Structural Design and Analysis of Initial 

Extended Area Protection and Survivability (EAPS) 

Projectile Configurations 

by Michael M. Chen 

ARL-TR-3866 August 2006 

Approved for public release; distribution is unlimited.
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Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5066 

ARL-TR-3866 August 2006 

Structural Design and Analysis of Initial 

Extended Area Protection and Survivability (EAPS) 

Projectile Configurations 

Michael M. Chen 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited.
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 Structural Design and Analysis of Initial Extended Area Protection and 

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14. ABSTRACT 

A mission program named Extended Area Protection and Survivability was initiated at the U.S. Army Research Laboratory to 

demonstrate guided ammunition technologies to defend the battle space against any presented targets, such as mortars, rockets, 

and artillery. This report introduces the first step in the development of the guided ammunition system. It presents high-level 

physics-based simulations of a 60-mm projectile system. The topology of the initial projectile was developed on the basis of 

gun barrel specifications and certain aerodynamics characteristics. A three-dimensional finite element model was created to 

present the projectile system. Three different projectile configurations were analyzed with the LS-DYNA1

 program and the 

results were compared. An acceptable deign demonstrated that the muzzle velocity reached only 85% of target value mainly 

because the launch package exceeded the desired mass by 25%. In addition, a characteristic centerline variation of a gun barrel 

was taken into account in this report. The outcome of the in-bore vertical displacements and accelerations attributable to the

variation was found to be significant. Note that the structural configuration of the initial projectile is not optimal. Rigorous 

optimization efforts will be made on the system, particularly on the sabot component, in order to meet performance 

requirements. 

1

LS-DYNA, which is not an acronym, is a trademark of Livermore Software Technology Corporation. 15. SUBJECT TERMS

 barrel centerline variation; EAPS projectile; in-bore dynamics; 60-mm projectile 

16. SECURITY CLASSIFICATION OF:

19a. NAME OF RESPONSIBLE PERSON

 Michael M. Chen 

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OF ABSTRACT 

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OF PAGES 

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 410-278-6146

 Standard Form 298 (Rev. 8/98) 

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iii

Contents 

List of Figures iv

List of Tables iv

Acknowledgments v

1. Introduction 1

2. Modeling and Analysis 3

3. Summary 11

5. References 13

Appendix A. Initial EAPS Projectile Configuration Data From PRODAS 15

Appendix B. Gun Barrel Specifications 19

Appendix C. IBHVG2 Input Parameter Values and Partial Output Data 23

Distribution List 28 
iv

List of Figures 

Figure 1. Configuration of the initial EAPS projectile. ................................................................. 2 

Figure 2. Characteristic centerline variation of a gun barrel. ........................................................ 3 

Figure 3. Material configuration of the initial EAPS projectile..................................................... 4 

Figure 4. Presentation of finite element model.............................................................................. 5 

Figure 5. Case I structural configuration of the initial EAPS projectile........................................ 6 

Figure 6. Case II structural configuration of the initial EAPS projectile....................................... 6 

Figure 7. Case III structural configuration of the initial EAPS projectile. .................................... 6 

Figure 8. Time history of in-bore base pressure. ........................................................................... 7 

Figure 9. In-bore travel distance versus travel............................................................................... 7 

Figure 10. In-bore travel velocities versus travel time. ................................................................. 7 

Figure 11. Contours of von Mises stress responses at 2.1 ms for (a) Case I, (b) Case II, and 

(c) Case III. ............................................................................................................................. 9 

Figure 12. Effective stress responses of inner components. ........................................................ 10 

Figure 13. Comparison of in-bore movements with and without centerline variation. ............... 11 

Figure 14. In-bore vertical accelerations versus travel time. ....................................................... 11 

List of Tables 

Table 1. Physical and mechanical properties of the initial EAPS projectile system. .................... 4 

Table 2. Responses of the initial EAPS projectile system to different weights of launch 

package. .................................................................................................................................. 8 
v

Acknowledgments 

The author wishes to thank Dr. Peter Plostins, Dr. Xiaogang Huang, and Dr. William Drysdale of 

the U.S. Army Research Laboratory (ARL) for their valuable advice throughout the research. The 

drawings of initial projectile configuration from Arrow Tech Associates, Inc., and of gun barrel 

specifications from BAE1 Systems (formally United Defense Limited Partnership) are greatly 

acknowledged. In addition, the author thanks Mr. Andrew Brant of ARL for helping derive timehistory breech pressures with IBHVG2 (interior ballistics of high velocity guns, version 2) and 

Dr. Mark Bundy of ARL for providing centerline variation data of a gun barrel. Many nomenclature clarifications on armor systems provided by Mr. Robert Keppinger of ARL are also 

appreciated. This work was supported in part by a grant of high-performance computing time 

from the U.S. Department of Defense High Performance Computing Modernization program at 

ARL’s Major Shared Resource Center, Aberdeen Proving Ground, Maryland. 

