U.S. Department Analysis of Accelerations

of Transportation Measured During Full­Scale

Federal Railroad

Administration Tank Car Impact Tests

Office of Research

and Development

Washington, DC 20590

DOT/FRA/ORD 07/08 Final Report This document is available to the

April 2007 public through the National Technical

Information Service, Springfield, VA 22161.

This document is also available on the FRA

Web site at www.fra.dot.gov.
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1. AGENCY USE ONLY (LEAVE BLANK) 2. REPORT DATE 

April 2007 

3. REPORT TYPE AND DATES COVERED 

Final Report 

April 2007 

4. TITLE AND SUBTITLE 

Analysis of Accelerations Measured During Full-Scale Tank Car Impact Tests 

5. FUNDING NUMBERS 

RR28/DB034 6. AUTHOR(S) 

Lyons, Matthew L.; Riddell, William T.; Koch, Kevin W. 

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

U.S. Department of Transportation 

Research and Special Programs Administration 

John A. Volpe National Transportation Systems Center 

55 Broadway 

Cambridge, MA 02142-0193 

8. PERFORMING ORGANIZATION 

REPORT NUMBER 

DOT VNTSC-FRA-07-03 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 

U.S. Department of Transportation 

Federal Railroad Administration 

Office of Research and Development 

1120 Vermont Avenue, NW–Mail Stop 20 

Washington, DC 20590 

10. SPONSORING/MONITORING 

 AGENCY REPORT NUMBER 

DOT/FRA/ORD-07/08 

11. SUPPLEMENTARY NOTES 

12A. DISTRIBUTION/AVAILABILITY STATEMENT 

This document is available to the U.S. public through the National Technical Information 

Service, Springfield, VA 22161. 

This document is also available on the FRA Web site at www.fra.dot.gov. 

12B. DISTRIBUTION CODE 

13. ABSTRACT (MAXIMUM 200 WORDS) 

Tank car impact responses were investigated using accelerometers mounted at various locations on a tank car. Several tests were 

run with both a full and an empty tank car, and varying the tank car impact speed. The data from the accelerometers went through 

a power spectral density (PSD) analysis for the longitudinal and vertical directions. The results from PSD analyses were 

compared with the peak coupler force and the dominant draft gear mechanism, also obtained from the data. 

The results showed that the dominant draft gear mechanism had a marked effect on the response of the tank car, and, as speed and 

energy increased, the draft gear mechanism changed. For the empty tank car impact test results, in longitudinal acceleration 

signals, a frequency of 0 Hz and a range of frequencies above 300 Hz were present in PSD analyses; in vertical acceleration 

signals, a frequency of 13 Hz was present in PSD analyses, coinciding with the first axial mode of a simply supported cylinder. 

For the full tank car impact test results, in the vertical acceleration signals, two distinct peaks, at 5 Hz and 26 Hz, were present. 

14. SUBJECT TERMS 

tank car, shock response spectrum, acceleration, impact, power spectral density 

15. NUMBER OF PAGES 

100 

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METRIC/ENGLISH CONVERSION FACTORS 

ENGLISH TO METRIC METRIC TO ENGLISH
 LENGTH (APPROXIMATE) 

1 inch (in) = 2.5 centimeters (cm) 

1 foot (ft) = 30 centimeters (cm) 

1 yard (yd) = 0.9 meter (m) 

1 mile (mi) = 1.6 kilometers (km) 

LENGTH (APPROXIMATE) 

1 millimeter (mm) = 0.04 inch (in) 

1 centimeter (cm) = 0.4 inch (in) 

1 meter (m) = 3.3 feet (ft) 

1 meter (m) = 1.1 yards (yd) 

1 kilometer (km) = 0.6 mile (mi) 

AREA (APPROXIMATE) 

1 square inch (sq in, in2

) = 6.5 square centimeters 

(cm2

) 

1 square foot (sq ft, ft2

) = 0.09 square meter (m2) 

1 square yard (sq yd, yd2

) = 0.8 square meter (m2) 

1 square mile (sq mi, mi2

) = 2.6 square kilometers 

(km2

) 

1 acre = 0.4 hectare (he) = 4,000 square meters (m2

) 

AREA (APPROXIMATE) 

1 square centimeter (cm2

) = 0.16 square inch (sq in, in2) 

1 square meter (m2

) = 1.2 square yards (sq yd, 

yd2

) 

1 square kilometer (km2

) = 0.4 square mile (sq mi, mi2) 

10,000 square meters (m2

) = 1 hectare (ha) = 2.5 acres 

MASS - WEIGHT (APPROXIMATE) 

1 ounce (oz) = 28 grams (gm) 

1 pound (lb) = 0.45 kilogram (kg) 

1 short ton = 2,000 pounds 

(lb) 

= 0.9 tonne (t) 

MASS - WEIGHT (APPROXIMATE) 

1 gram (gm) = 0.036 ounce (oz) 

1 kilogram (kg) = 2.2 pounds (lb) 

1 tonne (t) = 

= 

1,000 kilograms (kg) 

1.1 short tons 

VOLUME (APPROXIMATE) 

1 teaspoon (tsp) = 5 milliliters (ml) 

1 tablespoon (tbsp) = 15 milliliters (ml) 

1 fluid ounce (fl oz) = 30 milliliters (ml) 

1 cup (c) = 0.24 liter (l) 

1 pint (pt) = 0.47 liter (l) 

1 quart (qt) = 0.96 liter (l) 

1 gallon (gal) = 3.8 liters (l) 

1 cubic foot (cu ft, ft3

) = 0.03 cubic meter (m3) 

1 cubic yard (cu yd, yd3

) = 0.76 cubic meter (m3) 

VOLUME (APPROXIMATE) 

1 milliliter (ml) = 0.03 fluid ounce (fl oz) 

1 liter (l) = 2.1 pints (pt) 

1 liter (l) = 1.06 quarts (qt) 

1 liter (l) = 0.26 gallon (gal) 

1 cubic meter (m3

) = 36 cubic feet (cu ft, ft3) 

1 cubic meter (m3

) = 1.3 cubic yards (cu yd, yd3) 

TEMPERATURE (EXACT) 

[(x-32)(5/9)] °F = y °C 

TEMPERATURE (EXACT) 

[(9/5) y + 32] °C = x °F 

QUICK INCH - CENTIMETER LENGTH CONVERSION 

0 1 2 3 4 5

Inches 

Centimeters 

QUICK FAHRENHEIT - CELSIUS TEMPERATURE CONVERSION 

°F -40° -22° -4° 14° 32° 50° 68° 86° 104° 122° 140° 158° 176° 194° 212°
 

°C -40° -30° -20° -10° 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° 100°
 

For more exact and or other conversion factors, see NIST Miscellaneous Publication 286, Units of Weights and 

Measures. Price $2.50 SD Catalog No. C13 10286 Updated 6/17/98 

0 1 2 3 4 5 6 7 8 9 10 11 12 13

ii 
Preface 

The tests that are described in this report resulted from a cooperative effort between industry 

groups and Federal agencies. The Tank Car Operating Environmental Task Force was 

established by the Association of American Railroads (AAR)–Chemical Manufacturers 

Association–Railway Progress Institute (RPI) liaison team to oversee this project. This project 

was funded by RPI, AAR, and the Federal Railroad Administration (FRA) Office of Research 

and Development. 

The analysis discussed in this report was performed as part of the Tank Car Structural Integrity 

Program sponsored by FRA’s Office of Research and Development. 

