances the impulse captured by the plate is 
roughly inversely proportional to the angle of the plate.  More refined testing with 
additional standoff distances and plate angles is needed to better understand the 
relationship.  The addition of more ejecta due to the deeper depth of burial may have 
increased the effect target geometry has on total impulse at smaller standoffs.  At the 
1.0? and 1.5? standoffs, the loading is roughly constant regardless of target angle.  
This suggests the presence of a loading component unaffected by target shape or 
standoff distance (within the range tested), perhaps the soil cap impacting against the 
underside of the plate. 
 
 
 53  
0
0.5
1
1.5
0
5
10
15
20
0
1
2
3
4
Standoff Distance (in)
Plate Total Impulse Test, 0.25" Depth of Burial
Plate Angle (Degrees)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure 4.2: Total Impulse Tests at 0.25? Depth of Burial 
0" 0.5" 1" 1.5"
0? 3.28 1.80 1.33 1.16
7? 2.81 1.40 1.05 1.23
13? 1.99 1.09 1.05 0.96
20? 1.57 0.96 0.85 0.87
Standoff Distance
An
gle
 
Table 4.2: Average Total Impulse Values (lb-s) at 0.25? Depth of Burial
 
 54  
 Figure 4.3 and Table 4.3 show total impulse as a function of standoff distance 
and plate angle at a 0.5? depth of burial.  At the 0? standoff distance the impulse 
values are unusual; the impulse drops between the 0? and 7? plates, remains constant 
between the 7? and 13? plates, and then drops again as the dihedral angle increases to 
20?.  One possible explanation for this phenomenon is the direction of the blast.  
Deeply buried charges are believed to have more vertical soil movement than shallow 
charges, and the target may need to have a greater angle to deflect that blast.  At the 
0.5? standoff distance there is little difference between the 13? and 20? plates. At 
greater standoff distances there is a negligible difference among all of the angles 
tested.
 
 55  
0
0.5
1
1.5
0
5
10
15
20
0
1
2
3
4
Standoff Distance (in)
Plate Total Impulse Test, 0.5" Depth of Burial
Plate Angle (Degrees)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure 4.3:  Total Impulse Tests at 0.5? Depth of Burial 
0" 0.5" 1" 1.5"
0? 3.06 2.14 1.27 1.21
7? 2.45 1.62 1.20 1.10
13? 2.66 1.17 1.23 0.99
20? 1.74 1.23 0.90 1.03
Standoff Distance
An
gle
 
Table 4.3: Average Total Impulse Values (lb-s) at 0.5? Depth of Burial 
 
 56  
4.1.2 Results at Constant Plate Angle 
Figure 4.4 and Table 4.4 present captured impulse as a function of standoff 
distance and depth of burial for a 0? dihedral target plate.  The total impulse is 
greatest at the 0? standoff distance, and decreases steadily as the standoff distances 
increases up to the 0.5? standoff distance.  The total impulse then levels out between 
the 0.5? and 1.5? distances.  The performance of the 0? plate with respect to depth of 
burial is dependent on the standoff distance.  At 0? standoff distance, the total 
impulse decreases slightly as the depth of burial increases.  At 0.5? standoff, the 
impulse increases with depth of burial, while at 1.0? and 1.5? the impulse increases 
slightly between 0.04? and 0.25? depth of burial, and then levels off as the depth 
reaches 0.5?.  The performance of the 0? plate is used as a baseline against which the 
other angle plates are compared. 
 
 
 57  
0
0.5
1
1.5
0.1
0.2
0.3
0.4
0.5
0
1
2
3
4
Standoff Distance (in)
Plate Total Impulse Test, 0 Degree Dihedral Plate
Depth of Burial (in)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure 4.4:  Total Impulse Tests with 0 Degree Angled Plate 
0" 0.5" 1" 1.5"
0.04"' 3.42 0.98 0.75 0.96
0.25" 3.28 1.80 1.33 1.16
0.5" 3.06 2.14 1.27 1.21
Standoff Distance
Bu
ria
l 
De
pt
h
 
Table 4.4:  Average Total Impulse Values (lb-s) with 0 Degree Angled Plate 
 
 
 
 58  
Figure 4.5 and Table 4.5 show captured impulse as a function of standoff 
distance and depth of burial for a 7? dihedral target plate.  Seven degrees is the 
shallowest nonzero plate angle tested, and overall this provided trends similar to those 
of the 0? plate.  The highest impulse is located at 0.0? standoff and 0.04? depth of 
burial.  For all depths of burial the impulse decreases gradually as standoff distance is 
increased.  As with the 0? plate, the change in impulse with respect to depth of burial 
depends on the standoff distance.  At 0.0? standoff the impulse steadily decreases 
with increasing depth.  At the other standoff distances the impulse increases slightly 
between the 0.04? and 0.25? depths and the levels off between the 0.25? and 0.5? 
depths.  Overall the impulse is lower than that of the 0? plate.  This implies that the 
plate angle, when loaded in the center, deflects some of the ejecta to the sides.  This 
reduces the total vertical impulse. 
 
 
 59  
0
0.5
1
1.5
0.1
0.2
0.3
0.4
0.5
0
1
2
3
4
Standoff Distance (in)
Plate Total Impulse Test, 7 Degree Dihedral Plate
Depth of Burial (in)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure 4.5:  Total Impulse Tests with 7 Degree Angled Plate 
0" 0.5" 1" 1.5"
0.04"' 3.39 1.37 0.88 0.57
0.25" 2.81 1.40 1.05 1.23
0.5" 2.45 1.62 1.20 1.10
Standoff Distance
Bu
ria
l 
De
pt
h
 
Table 4.5:  Average Total Impulse Values (lb-s) with 7 Degree Angled Plate
 
 60  
Figure 4.6 and Table 4.6 display captured impulse as a function of standoff 
distance and depth of burial for a 13? dihedral target plate.  As with the 0? and 7? 
plates, the impulse decreases as the standoff distance goes from 0? to 1.0?, and then 
levels off between the 1.0? and 1.5?.  For the 0.5?, 1.0?, and 1.5? standoff distances, 
the impulse trends are similar to the other dihedral plates; the impulse increases 
slightly between the 0.04? and 0.25? depths of burial, and then levels off between the 
0.25? and 0.5? depths.  At the 0.0? standoff distance, the impulse captured by the 13? 
plate remains level between the 0.04? and 0.25? depth of burials, and then increases 
as the depth of burial goes to 0.5?.  This behavior at the 0.0? standoff is different from 
the other target shapes used in this test series.  This behavior can be explained by the 
presence of increasingly vertical flow of the ejecta as charge depth increases, as seen 
in Section 1.5.2.  As more of the ejecta flows at an angle close to perpendicular with 
respect to the surface, a steeper dihedral angle is required in order to better deflect the 
blast effects. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 61  
0
0.5
1
1.5
0.1
0.2
0.3
0.4
0.5
0
1
2
3
4
Standoff Distance (in)
Plate Total Impulse Test, 13 Degree Dihedral Plate
Depth of Burial (in)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure 4.6:  Total Impulse Tests with 13 Degree Angled Plate 
0" 0.5" 1" 1.5"
0.04"' 1.93 0.52 0.65 0.63
0.25" 1.99 1.09 1.05 0.96
0.5" 2.66 1.17 1.23 0.99
Standoff Distance
Bu
ria
l 
De
pt
h
 
Table 4.6:  Average Total Impulse Values (lb-s) with 13 Degree Angled Plate
 
 62  
Figure 4.7 and Table 4.7 show total impulse as a function of standoff distance 
and depth of burial for a 20? plate.  At the 0.0? standoff distance, the 20? plate 
demonstrates a decrease in total impulse between the 0.04? and 0.25? depth of burial, 
and then levels off as the depth increases to 0.5?.  The plate performs differently at 
the other standoff distances.  At standoff distances greater than 0?, the impulse 
increases slightly between the 0.04? and 0.25? depths of burial, and then the impulse 
levels off between the 0.25? and 0.5? burial depths.  The significant reduction in total 
impulse (relative to the 0? plate) implies that much of the blast effects are being 
deflected away by the 20? plate.  The similarity in performance between the 0.25? and 
0.5? depths of burial at 0.0? standoff is in contrast to the 13? plate.  This may mean 
that when facing charges buried at deeper depths, the more vertical flow of the ejecta 
and detonation products requires larger plate angles to maximize the deflection when 
compared to shallow buried charges. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 63  
0
0.5
1
1.5
0.1
0.2
0.3
0.4
0.5
0
1
2
3
4
Standoff Distance (in)
Plate Total Impulse Test, 20 Degree Dihedral Plate
Depth of Burial (in)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure 4.7:  Total Impulse Tests with 20 Degree Angled Plate 
0" 0.5" 1" 1.5"
0.04"' 2.23 0.61 0.56 0.60
0.25" 1.57 0.96 0.85 0.87
0.5" 1.74 1.23 0.90 1.03
Standoff Distance
Bu
ria
l 
De
pt
h
 
Table 4.7:  Average Total Impulse Values (lb-s) with 20 Degree Angled Plate
 
 64  
Figure 4.8 and Table 4.8 show total impulse as a function of plate angle and 
depth of burial at a 0.0? standoff distance.  Since the target is touching the ground the 
shock wave is able to load the target.  The close target placement also means the soil 
will have more time to act on the target and will be less dispersed than at greater 
standoff distances.  This standoff distance shows the highest impulses for all depths 
of burial and plate shapes. The relationship between impulse and plate shape changes 
with the depth of burial.  This may be a result of increased vertical flow of the soil 
and detonation products as a result of the deeper depth of burial.  At the 0.0? standoff 
distance the ejecta would not be able to change direction significantly before it hit the 
target.  Higher plate angles may be less susceptible to shock effects due to the greater 
spacing between the target surface and the ground as compared to the shallow plate 
angles.  Since the shock wave is mitigated in the presence of an air gap, the higher 
plate angles provide less area for the shock wave to act on as less of the target is close 
to the ground.
 
