CTH Analyses of Fragment Penetration 

Through Heat Sink Fins 

by Anand Prakash 

ARL-TR-3535 June 2005 

Approved for public release; distribution is unlimited. 
NOTICES 

Disclaimers 

The findings in this report are not to be construed as an official Department of the Army position 

unless so designated by other authorized documents. 

Citation of manufacturer’s or trade names does not constitute an official endorsement or 

approval of the use thereof. 

DESTRUCTION NOTICEDestroy this report when it is no longer needed. Do not return it to 

the originator. 
Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5068 

ARL-TR-3535 June 2005 

CTH Analyses of Fragment Penetration 

Through Heat Sink Fins 

Anand Prakash 

Survivability/Lethality Analysis Directorate, ARL 

Approved for public release; distribution is unlimited. 
ii

REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid 

OMB control number. 

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY)

 June 2005

2. REPORT TYPE 

Final 

3. DATES COVERED (From - To) 

 2003 to 2005 

5a. CONTRACT NUMBER 

5b. GRANT NUMBER 

4. TITLE AND SUBTITLE 

 CTH Analyses of Fragment Penetration Through Heat Sink Fins 

5c. PROGRAM ELEMENT NUMBER 

5d. PROJECT NUMBER 

 AH80 

5e. TASK NUMBER 

6. AUTHOR(S) 

 Anand Prakash (ARL) 

5f. WORK UNIT NUMBER 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 

 U.S. Army Research Laboratory 

 Survivability/Lethality Analysis Directorate 

 Aberdeen Proving Ground, MD 21005-5068

8. PERFORMING ORGANIZATION 

 REPORT NUMBER 

ARL-TR-3535

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S) 

11. SPONSOR/MONITOR'S REPORT 

 NUMBER(S) 

12. DISTRIBUTION/AVAILABILITY STATEMENT 

Approved for public release; distribution is unlimited. 

13. SUPPLEMENTARY NOTES 

14. ABSTRACT 

Vulnerability/lethality analysis codes (e.g., MUVES-S2) generally use the FATEPEN (fast air target encounter penetration) and 

THOR penetration models to determine damage produced by impacts of fragments. For simple impact scenarios, e.g., normal 

fragment impact on monolithic plates, these two models give reasonable predictions for penetration, perforation, and residual 

velocity. It is, however, not clear how realistic the predictions of these models are for more complicated scenarios. This report 

presents more detailed calculations of the penetration and perforation of an electronic box with cooling fins by a high velocity 

fragment that strikes the fins with an oblique impact. We do this by conducting physics-based, three-dimensional, numerical 

simulations with the CTH finite difference code. It is found that the presence of fins significantly reduces the residual velocity 

of the fragment. Predictions of CTH for oblique impact on plain walls are also compared with those from FATEPEN and 

THOR. 

15. SUBJECT TERMS

 CTH analysis; FATEPEN; fragment; heat sink fins; impact; lethality; modeling; penetration; projectile; simulation; THOR 

16. SECURITY CLASSIFICATION OF:

19a. NAME OF RESPONSIBLE PERSON

 Anand Prakash 

a. REPORT 

Unclassified

b. ABSTRACT 

Unclassified

c. THIS PAGE 

Unclassified 

17. LIMITATION 

OF ABSTRACT 

SAR

18. NUMBER 

OF PAGES 

30 19b. TELEPHONE NUMBER (Include area code) 

 410-278-5687

 Standard Form 298 (Rev. 8/98) 

 Prescribed by ANSI Std. Z39.18
iii

Contents 

List of Figures iv

List of Tables v

1. Introduction 1

1.1 Background .....................................................................................................................1 

1.2 Objective .........................................................................................................................1 

2. Methodology 1

2.1 Conventional Models ......................................................................................................1 

2.2 The CTH Simulations......................................................................................................2 

3. Results of the CTH Simulations 3

3.1 Simulation of the Actual Scenario With the Fins............................................................3 

3.2 Simulation Without the Fins ...........................................................................................4 

3.3 Simulation With Walls of Equivalent Thicknesses.........................................................8 

4. Summary and Discussion 13

5. References 15

Appendix A. CTH Input Details for the Actual Scenario With the Fins 17

Distribution List 21 
iv

List of Figures 

Figure 1. Driver’s integrated display with vertical cooling fins on the top wall. ...........................3 