The FRA Office of Research and Development tank car safety program manager is Mr. Jose 

Pena. Union Tank Car Company (or ACF) donated the tank car. Mr. Al Henzi facilitated this 

donation. Mr. Jim Rader (FRA-Office of Safety) helped with the historical aspects of the 

introduction and supplied the photograph for Figure 1. Mr. Keith Smith, of Southwest Research 

Institute, formerly of Transportation Technology Center, Inc. (TTCI), was responsible for much 

of the original vision and direction of the project. Thanks also to Todd Treichel, of RPI-AAR, 

and Christopher Barkan, University of Illinois, for support of this project. 

iii 

Table of Contents 

List of Figures............................................................................................................................... vii 

List of Tables ...................................................................................................................................x 

Executive Summary.........................................................................................................................1 

1. Introduction..................................................................................................................................3 

2. Experimental Procedure...............................................................................................................5 

2.1 Test Configuration..................................................................................................................5 

2.2 Equipment ..............................................................................................................................5 

2.3 Instrumentation.......................................................................................................................7 

3. Experimental Observations..........................................................................................................9 

3.1 Draft Gear Behavior ...............................................................................................................9 

3.2 Longitudinal Coupler Forces................................................................................................11 

3.3 Measured Accelerations .......................................................................................................12 

4. Analysis of Results ....................................................................................................................17 

4.1 Analysis of Measured Accelerations....................................................................................17 

4.2 Calculation of Anticipated Natural Frequencies ..................................................................31 

4.3 PSD Results..........................................................................................................................34 

4.4 Displacements ......................................................................................................................35 

5. Discussion..................................................................................................................................39 

5.1 Draft Gear Mechanism .........................................................................................................39 

5.2 Coupler Force, Impact Speed, and Draft Gear Mechanism .................................................39 

5.3 PSD Analyses.......................................................................................................................40 

5.4 The Relationship of PSD Results to Natural Frequencies....................................................41 

6. Summary and Conclusions ........................................................................................................43 

References......................................................................................................................................45 

Appendix A. PSD Results of Empty Car Impact Tests ................................................................47 

Appendix B. PSD Results of Full Car Impact Tests.....................................................................71 

Acronyms.......................................................................................................................................85
 

v 

List of Figures 

Figure 1. A Sill Pad on a Tank Car–The Arrow Points to a Crack that Was Caused by High 

Coupler Forces Resulting from an Over-Speed Impact .............................................3 

Figure 2. Configuration of Impact Tests–With the Brakes Applied on the Hopper Car at the 

End of the Consist ......................................................................................................5 

Figure 3. Dimensions of the Tank Car Used in the Impact Tests..............................................6 

Figure 4. Schematic of Draft Gear Used for Test......................................................................7 

Figure 5. Location of Accelerometers on Tank Car Body.........................................................8 

Figure 6. Coupler Force Plotted Against Time for Empty Tank Car Impacts at (a) 4.5 mph, 

(b) 6.1 mph, and (c) 7.4 mph, Representing Spring, Stick-Slip, and Solid Load 

Transfer Mechanisms, Respectively ........................................................................10 

Figure 7. Coupler Force Plotted Against Time for Full Tank Car Impacts at (a) 2.5 mph, 

(b) 4.2 mph, and (c) 7.5 mph, Representing Spring, Stick-Slip, and Solid Load 

Transfer Mechanisms, Respectively ........................................................................11 

Figure 8. Peak Longitudinal Coupler Forces Plotted Against Impact Velocity for an Empty 

and Full Tank Car.....................................................................................................12 

Figure 9. Vertical Accelerations Measured at Location 6 for Three Solid Impacts of an 

Empty Tank Car at (a) 8.0 mph (1052 kips Peak Coupler Force), (b) 7.8 mph 

(970 kips Peak Coupler Force), and (c) 7.9 mph (1004 kips Peak Coupler Force) .13 

Figure 10. Longitudinal Accelerations Measured at Location 6 for Three Solid Impacts of an 

Empty Tank Car at (a) 8.0 mph (1052 kips Peak Coupler Force), (b) 7.8 mph (970 

kips Peak Coupler Force), and (c) 7.9 mph (1004 kips Peak Coupler Force)..........14 

Figure 11. Vertical Accelerations Measured from Location 6 for Three Solid Impacts of a 

Full Tank Car at (a) 7.4 mph (1347 kips Peak Coupler Force), (b) 7.2 mph (1276 

kips Peak Coupler Force), and (c) 7.5 mph (1375 kips Peak Coupler Force)..........15 

Figure 12. Longitudinal Accelerations Measured from Location 6 for Three Solid Impacts of 

a Full Tank Car at (a) 7.4 mph (1347 kips Peak Coupler Force), (b) 7.2 mph (1276 

kips Peak Coupler Force), and (c) 7.5 mph (1375 kips Peak Coupler Force)..........16 

Figure 13. Example of Window Selection.................................................................................17 

vii 
List of Figures (cont.) 

Figure 14. PSD Results as a Function of Length of Signal Examined for Accelerometer 6 for 

the Empty Tank Car Impact at Stick-Slip–The PSD Plot Obtained for a Window 

of 0.35 Second, Selected as the Representative Response, Shown in Bold.............18 

Figure 15. PSD of Vertical Accelerations Measured at Location 6 for Empty Tank Car 

Impacts with Spring Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 375 kips, (b) 444 kips, and (c) 542 kips..............................................................19 

Figure 16. PSD of Longitudinal Accelerations Measured at Location 6 for Empty Tank Car 

Impacts with Spring Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 375 kips, (b) 444 kips, and (c) 542 kips..............................................................20 

Figure 17. PSD of Vertical Accelerations Measured at Location 6 for Empty Tank Car 

Impacts with Stick-Slip Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 582 kips, (b) 594 kips, and (c) 619 kips..............................................................21 

Figure 18. PSD of Longitudinal Accelerations Measured at Location 6 for Empty Tank Cars 

Impacts with Stick-Slip Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 582 kips, (b) 594 kips, and (c) 619 kips..............................................................22 

Figure 19. PSD of Vertical Accelerations Measured at Location 6 for Empty Tank Car 

Impacts with Solid Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 970 kips, (b) 1004 kips, and (c) 1052 kips..........................................................23 

Figure 20. PSD of Longitudinal Accelerations Measured at Location 6 for Empty Tank Car 

Impacts with Solid Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 970 kips, (b) 1004 kips, and (c) 1052 kips..........................................................24 

Figure 21. PSD of Vertical Accelerations Measured at Location 6 for Full Tank Car Impacts 

with Spring Load Transfer Mechanisms with Peak Coupler Forces of (a) 468 

kips, (b) 496 kips, and (c) 500 kips ..........................................................................25 

Figure 22. PSD of Longitudinal Accelerations Measured at Location 6 for Full Tank Car 

Impacts with Spring Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 468 kips, (b) 496 kips, and (c) 500 kips.............................................................26 

viii 
List of Figures (Cont.) 

Figure 23. PSD of Vertical Accelerations Measured at Location 6 for Full Tank Car Impacts 

with Stick-Slip Load Transfer Mechanisms with Peak Coupler Forces of (a) 479 

kips, (b) 486 kips, and (c) 495 kips ..........................................................................27 

Figure 24. PSD of Longitudinal Accelerations Measured at Location 6 for Full Tank Car 

Impacts with Stick-Slip Load Transfer Mechanisms with Peak Coupler Forces 

of (a) 479 kips, (b) 486 kips, and (c) 495 kips .........................................................28 

Figure 25. PSD of Vertical Accelerations Measured at Location 6 for Full Tank Car Impacts 

with Solid Load Transfer Mechanisms with Peak Coupler Forces of (a) 1276 

kips, (b) 1347 kips, and (c) 1375 kips ......................................................................29 

Figure 26. PSD of Longitudinal Accelerations Measured at Location 6 for Full Tank Car 

Impacts with Solid Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 1276 kips, (b) 1347 kips, and (c) 1375 kips........................................................30 

Figure 27. Schematic of the Cylinder Used to Determine the Natural Frequencies of the 

Tank Car...................................................................................................................31 

Figure 28. Examples of Mode Shapes for the Natural Frequencies of a Simply Supported 

Cylinder without Axial Constraint for (a) Bending, (b) Axial, (c) Radial, and 

(d) Radial-Axial........................................................................................................31 

Figure 29. PSD of Vertical Acceleration from Location 6 for Three Solid Impacts of an 

Empty Tank Car Are Superimposed–Natural Frequencies of a Simply Supported 

Cylinder for Mode Shapes with a Vertical Component Are Indicated by the Solid 

Vertical Line (j = 1) and Dashed Vertical Lines (j = 2 through 5)...........................34 

Figure 30. PSD of Longitudinal Acceleration from Location 6 for Three Solid Impacts of an 

Empty Tank Car Are Superimposed–Natural Frequencies of a Simply Supported 

Cylinder for Mode Shapes with a Longitudinal Component Are Indicated by the 

Solid Vertical Line (j = 1) and Dashed Vertical Lines (j = 2 through 5) .................35 

Figure 31. Vertical Displacement at Location 5 for an Empty Tank Car Impact at 8.0 mph....36 

Figure 32. Vertical Displacement at Location 6 for an Empty Tank Car Impact at 8.0 mph....37 

Figure 33. Longitudinal Displacement at Location 5 for an Empty Tank Car Impact at 

8.0 mph.....................................................................................................................38 

ix 
List of Tables 

Table 1. Parameters Used in Equations..................................................................................32 

Table 2. Calculated Natural Frequencies for a Simply Supported Cylinder ..........................33 

x 
Executive Summary 

Under in-service conditions, a railroad tank car is subjected to cyclic loads that can lead to 

structural damage. Under most conditions, the damage accumulates slowly through fatigue crack 

growth mechanisms. Fatigue crack damage resulting from normal service conditions is managed 

in tank cars through a program of periodic inspections. The inspections identify stub sills and 

tanks with cracks, resulting in either repair of the cracks or retirement of cars found with cracks. 