 65  
4.1.3 Results at Constant Standoff Distance 
0.1
0.2
0.3
0.4
0.5
0
5
10
15
20
0
1
2
3
4
Depth of Burial (in)
Plate Total Impulse Test, 0.0" Standoff Distance
Plate Angle (Degrees)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure 4.8:  Total Impulse Tests at 0.0? Standoff Distance 
0.04" 0.25" 0.5"
0? 3.42 3.28 3.06
7? 3.39 2.81 2.45
13? 1.93 1.99 2.66
20? 2.23 1.57 1.74
Depth of Burial
An
gle
 
Table 4.8:  Average Total Impulse Values (lb-s) at 0.0? Standoff Distance
 
 66  
Figure 4.9 and Table 4.9 display impulse as a function of plate angle and 
depth of burial at a 0.5? standoff distance.  The presence of an air gap between the 
surface and the target suggests the shock wave no longer provides a significant 
amount of loading.  Instead the target is loaded entirely by the impact and distributed 
load components.  The 0? plate shows the greatest impulse for all depths of burial 
because none of the material is deflected to the side.  The highest impulse is captured 
by the 0? plate at the 0.5? depth of burial, which suggests that the addition of soil over 
the charge produces an increased load on the plate.  As the target angle increases, less 
impulse is captured for all depths of burial.  There appears to be little difference in 
total impulse between the 13? and 20? target shapes for all depths of burial at the 0.5? 
standoff distance. 
 
 
 
 67  
0.1
0.2
0.3
0.4
0.5
0
5
10
15
20
0
1
2
3
4
Depth of Burial (in)
Plate Total Impulse Test, 0.5" Standoff Distance
Plate Angle (Degrees)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure 4.9:  Total Impulse Tests at 0.5? Standoff Distance 
0.04" 0.25" 0.5"
0? 0.98 1.80 2.14
7? 0.88 1.40 1.62
13? 0.52 1.09 1.17
20? 0.61 0.96 1.23
Depth of Burial
An
gle
 
Table 4.9:  Average Total Impulse Values (lb-s) at 0.5? Standoff Distance
 
 68  
Figure 4.10 and Table 4.10 plot total impulse as a function of plate angle and 
depth of burial at a 1.0? standoff distance.  The increased air gap between the charge 
and target underside allows the soil annulus and gas bubble to be more dispersed, 
which in turn reduces the total impulse captured by the target plate.  The 0? plate 
captures the most impulse, but the difference in impulse between various depths of 
burial and plate angles is significantly less than differences seen at closer standoff 
distances.  Total impulse increases for all angles between the 0.04? and 0.25? depth 
of burial.  There is little change in impulse between the 0.25? and 0.5? depths of 
burial for all plate angles.  The high standoff distance significantly reduces 
momentum transfer from the soil.  It is the author?s opinion that the majority of the 
loading at the higher standoff distances seems to come from the initial impact of the 
soil plug, which appears to be largely unaffected by standoff distance within the range 
tested.  If the soil plug were affected by standoff distance, the change in impulse 
between the 1.0? and 1.5? would be greater. 
 
 
 69  
0.1
0.2
0.3
0.4
0.5
0
5
10
15
20
0
1
2
3
4
Depth of Burial (in)
Plate Total Impulse Test, 1.0" Standoff Distance
Plate Angle (Degrees)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure 4.10:  Total Impulse Tests at 1.0? Standoff Distance 
0.04" 0.25" 0.5"
0? 0.75 1.33 1.27
7? 0.57 1.05 1.20
13? 0.65 1.05 1.23
20? 0.56 0.85 0.90
Depth of Burial
An
gle
 
Table 4.10:  Average Total Impulse Values (lb-s) at 1.0? Standoff Distance
 
 70  
Figure 4.11 and Table 4.11 show impulse as a function of plate angle and 
depth of burial at a 1.5? standoff distance.  The 0? plate captures the most impulse, 
but the difference in total impulse between the 0? plate and the other shapes for a 
given depth of burial is minimal.  As with the 1.0? standoff distance the impulse 
increases slightly between the 0.04? and 0.25? depths of burial, and then remains 
constant to the 0.5? depth for all target shapes.  At lower standoff distances, where the 
distributed load appears to be most significant, variations in the dihedral angle of the 
target change the total impulse captured by the plate.  At the higher standoff distances 
changes in geometry have a minimal effect on total captured impulse.  The change in 
behavior of total impulse with respect to target geometry suggests that a different load 
mechanism is prevalent at the higher standoff distances, such as the impact load from 
the soil plug.  This component appears to be largely unaffected by target geometry or 
standoff distance (within the range tested), and increases slightly as more soil is 
added above the charge. 
 
 
 
 
 
 71  
0.1
0.2
0.3
0.4
0.5
0
5
10
15
20
0
1
2
3
4
Depth of Burial (in)
Plate Total Impulse Test, 1.5" Standoff Distance
Plate Angle (Degrees)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure 4.11:  Total Impulse Tests at 1.5? Standoff Distance 
0.04" 0.25" 0.5"
0? 0.96 1.16 1.21
7? 0.71 1.23 1.10
13? 0.63 0.96 0.99
20? 0.60 0.87 1.03
Depth of Burial
An
gle
 
Table 4.11:  Average Total Impulse Values (lb-s) at 1.5? Standoff Distance
 
 72  
4.1.4 Pyramid v. Dihedral Shaped Plates 
Figure 4.12 and Table 4.12 show total impulse as a function of standoff 
distance for a 7? dihedral and pyramid shape at a constant 0.04? depth of burial.  The 
X-axis is standoff distance, the Y-axis is total captured impulse, and each colored line 
gives the values for the two target geometries.  The 7? dihedral plate (red line) 
captures more impulse than the 7? pyramid plate (blue line) at the 0.0? and 0.5? 
standoff distances, but at further standoff distances the total impulse is the same 
between the two.  The 7? pyramid plate shows no difference between the 0.5? and 
1.0? standoff distances.  This suggests that at 0.5? standoff distance the 7? pyramid 
shape has deflected the maximum amount of impulse possible and the only 
component of the load remaining is one unaffected by geometry or standoff distance. 
Appendix B contains additional information comparing dihedral and pyramid 
shapes to one another.  In addition to the 7? dihedral and pyramid tests, 13? dihedral 
and pyramid plates are compared.  The results indicate that there is no difference in 
total captured impulse between a 13? pyramid and dihedral plate, and furthermore 
that both plates captured the same total impulse as the 7? pyramid plate.  The results 
reinforce the concept that target geometry can only deflect a portion of the total 
impulse, and once that portion is fully deflected further changes in geometry have no 
effect.
 
 73  
Pyramid and Dihedral Shaped Plate Impulse Tests 
Depth of Burial: 0.04"
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.5 1 1.5 2
Standoff Distance (in)
Im
pu
lse
 (l
b-
s)
7? Pyramid
7? Dihedral
 
Figure 4.12:  Pyramid and Dihedral Shaped Plate Impulse Tests 
0" 0.5" 1" 1.5"
3.39 0.88 0.57 0.71
2.21 0.58 0.68 0.68
Standoff Distance
7? Dihedral
7? Pyramid  
Table 4.12:  Pyramid and Dihedral Shaped Plate Impulse Values (lb-s)
 
 74  
4.2 Discussion of Target Shape Findings 
4.2.1 Standoff Distance 
Testing confirmed what previous studies have found regarding standoff 
distance.  The standoff distance between the surface of the soil and the underside of 
the target plate has an inverse effect on the impulse captured by the target from an 
exploding charge.  At the 0? standoff distance, when the target is physically touching 
the soil, energy from the explosion can be directly channeled into the plate in the 
form of a shock wave.  In addition the close proximity of the plate to the charge 
maximizes the exposure of the target to soil and expanding gas.  Loading from the 
shock wave may be mitigated in targets with a steeper dihedral angle; these shapes 
have less material touching or near the surface when compared to the shallow 
dihedral angles and flat plates.  As a result the shock wave will come into contact 
with less material compared to a flat plate. 
Figure 4.13 through 4.15 are surface graphs showing the percentage change in 
total impulse as the standoff distance increases.    Tables 4.13 through 4.15 contain 
the values used to create the surface graphs.  The percentage is relative to the lower 
value.  For example, for a given combination of angle and burial depth in Figure 4.13, 
the percentage is the total change between 0.0? and 0.5? standoff distance, divided by 
the magnitude of impulse at the 0.0? standoff distance.  The largest change in total 
impulse is seen as the target moves away from the surface to the 0.5? standoff 
distance.  The presence of an air gap allows the soil annulus and detonation gases to 
expand before impacting on the target.  This dispersion causes some of the ejecta to 
 
 75  
escape without hitting the target, and as a result the impulse captured by the target 
plate is decreased.  
The impulse was nearly constant between the 1.0? and 1.5? standoff distances.  
Beyond 1.0? standoff distance, the air gap disperses the soil annulus and provides 
room for the gas bubble to expand.  It is this author?s opinion that this would 
minimize impulse transmitted from the soil, and as a result the impact of the soil plug 
(the impact load) would be the mechanism responsible for the majority of the load.  
The minimal change in total impulse between the 1.0? and 1.5? standoff distances for 
all angles suggests the soil plug is largely unaffected by standoff distance within the 
range tested.   
 