 1BAE is not an acronym.
vi

INTENTIONALLY LEFT BLANK
1

1. Introduction 

Research in high-supersonic guided projectiles that intend to intercept incoming missiles has 

been of interest in recent years. Examples, such as in-bore dynamic responses of projectiles to 

two distinct types of propellants, validation of steering forces generated by control pins for 

medium caliber munitions, cavity design around fin area to achieve desired aerodynamic forces, 

enhancements in embedded electronics for better guidance, etc., are available in the literature (1 

through 4). The U.S. Army Research Laboratory (ARL) initiated a program named Extended 

Area Protection and Survivability (EAPS) to investigate guided ammunition technologies to 

defend the battle space against any presented targets. The ultimate goal is to develop and 

demonstrate critical supporting technologies, including interceptor, sensor and fire controls, to 

enable stationary/mobile 360-degree hemispherical extended area protection from direct and 

indirect fire. This report presents the very first step for the development of the mission program, 

which is to perform preliminary structural design and analysis for the launch package. The 

guided ammunition system was designed to hit and destroy hostile objects, such as mortars, 

rockets, and artillery. The whole process must be undertaken with high accuracy at an extended 

range in a very short time frame. The launch package of study that supports the mission includes 

all payload, sabot, and projectile. With high launch acceleration, interactions among these 

components must be understood. The focus of the report falls on the design of the projectile 

system so that the structural integrity can hold during the launch. 

The topology of the initial EAPS projectile was designed on the basis of gun barrel specifications 

and certain aerodynamic characteristics. A drawing from the Projectile Design and Analysis 

System (PRODAS) software provided by Arrow Tech Associates, Inc., depicted the outer 

configuration of the projectile. The detailed information of the initial configuration is given in 

the appendix A. The drawing was thereafter transformed into a solid model as shown in figure 1. 

The projectile is equipped with a windscreen and a penetrator in the front, having an ogive length 

and radius of 70.5 mm and 1,380 mm, respectively. Four fins for stabilization are embedded in 

the tail with a fin span of 50 mm. Detailed fin configuration that had no structural significance 

was ignored. The projectile has a total length of 316.7 mm from nose to tail and an outer 

diameter of 23.5 mm. The inside of its body is divided into two cavity areas. The forward cavity 

may carry high explosive payload while the rear cavity was designed to accommodate electronic 

equipments. 

A 64-caliber smooth bore gun tube with an inner diameter of 60 mm was used to simulate the 

projectile firing. The detailed drawings of the gun barrel and the chamber specifications provided 

by the BAE Systems (formally United Defense Limited Partnership) are given in the appendix B. 

Note that all numbers on the drawings are in inches. The barrel has a total length of 3840 mm, 

i.e., in-bore travel distance for the projectile. M2 propellants with geometry of 7-perforation grain 
2

were used for the propulsion. Considering a chamber volume of 1.3 liters, a peak breech pressure 

of 470 MPa was derived from the interior ballistics code IBHVG2 (interior ballistics of high 

velocity guns, version 2). Detailed IBHVG2 input parameter values and output data are given in 

the appendix C. With the assumption of the charge mass equivalent to that of the launch package, 

approximately 2/3 of the breech pressure would act on the projectile system. Based on the 

pressure level, the wall thickness of the projectile body was determined to be at least of 4 mm so 

that its hoop and radial stresses do not exceed yield strength. The results of the calculations 

served as a baseline for solid modeling and finite element analysis. 

317 mm

50 mm

Figure 1. Configuration of the initial EAPS projectile. 

Another major task of the study was to develop the sabot. Methodologies for forecasting sabot 

for projectile systems have been undergoing research for decades (5,6). The design of the sabot 

depends heavily on different types of propulsion systems. For a solid propellant gun, a conventional double-ramp sabot is appropriate. Typically, the purposes of sabot are to (a) support the 

projectile during high acceleration of launch; (b) guide the projectile along the center of gun barrel; 

(c) seal the gun tube to high-pressure propellant gas; and (d) discard smoothly after muzzle exit. It 

is understood that the length of sabot that supports a kinetic energy projectile is a major factor 

affecting the structural integrity. By applying limit state theorem, one can determine the fore and 

aft unsupported projectile length to avoid axial stress exceeding allowable value. A preliminary 

calculation suggested that the fore unsupported length could be included with the entire ogive area 

and the aft unsupported length with fin area. Grooves were designed for the interface between the 

sabot and projectile to handle a great deal of force transfer by means of equivalent shear stresses. 

The modeling of the grooves is not addressed in this report. Instead, a friction type of surface-tosurface contact was adopted in this study. 