Figure 2. Initial state (0 μs) of CTH simulation of oblique impact of the projectile on the 

wall with fins............................................................................................................................4 

Figure 3. The impact at 20 μs for the actual scenario.....................................................................5 

Figure 4. The impact at 100 μs for the actual scenario...................................................................5 

Figure 5. The impact at 200 μs for the actual scenario...................................................................5 

Figure 6. The impact at 280 μs for the actual scenario...................................................................5 

Figure 7. Projectile velocity as a function of time for the actual scenario......................................6 

Figure 8. Initial state (0 μs) of CTH simulation of oblique impact of the projectile on the 

bare wall without fins...............................................................................................................7 

Figure 9. The simulation for the bare wall impact at 20 μs............................................................7 

Figure 10. The simulation for the bare wall impact at 40 μs..........................................................7 

Figure 11. The simulation for the bare wall impact at 100 μs........................................................7 

Figure 12. The simulation for the bare wall impact at 200 μs........................................................8 

Figure 13. The simulation for the bare wall impact at 100 μs........................................................8 

Figure 14. Initial state (0 μs) of CTH simulation of oblique impact of the projectile on a 

wall of thickness equal to that of the bare wall plus the thickness of two fins........................8 

Figure 15. The simulation with wall thickness increased by twice the fin thickness at 20 μs. ......8 

Figure 16. The simulation with wall thickness increased by twice the fin thickness at 40 μs. ......9 

Figure 17. The simulation with wall thickness increased by twice the fin thickness at 100 μs. ....9 

Figure 18. The simulation with wall thickness increased by twice the fin thickness at 200 μs. ....9 

Figure 19. The simulation with wall thickness increased by twice the fin thickness at 280 μs. ....9 

Figure 20. Projectile velocity as a function of time for the case when wall thickness is 

increased by twice the fin thickness.......................................................................................10 

Figure 21. Initial state (0 μs) of CTH simulation of oblique impact of the projectile on a 

 wall of thickness equal to that of the bare wall plus the thickness of three fins...................11 

Figure 22. The simulation with wall thickness increased by three times the fin thickness 

at 20 μs...................................................................................................................................11 

Figure 23. The simulation with wall thickness increased by three times the fin thickness 

at 40 μs...................................................................................................................................11 

Figure 24. The simulation with wall thickness increased by three times the fin thickness 

at 100 μs.................................................................................................................................11 

Figure 25. The simulation with wall thickness increased by three times the fin thickness 

at 200 μs.................................................................................................................................12 

Figure 26. The simulation with wall thickness increased by three times the fin thickness 

at 280 μs.................................................................................................................................12 
v

Figure 27. Projectile velocity as a function of time for the case when wall thickness is 

increased by three times the fin thickness..............................................................................12 

List of Tables 

Table 1. Summary of residual velocity magnitudes......................................................................12 
vi

INTENTIONALLY LEFT BLANK
1

1. Introduction 

1.1 Background 

For analyzing the survivability of crew and vehicle components on the battlefield, the 

vulnerability/lethality analysis code MUVES-S2 generally uses the empirical/analytical models 

FATEPEN (fast air target encounter penetration) and THOR (1, 2) for tracing the penetration, 

perforation, residual velocity, and residual mass of fragments that strike the system. For simple 

scenarios, such as the normal impact of a fragment-simulating projectile (FSP) on a monolithic 

armor plate, these models generally give sufficiently accurate predictions. For more complicated 

scenarios, such as the oblique impact of an FSP on complex component geometries, the response 

is much more complicated as well. Thus, it would be of interest to investigate the use of a 

physics-based finite difference code such as CTH (3) to predict the response and compare the 

results to FATEPEN and THOR. 

1.2 Objective 

The purpose of this project was to conduct three-dimensional (3-D) CTH analyses of an oblique 

impact of an FSP on an electronics box with cooling fins which has been used on the U.S. 

Army’s Stryker vehicle. The FSP impacts obliquely on the fins (ribs) on top of the box, and the 

question addressed is whether the presence of fins significantly reduces the lethality of the 

projectile. We obtained an answer to this by conducting 3-D, numerical simulations with the 

CTH code using the Department of Defense’s high performance computers at the U.S. Army 

Research Laboratory’s major shared resource center. In addition, the CTH results are also 

compared with the predictions of the conventional algorithms, FATEPEN and THOR. 