 
 76  
0
5
10
15
20
0.1
0.2
0.3
0.4
0.5
-100
-50
0
50
100
Plate Angle (Degrees)
Percent Total Impulse Change, 0.0" SOD to 0.5" SOD
Depth of Burial (in)
Pe
rce
nt 
Ch
an
ge
-80
-60
-40
-20
0
20
40
60
80
 
Figure 4.13:  Percent Total Impulse Change from 0? to 0.5? Standoff Distance 
0.04 0.25 0.5
0? -71.64 -45.12 -30.07
7? -74.04 -50.18 -33.88
13? -73.06 -45.23 -56.02
20? -72.65 -38.85 -29.31A
ng
le
Depth of Burial
 
Table 4.13:  Percent Total Impulse Change Values, 0? to 0.5? SOD 
 
 77  
0
5
10
15
20
0.1
0.2
0.3
0.4
0.5
-100
-50
0
50
100
Plate Angle (Degrees)
Percent Total Impulse Change, 0.5" SOD to 1.0" SOD
Depth of Burial (in)
Pe
rce
nt 
Ch
an
ge
-80
-60
-40
-20
0
20
40
60
80
 
Figure 4.14:  Percent Total Impulse Change from 0.5? to 1.0? Standoff Distance 
 
0.04 0.25 0.5
0? -22.68 -26.11 -40.65
7? -35.23 -25.00 -25.93
13? 25.00 -3.67 5.13
20? -8.20 -11.46 -26.83A
ng
le
Depth of Burial
 
Table 4.14:  Percent Total Impulse Change Values, 0.5? to 1.0? SOD 
 
 78  
0
5
10
15
20
0.1
0.2
0.3
0.4
0.5
-100
-50
0
50
100
Plate Angle (Degrees)
Percent Total Impulse Change, 1.0" SOD to 1.5" SOD
Depth of Burial (in)
Pe
rce
nt 
Ch
an
ge
-80
-60
-40
-20
0
20
40
60
80
 
Figure 4.15:  Percent Total Impulse Change from 1.0? to 1.5? Standoff Distance 
0.04 0.25 0.5
0? 28.00 -12.78 -4.72
7? 24.56 17.14 -8.33
13? -3.08 -8.57 -19.51
20? 7.14 2.35 14.44A
ng
le
Depth of Burial
 
Table 4.15:  Percent Total Impulse Change Values, 1.0? to 1.5? SOD
 
 79  
4.2.2 Depth of Burial 
The effect of burial depth on the impulse applied to a target by an exploding 
charge varies with the magnitude of that depth.  Deeper burial depths provide more 
soil over and around the charge.  At very shallow depths of burial there is little or no 
soil plug, and most of the impulse is transmitted through an expanding gas bubble and 
the impact of soil from the crater.  This results in a significant decrease in impulse if 
the target is not very close to the charge.   
Figures 4.16 and 4.18 show the percentage change in total impulse as the 
depth of burial increases.  Tables 4.16 and 4.17 contain the values used to create the 
respective surface graphs.  The percentages are with respect to the smaller depth of 
burial.  The additional soil reduces the shock wave (decreasing the total impulse at 
the 0.0? standoff distance), but provides more mass to impact against the target.  
Beyond the 0.25? depth the additional soil provides a negligible increase in impulse.  
As a result we see the impulse increase between the 0.04? and 0.25? depths of burial 
for all standoff distances in which there is an air gap.  This change can be seen most 
clearly in Figure 4.17, which is a 180? rotation of Figure 4.16.  There is little change 
between the 0.25? and 0.5? depths as seen in Figure 4.18.  The additional soil also 
increases the impulse at the 1.0? and 1.5? standoff distances, where the dispersed load 
is no longer a major loading mechanism and it is believed that most of the loading 
comes from the impact of the soil plug.
 
 80  
0
5
10
15
20
0
0.5
1
1.5
-100
-50
0
50
100
Plate Angle (Degrees)
Percent Total Impulse Change, 0.04" DOB to 0.25" DOB
Standoff Distance (in)
Pe
rce
nt 
Ch
an
ge
-80
-60
-40
-20
0
20
40
60
80
 
Figure 4.16:  Percent Total Impulse Change from 0.04? to 0.25? Burial Depth 
0" 0.5" 1" 1.5"
0? -4.09 85.57 77.33 20.83
7? -17.11 59.09 84.21 73.24
13? 3.11 109.62 61.54 52.38
20? -29.60 57.38 51.79 45.00A
ng
le
Standoff Distance
 
Table 4.16:  Percent Total Impulse Change Values, 0.04? to 0.25? DOB 
 
 81  
0
5
10
15
20 0
0.5
1
1.5
-100
-50
0
50
100
Standoff Distance (in)
Percent Total Impulse Change, 0.04" DOB to 0.25" DOB
Plate Angle (Degrees)
Pe
rce
nt 
Ch
an
ge
-80
-60
-40
-20
0
20
40
60
80
 
Figure 4.17:  180? Rotation of Figure 4.16 
 
 
 82  
0
5
10
15
20
0
0.5
1
1.5
-100
-50
0
50
100
Plate Angle (Degrees)
Percent Total Impulse Change, 0.25" DOB to 0.5" DOB
Standoff Distance (in)
Pe
rce
nt 
Ch
an
ge
-80
-60
-40
-20
0
20
40
60
80
 
Figure 4.18:  Percent Total Impulse Change from 0.25? to 0.5? Burial Depth 
0" 0.5" 1" 1.5"
0? -6.71 -18.89 -4.51 4.31
7? -12.81 -15.71 14.29 -10.57
13? 33.67 -7.34 17.14 3.13
20? 10.83 -28.13 5.88 18.39A
ng
le
Standoff Distance
 
Table 4.17:  Percent Total Impulse Change Values, 0.25? to 0.5? DOB 
 
 
 83  
4.2.3 Dihedral Plate Angle 
The shape of the target plays a significant role in determining the amount of 
impulse captured from an exploding buried charge, but the extent of the effect is 
dependent on the standoff distance and charge depth of burial.  Overall, the effect 
plate angle has on total impulse is roughly inversely proportional to standoff distance, 
and approximately proportional to depth of burial.  That is, as the standoff distance 
increases, the effect of a dihedral angle in reducing impulse compared to a flat plate at 
the same height goes down.  In all cases the steepest plate angles captured less 
impulse than the shallow plate angles. 
Figures 4.19 through 4.21 show the percentage change in impulse as the 
dihedral plate angle increases with respect to a flat plate.  Tables 4.18 through 4.20 
contain the values used to create the respective surface graphs.  Depending on the 
standoff distance and depth of burial, some increases in plate angle produced 
significant decreases in impulse while others produced little or none.  For all standoff 
distances in which an air gap existed, there was little difference between the 13? and 
20? plate angles.  At 0.0? standoff distances, the change in impulse with respect to 
target shape varied greatly depending on the depth of burial.  At the shallow depth of 
burial, there was little change between the 0? and 7? targets, a large change between 
the 0? and 13? targets, and a similar change between the 0? and 20?.  At the 0.25? 
depth of burial, the change was nearly linear with respect to target shape.  Finally at 
0.5? depth, there was a change between the 0? and 7?, a similar magnitude of change 
between 0? and 13?, and a larger decrease between the 0? and 20? targets.  
 
 84  
As depth of burial increases, more soil is thrown into the air and against the 
target, but at a slower speed.  The additional mass increases the effect of target shape 
on total impulse, particularly at closer standoff distances.  Deeply buried charges also 
produce a more vertical flow of ejecta.  Vertical flows require steeper angles to 
deflect the components away from the target, and shallow angled plates seem to act 
similarly to a 0? plate as the gas and soil annulus stagnate against the underside.  The 
result is that, as the depth of burial increases, a steeper plate angle is required to 
deflect the ejecta and reduce the total vertical impulse applied to the plate. 
Changes in target shape have little effect when the standoff distance is large.  
The presence of an air gap disperses the soil annulus; as the air gap increases, the soil 
annulus will impact over a larger area on the target.  The increased dispersion allows 
some of the ejecta to escape from the target without impacting against it.  The greatest 
change in impulse with respect to dihedral angle is around standoff distances close to 
the surface.  When the target is close to the ground, changes in target shape can have 
a dramatic effect on impulse (on the order of a 45% reduction).  
 