Please note that experimental validation will be performed at a later date to compare test results 

with simulation results. A preliminary design from this study will serve as a blueprint for the 

testing. To account for the influence of gun barrel centerline curvature, the gun tube to be used 
3

must be measured. However, because the data were not available, the author employed a 

characteristic centerline variation provided by Dr. Bundy (7) in this study. The lateral 

displacement along down-bore distance from rear face of tube is shown in figure 2. For 

modeling feasibility, the curve was fitted with a high-order polynomial as shown. This report 

compares the velocity and stress responses of the characteristic gun with those of an ideally 

perfect straight barrel. Overall, the research was targeting a muzzle velocity of 1650 m/s with a 

total launch mass of 1 kg. A high launch acceleration of 82,000 to 95,000 acceleration-to-gravity 

ratio (g’s) was pursued in the design. 

Figure 2. Characteristic centerline variation of a gun barrel. 

2. Modeling and Analysis 

According to the design baseline, a three-dimensional (3-D) solid model was created. Figure 3 

illustrates material configuration from a cross-sectional view of the projectile system. The sabot 

and windscreen cover were composed of 7075-T651 aluminum alloy, a high strength material that 

possesses a yield strength of 480 MPa. Tungsten with a 1240-MPa yield capacity was used for the 

penetrator. The gun barrel, projectile body, and fins were modeled with 17-4 PH2 stainless steel 

(with H925 conditions treatment) that has a yielding strength of 1070 MPa. The space inside 

windscreen may accommodate an antenna and seeker. High explosive payload and the other 

electronics equipments may be mounted into the cavity area. Table 1 provides the physical and 

mechanical properties of each component. Based on the density property employed, the total mass 

of the projectile system was approximately 1.24 kg. 

 217-4 PH is a registered trademark of AK Steel Corporation.

Centerline Variation of Gun Barrel

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 500 1000 1500 2000 2500 3000 3500

Down-bore Distance from RFT (mm)

Lateral Displacement (mm)
4

Cavity 

(Electronics)

Body 

(Steel)

Fin (Steel)

Windscreen 

(Aluminum)

Sabot 

(Aluminum)

Penetrator 

(Tungsten)

Nose 

(Electronics)

Cavity 

(Electronics)

Body 

(Steel)

Fin (Steel)

Windscreen 

(Aluminum)

Sabot 

(Aluminum)

Penetrator 

(Tungsten)

Nose 

(Electronics)

Figure 3. Material configuration of the initial EAPS projectile. 

Table 1. Physical and mechanical properties of the initial EAPS projectile system. 

Part No. Part Name Material Density 

(kg/mm^3) 

Elastic Modulus 

(MPa) 

Poisson’s 

Ratio 

Weight 

(kg) 

1 Bore Steel 7.75E-06 1.96E05 0.28 - 

2 Body & Fin Steel 7.75E-06 1.96E05 0.28 5.03E-01 

3 Penetrator Tungsten 1.80E-05 3.65E05 0.28 2.71E-01 

4 Windscreen Aluminum 3.60E-06 6.90E04 0.33 9.51E-03 

5 Sabot Aluminum 3.60E-06 6.90E04 0.33 4.07E-01 

6 Cavity Electronics 7.10E-07 1.00E04 0.35 4.85E-02 

As prescribed, the launch package consisted of projectile body, penetrator, windscreen, fins and 

sabot. A full-scale finite element model was generated to represent the projectile system, as shown 

in figure 4. All material throughout the model was assumed to be isotropic elastic material, i.e., 

material type 1 in LS-DYNA3 (8). Constant stress property was specified for section solid 

elements. The model included a total of 237,232 8-node hexahedral elements and 231,456 nodes. 

Figure 5 displays time-dependent base pressure, which was derived from IBHVG2 output based on 

a 1.3-liter gun chamber and 1-kg launch mass. The duration of the pressure loading was 5 ms and 

the peak pressure of 335 MPa took place at 2.1 ms from the start of ignition. A load segment set 

was created as part of LS-DYNA key word file to include all surface elements in the chamber area. 

Subsequently, the load curve attribute of the segment set was linked to the base pressure curve, i.e., 

all surface elements subject to the pressure load. 

It is important that the interfaces between bore-sabot, sabot-sabot and sabot-body be defined as 

contact surfaces in order to avoid element overlapping. LS-DYNA offers a variety of contact 

algorithms to treat interaction between disjoint parts. Surface-to-surface contact type was chosen 

for all the interfaces. Because the sabot moved along the in-bore surface, bore elements were 

defined as a master segment set type while the elements of bulkhead and bore-rider fell into slave 

 3LS-DYNA, which is not an acronym, is a trademark of Livermore Software Technology Corporation.
5

segments. The master-slave type can be arbitrarily chosen for sabot-sabot interfaces since no 

significance was found. The sabot-body interface was modeled as surface-to-surface contact as 

well. A high friction coefficient of 0.9 was assigned to simulate shear force transfer. In reality, 

grooves were designed to be responsible for the transfer but it was simplified in the simulation. 

Sabot interfaces were modeled 

surface to surface contacts

Time-dependent pressure was applied at the 

surfaces in the chamber area

Sabot interfaces were modeled as 

surface-to-surface contacts

Time-dependent pressure was applied at the 

surfaces in the chamber area

Figure 4. Presentation of finite element model. 