2. Methodology 

2.1 Conventional Models 

The vulnerability analysis code MUVES-S2 uses the models THOR and FATEPEN for fragment 

penetration. THOR is a semi-empirical model based on curve fitting to fairly extensive 

experimental data regarding the penetration of plates by projectiles. Given an initial state, 

THOR’s algebraic equations calculate the final state. For example, the THOR equation for 

residual velocity is as follows. 

(10 * * * * * [ ] { } ) c V V e A M Sec V rs s s

α γ β λ = −   θ  
2

in which 

 Vr = fragment residual velocity in feet per second. 

 Vs = fragment striking velocity in feet per second. 

 e = target thickness in inches. 

 A = average impact area of the fragment in square inches. 

 Ms = weight of original fragment in grains. 

 θ = angle between trajectory of fragment and target normal. 

 c, α, β, γ, λ = constants determined for each target material. 

FATEPEN uses “engineering” models of terminal ballistic penetration. For core penetration 

models, FATEPEN makes assumptions of ideal impact geometries and applies laws of 

mechanics in a simplified way to the dominant terminal ballistic loading and response 

mechanisms; this allows FATEPEN to obtain algebraic equations relating the known initial 

conditions to a simplified final configuration. In both FATEPEN and THOR, one specifies the 

initial projectile parameters (shape, mass, and velocity, etc.) and the target parameters (plate 

material, thickness, etc.) and the model calculates, via several subroutines, the final state of 

affairs after the terminal ballistic interaction is finished. 

2.2 The CTH Simulations 

In contrast to the conventional engineering and semi-empirical models, the CTH code calculates 

the time development of the terminal ballistic event from “first principles.” CTH is an Eulerian 

finite difference code in which the differential equations of continuum mechanics are integrated 

over a fixed spatial mesh in small time steps to obtain the time development of the physical 

event. CTH has a Lagrangian first phase and a second phase that uses a mesh re-mapping to 

bring the distorted mesh back to the stationary Eulerian mesh by the use of a second order 

accurate advection scheme. The code uses experimentally determined material properties as an 

input in the form of material model parameters. For a thorough description of CTH, the reader is 

referred to the standard reference (3). 

3-D simulations of an oblique impact of an FSP on an electronics box with the geometry of the 

driver’s panel on a Stryker vehicle were conducted with the CTH code. The physical assumptions 

in the CTH simulations are the material models. For the aluminum target, the simulations used the 

Mie-Gruneisen equation of state, with parameters from CTH library under the key word 1100-

aluminum. It is known that metals are well represented by the Mie-Gruneisen equation of state. 

For the steel projectile of density 7.87g/cm2

, the tabular equation of state for steel, given in the 

“sesame” data set of CTH library, was used. The first simulation was also re-run with the MieGruneisen parameters of key word 304_SS, and no appreciable differences in results were seen. 

For both materials, the Johnson-Cook constitutive model (4) was used. The model describes the 

yield surface of the material based on strain, strain rate, and temperature. The model parameters 

used were those in CTH library corresponding to 4340-steel and 1100-aluminum. In addition, the 

Johnson-Cook fracture model (5) was used for the projectile, with parameters under the key word 
3

steel in the CTH library, and the Grady-Kipp model (6) was chosen for the target since this model 

was specifically developed to reproduce spall. Two sets of Grady-Kipp model parameters for 

aluminum are available in the CTH library; the one corresponding to the density of 

1100_aluminum was used. These models are strain rate dependent and keep track of accumulated 

damage in each cell over the various time steps. CTH input details for the actual scenario with the 

fins are shown in appendix A. 

The electronics box with fins on a Stryker is the driver’s integrated display (figure 1). The top 

panel (wall) has a thickness of 0.4 inch and it has vertical cooling fins (ribs) which are 0.75 inch 

high, 0.16 inch thick, with 0.24-inch air gaps. This electronics box (including the fins) is made 

of aluminum. The case scenario simulated is the impact of a 4340-steel FSP of mass 3.06 g, with 

a length-to-diameter ratio L/D = 1.17, arriving at an obliquity of 45 degrees to the top panel with 

a striking velocity of 1 km/s which overmatches 0.4-inch-thick aluminum. In the CTH simulations, a uniform mesh with a cell size of 0.08 cm by 0.08 cm by 0.08 cm was used. This gives 

five cells across a fin thickness. 