 85  
0
0.5
1
1.5
0.1
0.2
0.3
0.4
0.5
-100
-50
0
50
100
Standoff Distance (in)
Percent Total Impulse Change, 0 Degree Plate to 7 Degree Plate
Depth of Burial (in)
Pe
rce
nt 
Ch
an
ge
-80
-60
-40
-20
0
20
40
60
80
 
Figure 4.19:  Percent Total Impulse Change from 0? to 7? Dihedral Plate 
0.04" 0.25" 0.5"
0" -0.88 -14.33 -19.93
0.5" -9.28 -22.22 -24.30
1" -24.00 -21.05 -5.51
1.5" -26.04 6.03 -9.09St
an
do
ff 
Di
sta
nc
e
Depth of Burial
 
Table 4.18:  Percent Total Impulse Change Values, 0? to 7? Dihedral Plate 
 
 86  
0
0.5
1
1.5
0.1
0.2
0.3
0.4
0.5
-100
-50
0
50
100
Standoff Distance (in)
Percent Total Impulse Change, 0 Degree Plate to 13 Degree Plate
Depth of Burial (in)
Pe
rce
nt 
Ch
an
ge
-80
-60
-40
-20
0
20
40
60
80
 
Figure 4.20:  Percent Total Impulse Change from 0? to 13? Dihedral Plate 
0.04" 0.25" 0.5"
0" -43.57 -39.33 -13.07
0.5" -46.39 -39.44 -45.33
1" -13.33 -21.05 -3.15
1.5" -34.38 -17.24 -18.18St
an
do
ff 
Di
sta
nc
e
Depth of Burial
 
Table 4.19:  Percent Total Impulse Change Values, 0? to 13? Dihedral Plate 
 
 87  
0
0.5
1
1.5
0.1
0.2
0.3
0.4
0.5
-100
-50
0
50
100
Standoff Distance (in)
Percent Total Impulse Change, 0 Degree Plate to 20 Degree Plate
Depth of Burial (in)
Pe
rce
nt 
Ch
an
ge
-80
-60
-40
-20
0
20
40
60
80
 
Figure 4.21:  Percent Total Impulse Change from 0? to 20? Dihedral Plate 
0.04" 0.25" 0.5"
0" -34.80 -52.13 -43.14
0.5" -37.11 -46.67 -42.52
1" -25.33 -36.09 -29.13
1.5" -37.50 -25.00 -14.88St
an
do
ff 
Di
sta
nc
e
Depth of Burial
 
Table 4.20:  Percent Total Impulse Change Values, 0? to 20? Dihedral Plate 
 
 
 88  
4.3 Scaling and Expected Values 
 During the course of the research an attempt was made to correlate the 0? 
plate tests with an equation developed from small-scale tests previously conducted at 
the University of Maryland Dynamic Effects Lab and full scale tests conducted at the 
US Army Aberdeen Proving Grounds.  These results were plotted to a surface graph 
by Mr. W. McDonald [15], and an equation was derived from the result.  The 
equation is presented below, and Figure 4.22 shows the data points and the resulting 
surface graph from the equation.  Red dots represent the 24 small scale tests (.609 g 
charges using Reynolds detonators), and blue dots are the seven full scale (Table 
4.21) tests.  In order to compare the values across difference scales, the values were 
reduced to units that are independent of scale.  Standoff distance (called HOT, or 
height of target in the figure) and depth of burial are in units of 3 lbin , and impulse 
is in units of lbslb ? . 
 
 
 The derived equation was then used by LC Taylor at the Dynamic Effects Lab 
to determine expected reduced total impulse with respect to reduced depth of burial 
when the reduced standoff distance was held constant [15].  The equation is limited 
by the data it was derived from, and as a result may not be accurate for combinations 
of variables that are outside the range tested.  The depth of burial tested ranged from a 
reduced value of 1.86 to about 14 3 lbin .  Reduced target height ranged from 0 to 14 
3 lbin ,  however most of the tests were conducted at a reduced height of target of 
3.7 to 6.89 3 lbin .   
2 2 3
1/3 1/3 1/3 1/3 1/3( , ) / 3077 128 9.37 624 65.1 2.22
d d h h hI d h W
W W W W W
? ? ? ? ? ? ? ? ? ?= + ? ? + ?? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ?
 
 89  
 
 
Figure 4.22:  Surface Graph of Reduced Small and Full Scale Tests Values [15] 
The equation was used to examine how well the results of the flat plate testing 
in this research compared to results from previous impulse testing.  External 
correlation is important in order to validate the results and ensure that the data are 
useful for directly predicting full scale results.  The data developed in this research 
are internally consistent, meaning repeated tests show little variation and valid 
conclusions can be drawn by comparing one data point to another within these test 
 
 90  
results.  External consistency would mean that data coincides with results from other 
tests, and that valid expectations can be drawn directly regarding full scale values.   
 Figures 4.23 through 4.25 compare the expected impulse values from 
the model equation (dashed line) with the actual results found during shaped target 
testing (solid line) for three constant reduced heights of target.  Table 4.22 displays 
the small scale test values. 
Charge DoB Reduced DoB HoT Reduced HoT Reduced Impulse Expected Impulse
lb in in/(lb^[1/3]) in in/(lb^[1/3]) (lb-s)/lb (lb-s)/lb
0.001402 0.04 0.36 0.50 4.47 691 1435
0.001402 0.25 2.23 0.50 4.47 1283 1630
0.001402 0.5 4.47 0.50 4.47 1384 1775
0.001402 0.04 0.36 1.00 8.93 528 1160
0.001402 0.25 2.23 1.00 8.93 991 1354
0.001402 0.5 4.47 1.00 8.93 906 1500
0.001402 0.04 0.36 1.50 13.40 685 1108
0.001402 0.25 2.23 1.50 13.40 827 1302
0.001402 0.5 4.47 1.50 13.40 863 1448  
Table 4.21:  0? Plate Small Scale Test Results 
Reduced Impulse vs Reduced Burial Depth
4.47 in/lb^[1/3] Constant Reduced Standoff Distance
636mg Actual Charge Size
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
0 1 2 3 4 5
Reduced Burial Depth (in/lb^[1/3])
Re
du
ce
d I
mp
uls
e (
lb-
s/l
b)
Measured Impulse @ 4.467 HOT Expected Impulse @ 4.467 HOT
 
Figure 4.23:  4.467 3 lbin  Reduced Impulse: Expected vs. Actual Values [15] 
 
 91  
Reduced Impulse vs Reduced Burial Depth
8.93 in/lb^[1/3] Constant Reduced Standoff Distance
636mg Actual Charge Size
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
0 1 2 3 4 5
Reduced Burial Depth (in/lb^[1/3])
Re
du
ce
d I
mp
uls
e (
lb-
s/l
b)
Measured Impulse @ 8.93 HOT Expected Impulse @ 8.93 HOT
 
Figure 4.24:  8.93 SOD Reduced Impulse: Expected vs. Actual Values [15] 
Reduced Impulse vs Reduced Burial Depth
13.4 in/lb^[1/3] Constant Reduced Standoff Distance
636mg Actual Charge Size
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
0 1 2 3 4 5
Reduced Burial Depth (in/lb^[1/3])
Re
du
ce
d I
mp
uls
e (
lb-
s/l
b)
Measured Impulse @ 13.4 HOT Expected Impulse @ 13.4 HOT
 
Figure 4.25:  13.4 SOD Reduced Impulse: Expected vs. Actual Values [15] 
 
 92  
 The reduced values of the flat plate tests reported in this thesis are consistently 
lower than the expected values calculated by the McDonald equation.  Because the 
data used to create the McDonald equation did not contain any tests at a depth of 
burial less than 1.86 3 lbin , the expected values at the shallower depths of burial are 
not predicted.  The differences at the 2.23 and 4.47 3 lbin  reduced depths of burial 
are within a region that was extensively tested and incorporated into the model, and 
are therefore more believable.  Ignoring the values for the 0.36 3 lbin  reduced depth 
of burial, on average the measured impulse values in this study are 31% lower than 
the expected values.   
 An inconsistency between the expected values derived from previous testing 
and the results obtained from the shaped target testing would indicate the presence of 
a problem with testing that needs to be resolved.  Assuming the equation is correct, 
the most likely source of error is miscalculation of charge size.  Hopkinson scaling 
only applies to ideal explosives, so a correlation factor may be required if the charge 
output is not what is expected. 
The equation and test data have similar trends with regards to impulse as a 
function of height of target, as seen in Figure 4.26.   
 