In rare cases, however, a tank car can be subjected to an extreme force that leads to a sudden 

fracture. It is believed that many of the largest coupler-force events encountered by tank cars are 

induced by rail yard impacts. 

A study of the technical requirements for a system to remotely monitor coupler forces on tank 

cars operating in revenue service was performed [1]. Based on the study of the technical 

requirements, an accelerometer-based system was recommended as a means to monitor coupler 

forces resulting from yard impacts. The first step toward developing such a system was 

performing a series of full-scale impact tests [2]. These tests involved impacting a tank car into a 

stationary consist of hopper cars. The tests consisted of a series of empty tank car impacts at 

nominal impact velocities of 2, 4, 6, and 8 miles per hour (mph) and a series of full tank car 

impacts at nominal impact velocities of 2, 4, 6, and 7 mph. For each empty tank car impact at 8 

mph, 3 to 5 inches of movement occurred in the anvil string. For the other impacts in this series, 

the anvil cars essentially remained stationary. Strains, accelerations, and longitudinal coupler 

force were recorded as a function of time for each impact. For each impact test of the empty 

tank car, the coupler on the tank car was approximately 1.5 inches higher than the coupler on the 

impacted hopper car. 

The purpose of this report is to investigate the response of accelerometers mounted at various 

locations on a tank car that was subjected to coupler impacts. This work was performed as part 

of the Tank Car Structural Integrity Program sponsored by the Office of Research and 

Development of the Federal Railroad Administration (FRA). The research team considered the 

effects of tank car lading, peak coupler force, dominant draft gear mechanism, and accelerometer 

location on the accelerometer responses. Power spectral density (PSD) analyses were performed 

on accelerations to quantify the response of the tank car to the impacts. The team compared 

frequencies identified by the PSD analyses to calculated natural frequencies for a simple thinwalled cylinder. 

The dominant draft gear mechanism has a marked effect on the response of the tank car. In 

general, as speed and energy increase, the draft gear mechanism changes from spring to stick-slip 

to solid. For spring type impacts for empty tank cars, peak coupler force increased as impact 

speed increased. For spring type impacts, little difference existed in peak coupler force for full 

tank car impacts for the range of speeds investigated. Peak coupler force was nearly constant for 

all stick-slip impacts. The forces were approximately the same for the empty and full tank car 

impacts, but the impact speeds at which the stick-slip mechanism occurs were lower for the full 

1 
 cars. For solid impacts, as speed increases, peak coupler force increases. For a given impact 

speed and a solid load transfer mechanism, full tank car impacts generated higher peak coupler 

force than empty cars. 

The frequencies that were significantly and consistently excited differed between the empty and 

full tank car impact tests. For the empty tank car impact test results, a frequency near 0 Hz was 

present in the PSDs of longitudinal acceleration signals. The lack of vibrations and similar 

magnitude of integrated longitudinal displacements at locations 5 and 6 suggest that this is a 

rigid body vibration. A frequency of 13 Hz was present in the PSDs of the vertical acceleration 

signals, coinciding with the first radial-axial mode of a simply supported cylinder. The 

difference in magnitude of integrated vertical displacements at locations 5 and 6 suggest that this 

is a structural, not a rigid body vibration. In addition, frequencies of approximately 100 Hz were 

present in the vertical acceleration signals from impacts with a stick-slip coupler mechanism. 

The 100 Hz peak coincides with a frequency observed in the force-time traces for impacts with 

stick-slip draft gear mechanisms and was likely induced by the periodic nature of the couplerforce versus time relationship of the stick-slip coupler mechanism. Additional peaks greater than 

250 Hz were present, but these occurred above most of the structural frequencies estimated by a 

simple model of a cylinder. In the full tank car impact tests, two distinct peaks, at approximately 

5 Hz and 26 Hz, were present in the vertical acceleration response. A frequency at 0 Hz and a 

range of frequencies above 300 Hz were present in the PSDs of longitudinal acceleration signals. 

Additional work with filtering and calculation of stock response spectrum (SRS) are required to 

develop a model for response of tank car to impact. Results suggest that structural response of a 

tank car subjected to coupler impact can be characterized by vibration at relatively few 

frequencies. As a result, the response of accelerometers at locations 5 and 6 might be able to be 

characterized with only a few degrees of freedom. 

2
1. Introduction 

During regular service, a railroad tank car is subjected to cyclic loads that can lead to structural 

damage. Under most conditions, the damage accumulates slowly through fatigue crack growth 

mechanisms. Fatigue crack damage resulting from normal service conditions is managed in tank 

cars through a program of periodic inspections. The inspections identify stub sills and tanks with 

cracks, resulting in either repair of the cracks or retirement of cars found with cracks. In rare 

cases, however, a tank car can be subjected to an extreme force that leads to a sudden fracture. 

The cracked head pad, shown in Figure 1, is the result of an extreme coupler force event. In this 

case, the fracture remained in the head pad and did not extend into the tank shell. However, if 

the damage resulting from an extreme case such as this were not noticed, a fatigue failure could 

occur after very little additional service, regardless of when the last inspection occurred. 

Therefore, the effect of especially damaging impacts on the reliability of tank cars must be 

considered carefully. 

Figure 1. A Sill Pad on a Tank Car–The Arrow Points to a Crack that Was Caused by 

High Coupler Forces Resulting from an Over-Speed Impact 

It is believed that many of the largest coupler-force events encountered by tank cars are induced 

by rail yard impacts. To address the frequency of these damaging events, a tank car operating 

environment task force was formed by the Association of American Railroads (AAR), the 

Chemical Manufacturers Association (now the American Chemistry Council), and the Railway 

Progress Institute (Association of American Railroads–Chemical Manufacturers Association– 

Railway Progress Institute) liaison team. Industry representatives, U.S. regulators, and Canadian 

regulators participated in this task force. A conclusion of this task force was that sufficient data 

did not exist to assess the extent of this problem. As a result of this conclusion, a study of the 

technical requirements for a system to remotely monitor coupler forces on tank cars operating in 

revenue service was performed [1]. 

3
 
Based on the study of the technical requirements, an accelerometer-based system was 

recommended as a means to monitor coupler forces resulting from yard impacts. The first step 

toward developing such a system was to perform a series of full-scale impact tests [2]. These 

tests involved impacting an empty tank car into a stationary consist. The results of these tests 

showed a relationship between the SRS [3] of measured accelerations and peak longitudinal 

coupler force. These tests, however, considered only an unloaded tank car in a single impact 

configuration. To develop a system that is applicable to in-service conditions, the effect of 

different impact configurations, tank car design, and lading in the tank car must be accounted for 

in the relationship between coupler force and dynamic response. The next step toward 

developing a useful system to monitor coupler forces is to account for lading in the tank car. 

Therefore, the research team performed a second series of tests where the tank car was full. 

Whether the car is empty or full, the primary draft gear mechanism and the peak coupler force 

are observed to affect the response. 

4
 
2. Experimental Procedure 

This report discusses two series of impact tests. The first series of impacts involved an empty 

tank car, and the second series of impacts involved a full tank car. Each series will be discussed 

further. 

2.1 Test Configuration 

Each test discussed in this report consisted of an instrumented tank car rolled into a stationary 

consist of three full hopper cars, as shown in Figure 2. The brakes of the last hopper car in the 

consist were applied for all impacts. 

The series of empty tank car impacts consisted of nominal impact velocities of 2, 4, 6, and 8 

mph. For each impact at 8 mph, 3 to 5 inches of movement occurred in the anvil string. During 

the other impacts in this series, the anvil cars essentially remained stationary. For each impact 

test of the empty tank car, the coupler on the tank car was approximately 1.5 inches higher than 

the coupler on the impacted hopper car. 

The series of full tank car impacts consisted of nominal impact velocities of 2, 4, 6, and 7 mph. 

For each impact test of the full tank car, the coupler on the tank car was approximately at the 

same height as the coupler on the impacted hopper car. Strains, accelerations, and the 

longitudinal coupler force were recorded as a function of time for each impact. 

Figure 2. Configuration of Impact Tests–With the Brakes Applied on the Hopper Car 

at the End of the Consist 

2.2 Equipment 

A tank car manufactured by American Car and Foundry (ACF) was used for the tests. Figure 3 

shows some critical dimensions of this car. The tank design is denoted ACF 4-B-7188, and the 

underframe design is denoted ACF 4-B-7190 Stub Sill. The tank consists of a steel shell 7/16-

inch thick with a 4-inch layer of fiberglass insulation covering the exterior of the shell. A 

7/8-inch thick jacket covers the insulation. The car weighs 75.4 kips empty and 263 kips with a 

full payload of 22,577 gallons of detergent alkylate. The coupler is a 6 1/4 x 8 type E. 