Figure 1. Driver’s integrated display with vertical cooling fins on the top wall. 

3. Results of the CTH Simulations 

3.1 Simulation of the Actual Scenario With the Fins 

The cross-sectional view of the initial state (time = 0 μs) of the first 3-D CTH simulation is 

shown in figure 2. The geometry was rotated so that the top panel is vertical. The cylindrical 
4

FSP is moving upward at 45 degrees from the lower left corner. The fins are shown in different 

colors in order to distinguish them as they become distorted and perforated during the impact 

event. 

Figure 2. Initial state (0 μs) of CTH simulation of oblique impact of the 

projectile on the wall with fins. 

The next four figures (figures 3 through 6) show the time sequence of events at 20 μs, 100 μs, 

200 μs, and 280 μs. From figure 3, we see that at 20 μs, one fin (yellow) was perforated, and this 

fin is impacting the next (green) fin together with the projectile. Figure 4 shows that at 100 μs, 

the third (dark blue) fin has been perforated and the FSP has nearly perforated the wall of the box 

(pink). Figure 5 shows the situation at 200 μs when the FSP is moving freely after perforation 

with behind-armor debris (BAD) next to it. Figure 6 (at 280 μs) shows that the fifth fin (yellow) 

survives and the FSP and wall debris (pink) fly into the box. The magnitude of the FSP velocity 

as a function of time is plotted in figure 7. The figure shows that during the FSP’s interaction 

with the fins and the panel wall, the velocity of the FSP rapidly falls from its initial value of 

1000 m/s and, after perforation, the residual velocity magnitude settles to 222 m/s. According to 

CTH simulations, there is no discernible mass erosion of the FSP. 

3.2 Simulation Without the Fins 

Prior MUVES-S2 analyses involving Stryker’s electronics box did not include the cooling fins. 

Thus, a CTH simulation of the FSP impact without the fins was also conducted and compared 

with the results in section 3.1. 
5

Figure 3. The impact at 20 μs for the actual scenario. Figure 4. The impact at 100 μs for the actual scenario. 

Figure 5. The impact at 200 μs for the actual scenario. Figure 6. The impact at 280 μs for the actual scenario. 

To ascertain what difference the fins made in resisting the wall penetration, the previous 

simulation was repeated without the fins. Figures 8 through 12 show the time sequence of the 

motion of the FSP (starting from the same initial position as before) and its interaction with the 

0.4-inch-thick bare wall of the electronics box (now shown in green). The FSP moves freely 

until it strikes the bare wall of the box at about 30 μs. Figure 10 shows the beginning stages of 

penetration at 40 μs. Figure 11 shows that the perforation has been completed well before 

100 μs and the projectile and the debris are flying freely inside the box. In the first scenario with 

fins, the perforation was incomplete at 100 μs. In figure 12, we see that because of the higher 

residual velocity, the FSP has traveled much farther (to the edge of the computational mesh) in 

200 μs than was the case when fins were included (figure 5). Figure 13 shows that the residual 

velocity magnitude is now 508 m/s compared to 222 m/s for the case when fins were included 
6

(figure 7). (It may be noted that the sudden decrease in velocity shortly after 200 μs in figure 13 

is fictitious; the FSP is merely leaving the computational mesh.) According to CTH simulations, 

there is no discernible mass erosion of the projectile. 

Figure 7. Projectile velocity as a function of time for the actual scenario. 

For this simple scenario, THOR gives the residual velocity magnitude to be 622 m/s, and 

FATEPEN (version 3.0.0b) gives 504 m/s. We see that FATEPEN gives a value close to that 

obtained by CTH simulation without the fins, but THOR gives a value 20% in excess of that 

obtained by CTH. FATEPEN gives a residual mass of 2.77 g, i.e., a mass loss of 0.29 g (9%). 

THOR gives a residual mass of 2.68 g, i.e., a mass loss of 0.38 g (12%). 