 93  
Reduced Impulse vs Reduced Height of Target
Constant Reduced Burial Depth
636mg Charge Size
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Reduced Height of Target (in/lb^[1/3])
Re
du
ce
d I
mp
uls
e (
lb-
s/l
b)
Measured DOB = 2.23 Expected DOB = 2.23
Measured DOB = 4.47 Expected DOB = 4.47
 
Figure 4.26:  Measured vs Expected Total Impulse for Constant Reduced DoB 
 For the reduced depths of burial within the range of the model, the expected 
and measured values show similar trends with respect to the different heights of 
target.   
 Comparisons show that the total impulse measured using the flat plate for the 
given height of target and depths of burial are consistently lower than what the 
McDonald equation predicts for a 636mg size charge.  Although the output of the 
charge is less than expected, it is consistent among repeated tests.  This suggests that 
the results from this research using the 636mg charge may be compared to external 
data if a correlation (or ?correction?) factor is used for the charge size.  Since the 
charge output is consistent but lower than expected, we can correlate the results by 
using an effective charge size that is smaller than the 636mg of output explosive used.  
 
 94  
This is similar to the use of a correlation factor suggested by Fu [7] when scaling 
nonidealized explosives. 
 The expected values from the McDonald equation coincide more closely with 
the reduced values from the 0? plate tests if a charge size of 460mg is used instead of 
636mg, as seen in Figures 4.27 through 4.29 and Table 4.22. 
Charge DoB Reduced DoB HoT Reduced HoT Reduced Impulse Expected Impulse
lb in in/(lb^[1/3]) in in/(lb^[1/3]) (lb-s)/lb (lb-s)/lb
0.001014 0.04 0.40 0.50 4.98 956 1360
0.001014 0.25 2.49 0.50 4.98 1775 1571
0.001014 0.5 4.98 0.50 4.98 1913 1715
0.001014 0.04 0.40 1.00 9.95 730 1176
0.001014 0.25 2.49 1.00 9.95 1371 1387
0.001014 0.5 4.98 1.00 9.95 1252 1531
0.001014 0.04 0.40 1.50 14.93 947 933
0.001014 0.25 2.49 1.50 14.93 1144 1144
0.001014 0.5 4.98 1.50 14.93 1193 1289  
Table 4.22:  0? Plate Small Scale Test Results for 460mg Effective Charge Size
 
 95  
Reduced Impulse vs Reduced Burial Depth
4.98 in/lb^[1/3] Constant Reduced Standoff Distance
460mg Effective Charge Size
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
0 1 2 3 4 5
Reduced Burial Depth (in/lb^[1/3])
Re
du
ce
d I
mp
uls
e (
lb-
s/l
b)
Measured Impulse @ 4.98 HOT Expected Impulse @ 4.98 HOT
 
Figure 4.27:  4.98 3 lbin  Reduced Impulse Values for 460mg Charge Size 
Reduced Impulse vs Reduced Burial Depth
9.95 in/lb^[1/3] Constant Reduced Standoff Distance
460mg Effective Charge Size
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
0 1 2 3 4 5
Reduced Burial Depth (in/lb^[1/3])
Re
du
ce
d I
mp
uls
e (
lb-
s/l
b)
Measured Impulse @ 9.95 HOT Expected Impulse @ 9.95 HOT
 
Figure 4.28:  9.95 SOD Reduced Impulse Values for 460mg Charge Size 
 
 96  
Reduced Impulse vs Reduced Burial Depth
14.93 in/lb^[1/3] Constant Reduced Standoff Distance
460mg Effective Charge Size
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
0 1 2 3 4 5
Reduced Burial Depth (in/lb^[1/3])
Re
du
ce
d I
mp
uls
e (
lb-
s/l
b)
Measured Impulse @ 14.93 HOT Expected Impulse @ 14.93 HOT
 
Figure 4.29:  14.93 SOD Reduced Impulse Values for 460mg Charge Size 
Scaling the results with a 460mg effective charge size places the expected and 
actual reduced impulse values much closer than if they were scaled with the actual 
charge size of 636mg.  Ignoring the values at the 0.36 3 lbin reduced depth of burial 
(since this value is outside the range of validity for the McDonald equation), the 
average difference between the measured and expected values is 9%, with the greatest 
difference at 18%.  In particular, the measured 14.93 3 lbin height of target values 
(green lines in Figure 4.29) are right on top of their expected values.  Using the 
460mg effective charge size as a correlation factor allows the results of the small 
scale shape tests to be reduced and compared to tests conducted at other scales.  In 
order to determine if the difference between measured and expected values was due 
to charge size, a series of tests involving three separate charge sizes was conducted.  
 
 97  
0? plate impulse tests were conducted with 0.636g, 1.0g, and 2.5g charges.  There 
was no agreement between expected and measured values until the charge size was 
2.5g.   Values at the 2.5g charge size were within 10% of those predicted by the 
McDonald equation.  In order to validate this correlation, larger scale testing should 
be conducted and the results compared to both the small scale tests and the McDonald 
equation.   
 
 98  
4.4 Blast Damage Effects: Erosion and Impact 
Testing of the flat and dihedral plates produced wear on the target faces from 
repeated detonations.  Analysis of the worn target plates provided additional 
information about the loading mechanisms experienced by the plate from the 
detonation of a buried charge.  Repeating tests with a new and worn plate indicated 
that change in total captured impulse due to wear on the plate was within 10% scatter.  
Figure 4.30 compares a new 13? dihedral plate to one damaged after multiple tests. 
Figure 4.30:  New and Worn 13? Dihedral Target Plates 
 
 
 99  
 Close examination of the damage to the worn plate shows two regions.  The 
target face is radially eroded and pitted in a large circle, a result of sand tangentially 
striking the plate during the course of repeated blasts.  This area of effect will be 
referred to as the erosion region.  In the center of the plate is a distinct crater with a 
wear pattern different from that of the erosion region.  This area will be called the 
impact region.  Figures 4.31 and 4.32 show the target plate and the approximate 
distribution of the impact and erosion damage regions.   
 
Figure 4.31: Worn 13? Plate 
 
 100  
 
Figure 4.32:  Erosion and Impact Damage Regions 
Figure 4.33 is a picture of the underside of the 13? plate after a test.  The plate 
flipped over after being loaded by the charge detonation, which preserved the sand 
pattern.  The center of the target plate features a glob of sand over the impact region.  
A radial pattern of scorch marks and sand spray splays out from the center, and is 
surrounded on the outside by arcs of sand.  Because only one pattern was recorded, 
further research is required before any assertions can be made regarding this 
phenomena. 
 
 101  
 
Figure 4.33:  Spray Pattern on the Underside of the 13? Plate 
4.4.1 Impact Region 
The impact of ejecta against the center of the target left it deeply pitted 
(Figure 4.34).  The walls of the impact region are concave, and there is a distinct lip 
at the edge of the crater.  The appearance of the center of the plate suggests that the 
sand that hit the center traveled perpendicular to the surface of the ground.  Using the 
circles pictured in Figure 4.32 as a reference, the impact region was struck by sand 
traveling perpendicular to the surface.  This is in contrast to the surrounding region, 
where the pitting travels outward in a radial direction.  The sand seen in the center of 
the plate in Figure 4.33 completely covers the impact region. 
 
 102  
 
Figure 4.34:  Impact Crater Close-Up 
The cratered shape of the impact region supports the presence of an intense, 
concentrated loading acting against the center of the plate.  The most likely candidate 
for this load comes from the impact of the soil plug as it is propelled by the rapidly 
expanding detonation gases beneath it.  The collision of the soil plug against the 
target plate deformed the center, and eventually a crater was formed after repeated 
strikes from testing.  The size of the crater is slightly larger than the diameter of the 
636 mg charge used in the impulse testing (Figure 4.35).  The similarity in size 
between the charge and the impact region supports the idea that the cratering is from 
the impact of the soil plug against the target.   
 
 103  
 
Figure 4.35:  Impact Region as Compared to 636 mg Charge 
 
 104  
4.4.2 Erosion Region 
Surrounding the crater is an area pitted and worn in a radial pattern emanating 
outward from the center.  This damage region is evenly distributed over a wide area 
on the plate, and hints at the presence of sand tangentially impacting against the 
surface of the target.  The sand is most concentrated in two perpendicular lines, 
forming an ?X? across the center of the target.  The ?X? pattern of soil and scorch 
marks in Figure 4.33 is spread out radially from the center of the target, and partial 
arcs of sand surround the outside.   
The sand pattern in Figure 4.33, as well as the wear pattern in Figure 4.32, 
supports the presence of a distributed load mechanism acting over a wide area of the 
plate.  The spray of ejecta from the charge located underneath the center of the target 
impacted over the surface the target in an outward direction, which caused the radial 
pitting seen in Figure 4.33.  Portions of the spray struck and then stuck to the target, 
and formed the arcs seen in Figure 4.33.  The ?X? shape of the spray pattern suggests 
that the distributed load is influenced by the target shape.  The regions of the dihedral 
shape closest to the surface are clean of spray, as are the center of the dihedral faces.   
 