5
 
7 4 " 

8 

"' 

8 

7 − 354 

− 742 "' 

"' 

8 

7 − 046 

" 

8 

1 108 

− 010 "' 

" 

4 

3

'4 

" 

4 

1 103 

R 

Shell Gap between 

shell and shell 

jacket 

Figure 3. Dimensions of the Tank Car Used in the Impact Tests 

A Cardwell Westinghouse Mark 50 all-steel design draft gear was used on both the tank car and 

the hopper cars that are used as anvil cars. Figure 4 shows a schematic of this draft gear. This 

gear employs friction wedges plus springs. When first loaded, the draft gear transmits forces 

through the friction wedges. Under quasi-static loading conditions, as much as 800 to 1000 kips 

(3600 to 4400 kN) can be developed without breaking the friction bond. Substantially less force, 

however, can break the friction bond under dynamic loading conditions. After the friction bond 

is broken, the internal spring-pack results in a nonlinear force-displacement relationship. The 

stiffness of the spring pack increases as the displacement increases to the full 3.25 inches (82.6 

mm) of travel. The load-time trace between the time that the friction bond breaks and the 

internal spring force develops fully tends to be erratic. As impact speeds increase, this transition 

tends to become smoother. 

6
 
Figure 4. Schematic of Draft Gear Used for Test 

2.3 Instrumentation 

The tank car was instrumented with 37 accelerometers mounted at 20 locations. Figure 5 shows 

these locations. At each accelerometer location, except 11, 12, and 17, one accelerometer was 

oriented in the longitudinal direction, and one accelerometer was oriented in the vertical 

direction. Locations 11, 12, and 17 had a single accelerometer oriented in the longitudinal 

direction. The accelerometers mounted near the center and A-end (impacted end) of the car had 

a capacity of +/- 100 Gs, and those mounted near the B-end of the car had a capacity of +/- 50 

Gs. The acceleration data was sampled at 5000 samples/second. These signals were filtered at 

about 1000 cycles/second. An instrumented coupler was installed at the A-end of the car and 

used to measure longitudinal coupler force as a function of time during each test. 

7
 
A-End B-End 

Figure 5. Location of Accelerometers on Tank Car Body 

8
 
3. Experimental Observations 

This section describes draft gear behavior, longitudinal coupler forces, and accelerations 

measured during the test. 

3.1 Draft Gear Behavior 

The longitudinal coupler force history resulting from each impact reveals the dominant load 

transfer mechanism that occurred during that impact. Previous work has shown that changes in 

the dominant load transfer mechanism resulted in distinct changes in the relationship between 

SRS values of measured accelerations and peak coupler force [2]. Longitudinal coupler force 

is plotted against time in Figure 6 for sample tests representing (a) spring, (b) stick-slip, and 

(c) solid coupler mechanisms for an empty tank car, and in Figure 7 for sample tests representing 

the same coupler mechanisms for a full tank car. For each impact on the full tank car, additional 

load peaks follow the primary load peaks. These additional peaks are believed to be induced by 

the motion of the fluid in the tank car. 

9
 
1500 

1000 

4.5 mph 

Empty Car 

(a) 

500 

0 

1500 

1000 

6.1 mph (b) 

Empty Car 500 

0 

1500 

1000 7.4 mph (c) Empty Car 500 

0 

time (s) 

Figure 6. Coupler Force Plotted Against Time for Empty Tank Car Impacts at 

(a) 4.5 mph, (b) 6.1 mph, and (c) 7.4 mph, Representing Spring, Stick-Slip, and 

Solid Load Transfer Mechanisms, Respectively 

Force (kips) Force (kips) Force (kips) 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 

time (s) 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 

time (s) 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
 

10
 
(a) 

(b) 

(c) 

Force (kips) Force (kips) Force (kips) 

1500 

1000 

500 

0 

1500 

1000 

500 

0 

1500 

1000 

500 

0 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 

time (s) 

2.5 mph 

Full Car 

4.2 mph 

Full Car 

7.5 mph 

Full Car 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 

time (s) 

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
 

time (s) 

Figure 7. Coupler Force Plotted Against Time for Full Tank Car Impacts at 

(a) 2.5 mph, (b) 4.2 mph, and (c) 7.5 mph, Representing Spring, Stick-Slip, and 

Solid Load Transfer Mechanisms, Respectively 

3.2 Longitudinal Coupler Forces 

The peak longitudinal coupler forces resulting from both sequences of tests are plotted against 

impact velocity in Figure 8. Open symbols indicate empty car impacts, and solid symbols 

indicate full tank car impacts. A triangle, a square, and a circle represent spring, stick-slip, and 

solid draft gear mechanisms, respectively. Three observed trends are: 

1.	 For the empty tank car, as impact speed increases, peak longitudinal coupler force 

tends to increase. 

2.	 The loaded tank car tends to develop higher coupler forces than the unloaded car, 

except for impacts where the primary mechanism is stick-slip. 

11
 
3.	 For impacts where stick-slip behavior is the dominant mechanism, peak coupler 

force is relatively insensitive to impact speed. 

These observations for spring and solid impacts are consistent with trends predicted by 

simple lumped mass analyses, which model the couplers as springs. Figure 8 suggests 

that the complex behavior during stick-slip dominated impacts cannot be modeled as a 

simple spring. 

1500 

Full Empty

Car Car
 

Spring 1000 

Stick-Slip 

Solid 

500 

0 

Impact Velocity (mph) 

Figure 8. Peak Longitudinal Coupler Forces Plotted Against Impact Velocity for an 

Empty and Full Tank Car 

3.3 Measured Accelerations 

For each impact, the responses of all accelerometers were recorded over time. Acceleration was 

recorded before each impact, so the start time of each impact is assumed to be at the first 

significant change in the acceleration time history. 

As examples, Figure 9 plots the vertical accelerations measured at location 6 resulting from three 

impacts dominated by the solid load transfer mechanism. Location 6 is near the manway 

opening on the tank (refer to Figure 5). Figure 10 plots the longitudinal accelerations measured 

at location 6 resulting from three solid impacts. The resulting peak coupler forces for these 

impacts are 1052, 970, and 1004 kips for the tests plotted in Figures 9a, 9b, and 9c, and Figures 

10a, 10b, and 10c, respectively. Peak Coupler Force (kips)

0 1 2 3 4 5 6 7 8 9
 

12
 
50 

8.0 mph (a) 0 Empty Car 

-50 

time (s) 50 

7.8 mph 

(b) 0 Empty Car 

-50 

time (s) 50 

7.9 mph 

(c) 0 Empty Car 

-50 

time (s) 

Acceleration (g) Acceleration (g) Acceleration (g) 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
 

Figure 9. Vertical Accelerations Measured at Location 6 for Three Solid Impacts of an 

Empty Tank Car at (a) 8.0 mph (1052 kips Peak Coupler Force), (b) 7.8 mph 

(970 kips Peak Coupler Force), and (c) 7.9 mph (1004 kips Peak Coupler Force) 

13
 
50 

8.0 mph (a) 0 

Empty Car 

-50 

time (s) 50 

7.8 mph (b) 0 

Empty Car 

-50 

time (s) 50 

7.9 mph (c) 0 Empty Car 

-50 

Acceleration (g) Acceleration (g) Acceleration (g) 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
 

time (s) 

Figure 10. Longitudinal Accelerations Measured at Location 6 for Three Solid 

Impacts of an Empty Tank Car at (a) 8.0 mph (1052 kips Peak Coupler Force), 

(b) 7.8 mph (970 kips Peak Coupler Force), and (c) 7.9 mph (1004 kips Peak 

Coupler Force) 

For each of these impacts, the greatest absolute value of vertical acceleration for these impacts 

occurs approximately 0.06 to 0.10 seconds after the impact starts. This time period coincides 

with a large spike in the longitudinal force versus time relationship, similar to that observed in 

Figures 6c and 7c. 

14
 
50 

(a) 7.4 mph 0 

Full Car 

-50 

time (s) 50 

7.2 mph (b) 0 

Full Car 

-50 

time (s) 50 

7.5 mph (c) 0 Full Car 

-50 

Acceleration (g) Acceleration (g) Acceleration (g) 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
 

time (s) 

Figure 11.	 Vertical Accelerations Measured from Location 6 for Three Solid Impacts 

of a Full Tank Car at (a) 7.4 mph (1347 kips Peak Coupler Force), 

(b) 7.2 mph (1276 kips Peak Coupler Force), and (c) 7.5 mph (1375 kips 

Peak Coupler Force) 

Figure 11 plots the vertical accelerations measured at location 6, resulting from three full tank 

car impacts dominated by the solid load transfer mechanism. Figure 12 plots the longitudinal 

accelerations measured at location 6, resulting from three solid full tank car impacts. The 

resulting peak coupler forces for these impacts are 1347, 1276, and 1375, respectively. 