Another way to examine the penetration and generation of BAD for the case when the fins are 

included (section 3.1) would be to put a layer of material (aluminum) on top of the bare wall of 

the box to represent the fins. In the simulation of section 3.1, the FSP interacts directly with at 

least two fins, perhaps three (figures 3 and 4). Accordingly, CTH, THOR, and FATEPEN can be 

used to analyze cases when a layer of aluminum equal to two fin thicknesses is added to the bare 

wall and when the layer thickness is taken to be equal to three fin thicknesses. 
7

Figure 8. Initial state (0 μs) of CTH simulation of Figure 9. The simulation for the bare wall impact at 20 μs. 

oblique impact of the projectile on the bare 

wall without fins. 

 

Figure 10. The simulation for the bare wall impact at Figure 11. The simulation for the bare wall impact at 

 40 μs. 100 μs. 
8

Figure 12. The simulation for the bare wall impact at Figure 13. The simulation for the bare wall impact 

 200 μs. at 100 μs. 

3.3 Simulation With Walls of Equivalent Thicknesses 

The results of the CTH simulation with the bare wall of the box covered with a layer equivalent 

to twice the fin thickness is shown in time sequence at 0 μs, 20 μs, 40 μs, 100 μs, 200 μs, and 

280 μs in figures 14 through 19. The wall is shown in green color. From 100 μs onward, we do 

see some similarity between these figures and the corresponding figures of section 3.1 (figures 4 

through 6). 

Figure 14. Initial state (0 μs) of CTH simulation of Figure 15. The simulation with wall thickness increased 

oblique impact of the projectile on a wall by twice the fin thickness at 20 μs. 

of thickness equal to that of the bare wall 

plus the thickness of two fins. 
9

Figure 16. The simulation with wall thickness increased Figure 17. The simulation with wall thickness increased 

 by twice the fin thickness at 40 μs. by twice the fin thickness at 100 μs. 

Figure 18. The simulation with wall thickness increased Figure 19. The simulation with wall thickness increased 

 by twice the fin thickness at 200 μs. by twice the fin thickness at 280 μs. 

To see quantitatively the new residual velocity magnitude, the time history of the magnitude of 

the FSP velocity is plotted in figure 20. It is seen that the residual velocity magnitude for this 

adjusted bare wall thickness is 218 m/s, which is close to that obtained (222 m/s) in the CTH 

simulation of the actual scenario with fins. However, the direction of the residual velocity vector 

is slightly different. This is because the x- and z- components of velocity in the CTH simulation 

of section 3.1 were 174 m/s and 138 m/s, respectively, whereas now they are 184 m/s and 

117 m/s, respectively. This indicates that the replacement of the fins by a layer twice the fin 

thickness on the wall is a close approximation but is not exactly equivalent to the actual scenario 

for the purpose of obtaining the residual velocity. 
10

For the case of the bare wall to which a layer of aluminum equivalent to twice the fin thickness is 

added, THOR gives a residual velocity magnitude of 385 m/s, which is more than 50% larger 

than the residual velocity magnitude (218 m/s) obtained from the corresponding CTH simulation 

described before. As for FATEPEN, it shows no perforation (residual velocity of 0 m/s). 

According to CTH, there is no mass erosion of the FSP. FATEPEN also predicts no mass loss. 

However, THOR gives a residual mass of 2.62 g, i.e., a mass loss of 0.44 g (14%). 

Figure 20. Projectile velocity as a function of time for the case when 

wall thickness is increased by twice the fin thickness. 

To complete the set of simulations described at the end the last section, an additional 3-D CTH 

simulation was conducted with a thicker bare wall, comprised of the original wall plus a layer of 

aluminum of three times the fin thickness. The results are shown in time sequence 0 μs, 20 μs, 

40 μs, 100 μs, 200 μs, and 280 μs in figures 21 through 26. It is seen that the FSP just manages 

to perforate this wall. However, CTH shows no discernible mass erosion of the projectile. To 

obtain a quantitative idea of the deceleration of the FSP, the magnitude of FSP velocity is plotted 

as a function of time in figure 27. It is seen that the FSP rapidly decelerates to attain a residual 

velocity magnitude of 73.8 m/s. 