Similarly, the bore-sabot interfaces were also represented by contact surfaces. To be precise, 

obturator would be the interfacing material. In this study, a number of different friction coefficients were used on the contact surfaces. Since the friction depends on the relative velocity and 

pressure between the two objects in addition to potential phase changes of obturator, the actual 

physics mechanism is rather complex. The sole intention of varying the attribute of the contact 

analysis was to look into the sensitivity of the results in response to various friction coefficients. 

This report studied three different structural configurations for the EAPS projectile. Their 

descriptions are as follow: Case I: The body wall had a uniform thickness of 4 mm and the area 

between bulkhead and bore-rider of sabot was flat as given in figure 5. Case II: The wall thickness of the body was 5 mm in the front half and 4 mm in the tail portion. The rest remained the 

same as Case I, as demonstrated in figure 6. Case III: Sabot had a taper through the fore ramp 

and the other conditions stayed the same as Case I, as shown in figure 7. 

Explicit dynamic analyses were performed with LS-DYNA tool on the Linux Networx Evolocity 

II cluster at the ARL Major Shared Resource Center. Each analysis took approximately 5 hours 

of central processing unit time on 16-thread parallel executions. LS-DYNA d3plot output files, a 

binary database, were requested at 0.1-ms intervals. From the result of the Case I analysis, it 

yielded a total of 5.0 ms in-bore travel time, as shown in figure 9. Note that the computed travel 

time was relatively longer than the applied pressure duration because the pressure was derived on 

the basis of 1-kg launch package mass, which was lighter than the model. Figure 10 displays inbore travel velocity against travel time, which indicated that a muzzle velocity of approximately 

1500 m/s was reached. The velocity curve was in line with the base pressure history, where the 

maximum slope took place at 2.1 ms after ignition. Since acceleration responses varied over the 
6

entire model, an average number at the centers of the nose and the tail was used. The result 

shows a peak acceleration of 76 kilo-g’s at 2.1 ms. 

Figure 5. Case I structural configuration of the initial EAPS projectile. 

Figure 6. Case II structural configuration of the initial EAPS projectile. 

Figure 7. Case III structural configuration of the initial EAPS projectile. 

The analytical results are summarized in table 2. The total weights of the launch package for 

Cases I, II, and III were 1.239 kg, 1.269 kg, and 1.375 kg, respectively. Given the loading history 

and duration of 5 ms as shown in figure 9, the Case I projectile traveled a distance of 3721 mm, 

close to the gun muzzle. The maximum acceleration of 76 kilo-g’s took place at 2.1 ms from 

firing. Figure 11(a) displays contours of effective stress response in which a peak stress of 

1210 MPa occurred at the projectile body area between bore-rider and bulkhead. It was obtained 

as a result of significant compression stress coming from the base pressure. Given 17-4 PH steel 

material, the Case I projectile would fail accordingly. 
7

Figure 8. Time history of in-bore base pressure. 

Figure 9. In-bore travel distance versus travel. 

Figure 10. In-bore travel velocities versus travel time. 

0

50

100

150

200

250

300

350

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Time (milisecond)

Base Pressure (MPa)

Time History of Projectile Velocity

0.0E+00

2.0E+02

4.0E+02

6.0E+02

8.0E+02

1.0E+03

1.2E+03

1.4E+03

1.6E+03

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Time (milisecond)

Vx (m/s)

0.0E+00

5.0E+02

1.0E+03

1.5E+03

2.0E+03

2.5E+03

3.0E+03

3.5E+03

4.0E+03

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Time (milisecond)

In-Bore Travel Distance (mm)
8

The Case II projectile, which increased the wall thickness by 1 mm, was developed to alleviate 

stress magnitude in the fore ramp area. Consequently, the peak stress was reduced to 985 MPa, 

as displayed in figure 11(b) contours. Because the maximum stress was below yielding strength, 

no permanent deformation was anticipated. However, because of the addition of mass by 30 g, 

the in-bore travel distance, peak velocity, and acceleration lowered to 3514 mm, 1398 m/s and 

74 kilo-g’s, respectively. In order to reach a target muzzle velocity of 1650 m/s, the breech 

pressure would need to be increased, which might result in re-adjustment of the structural 

configuration. Understandably, an iterative design and analysis process would be required. 

Instead of increasing the wall thickness, the Case III augmented the sabot, i.e., it made the fore 

ramp go all the way to the bore-rider so that it could absorb more stress and obtain uniform stress 

response distributions because of increasing stiffness ratio between the sabot and projectile. The 

corresponding stress contours are shown in figure 11(c). The configuration changes resulted in a 

reduction of peak von Mises stress from 1210 MPa to 1035 MPa. The decrease in stress would 

prevent the steel material from yielding. Note that this alteration added significant mass to the 

launch system. The in-bore travel distance, peak velocity, and acceleration were all dropped to 

3351 mm, 1345 m/s and 70 kilo-g’s, respectively. Therefore, a trade-off was seen between free 

space for electronics and sabot mass. 