15
 
50 

7.4 mph (a) 0 Full Car 

-50 

time (s) 50 

7.2 mph 

(b) 0 Full Car 

-50 

time (s) 50 

7.5 mph (c) 0 Full Car 

-50 

Acceleration (g) Acceleration (g) Acceleration (g) 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
 

time (s) 

Figure 12. Longitudinal Accelerations Measured from Location 6 for Three Solid 

Impacts of a Full Tank Car at (a) 7.4 mph (1347 kips Peak Coupler Force), 

(b) 7.2 mph (1276 kips Peak Coupler Force), and (c) 7.5 mph (1375 kips Peak 

Coupler Force) 

16
 
4. Analysis of Results 

This section discusses the methodology of the analysis of the recorded acceleration signals. 

4.1 Analysis of Measured Accelerations 

A PSD analysis was performed on each time history of acceleration to determine the dominant 

frequencies of the response of the tank cars. Accelerations in both the vertical and longitudinal 

directions for the empty tank car tests for representative impacts with spring, stick-slip, and solid 

load transfer mechanisms and for the full car for representative impacts with spring, stick-slip, 

and solid load transfer mechanisms from all locations were examined. 

The results of PSD analyses are dependent on the portion of the signal that is analyzed. To 

determine the optimum portion of the signal to analyze for the PSD calculations, a consistent 

method to identify a start time and a constant window size were established for the accelerations 

signals. Figure 13 shows an example of the process. Double-differentiating the acceleration 

signal and setting a reasonable threshold value, determined to be 2x10+7 (g/sec2

), identifies the 

start time. No sensitivity studies were performed on the start time, but this value resulted in the 

same start time obtained when using engineering judgment. To investigate the most appropriate 

value for the window, the window of signal was varied between 0.2 and 1.0 second in increments 

of 0.05 second. To visualize these results, a plot of PSD analyses, frequency, and the window 

was developed. 

Figure 13. Example of Window Selection 

17
 
window

(s) 

frequency (Hz) 

Figure 14 shows a sample 3D plot. For a given window, certain frequencies exhibit PSD peaks. 

When these peaks are consistent for a range of window values, the peaks appear as fans in the 

three-dimensional plot that run parallel to the window axis and perpendicular to the frequency 

axis. It was assumed that the peaks that are consistent throughout a range of windows were the 

most significant. A window of 0.35 second captures most of the fans and was used for all 

additional analyses. 

0.5 1500 0.6 

0.4 

0.7 

0.8 

0.9 

100 200 1.0 300 400 500 600 700 

0.0 

0.1 

3000 0.2 

2500 0.3 

PSD (g

2/Hz) 

2000
 

1000 

500 

0 

Figure 14. PSD Results as a Function of Length of Signal Examined for Accelerometer 

6 for the Empty Tank Car Impact at Stick-Slip–The PSD Plot Obtained for a 

Window of 0.35 Second, Selected as the Representative Response, Shown in Bold 

Figures 15-20 show plots of the PSDs for the vertical and longitudinal acceleration signals from 

location 6 for one empty tank car impact for each type (spring, stick-slip, and solid). Figures 21-

26 show plots of the PSDs for the vertical and longitudinal acceleration signals from location 6 

for a loaded tank car impact of each type (spring, stick-slip, and solid). 

Accelerations measured at other locations were also analyzed. Results of the PSD analyses on 

accelerations measured at locations 1, 1A, 2, 2A, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, and 18 on the 

empty tank car are shown in Appendix A, Figures A1-A23, and at locations 1, 1A, 5, 6, 9, 10, 

and 18 on the full tank car are shown in Appendix B, Figures B1-B14. 

18
 
3000
 

2000
 

375 kips (a) 

Empty Car 1000
 

0 

3000
 

2000
 444 kips (b) Empty Car 1000
 

0 

3000
 

2000
 542 kips (c) Empty Car 1000
 

0
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

Figure 15. PSD of Vertical Accelerations Measured at Location 6 for Empty Tank Car 

Impacts with Spring Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 375 kips, (b) 444 kips, and (c) 542 kips 

19
 
1000 

(a) 375 kips 500 

Empty Car 

0 

1000 

444 kips (b) 500 

Empty Car 

0 

1000 

542 kips (c) 500 Empty Car 

0 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700 

frequency (Hz) 

0 100 200 300 400 500 600 700 

frequency (Hz) 

0 100 200 300 400 500 600 700 

frequency (Hz) 

Figure 16. PSD of Longitudinal Accelerations Measured at Location 6 for Empty 

Tank Car Impacts with Spring Load Transfer Mechanisms with Peak Coupler 

Forces of (a) 375 kips, (b) 444 kips, and (c) 542 kips 

20
 
3000 

2000 

(a) 

1000 

0 

frequency (Hz) 3000 

2000 

(b) 

1000 

0 

frequency (Hz) 3000 

2000 

(c) 

1000 

0 

frequency (Hz) 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

582 kips 

Empty Car 

594 kips 

Empty Car 

619 kips 

Empty Car 

Figure 17. PSD of Vertical Accelerations Measured at Location 6 for Empty Tank Car 

Impacts with Stick-Slip Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 582 kips, (b) 594 kips, and (c) 619 kips 

21
 
1000 

582 kips (a) 500 Empty Car 

0 

1000 

594 kips

(b) 500 Empty Car 

0 

1000 

619 kips 

(c) 500 Empty Car 

0 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700 

frequency (Hz) 

0 100 200 300 400 500 600 700 

frequency (Hz) 

0 100 200 300 400 500 600 700 

frequency (Hz) 

Figure 18. PSD of Longitudinal Accelerations Measured at Location 6 for Empty 

Tank Car Impacts with Stick-Slip Load Transfer Mechanisms with Peak Coupler 

Forces of (a) 582 kips, (b) 594 kips, and (c) 619 kips 

22
 
3000
 

2000
 

970 kips 

Empty Car 

(a) 

1000
 

0
 

3000
 

2000
 1004 kips (b) 

Empty Car 1000
 

0
 

3000
 

2000
 1052 kips (c) Empty Car 1000
 

0
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

Figure 19. PSD of Vertical Accelerations Measured at Location 6 for Empty Tank Car 

Impacts with Solid Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 970 kips, (b) 1004 kips, and (c) 1052 kips 

23
 
1000 

(a) 970 kips 500 

Empty Car 

0 

1000 

1004 kips (b) 500 

Empty Car 

0 

1000 

1052 kips (c) 500 Empty Car 

0 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700 

frequency (Hz) 

0 100 200 300 400 500 600 700 

frequency (Hz) 

0 100 200 300 400 500 600 700 

frequency (Hz) 

Figure 20. PSD of Longitudinal Accelerations Measured at Location 6 for Empty 

Tank Car Impacts with Solid Load Transfer Mechanisms with Peak Coupler Forces 

of (a) 970 kips, (b) 1004 kips, and (c) 1052 kips 

24
 
PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

3000
 

2000
 

1000
 

0
 

3000
 

2000
 

1000
 

0
 

3000
 

2000
 

1000
 

0 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

(a) 

(b) 

(c) 

468 kips 

Full Car 

496 kips 

Full Car 

500 kips 

Full Car 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

Figure 21. PSD of Vertical Accelerations Measured at Location 6 for Full Tank Car 

Impacts with Spring Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 468 kips, (b) 496 kips, and (c) 500 kips 

25
 
PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

1000 

500
 

0
 

1000
 

500
 

0
 

1000
 

500
 

0 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

(a) 

(b) 

(c) 

468 kips 

Full Car 

496 kips 

Full Car 

500 kips 

Full Car 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

Figure 22. PSD of Longitudinal Accelerations Measured at Location 6 for Full Tank 

Car Impacts with Spring Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 468 kips, (b) 496 kips, and (c) 500 kips 

26
 
PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

3000
 

2000
 

1000
 

0
 

3000
 

2000
 

1000
 

0
 

3000
 

2000
 

1000
 

0 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

(a) 

(b) 

(c) 

479 kips 

Full Car 

486 kips 

Full Car 

495 kips 

Full Car 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

Figure 23. PSD of Vertical Accelerations Measured at Location 6 for Full Tank Car 

Impacts with Stick-Slip Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 479 kips, (b) 486 kips, and (c) 495 kips 