 
 105  
Chapter 5: Summary & Conclusions 
5.1 Summary 
Research was conducted to examine the effect of changes in target geometry 
on loading applied by a blast from a buried charge centered under the target plate.  
The testing involved very small scale charges (636mg of explosive) and utilized high 
speed digital imagery to capture the motion of specially fabricated target plates.  The 
primary test set involved charges buried in saturated sand at three depths (0.04?, 
0.25?, and 0.5? to the top of the charge).  The targets were aluminum billets machined 
into non-deforming shapes with 0?, 7?, 13?, and 20? dihedral angles.  The plane area 
parallel to the soil surface and target mass were held constant.  The target plates were 
suspended at four different heights from the surface: 0?, 0.5?, 1?, and 1.5?.  The 
height (called the standoff distance) was measured from the surface to the lowest 
point on the target.  Analysis of high speed video was used to determine the total 
impulse transmitted from the detonated charge to the target plate.   
The blast from a buried charge can act on the target plate with three distinct 
mechanisms.  The first is a shock wave transmitted from the explosive directly into 
the target.  This loading mechanism only affects the target when it is touching the 
surface, or at extremely low standoff distances.  The other two loading mechanisms 
are caused by the expanding detonation gases in the form of a gas bubble.  The 
second loading mechanism is the perpendicular impact of the soil above the charge 
(the soil plug) against the target.  The expanding gas acts on the soil directly over the 
charge to propel the soil plug upward like a piston.  The third loading mechanism is a 
 
 106  
distributed load from an annulus of soil and ejecta thrown from the charge area by the 
expanding gas bubble.  The distributed load is responsible for most of the total 
impulse, and in most cases is also the most affected by target geometry and standoff 
distance.  Analysis of the damage caused to the plate by repeated tests supports the 
division of the load into an impact and distributed mechanism. 
 
 107  
5.2 Conclusions 
The dihedral angle of the target plays a significant role in reducing the total 
impulse applied to a target by the explosion of a buried charge.  For a given standoff 
distance and depth of burial, there is a cutoff angle beyond which there is no 
reduction in total impulse over the range of variables investigated.  This cutoff angle 
increases with depth of burial, and decreases with standoff distance.  Comparisons 
between dihedral and pyramid target shapes confirmed the idea that only a portion of 
the total impulse (the distributed load mechanism) is affected by target geometry.  
Once the distributed load has been mitigated (and only the impact load remains), 
further changes in target geometry will not affect total impulse. 
Changes in the depth of burial affect the amount of ejecta that was flung 
towards the plate and the size of the soil plug.  Increases in depth of burial increase 
total impulse up to a point, beyond which changes had a negligible effect within the 
range of depths tested.  The addition of more ejecta from increasing the depth of 
burial increases the influence of plate shape on total impulse. 
Standoff distance has a roughly inverse relationship with total impulse; at 
higher standoff distances, the impulse is lower.  For a given plate shape and depth of 
burial, there appears to be a cutoff height at which increases in standoff distance 
caused negligible changes in total impulse (within the range tested).  Standoff 
distance determined the proportion of loading mechanisms.  At extremely close 
distances, the shock wave imparts significant impulse to the target.  Increasing 
standoff creates an air gap that mitigates the effect of the shock wave. At large 
 
 108  
distances the distributed load mechanism is significantly reduced.  The speculated 
impact load is largely unaffected by standoff distance within the range tested. 
Comparisons between the test data and a model derived from previous 
experiments revealed a disparity.  The measured total impulse per gram of explosive 
in this research seems to be lower than the expected values.  The model itself has 
provided predicted results that are consistent with previous small-scale testing, and as 
a result the problem appears to be with the charge size.  The lower values (relative to 
the expected values) suggest the possibility that the charge output may not be as much 
as the total explosive mass suggests it should be.  Correlations between this data and 
the model were more successful when an effective charge weight approximately 70% 
that of the actual charge weight was used. 
 
 109  
5.3 Future Work 
There are several areas that need additional research.  Additional standoff 
distances, plate angles, and depths of burial should be tested in order to refine the 
matrix and obtain a better understanding of the transition regions and cutoff angles.  
Particular attention should be paid to standoff distances and depths of burial near to 
the surface, since these areas show the greatest sensitivity to changes in the 
parameters.  New plate shapes incorporating additional dihedral angles, as well as 
other geometries such as rounded shapes, should be tested.  A new testing regimen 
involving charges placed in areas other than directly underneath the plate is needed to 
replicate the fact that most explosions do not occur directly underneath the center of 
the vehicle.  Additional focus should be placed on the spray pattern on the underside 
of the plates after a test, as they provide insight into the distribution of load 
mechanisms on the target.  Finally, larger scale tests should be conducted to ensure 
proper consistency between very small and full scale events.  The research discussed 
in this thesis only scratches the surface of the dynamic effects surrounding a buried 
charge explosion.  Further experiments based on results found here and elsewhere 
will eventually provide insight, but there remains an extensive amount of work to be 
done
 
 110  
Appendix A:  Deformable Plate Shapes 
In the earliest stages of this research, an attempt was made to fabricate a target 
plate by bending a flat plate of aluminum into a dihedral shape.  A 0.125? wide by 
0.375? deep channel was milled out of the center of an 8? x 8? x 0.5? aluminum plate 
to provide a bending axis (Figure A.1).  When bent, the plate formed a dihedral angle 
of approximately 13 degrees.  Testing used a charge consisting of 3 RP-80 detonators 
laid side-by-side; the total charge size was 609mg (Figure A.2).  A total of three tests 
were conducted before the plate was too damaged by erosion to use.  By the third test 
a crack had formed in the center of the plate into the milled channel. 
 
Figure A.1:  13? Deformable ?Bent? Plate 
 
 111  
 
Figure A.2:  609mg Charge Consisting of 3 RP-80 Detonators 
Testing of the bent plate revealed that during the initial stages of loading the 
plate would deform before it displaced.  Figure A.3 is a series of images showing the 
first 5ms of the bent plate being loaded by a buried charge in saturated soil.  The test 
was conducted at a 0.04? depth of burial and a standoff distance of 0.11?.  In the first 
frame we see the target resting before the charge is detonated.  1ms later we see the 
charge detonate and an initial spray of ejecta.  1 ms later the center locally deforms 
and flattens out to an angle of 4?.  The plate does not experience any global 
movement.  3 ms after the explosion, in the third frame, the plate begins to move with 
rigid body motion.  The plate regains a portion of its original shape between the third 
and fourth frame.  After the test the plate was found to have a dihedral angle of 10?, 
indicating that a portion of the deformation was plastic. 
 
 112  
 
Figure A.3:  Time Elapse (1 ms/frame) of Bent Plate Starting at 0ms 
 
 113  
Since the bent plate deforms during loading, it was less useful for examining 
the role shape plays in reducing total impulse from a buried charge.  Testing was 
instead conducted with solid plates machined out of solid aluminum billets, which 
maintained their shape during loading.  While they did not solve the problem they 
were designed for, the bent plate tests provided an opportunity to examine how 
deformation affects the total impulse captured by a shaped plate.   
Figure A.4 compares the reduced impulse values of the bent plate tests to the 
13? dihedral tests for the same 0.04? depth of burial.  The X-axis is reduced standoff 
distance, the Y-axis is reduced total captured impulse, and the three colored lines are 
three different targets.  The black line is the 0? plate, the red line the deformable 13? 
plate, and the blue line the rigid 13? plate.  The circles, triangles, and squares 
represent the data points rigid 13?, and deformable 13?, and 0? plates respectively.  
The reduced values are used because of the different charge sizes; 609mg is used to 
scale the bent plate values, and the effective value of 460mg from Section 4.3 is used 
to scale the 0? and rigid 13? plate values.  Table A.1 contains the impulse values for 
Figure A.4. 
 
 114  
Rigid and Deformable Shaped Plate Impulse Tests 
Reduced Depth of Burial: 0.04"
0
500
1000
1500
2000
2500
3000
3500
4000
0 2 4 6 8 10 12 14 16
Reduced Standoff Distance (in/(lb^[1/3]))
Re
du
ce
d T
ot
al 
Im
pu
lse
 (l
b-
s/l
b) Rigid 13? Plate
Deformable 13? Plate
0? Plate
 
Figure A.4:  Rigid and Deformable 13 Degree Plates at 0.04? Burial Depth 
Charge Reduced SD Reduced Imp
g in/(in^[1/3]) lb-s / lb
0.609 1.00 2044.56
0.609 1.00 2170.14
0.609 5.26 1044.88
0.460 0.00 3371.88
0.460 4.98 840.20
0.460 4.98 1010.90
0.460 4.98 1030.85
0.460 9.95 722.70
0.460 9.95 744.87
0.460 14.93 944.39
0.460 19.91 625.16
0.609 1.00 2394.53
0.609 8.25 907.58
0.460 0.00 1910.95
0.460 4.98 512.10
0.460 9.95 645.11
0.460 14.93 616.29
0.460 19.91 563.09
Flat Plate
Rigid 13? Plate
Plate
Deformable 
13? Plate
 
Table A.1:  Rigid and Deformable Plate Impulse Test Values 
 
 
 115  
In Figure A.4 we see the bent plate consistently shows higher levels of total 
impulse within the range of standoff distances tested compared to the rigid shape.  
The values of the bent plate coincide very closely with those of the 0? plate, even 
though the bent plate still had a 10? dihedral angle after being loaded by the buried 
charge.  Although more tests are required to confirm these results, the initial data 
suggests that the deformation of the bent plate can have a significant effect on total 
captured impulse.  The impulse captured by the bent plate is the same as a flat plate.  
The deformable target is formed by the blast into a flatter shape that captures more 
impulse than a rigid target.
 