Table 2. Responses of the initial EAPS projectile system to different weights of launch package. 

 Case I Case II Case III 

Total weight (kg) 1.239 1.269 1.375 

In-bore travel distance (mm) at 5 ms from ignition 3721 3514 3351 

Projectile velocity (m/s) at 5 ms 1492 1398 1345 

Peak acceleration (kilo-g’s) at 2.1 ms 76 74 70 

Peak von Mises Stress (MPa) at 2.1 ms 1210 985 1035 

Inside the projectile, the tungsten joint between the penetrator and body exhibited a high effective 

stress of 700 MPa, as shown in figure 12. However, the stress level was safely below its material 

strength. The disconnection area shown in the figure was a void inside the system. The aluminum 

windscreen and sabot are both subjected to pressure below yield strength. The encapsulation 

material and electronics appeared to have low and safe stresses as well. Because of the relatively 

long duration of pressure load, the effect of wave propagation was not significant. 

To prevent the loss of propellant pressure during launch, an obturator was used to isolate the 

projectile from the bore of the gun barrel. Five different friction coefficients, i.e., 0.0, 0.1, 0.2, 0.3, 

and 0.5, for the sliding contact were used to investigate the influence on the exit velocity and stress 

responses. The results indicated that the differences in the responses among the coefficients of 

friction were marginal. However, the friction for the sabot-projectile interface must be sufficiently 

high in order to simulate force transfer and be able to move the projectile along. From simulation 

results, a coefficient of 0.5 is adequate. 
9

Figure 11. Contours of von Mises stress responses at 2.1 ms for (a) Case I, (b) Case II, and (c) Case III. 

It is understood that the centerline curvature of a gun barrel influences the location of projectile 

shot impacts. In addition to investigating projectile response to configuration changes, this report 

also studied how the barrel with centerline variations would affect in-bore projectile movements. 

Two types of barrels, one with a perfectly straight centerline and another with characteristic centerline variation as provided in figure 2, were used. The Y movement (vertical plane perpendicular to 

axial direction) of the projectile at the nose while the projectile traveled in each barrel was captured 

and compared in figure 13. It can be seen that the projectile started balloting at 1.2 ms from ignition for both cases. However, after 1.8 ms, the blue line (the one with centerline variation) oscillated dramatically. The results indicated that in-bore Y displacement with centerline variation 

underwent as much as 0.22 mm, five times larger than that with the perfectly straight barrel. 

(a) 

(b) 

(c) 
10

Therefore, caution must be taken when one is considering gun manufacturing error since the 

muzzle exit yaw and pitch movements play a vital role in aerodynamic stability. 

Figure 12. Effective stress responses of inner components. 

Finally, the projectile system has been undergoing planning and development to possess a high 

probability of hit of 90%. This capability requires sophisticated guidance control to achieve high 

accuracy and to conduct the mission. Because of high acceleration launch, one must pay attention 

to the survivability of fragile electronics, such as seeker, antenna, transceiver, etc. It would not be 

possible for the projectile to accomplish its mission when any one of the components failed during 

launch. Furthermore, because of the centerline variations of a gun barrel, the electronics would be 

subject to extra vibrating accelerations. Figure 14 demonstrates in-bore vertical accelerations of 

the projectile with the characteristic gun barrel. It is shown that an acceleration as high as 26 kilog’s may occur around 1.7 ms when the projectile started to deviate greatly from the centerline. 

Care must be taken in the analysis since the additional unanticipated loading may cause damage to 

the electronic equipment. 
11

Figure 13. Comparison of in-bore movements with and without centerline variation. 

Figure 14. In-bore vertical accelerations versus travel time. 

3. Summary 

A mission program named EAPS was initiated to develop guided ammunition technologies to 

defend the battle space against any presented targets, such as mortars, artillery, and rockets. This 

report outlined a preliminary structural design and analysis of the initial EAPS projectile 

In-Bore Movement of the Projectile Nose

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Time (milisecond)

Displacement Y (mm)

Barrel with centerline variation Straight centerline 

In-Bore Vertical Acceleration at Projectile Nose

-30,000

-25,000

-20,000

-15,000

-10,000

-5,000

0

5,000

10,000

15,000

20,000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Travel Time (ms)

Y Acceleration (g)
12

configurations. It was the first step in the iterative development process of a guided ammunition 

system. The projectile launch package was intended to survive high g loading and to achieve high 

muzzle velocity. The development started with a pre-determined outer configuration, based on 

gun barrel specifications and certain aerodynamic characteristics. The system of the study 

included gun barrel, sabot, projectile body, tungsten nose, fin, and windscreen. A total of 22 

components along with six different material properties were created and assembled for finite 

element analysis. The LS-DYNA computer code was employed to investigate the dynamics of the 

EAPS projectile. The simulation results will be validated by experimental tests that will be 

conducted later at ARL. 