27
 
1000 

479 kips (a) 500 

Full Car 

0 

1000 

486 kips (b) 500 

Full Car 

0 

1000 

495 kips (c) 500 Full Car 

0 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700 

frequency (Hz) 

0 100 200 300 400 500 600 700 

frequency (Hz) 

0 100 200 300 400 500 600 700 

frequency (Hz) 

Figure 24. PSD of Longitudinal Accelerations Measured at Location 6 for Full Tank 

Car Impacts with Stick-Slip Load Transfer Mechanisms with Peak Coupler Forces 

of (a) 479 kips, (b) 486 kips, and (c) 495 kips 

28
 
3000
 

2000
 

1276 kips 

Full Car

(a) 

1000
 

0 

3000
 

2000
 1347 kips (b) 

Full Car 1000
 

0 

3000
 

2000
 1375 kips (c) Full Car 

1000
 

0 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

Figure 25. PSD of Vertical Accelerations Measured at Location 6 for Full Tank Car 

Impacts with Solid Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 1276 kips, (b) 1347 kips, and (c) 1375 kips 

29
 
PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

1000 

500
 

0
 

1000
 

500
 

0
 

1000
 

500
 

0 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

(a) 

(b) 

(c) 

1276 kips 

Full Car 

1347 kips 

Full Car 

1375 kips 

Full Car 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

0 100 200 300 400 500 600 700
 

frequency (Hz)
 

Figure 26. PSD of Longitudinal Accelerations Measured at Location 6 for Full Tank 

Car Impacts with Solid Load Transfer Mechanisms with Peak Coupler Forces of 

(a) 1276 kips, (b) 1347 kips, and (c) 1375 kips 

30
 
4.2 Calculation of Anticipated Natural Frequencies 

The natural frequencies of a simple cylinder [5], shown in Figure 27, were calculated using 

equation (1) to approximate the natural frequencies, fi,j , of an empty tank car. These frequencies 

were then compared to results of the PSD analyses of the recorded acceleration data. Table 1 

gives the parameters used for these equations. These values were chosen to represent the 

(greatly simplified) geometry of the car. The value of Λ was calculated using equations 2-5 for 

bending, radial, radial-axial, and axial modes, respectively. Mode shapes were calculated using 

equations 6-9 for bending, radial, radial-axial, and axial modes, respectively. Figure 28 shows 

examples of the first mode shape for each mode. Table 2 lists the resulting natural frequencies 

for the first five modes for each mode shape. 

t R 

L 

Z 

X 

Z 

Y 

Figure 27. Schematic of the Cylinder Used to Determine the Natural Frequencies of 

the Tank Car 

(a) (b) 

(c) 

i = 1 j = 1 i = 1 j = 1 

(d) 

i = 1 j = 1 i = 1 j = 2 

Figure 28. Examples of Mode Shapes for the Natural Frequencies of a Simply 

Supported Cylinder without Axial Constraint for (a) Bending, (b) Axial, (c) Radial, 

and (d) Radial-Axial 

31
 
⎡

⎛

⎜

⎝

⎢

⎢ ⋅
 

⎣ Λ
 =

0.5 

⎡ ⎤

i, j 

⋅π ⋅

⎛

⎜ Λ

⎜

⎜

⎞

⎟

⎟

⎟

E
 (1) ⎢

⎢

⎢

⎢

⎣

⎥

⎥

⎥

⎥

⎦

fi, j =
 ⋅ 2 ) 2 R ⎝ ⎠ u v ⋅(1−

0.5 4 ⎤ R 4

⎞

⎟

⎠

⋅⋅ 2 ⎛ 2 ⎡ ⎤ ⎜

⎝

⎜

⎞

⎟

⎠

⎟⋅

R 

j 

L 

π j R ⋅π ⋅

R (5) 

⎛

⎜

⎝

⎞

⎟

⎠

t ⎥

⎥

2 2 

⎞

⎟

⎠

⎢

⎢⎣

(1− )⋅ i ⎥

⎥⎦

v + 2 12 ⋅ R L
 (2) ⎦

i, j 2 ⎛ j ⋅π ⋅ ⎜

⎝ i

2 +

L
 

 (3) Λ =1 

2 0.5 2 

i, j 

2 2 j ⋅π ⋅(1− v ) R

 (4) Λ =
 ⋅ i, j 0.5 L2 2
 

2 0.5 Λi, j = j ⋅π ⋅(1− v ) ⋅

L
 

Table 1. Parameters Used in Equations 

R 54.125 inches 

u 0.00074 slugs/in3 

ν 0.32 

E 29000000 ksi 

L 575.375 inches 

t 0.4375 inches 

j ⋅ π

0 

⎛ ⋅ x ⎜

⎜

⎜

⎜

⎜

⎞

⎟

⎟

⎟

⎟

⎟

u

~ cos( ) ⎛

⎜

⎜

⎜

⎞

⎟

⎟

⎟

⎠i,j 

=
 L
 ~
 (6) v 

~ 0
 

⎝ ⎠ ⎝w

32
 
⋅

⋅

⋅

⎛

⎜

⎜

⎜

⎜

⎞

⎟

⎟

⎟

⎟

~
 ⎛ 0 ⎜

⎜

⎜

i,j 

⎞

⎟

⎟

⎟

⎠

u 

~ (7) v 0

~
 

=
 

j π ⋅

π ⋅

⋅

j ⋅ x

) 

x 

w sin( ⎝ ⎝ L ⎠

⎞

⎟

⎟

⎟

⎟

⎛

⎜

⎜

⎜

⎜

~
 ⎛ 0 ⎜

⎜

⎜

i,j 

⎞

⎟

⎟

⎟

⎠

u 

~ (8) v 0

~
 

=
 

w sin( ) ⎝ ⎝ L

π ⋅

⎠

⎛ i ⋅ ⎜

⎜

⎜

⎜

⎜

⎜

⎞

⎟

⎟

⎟

⎟

⎟

⎟

x A ⋅ cos(i ⋅θ) cos( )

) cos( 

) cos( 

~
 ⎛ L ⎜

⎜

⎜

i,j

⎞

⎟

⎟

⎟

⎠

u 

i ⋅π ⋅ x

) ~ (9) v =
 B cos(i ⋅⋅ θ

L ~
 ⎝w i ⋅π ⋅ x C cos(i ⋅⋅ θ ) ⎝ L ⎠

Table 2. Calculated Natural Frequencies for a Simply Supported Cylinder 

Mode 

j 

Bending 

(Hz) 

Axial 

(Hz) 

Radial 

(Hz) 

RadialAxial 

(Hz) 

1 36.07 172.61 616.50 13.80 

2 144.28 345.23 616.50 47.33 

3 324.64 517.84 616.50 96.17 

4 577.13 690.45 616.50 151.42 

5 901.77 863.07 616.50 206.44 

33
4.3 PSD Results 

PSD plots from three solid type impacts are plotted in Figures 29 and 30 for vertical and 

longitudinal accelerations, respectively. Natural frequencies calculated using a simply supported 

cylinder have been superimposed over the PSD traces. The solid vertical lines show the primary 

mode (j = 1), and the dashed vertical line show the remaining modes (j = 2 through 5). 

10000 

8000 

6000 

4000 

2000 

0 

PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

frequency (Hz) 

Figure 29. PSD of Vertical Acceleration from Location 6 for Three Solid Impacts of 

an Empty Tank Car Are Superimposed–Natural Frequencies of a Simply Supported 

Cylinder for Mode Shapes with a Vertical Component Are Indicated by the Solid 

Vertical Line (j = 1) and Dashed Vertical Lines (j = 2 through 5) 

34
 
3000 

2500 

2000 

1500 

1000 

500 

0 

frequency (Hz) 

Figure 30. PSD of Longitudinal Acceleration from Location 6 for Three Solid Impacts 

of an Empty Tank Car Are Superimposed–Natural Frequencies of a Simply 

Supported Cylinder for Mode Shapes with a Longitudinal Component Are 

Indicated by the Solid Vertical Line (j = 1) and Dashed Vertical Lines 

(j = 2 through 5) 

4.4 Displacements 

Vertical and longitudinal accelerations from a solid type impact were integrated twice to 

determine displacements at the middle of the tank car for location 5, shown in Figures 31 and 32, 

and for location 6, shown in Figures 33 and 34. To integrate the acceleration signals, initial and 

final conditions were assumed. In the vertical direction, initial and final position and velocity 

were assumed to be zero. In the longitudinal direction, initial displacement was assumed to be 

zero, and the initial velocity was set to the impact velocity for the test. Final velocity was 

assumed to be zero. The acceleration signals were adjusted slightly to achieve these conditions 

by adding or subtracting a constant factor to the acceleration signal. The adjustment was small 

in magnitude compared to the acceleration signal. PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

35
 
Figure 31. Vertical Displacement at Location 5 for an Empty Tank Car Impact at 

8.0 mph 

36
 
Figure 32. Vertical Displacement at Location 6 for an Empty Tank Car Impact at 

8.0 mph 

37
 
Figure 33. Longitudinal Displacement at Location 5 for an Empty Tank Car Impact 

at 8.0 mph 

38
 
5. Discussion 

The following sections will discuss the effect of tank car loading, peak coupler force, the 

dominant draft gear mechanism on the response of the accelerometers, and the results from PSD 

analyses that were performed on the measured accelerations. 