For this thick wall, FATEPEN does not predict any perforation (residual velocity of 0 m/s), but 

THOR does, with a residual velocity of 270 m/s and a residual mass of 2.60 g, i.e., a mass loss of 

0.46 g. This mass loss is relatively small (15%). However, the residual velocity predicted by 

THOR is more than three times the predicted residual velocity obtained by the CTH simulation. 

The results of residual velocities for the various cases are summarized in table 1. 
11

Figure 21. Initial state (0 μs) of CTH simulation of Figure 22. The simulation with wall thickness increased 

oblique impact of the projectile on a wall by three times fin thickness at 20 μs. 

of thickness equal to that of the bare wall 

plus the thickness of three fins. 

 

Figure 23. The simulation with wall thickness increased Figure 24. The simulation with wall thickness increased 

 by three times fin thickness at 40 μs. by three times fin thickness at 100 μs. 
12

 

Figure 25. The simulation with wall thickness increased Figure 26. The simulation with wall thickness increased 

 by three times fin thickness at 200 μs. by three times fin thickness at 280 μs. 

Figure 27. Projectile velocity as a function of time for the case when 

wall thickness is increased by three times the fin thickness. 

Table 1. Summary of residual velocity magnitudes. 

Wall Thickness CTH FATEPEN THOR 

1.02 cm 

(fins present) 

222 m/s N/A N/A 

1.02 cm 508 m/s 504 m/s 622 m/s 

1.82 cm 218 m/s 0 m/s 385 m/s 

2.23 cm 74 m/s 0 m/s 270 m/s 
13

The reasons for these differences between the predictions of CTH, FATEPEN, and THOR are not 

fully understood at this time. Further investigations would be needed to identify what causes these 

differences. It is recommended that experiments be conducted first to validate the CTH results of 

table 1. In addition, one could consider using the existing experimental database that was used to 

develop FATEPEN and THOR to conduct CTH simulations for cases for which experimental 

details required for CTH input exist. If the predictions of CTH are found to be reasonable, one 

should look into the details of THOR and FATEPEN calculations to identify the causes of the 

differences in the predictions and to determine, if possible, what those differences might mean to 

MUVES-S2 analyses using THOR and FATEPEN. 

4. Summary and Discussion 

Physics-based 3-D simulations with the CTH hydrocode have been conducted to study the penetration into the driver’s integrated display of a Stryker vehicle of a high velocity FSP impacting 

obliquely (at 45 degrees) on the top wall. This display is an aluminum electronics box which has 

vertical cooling fins on the top wall. These simulations provide details of the perforation of the 

FSP into this complex configuration. By conducting CTH simulations with and without the fins, 

we quantitatively determined the effect of fins on the residual velocity of an FSP impacting the 

box through the fins. The effect of fins on the residual velocity was found to be significant. Based 

on this result, it is recommended that future MUVES-S2 analyses involving vehicles with electronics boxes that have cooling fins should consider this detail in the geometric modeling. 

We conducted more CTH simulations in which the fins were replaced by the addition of 

equivalent wall thicknesses. It was found that a CTH simulation with an added wall thickness 

equal to the thickness of two fins gave a residual velocity magnitude close to that obtained in the 

simulation with the actual fin geometry. Since MUVES-S2 uses the algorithms FATEPEN or 

THOR to calculate the residual velocity magnitude of the impacting projectile, the CTH 

predictions of the residual velocity magnitudes for different wall configurations were also 

compared with the predictions of FATEPEN and THOR. 

It is only noted here that for the geometry of the thin bare wall (table 1, second row of data) 

without any fins, FATEPEN gives a prediction close to that of CTH. For the thicker wall 

(table 1, third row of data), which was found by CTH to be equivalent to the finned wall for 

reproducing the residual velocity magnitude, FATEPEN does not predict perforation. THOR 

predicts a perforation for this wall, but it gives a higher residual velocity when this velocity is 

compared to the CTH prediction. The higher residual velocity predicted by THOR, as compared 

to CTH, is also seen for the thicker wall (table 1, fourth row of data). 