Three different configuration projectiles were studied and the results were compared. The projectile that had a uniform wall thickness of 4 mm with a flat fore ramp component was expected to 

encounter yielding failure. It would not survive the launch unless the sabot were altered so that it 

can transfer forces to the projectile body more uniformly. However, the alteration signifi-cantly 

increased the total mass of the launch package, which considerably impaired muzzle velocity. 

Alternatively, the author proposed to reinforce the projectile body by augmenting the thickness in 

the fore ramp area. As a result, the strength of the projectile was significantly improved and the 

integrity of the structure held. The muzzle velocity was not offset considerably. One negative 

influence from the change was slight reduction of free space. The free space could be designed to 

accommodate a warhead if applicable. Therefore, the actual impact would depend. 

Note that the time-dependent breech pressure employed in this study was derived from IBHVG2 

based on empty gun chamber and initially specified mass. On one hand, both factors exhibited 

certain degree of deviations from actual volume and weight in this study. More accurate 

measurements shall be undertaken. On the other hand, the lumped parameter code IBHVG2 

assumed uniform and simultaneous ignition of the entire propellant charge. This unrealistic 

assumption has been relaxed by a complex computer program called the Next Generation 

(NGEN) Interior Ballistics code (9), which can account for multi-dimensional and multi-phase 

computational fluid dynamic physics problems. For continuing efforts in the EAPS projectile 

development, the incorporation of NGEN into the analysis becomes important. 

The effects of centerline variations of a characteristic gun barrel on the initial EAPS projectile 

were also evaluated. It was found that the maximum in-bore vertical movement was five times 

larger than that for a gun barrel with a straight centerline. In addition, the vertical acceleration 

loads attributable to centerline curvature were substantial and may have a significant impact on 

the electronics. The actual gun barrel to be used for experimental firing would need to be 

carefully measured upon delivery. The actual variations would be used in later simulations for 

better prediction. Finally, the muzzle velocity from the study did not reach the target value. The 

total mass of the launch package required considerable reduction from the preliminary design. 

Rigorous optimization efforts will be made, particularly on the sabot component. 
13

5. References 

1. Huang, X.; Newill, J.; Garner, J. Hit-to-Kill Sabot and projectile Design and In-Bore 

Dynamic Response; ARL-TR-3081; U.S. Army Research Laboratory: Aberdeen Proving 

Ground, MD, September 2003. 

2. Silton, S. Validation of Asymmetric Lift to Produce Roll Torque for a Medium-Caliber 

Guided Munition; ARL-TR-3342; U.S. Army Research Laboratory: Aberdeen Proving 

Ground, MD, September 2004. 

3. Sahu, J.; Heavey, K. Application of Computational Fluid Dynamics to the Hit-to-Kill 

Projectile at Supersonic Speeds; ARL-TR-3207; U.S. Army Research Laboratory: Aberdeen 

Proving Ground, MD, August 2004. 

4. Peters, B.; Patron, H.; Strickland, B.; Lianos, D. Development of a Telescope for a 

Miniature Hit-to-Kill Interceptor; ADB285029; U.S. Army Research Laboratory: Aberdeen 

Proving Ground, MD, March 2002. 

5. Drysdale W. Design of Kinetic Energy projectiles for Structural Integrity; Technical Report 

ARBRL-TR-02365; U.S. Army Research Laboratory: Aberdeen Proving Ground, MD, 

September 1981. 

6. Burns, B.; Burton, L.; Drysdale, W. Methodologies for Forecasting Sabot Mass for 

Advanced Gun and projectile Systems; BRL-TR-3387; U.S. Army Research Laboratory: 

Aberdeen Proving Ground, MD, September 1992. 

7. Bundy, M.; Newill, J. A Methodology for Characterizing Barrel Flexure Due to Tank 

Motion; ARL-MR-479; U.S. Army Research Laboratory: Aberdeen Proving Ground, MD, 

June 2000. 

8. LS-DYNA Keyword User’s Manual Version 970, Livermore Software Technology 

Corporation. 

9. Nusca, M. J.; Horst, A. W.; Newill, J. F. Multidimensional, Two-Phase Simulations of 

Notional Telecoped Ammunition Propelling Charge; ARL-TR-3306; U.S. Army Research 

Laboratory: Aberdeen Proving Ground, MD, September 2004. 
14

INTENTIONALLY LEFT BLANK
15

Appendix A. Initial EAPS Projectile Configuration Data From PRODAS 
16
17
18

INTENTIONALLY LEFT BLANK
19

Appendix B. Gun Barrel Specifications 
20
21
22
23

Appendix C. IBHVG2 Input Parameter Values and Partial Output Data 

ERRTOL= 2.2204460E-16 

1 IBHVG2.506 DATE TIME 

0 CARD 1 --> $INFO 

CARD 2 --> POPT = 1, 1, 1, 0 

CARD 3 --> RUN = '57MM' 

CARD 4 --> GRAD = 1 

CARD 5 --> DELT=5E-6 DELP=1E-5 

CARD 6 --> $GUN 

CARD 7 --> NAME = '57MM' 