5.1 Draft Gear Mechanism 

Three distinct mechanisms by which the draft gear transfers forces to the tank car were observed: 

spring, stick-slip, and solid. Previous work defined these mechanisms and identified an effect of 

the draft gear mechanism on the shock response spectrum-peak coupler force relationship [2]. 

Coupler force versus time plots from impacts characterized by these transfer mechanisms are 

shown in Figures 6 and 7 for tests on the empty and full tank cars, respectively. The smooth 

force versus time trace, shown in Figures 6a and 7a, is typical of the spring type load transfer. 

Under this mechanism, the load is transferred to the friction wedges in the draft gear without the 

friction wedges slipping. For these impacts, peak coupler force tends to increase with increasing 

impact speed, up to slipping of the wedges. Once the friction wedges slip, the stick-slip load 

transfer mechanism occurs. The stick-slip load transfer is characterized by large oscillations, in 

this case at approximately 100 Hz, in the force versus time history, as shown in Figures 6b and 

7b. The stick-slip behavior tends to be not as pronounced in the full tank car impact tests as in 

the empty tank car tests. The draft gear can travel 3.25 inches under the stick-slip mechanism 

before developing a solid load transfer mechanism, where the force is transferred directly to the 

stub sill. Figures 6c and 7c show force versus time traces of impacts dominated by the solid type 

load transfer mechanism. The solid load transfer mechanism is characterized by small 

oscillations in the force versus time trace (where the stick-slip mechanism is operative) followed 

by a single peak with a large force value. The value of the peak force tends to increase with 

increasing impact speed. The transfer of the impact load directly through the draft gear into the 

stub sill causes a single large peak in coupler force. The force versus time traces for full tank car 

impact tests exhibit low frequency oscillations after the peak impact force (at approximately 11 

Hz). These oscillations are not present in the force versus time traces for empty tank car impacts 

and are most likely caused by the sloshing of the lading after the initial impact. 

5.2 Coupler Force, Impact Speed, and Draft Gear Mechanism 

This study examined the relationship between peak coupler force, impact speed, and primary 

draft gear mechanism. The peak coupler force from each impact is plotted against impact speed 

in Figure 8. In general, peak coupler force increases, and the dominant coupler mechanism 

changes from spring to stick-slip to solid as the impact speed increases. The full tank car impact 

tests tend to transition from spring to stick-slip at lower speeds than the empty tank car impact 

tests. For the full car tests, peak coupler force remains relatively constant between 2 mph and 4 

mph and does not increase as the dominant coupler mechanism changes from spring to stick-slip. 

Peak coupler force then increases with increasing impact speed during the impacts where the 

solid coupler mechanism becomes dominant. A higher peak coupler force was observed in the 

empty tank car slip-stick impacts than in the full tank car stick-slip impacts. A higher speed was 

required to induce stick-slip in the empty tank car impacts than for full tank car impacts. The 

39
 
increase in impact velocity required to transition to stick-slip behavior results from the lower 

mass of the empty tank. It is likely that this trend would be observed for the solid mechanism as 

well, but no impacts exist in the range of 4 to 6 mph for the full tank car impact tests to check 

this hypothesis. 

5.3 PSD Analyses 

PSD analyses were performed on accelerations that were measured during empty and full car 

impact tests. The purpose of these analyses was to identify frequencies that were excited by the 

coupler impacts. For a given impact, the peaks for locations at the A-end (impacted) of the tank 

car (1, 1A, 3, 7, 11, 13, and 15) have greater power than the peaks for locations at the B-end of 

the tank car (2, 2A, 4, 8, 10, 14, and 16). Furthermore, the PSD analyses for locations at the Aend of the car exhibit numerous peaks at frequencies above 250 Hz, which were above most of 

the structural natural frequencies that were deemed most likely to occur and were not 

consistently excited from test to test. These high frequencies are considered to be noise. This 

trend was consistent for all coupler mechanisms for both empty and full tank car impacts. In 

both types of impacts, these frequencies appear in the PSD results from locations at the A-end of 

the car and locations in the middle of the car but are not significant at the B-end of the car. It 

was observed that locations at the A-end of the car introduced more noise than locations in the 

middle of the tank car. As a result, accelerations measured in the middle of the car (locations 5 

and 6) were felt to be the best locations to observe structural response. Furthermore, location 5 

has additional interaction from stiffener beams and lading (for full car impacts). As a result, 

location 6 was chosen for careful consideration. 

Accelerations measured at location 6 were examined for three solid impacts for empty and full 

tank car tests. Vertical and longitudinal accelerations measured at location 6 are plotted against 

time for empty tank car impacts in Figures 9 and 10, respectively. Vertical and longitudinal 

accelerations measured at location 6 are plotted against time for full tank car impacts in Figures 

11 and 12, respectively. The accelerations from the three empty tank car impact tests are similar 

qualitatively. Peak accelerations differ slightly between the acceleration signals, but all of the 

acceleration signals have an underlying sinusoidal oscillation through the signal following the 

initial portion before the impact. The accelerations from the three full tank car impact tests are 

similar qualitatively and quantitatively. The vertical accelerations from the full tank car test 

damp out considerably quicker than the vertical accelerations from the empty tank cars tests 

damp out. This is possibly due to the lading in the full tank car. 

PSD results from location 6, for empty and full tank car impacts with spring, stick-slip, and solid 

draft gear mechanisms, were examined to determine any frequencies that were repeatedly excited 

by the tank car impacts. The PSD results from the empty tank car impacts, shown in Figures 18-

21, exhibit dominant peaks near 0 Hz in the longitudinal direction and 13 Hz in the vertical 

direction. The PSD results from the full tank car test, shown in Figures 22-26, exhibit dominant 

peaks near 0 Hz in the longitudinal direction and at both 5 Hz and 23 Hz in the vertical direction. 

A frequency of 100 Hz was also apparent in the vertical direction in the empty tank car impacts 

with a stick-slip coupler mechanism. This peak also occurs for full tank car impact, but these are 

not as significant during the full tank car impacts. These peaks correspond to 100 Hz oscillations 

in the coupler force versus time traces observed for impacts with a stick-slip draft gear 

mechanism. 

40
 
5.4 The Relationship of PSD Results to Natural Frequencies 

Figure 29 shows a plot of the PSD results for the vertical accelerations from location 6, for three 

empty car impacts with a solid coupler mechanism characteristic. The solid vertical lines show 

the first mode of the calculated natural frequencies for various types of vibrations. The dashed 

vertical lines show the second through fifth modes. The first mode of the radial-axial mode, 13 

Hz, corresponds with a significant peak in the PSD. Figure 30 shows a plot of the PSD results 

of longitudinal accelerations from location 6, for three empty car impacts with solid coupler 

mechanism characteristics. The solid vertical line shows the first mode of the calculated natural 

frequencies. The dashed vertical lines show the second through fifth modes. The peak at 0 Hz 

represents rigid body motion. 

Vertical and longitudinal accelerations recorded from locations 5 and 6 from an empty tank car 

impact with a solid draft gear mechanism were integrated to examine the displacement versus 

time history during the impact. Displacements integrated from vertical accelerations at locations 

5 and 6 are plotted against time in Figures 31 and 32, respectively. A frequency of 

approximately 13 Hz (coinciding with PSD results) is present in the oscillations of the vertical 

displacements at locations 5 and 6. For a given vibration cycle, vertical displacement at location 

6 has approximately twice as the amplitude as vertical displacements at location 5. If these 

displacements were the result of rigid body movement, the amplitude would be the same at both 

locations. Therefore, these results suggest the 13 Hz vibration results from structural, not rigid 

body, vibration. Displacements integrated from longitudinal accelerations at location 5 are 

plotted against time in Figure 33. Although some small oscillations are present, the resulting 

displacements are dominated by a single translation on the order of 2 feet. This, coupled with a 

strong PSD response at 0 Hz, suggests that the longitudinal accelerations result largely from rigid 

body displacements. 