Although CTH code has undergone general validation testing, it is recommended that laboratory 

experiments of the scenarios be conducted to validate the absolute values of residual velocities 

predicted by CTH for the specific cases simulated here. Once the CTH predictions have been 
14

validated, further investigations should be conducted to determine the factors responsible for 

differences between CTH predictions and those of FATEPEN and THOR penetration equations. 
15

5. References 

1. Yatteau, J. D.; Zernow, R. H.; Recht, G. W.; Edquist, K. T. FATEPEN (Version 3.0.0b) 

Terminal Ballistic Penetration Model; ARA Project 4714, Prepared for Naval Surface 

Warfare Center: Dahlgren, VA, Under CBDCOM Contract DAAA15-94-D-0005, D.O. 

0073, January 1999. 

2. Project THOR. The Resistance of Various Metallic Materials to Perforation by Steel 

Fragments; Empirical Relationships for Fragment Residual Velocity and Residual Weight; 

TR-47, U.S. Army Ballistics Research Laboratory, Institute for Cooperative Research, The 

Johns Hopkins University, April 1961. 

3. McGlaun, J. M.; Thompson, S. L.; Elrick, M. G. CTH: A Three-Dimensional Shock Wave 

Physics Code. Int. J. Impact Engng. 1990, 10, 351-360. 

4. Johnson, G. R.; Cook, W. H. A Constitutive Model and Data for Metals Subjected to Large 

Strains, High Strain Rates and High Temperatures. in Proc. of the Seventh International 

Symposium on Ballistics, The Hague, The Netherlands, 1983. 

5. Johnson, G. R.; Cook, W. H. Fracture Characteristics of Three Metals Subjected to Various 

Strains, Strain Rates, Temperatures, and Pressures. J. of Engineering Fracture Mechanics

1985, 1, 31-48. 

6. Grady, D. E.; Kipp, M. E. Geometric Statistics and Dynamic Fragmentation. J. Appl. Phys.

1985, 58, 1210-1222,. 
16

INTENTIONALLY LEFT BLANK
17

Appendix A. CTH Input Details for the Actual Scenario With the Fins 
18
19
20
21 

NO. OF 

COPIES ORGANIZATION 

 * ADMINISTRATOR 

 DEFENSE TECHNICAL INFO CTR 

 ATTN DTIC OCA 

 8725 JOHN J KINGMAN RD STE 0944 

 FT BELVOIR VA 22060-6218 

 *pdf file only 

 1 DIRECTOR 

 US ARMY RSCH LABORATORY 

 ATTN IMNE ALC IMS MAIL & REC MGMT 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

 1 DIRECTOR 

 US ARMY RSCH LABORATORY 

 ATTN AMSRD ARL CI OK TL TECH LIB 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

 1 DIRECTOR 

 US ARMY RSCH LABORATORY 

 ATTN AMSRD ARL SL ES J GONZALEZ 

 BLDG 1648 

 WSMR NM 88002-5513 

 ABERDEEN PROVING GROUND

 1 DIRECTOR 

 US ARMY RSCH LABORATORY 

 ATTN AMSRD ARL CI OK (TECH LIB) 

 BLDG 4600 

 2 US ARMY RESEARCH LAB 

 ATTN AMSRD ARL SL P TANENBAUM 

 J BEILFUSS 

 BLDG 328 

 3 US ARMY RESEARCH LAB 

 ATTN AMSRD ARL SL B D BELY 

 J FRANZ M PERRY 

 BLDG 328 

 7 DIRECTOR 

 US ARMY RSCH LABORATORY 

 ATTN AMSRD ARL SL BB S JUARASCIO 

 D FARENWALD R DIBELKA 

 G KUCINSKI P KUSS 

 J PLOSKONKA W WINNER 

 BLDG 328 

 1 US ARMY RESEARCH LAB 

 ATTN AMSRD ARL SL BD R GROTE 

 BLDG 1068 

NO. OF 

COPIES ORGANIZATION 

 7 US ARMY RESEARCH LAB 

 ATTN AMSRD ARL SL BE L ROACH 

 A PRAKASH (5 CYS) R SAUCIER 

 BLDG 328 

 1 US ARMY RESEARCH LAB 

 ATTN AMSRD ARL SL E M STARKS 

 BLDG 328 

 1 US ARMY RESEARCH LAB 

 ATTN AMSRD ARL SL EC J FEENEY 

 BLDG 328 

 1 US ARMY RESEARCH LAB 

 ATTN AMSRD ARL SL EM D BAYLOR 

 BLDG 328