 116  
Appendix B:  Additional Target Shapes 
 A small series of tests was conducted in order to compare the total impulse 
captured by a dihedral shape to a single pyramid shape of the same angle (Figure B.1, 
Top).  Two angles were tested: 7? and 13?.  A second series of tests were conducted 
comparing shapes with a grid of 45? pyramids (Figure B.1, Bottom).  Two pyramid 
heights were tested: 0.5? and 0.25?.  Pyramid grid height refers to the distance from 
the base of the pyramid to the top point.  Two different charges were used dependeing 
on the test.  The first was the 609mg RP-80 charge described in Appendix A, and the 
second was the 636mg charge described in Section 2.1.  In order to compare the 
results the standoff and impulse values were reduced to a scale-independent form.  
The effective charge size of 460mg from Section 4.3 was used for the 636mg charges. 
 
Figure B.1:  13? Dihedral & Pyramid (Top) and Pyramid Grids (Bottom) 
 
 117  
B.1 Pyramid and Dihedral Shapes 
Table B.1 and Figures B.2 and B.3 present the scale-independent values 
recorded from a series of tests comparing 7? and 13? dihedral and pyramid shapes.  
All values are presented in a scale-independent reduced format.   
Charge Reduced SOD Reduced Impulse
g in / (in^[1/3]) lb-s / lb
0.460 0.00 3371.88
0.460 4.98 840.20
0.460 4.98 1010.90
0.460 4.98 1030.85
0.460 9.95 722.70
0.460 9.95 744.87
0.460 14.93 944.39
0.460 19.91 625.16
0.609 1.00 2394.53
0.609 8.25 907.58
0.460 0.00 3300.94
0.460 3.78 1352.30
0.460 4.98 558.65
0.609 0.00 1850.32
0.609 0.00 2550.25
0.609 3.44 941.07
0.609 7.25 654.73
0.609 18.13 606.17
0.460 0.00 2176.98
0.460 4.98 576.39
0.460 9.95 671.72
0.460 14.93 669.50
0.460 19.91 620.73
0.460 0.00 1910.95
0.460 4.98 512.10
0.460 9.95 645.11
0.460 14.93 616.29
0.460 19.91 563.09
0.460 0.00 1857.75
0.460 19.91 538.70
0.609 0.00 1585.75
0.609 4.53 532.49
0.609 4.53 582.72
0.609 7.25 577.70
0.609 7.25 601.14
0.609 9.97 592.77
Plate
13? Pyramid
0? Flat Plate
7? Dihedral
7? Pyramid
13? Dihedral
 
Table B.1:  Dihedral and Pyramid Plate Test Values 
 
 118  
7? Pyramid and 7? Dihedral Shaped Plate Impulse Tes ts 
Reduced Depth of Burial: 0.4 (in/(lb^[1/3]))
0
500
1000
1500
2000
2500
3000
3500
4000
0 5 10 15 20 25
Reduced Standoff Distance (in/(lb^[1/3]))
Re
du
ce
d I
mp
uls
e (
lb-
s/l
b)
0? Flat Plate
7? Dihedral
7? Pyramid
 
Figure B.2:  7? Pyramid and Dihedral Plate Tests 
13? Pyramid and 13? Dihedral Shaped Plate Impulse T ests 
Reduced Depth of Burial: 0.4 (in/(lb^[1/3]))
0
500
1000
1500
2000
2500
3000
3500
4000
0 5 10 15 20 25
Reduced Standoff Distance (in/(lb^[1/3]))
Re
du
ce
d I
mp
uls
e (
lb-
s/l
b)
0? Flat Plate
13? Dihedral
13? Pyramid
 
Figure B.3:  13?Pyramid and Dihedral Plate Tests 
 
 119  
 Both Figure B.2 and B.3 show impulse as a function of standoff distance for a 
dihedral and pyramid plate.  The red lines and diamonds represent the values from 
dihedral shape tests, the blue lines and triangles are the pyramid shape test values, and 
the black line and squares are the 0? flat plate values.  As discussed in Section 4.1.4 
the 7? dihedral and pyramid shape differ slightly within the first range of standoff 
distances tested (from 0 to 4.98 3 lbin ), and then captured the same total impulse up 
to the maximum standoff distance tested.  When all the values for a given standoff 
distance are averaged, the 7? degree dihedral target plate captures slightly more 
impulse than the 7? pyramid target.  The 13? dihedral and pyramid target plates 
capture the same total impulse for the entire range of standoff distances tested.   
 The values for the dihedral and pyramid impulse tests support the idea that 
there is a maximum portion of the total impulse (the distributed load mechanism) that 
can be deflected by shaping the target.  It is speculated that once this portion of the 
load is deflected, and only the impact load mechanism remains, further changes in the 
target geometry will have a negligible effect on total captured impulse.  
 
 120  
B.2 Pyramid Grid Target Shapes 
 A second series of tests was conducted using plates machined with grid arrays 
of 45? pyramids of varying heights.  Two target plates were tested; one with an array 
of pyramids 0.5? high (Figure B.1, Bottom Left, p. 115), and a second with an array 
of pyramids 0.25? high (Figure B.1, Bottom Right, p.115).  Figure B.4 shows the 
results of the testing.  The graph shows reduced impulse as a function of reduced 
standoff distance.  The black squares and line represents the data for the 0? plate, the 
red line and diamonds are the data points of the 0.25? grid plate, and the blue line and 
triangles are data points for the 0.5? grid plate.  Table B.2 provides the data values for 
the information graphed in Figure B.4. 
0.25" and 0.5" Pyramid Grid Plate Impulse Tests 
Reduced Depth of Burial: 0.4 (in/(lb^[1/3]))
0
500
1000
1500
2000
2500
3000
3500
4000
0 2 4 6 8 10
Reduced Standoff Distance (in/(lb^[1/3]))
Re
du
ce
d I
mp
uls
e (
lb-
s/l
b)
0? Flat Plate
0.25" Pyramid Grid
0.5" Pyramid Grid
 
Figure B.4:  0.25? and 0.5? Pyramid Grid Plate Tests 
 
 121  
Charge Reduced SOD Reduced Impulse
g in / (in^[1/3]) lb-s / lb
0.460 0.00 3371.88
0.460 4.98 840.20
0.460 4.98 1010.90
0.460 4.98 1030.85
0.460 9.95 722.70
0.460 9.95 744.87
0.460 14.93 944.39
0.460 19.91 625.16
0.609 1.00 2394.53
0.609 8.25 907.58
0.609 0.00 2260.57
0.609 3.63 1351.32
0.609 3.63 1155.40
0.609 5.26 1247.50
0.609 0.00 1977.58
0.609 3.26 1018.09
0.609 3.26 1232.43
0.609 5.26 832.22
0.25" Pyramid Grid
0.5" Pyramid Grid
0? Flat Plate
Plate
 
Table B.2:  0.25? and 0.5? Pyramid Grid Plate Test Values 
The graph and table shows a change in relative performance of the grid plates 
with respect to the 0? plate depending on the standoff distance.  At the 0 3 lbin  
reduced standoff distance, the 0.25? and 0.5? pyramid grid plates capture roughly 
60% of the total impulse that the flat plate captures.  This can be explained by the 
influence of the shock wave loading mechanism at close standoff distances.  The 
pyramid grid plates are stood off from the ground by some distance, and only the 
points of the pyramid array are touching the sand.  As a result there is only limited 
material for the shock wave to travel through, and also gaps for the expanding gas to 
flow through.  In contrast the flat plate completely covers the soil at the 0 3 lbin  
standoff distance, and captures the maximum amount of impulse. 
The pyramid grid shapes capture more total impulse relative to the 0? plate as 
the standoff distance increases.  As the standoff distance approaches 5.26 3 lbin  the 
two pyramid grid plates capture the same total impulse as the 0? plate.  In the case of 
 
 122  
the 0.25? pyramid grid plate, the total captured impulse is actually 25% higher than 
the 0? plate at the 5.26 3 lbin  reduced standoff distance.  The increase in standoff 
relative to the 0? plate can be explained by the way the detonation gases and ejecta act 
against the pyramid grid structures.  In the flat plate, the target is shaped in such a 
way that none of the ejecta can be captured by the geometry of the plate, and instead 
all of the escaping soil and gases are deflected away.  ,In contrast portions of the 
underside of the pyramid grid plate are facing the center of the explosion.  Escaping 
ejecta and detonation gases have to flow around these faces, and in doing so impact 
against the target.  The surface features capture more impulse relative to a flat plate.   
 
Figure B.5:  Wear on 0.5? Pyramid Grid Plate After Testing 
 
 123  
 Figure B.5 is an expanded image of the 0.5? pyramid grid plate from Figure 
B.1.  The majority of the wear is located in the center of the target plate, but at 
portions of the plate away from the center we begin to see a change in the erosion 
pattern.  The wear is most concentrated on the sides of the pyramids that face the 
center of the target, and lest evident on sides facing away from the center. As the soil 
and gas bubble expanded, they impacted against the pyramid features facing the 
explosion and were then diverted around them.  We can see this diversion in Figure 
B.6, which is a frame from a 0.5? pyramid grid plate test taken 5ms after the charge 
was detonated.  Jets of sand and gas are projected from between the pyramid arrays, 
with most of the ejecta coming from the center of the pyramid plates.  The results 
support the idea that a portion of the total impulse is heavily dependent on target 
geometry, and depending on the shape of the target can be increased or decreased 
significantly. 
 