CARD 8 --> GRVE = 0.060 LAND = 0.060 

CARD 9 --> TRAV = 3.84 TWST = 99.0000 

CARD 10 --> CHAM=0.001007 

CARD 11 --> $PROJ 

CARD 12 --> NAME = 'SLUG' PRWT = 1.2 

CARD 13 --> $RESI 

CARD 14 --> NPTS = 4 AIR = 1 

CARD 15 --> TRAV = 0.0, 0.001, 0.02, 4.0 

CARD 16 --> PRES = 2.0, 10.0, 1, 1 

CARD 17 --> $HEAT 

CARD 18 --> HL = 1 

CARD 19 --> $PRIM 

CARD 20 --> NAME = 'BENITE' CHWT = 0.00015 

CARD 21 --> GAMA = 1.221 FORC = 548700. 

CARD 22 --> COV = 0.0009747145 TEMP = 2041 

CARD 23 --> $PROP 

CARD 24 --> NAME = 'M30' 

CARD 25 --> CHWT = 0.9 

CARD 26 --> RHO = 1660. GAMA = 1.251 

CARD 27 --> FORC = 1109000. COV = 0.001029 
24

CARD 28 --> TEMP = 3118.0 

CARD 29 --> GRAN = '7PF' LEN = 0.0047625 PD = 0.00029972 

CARD 30 --> WEB = 0.00040 

CARD 31 --> BETA = 0.002546 

CARD 32 --> ALPH = 0.727 

CARD 33 --> $COMM $PROP 

CARD 34 --> NAME = 'JA2 7P' CHWT = 1 GRAN = '7P' 

CARD 35 --> RHO = 1595.2 GAMA = 1.2268 FORC = 1150907. 

CARD 36 --> COV = 0.0009747145 TEMP = 3436 EROS = 0.0000000 

CARD 37 --> NTBL = -2 PR4L=68.96,700. CF4L=.003559,.0018033 EX4L=.7162,.8796 

CARD 38 --> LEN = 0.004841 DIAM = 0.002146 PD = 0.000406 

CARD 39 --> WEB=.00087 

CARD 40 --> $COMM $PROP 

CARD 41 --> NAME = 'M2' GRAN = '7PF' 

CARD 42 --> CHWT = .86 

CARD 43 --> RHO = 1650. GAMA = 1.2235 

CARD 44 --> FORC = 1096000. COV = 0.000975 

CARD 45 --> TEMP = 3373.0 

CARD 46 --> LEN = 0.0048 PD = 0.0003 

CARD 47 --> WEB = 0.0004728 

CARD 48 --> BETA = 0.0019408 

CARD 49 --> ALPH = 0.765 

CARD 50 --> $PMAX 

CARD 51 --> VARY='WEB' NTH=1 PMAX = 470. TRY1=.0004 TRY2=.00053 LOOP=60 

CARD 52 --> 

CARD 53 --> $COMM $PARA 

CARD 54 --> VARY = 'CHWT' DECK = 'PROP' NTH = 1 

CARD 55 --> FROM = .7 BY = .02 TO = .9 

157MM IBHVG2.506 DATE TIME 

0 CARD 56 --> $END 

157MM IBHVG2.506 DATE TIME 

------------ 
25

- GUN TUBE - 

------------ 

TYPE: 57MM CHAMBER VOLUME (M3): 0.00101 TRAVEL (M): 3.84000 

GROOVE DIAMETER (M): 0.06000 LAND DIAMETER (M): 0.06000 GROOVE/LAND RATIO (-): 0.000 

TWIST (CALS/TURN): 99.0 BORE AREA (M2): 0.00283 HEAT-LOSS OPTION: 1 

**WARNING: GROOVE/LAND RATIO .LE. 0., GUN TUBE IS ASSUMED TO BE SMOOTH-BORE OF DIAMETER 

0.60000E-01 

SHELL THICKNESS (M): 0.000102 SHELL CP (J/KG-K): 460.3163 SHELL DENSITY (KG/M3): 7861.0918 

INITIAL SHELL TEMP (K): 293. AIR H0 (W/M**2-K): 11.3482 

-------------- 

- PROJECTILE - 

-------------- 

TYPE: SLUG TOTAL WEIGHT (KG): 1.200 WEIGHT PREDICTOR OPTION: 0 

-------------- 

- RESISTANCE - 

-------------- 

AIR RESISTANCE OPTION: 1 TUBE GAS INITIAL PRES (MPA) 0.000 WALL HEATING FRACTION: 0.000 

RESISTIVE PRESSURE MULT INDEX: 3 RESISTIVE FACTOR 1.000 FRICTION TABLE LENGTH: 4 

I TRAVEL (M) PRESSURE (MPA) I TRAVEL (M) PRESSURE (MPA) I TRAVEL (M), PRESSURE (MPA) 

1 0.000 2.000 3 0.020 1.000 4 4.000 1.000 

2 0.001 10.000 

----------- 

- GENERAL - 

----------- 

MAX TIME STEP (S): 0.000005 PRINT STEP (S): 0.000010 MAX RELATIVE ERROR (-): 0.00200 

PRINT OPTIONS: 1 1 1 0 1 1 STORE OPTION: 0 CONSTANT-PRESSURE OPTION: 0 

GRADIENT MODEL: LAGRANGIAN 

---------- 

- RECOIL - 

---------- 

RECOIL OPTION: 0 TYPE: RECOILING WEIGHT (KG): 0. 