Figure B.6:  0.5? Pyramid Grid Plate, 0.04? DOB, 0.58? SOD, 5ms Elapsed Time
 
 124  
Appendix C:  Standoff Distance Measured from Centroid 
Standoff distance was found to play a significant role in the total impulse 
captured by a target plate from a buried charge, and where that standoff distance is 
measured from can greatly alter the measured values.  The shape of the target plates 
used in this research makes choosing a reference point difficult.  The decision to 
measure standoff distance from the surface to the lowest point on the target plate was 
designed to allow standoff distance to translate into the ground clearance beneath a 
vehicle.  The disadvantage of using the lowest point on the target as the reference for 
standoff distance is that the average distance between the surface of the target and the 
ground varies with the shape of the target.  In the case of dihedral and pyramid 
shapes, the average distance increases when the dihedral angle becomes larger. 
An alternate reference point is the centroid 
(geometric center) of the shape on the target.  Using 
the centroid as the reference point for standoff 
distance mitigates the geometry of the target, and 
transforms the target into a flat plate at an 
equivalent distance from the surface.  Table C.1  
Plate
Distance from 
Bottom to 
Centroid (in)
13? Bent Plate 0.53
0.25" Pyramid 0.17
0.5" Pyramid 0.33
7? Pyramid 0.33
13? Pyramid 0.60
0? Flat Plate 0.00
7? Dihedral 0.32
13? Dihedral 0.60  
Table C.1:  Centroid Distances
contains the distance from the bottom of each target plate to centroid of the dihedral 
or pyramid shape.  Figures C.1 through C.3, and Table C.2 through C.4, contain the 
graphs and values for the constant depth of burial tests using a standoff distance 
referencing the centroid.  Regardless of whether the centroid or lowest point of the 
target is used as the reference for the standoff distance, the results are the same.
 
 125  
0
0.5
1
1.5
2
0
5
10
15
20
0
1
2
3
4
Distance to Centroid (in)
Plate Total Impulse Test, 0.04" Depth of Burial
Plate Angle (Degrees)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure C.1:  Impulse Test and Centroid Standoff Distances, Constant 0.04? DOB 
Plate 
Angle
Burial 
Depth
Centroid 
Standoff
Total 
Impulse
(?) (in) (in) (lb-s)
0 0.04 0 3.42
0 0.04 0.5 0.97
0 0.04 1 0.75
0 0.04 1.5 0.96
0 0.04 2 0.63
7 0.04 0.32 3.39
7 0.04 0.7 1.37
7 0.04 0.82 0.88
7 0.04 1.32 0.57
7 0.04 1.82 0.71
13 0.04 0.6 1.93
13 0.04 1.1 0.52
13 0.04 1.6 0.65
13 0.04 2.1 0.63
20 0.04 0.6 2.23
20 0.04 1.1 0.61
20 0.04 1.6 0.56
20 0.04 2.1 0.60  
Table C.2:  Impulse Values for Figure C.1 
 
 126  
0
0.5
1
1.5
2
0
5
10
15
20
0
1
2
3
4
Distance to Centroid (in)
Plate Total Impulse Test, 0.25" Depth of Burial
Plate Angle (Degrees)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure C.2:  Impulse Test and Centroid Standoff Distances, Constant 0.25? DOB 
Plate 
Angle
Burial 
Depth
Centroid 
Standoff
Total 
Impulse
(?) (in) (in) (lb-s)
0 0.25 0 3.28
0 0.25 0.5 1.80
0 0.25 1 1.33
0 0.25 1.5 1.16
7 0.25 0.32 2.81
7 0.25 0.82 1.40
7 0.25 1.32 1.05
7 0.25 1.82 1.23
13 0.25 0.6 1.99
13 0.25 1.1 1.09
13 0.25 1.6 1.05
13 0.25 2.1 0.96
20 0.25 0.6 1.57
20 0.25 1.1 0.96
20 0.25 1.6 0.85
20 0.25 2.1 0.87  
Table C.3:  Impulse Values for Figure C.2 
 
 127  
0
0.5
1
1.5
2
0
5
10
15
20
0
1
2
3
4
Distance to Centroid (in)
Plate Total Impulse Test, 0.5" Depth of Burial
Plate Angle (Degrees)
Im
pu
lse
 (lb
-s)
0.5
1
1.5
2
2.5
3
3.5
 
Figure C.3:  Impulse Test and Centroid Standoff Distances, Constant 0.5? DOB 
Plate 
Angle
Burial 
Depth
Centroid 
Standoff
Total 
Impulse
(?) (in) (in) (lb-s)
0 0.5 0 3.06
0 0.5 0.5 2.14
0 0.5 1 1.27
0 0.5 1.5 1.21
7 0.5 0.32 2.45
7 0.5 0.82 1.62
7 0.5 1.32 1.20
7 0.5 1.82 1.10
13 0.5 0.6 2.66
13 0.5 1.1 1.17
13 0.5 1.6 1.23
13 0.5 2.1 0.99
20 0.5 0.6 1.74
20 0.5 1.1 1.23
20 0.5 1.6 0.90
20 0.5 2.1 1.03  
Table C.4:  Impulse Values for Figure C.3
 
 128  
Glossary 
Acoustic Impedance:  A material constant indicating the ability of a material to 
transmit sound in units of kg/s m?.  It is measured by multiplying the density by the 
speed of sound in the material.  Sound travels better through materials with high 
acoustic impedance, such as solids or liquids. 
Centroid:  The geometric center of a two-dimensional shape. 
Centroid Standoff Distance:  The perpendicular distance from the ground to the 
centroid of the target shape. 
Depth of Burial (DOB):  The distance between the surface of the sand and the top of 
the charge.  This measurement is taken before the sand is saturated, and is measured 
in inches (in.). 
Dispersed Load:  A component mechanism of blast loading that acts over a wide area 
of the target, imparting a significant amount of energy and momentum.  It is 
composed of the gas bubble and soil annulus. 
Ejecta:  Soil, water, and other bits that are thrown into the air by an explosion. 
Gas Bubble:  An area of extremely high pressure caused by expanding gas from the 
detonation of an explosive charge. 
Height of Target (HOT):  See standoff distance.  This term is primarily used when 
referring to reduced values ( 3 lbin ) that compare results between tests of different 
scales.   
Impact Load:  A component mechanism of blast loading that is defined by a very 
rapid and concentrated impact.  When the charge explodes, the expanding gas acts 
like a piston to project the soil plug into the target like a bullet. 
 
 129  
Impulse:  The change in the momentum of a target plate as a result of loading from a 
buried charge, which is the integral of the applied force with respect to time.  It is 
measured in lb-s, and was calculated by multiplying the mass of the target by the 
velocity. 
Plate Angle:  The dihedral angle of a target plate between the front face of the target 
(the side facing the ground) and the ground itself.  It is measured in degrees. 
Pyramid Height:  For the pyramid grid shapes, this variable measures the height of 
the triangles from the base to their top point.  It is measured in inches. 
Reduced Value:  A value that is unchanging with respect to scale, used to compare 
tests involving different charge sizes. 
Shock Load:  A component mechanism of blast loading consisting of the shock wave 
emitted by the detonation of an explosive charge. 
Soil Annulus:  A spray of ejecta that loads the plate and forms the dispersed load.  It 
does not include the soil plug. 
Soil plug:  The portion of the soil directly above the charge.  It is part of the impact 
load. 
Standoff Distance (SOD):  The perpendicular distance between the surface of the 
ground and the point of the target closest to the ground.  This measurement is taken 
before the sand is saturated, and is measured in inches (in.).
 
 130  
References 
[1] Tremblay, J.E., Bergeron, D.M., and Gonzalez, R., Protection of Soft-Skinned 
Vehicle Occupants from Landmine Effects, The Technical Cooperation Program, 
Subcommittee on Conventional Weapons Technology, Technical Panel W-1, Key 
Technical Activity 1-29, August 1998 
[2] Bergeron, D.M., and Gonzalez, R., Towards a Better Understanding of Land 
Mine Blast Loading, The Technical Cooperation Program, Weapons Group, 
Conventional Weapons Technology, WPN TP-1 Terminal Effects, Key Technical 
Activity 1-34, June 2004 
[3] Fourney, W.L., Leiste, U., Bonenberger, R., and Goodings, D., Mechanism of 
Loading on Plates Due to Explosive Detonation, FRAGBLAST: International Journal 
for Blasting and Fragmentation, Vol. 10, No. 3, September 2006 
[4] Gupta, A.D., Skaggs, R.R, Effect of Deflector Shapes on Mine-Blast Loading, 
ARL-TR-3042, Aberdeen Research Laboratory, September 2003 
[5] Baker, W.E.  Similarity Methods in Engineering Dynamics: Theory and 
Practice of Scale Modeling, Rev. Ed., Elsevier, NY, 1991 
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[15] Personal communication with Leslie C. Taylor