---------- 

- PRIMER - 
26

---------- 

TYPE: BENITE GAMMA (-): 1.2210 FORCE (J/KG): 548700. 

COVOLUME (M3/KG): 9.7471E-04 FLAME TEMP (K): 2041.0 WEIGHT (KG): 0.000150 

157MM IBHVG2.506 DATE TIME 

------------ 

- CHARGE 1 - 

------------ 

TYPE: M30 GRAINS: 13936. 7PF WEIGHT (KG): 0.9000 

EROSIVE COEFF (-): 0.000000 CHARGE IGN CODE: 0 CHARGE IGN AT (S): 0.00000E+00 

GRAIN LENGTH (M): 0.004763 GRAIN DIAMETER (M): 0.003321 PERF DIAMETER (M): 0.000300 

INNER WEB (M): 0.000605 OUTER WEB (M): 0.000605 

PROPERTIES AT LAYER BOUNDARIES OF PERF SURFACES PROPERTIES AT LAYER BOUNDARIES OF END 

SURFACES 

1ST 2ND 3RD 4TH 1ST 2ND 3RD 4TH 

AT DEPTH (M): ------ ------ ------ 0.00000 ------ ------ ------ 0.00000 

ADJACENT LAYER WT %: ------ ------ ------ 100.000 ------ ------ ------ 100.000 

DENSITY (KG/M3): ------ ------ ------ 1660.000 ------ ------ ------ 1660.000 

GAMMA (-): ------ ------ ------ 1.2510 ------ ------ ------ 1.2510 

FORCE (J/KG): ------ ------ ------ 1109000. ------ ------ ------ 1109000. 

COVOLUME (M3/KG): ------ ------ ------ 1.0290E-03 ------ ------ ------ 1.0290E-03 

FLAME TEMP (K): ------ ------ ------ 3118.0 ------ ------ ------ 3118.0 

BURNING RATE EXPS: ------ ------ ------ 0.7270 ------ ------ ------ 0.7270 

BURNING RATE COEFFS: ------ ------ ------ 2.5460E-03 ------ ------ ------ 2.5460E-03 

PROPERTIES AT LAYER BOUNDARIES OF LAT SURFACES 

1ST 2ND 3RD 4TH 

AT DEPTH (M): ------ ------ ------ 0.00000 

ADJACENT LAYER WT %: ------ ------ ------ 100.000 

DENSITY (KG/M3): ------ ------ ------ 1660.000 

GAMMA (-): ------ ------ ------ 1.2510 

FORCE (J/KG): ------ ------ ------ 1109000. 

COVOLUME (M3/KG): ------ ------ ------ 1.0290E-03 

FLAME TEMP (K): ------ ------ ------ 3118.0 

BURNING RATE EXPS: ------ ------ ------ 0.7270 
27

BURNING RATE COEFFS: ------ ------ ------ 2.5460E-03 

. 

. 

Lengthy time-history breech pressures are omitted here 

. 

. 

CONDITIONS AT: PMAX MUZZLE 

TIME (MS): 1.522 4.712 

TRAVEL (M): 0.1489 3.8400 

VELOCITY (M/S) 440.85 1476.61 

ACCELERATION (G): 81885. 7996. 

BREECH PRESS (MPA): 470.0002 49.9707 

MEAN PRESS (MPA): 427.3918 45.8103 

BASE PRESS (MPA): 342.1750 37.4894 

MEAN TEMP (K): 2749. 1565. 

Z CHARGE 1 (-): 0.363 1.000 

ENERGY BALANCE SUMMARY JOULE % 

TOTAL CHEMICAL: 3976870. 100.00 

(1) INTERNAL GAS: 1996360. 50.20 

(2) WORK AND LOSSES: 1980510. 49.80 

(A) PROJECTILE KINETIC: 1308220. 32.90 

(B) GAS KINETIC: 327109. 8.23 

(C) PROJECTILE ROTATIONAL: 659. 0.02 

(D) FRICTIONAL WORK TO TUBE: 0. 0.00 

(E) OTHER FRICTIONAL WORK: 11113. 0.28 

(F) WORK DONE AGAINST AIR: 24479. 0.62 

(G) HEAT CONVECTED TO BORE: 308930. 7.77 

(H) RECOIL ENERGY: 0. 0.00 

LOADING DENSITY (KG/M3): 893.893 

CHARGE WT/PROJECTILE WT: 0.750 

PIEZOMETRIC EFFICIENCY: 0.256 

EXPANSION RATIO: 11.782 
28

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