41
 

6. Summary and Conclusions 

The purpose of this report was to investigate the response of accelerometers mounted at various 

locations on a tank car that was subjected to coupler impacts. The effects of tank car loading, 

peak coupler force, and dominant draft gear mechanism on the accelerometer responses were 

considered. PSD analyses were performed on accelerations to quantify the response of the tank 

car to the impacts. Frequencies identified by the PSD analyses were compared to calculated 

natural frequencies for a simple thin-walled cylinder. 

The dominant draft gear mechanism has a marked effect on the response of the tank car. In 

general, as speed and energy increase, the draft gear mechanism changes from spring to stick-slip 

to solid. For spring-type impacts on empty tank cars, peak coupler force increased as impact 

speed increased. For spring-type impacts, little difference existed in peak coupler force for full 

tank car impacts for the range of speeds investigated. At very low speeds these coupler forces 

would presumably be lower. Peak coupler force was nearly constant for all stick-slip impacts. 

The forces were approximately the same for the empty and full tank car impacts, but the impact 

speeds at which the stick-slip mechanism occurred were lower for the full cars. For solid 

impacts, as speed increases peak coupler force increases. For a given impact speed and a solid 

load transfer mechanism, full tank car impacts generated higher peak coupler force than empty 

cars. 

Accelerations measured at various locations on the tank car were examined for both the empty 

and full tank car impact tests, with spring, stick-slip, and solid draft gear load transfer 

mechanisms. For a given impact, the strength of the peaks in the PSDs tends to decrease from 

the A-end (impact) to the B-end of the tank car. Locations at the A-end of the vehicle introduced 

significant amount of noise into the PSD plots. Locations at the B-end of the vehicle tend to not 

produce a strong response to the impact. The middle of the tank car, such as locations 5 and 6, 

provides a compromise in the amount of noise versus strength of signal from the impacts and the 

response of the vehicle. Therefore, location 6 was chosen as the primary location to examine. 

The frequencies that were significantly and consistently excited differed between the empty and 

full tank car impact tests. For the empty tank car impact test results, a frequency near 0 Hz was 

present in the PSDs of longitudinal acceleration signals. The lack of vibrations and similar 

magnitude of integrated longitudinal displacements at locations 5 and 6 suggests that this is a 

rigid body vibration. A frequency of 13 Hz was present in the PSDs of the vertical acceleration 

signals and coincides with the first radial-axial mode of a simply supported cylinder. The 

difference in magnitude of integrated vertical displacements at locations 5 and 6 suggests that 

this is a structural, not a rigid body, vibration. In addition, frequencies of approximately 100 Hz 

were present in the vertical acceleration signals from impacts with a stick-slip coupler 

mechanism. The 100 Hz peak coincides with a frequency observed in the force-time traces for 

impacts with stick-slip draft gear mechanisms and was likely induced by the periodic nature of 

the coupler force versus time relationship of the stick-slip coupler mechanism. Additional peaks 

greater than 250 Hz were present, but these occurred above most of the structural frequencies 

estimated by a simple model of a cylinder. In the full tank car impact tests, two distinct peaks, at 

approximately 5 Hz and 26 Hz, were present in the vertical acceleration response. A frequency 

43
 
at 0 Hz and a range of frequencies above 300 Hz were present in the PSDs of longitudinal 

acceleration signals. 

Additional work with filtering and calculation of SRS is required to develop a model for 

response of tank car to impact. Results suggest that structural response of a tank car subjected to 

coupler impact can be characterized by vibration at relatively few frequencies. As a result, the 

response of accelerometers at locations 5 and 6 might be able to be characterized with only a few 

degrees of freedom. 

44
 
References 

1. Smith, K.B., Parker, E.S., Iler, D.J., “Rail Car Service Spectra Generation for Full-Scale 

Accelerated Fatigue Testing,” in Applications of Automated Technology in Fatigue and 

Fracture Testing and Analysis, ASTM STP 1411, A.A. Braun, P.C. McKeighan, M.A. 

Nicholson and P.R. Lohr, eds. American Society for Testing and Materials, West 

Conshohocken, PA, 2002. 

2. Koch, K.D., Riddell, W.T., Treichel, T.T., Barkan, C P.L., “Structural Response and 

Coupler Forces During Tank Car Impacts,” 43rd Mechanical Working and Steel Processing 

Conference Proceedings, Vol. XXXIX, Iron and Steel Society, Warrendale, PA, pp. 837-848, 

2001. 

3. Thompson, W.T., “Transient Vibration,” Theory of Vibrations with Applications, Third 

Edition, Prentice Hall, New Jersey, 1988, pp. 96-100. 

4. Sommerfield, H. (Engineer at Cardwell/Westinghouse Air Brake Company), personal 

communication, January 2001. 

5. Blevins, R.D., Formulas for Natural Frequency and Mode Shape, Krieger Publishing 

Company, Melbourne, Florida, 1979, pp. 300-305. 

45
 

Appendix A. 

PSD Results of Empty Car Impact Tests 

3000
 

0 100 200 300 400 500 600 700
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

2000
 

1000
 

0
 

frequency (Hz) 3000
 

0 100 200 300 400 500 600 700
 

2000
 

1000
 

0
 

frequency (Hz) 3000
 

0 100 200 300 400 500 600 700
 

2000
 

1000
 

0
 

(a) 

(b) 

(c) 

frequency (Hz) 

Figure A-1. PSD of Vertical Acceleration from Location 1 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Empty Tank 

47 
1000 

(a) Spring 500 

0
 

frequency (Hz)
 1000 

Stick-Slip (b) 500 

0
 

frequency (Hz)
 1000 

Solid (c) 500 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-2. PSD of Longitudinal Acceleration from Location 1 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car
 

48 
Figure A-3. PSD of Vertical Acceleration from Location 1A for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

3000 

2000 

/Hz) 

(a) 

PSD (g2

Spring 

1000 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(b) 

2000 

PSD (g2 /Hz) 

Stick-Slip 

1000 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(c) 

2000 

PSD (g2 /Hz) 

Solid 

1000 

0 

0 100 200 300 400 500 600 700 

frequency (Hz) 

49 
1000 

Spring (a) 500
 

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-4. PSD of Longitudinal Acceleration from Location 1A for (a) Spring, 

(b) Stick-Slip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

50 
Figure A-5. PSD of Vertical Acceleration from Location 2 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

3000 

2000 

/Hz) 

(a) 

2 (g

Spring 

1000 

PSD 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(b) 

1000 

2000 

PSD (g2 /Hz) 

Stick-Slip 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

2000 

/Hz) 

(c) 

PSD (g2

Solid 

1000 

0 

0 100 200 300 400 500 600 700 

frequency (Hz) 

51 
1000 

(a) Spring 500
 

0
 

frequency (Hz)
 1000
 

Stick-Slip (b) 500
 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-6. PSD of Longitudinal Acceleration from Location 3 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car
 

52 
Figure A-7. PSD of Vertical Acceleration from Location 2A for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

3000 

2000 

/Hz) 

(a) 

2 (g

Spring 

1000 

PSD 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(b) 

1000 

2000 

PSD (g2 /Hz) 

Stick-Slip 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

2 

2000 

/Hz) 

Solid 

(c) 

1000 

PSD (g

0 

0 100 200 300 400 500 600 700 

frequency (Hz) 

53 
1000 

(a) 500
 Spring 

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-8. PSD of Longitudinal Acceleration from Location 2A for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

54 
Figure A-9. PSD of Vertical Acceleration from Location 5 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

3000 

(a) 

1000 

2000 

PSD (g2 /Hz) 

Spring 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(b) 

1000 

2000 

PSD (g2 /Hz) 

Stick-Slip 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(c) 

1000 

2000 

PSD (g2 /Hz) 

Solid 

0 

0 100 200 300 400 500 600 700 

frequency (Hz) 

55 
1000 

(a) 500
 Spring

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-10. PSD of Longitudinal Acceleration from Location 5 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

56 
Figure A-11. PSD of Vertical Acceleration from Location 6 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

3000 

2000 

/Hz) 

(a) 

2 (g

Spring 

1000 

PSD 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

2000 

/Hz) 

(b) 

1000 

PSD (g2

Stick-Slip 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

2000 

/Hz) 

(c) 

PSD (g2

Solid 

1000 

0 

0 100 200 300 400 500 600 700 

frequency (Hz) 

57 
1000 

(a) 500
 Spring

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-12. PSD of Longitudinal Acceleration from Location 6 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

58 
1000 

(a) 500
 Spring 

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-13. PSD of Longitudinal Acceleration from Location 8 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

59 
1000 

(a) 500
 Spring 

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) Solid 500
 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-14. PSD of Longitudinal Acceleration from Location 9 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

60 
1000 

(a) 500
 Spring 

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-15. PSD of Longitudinal Acceleration from Location 11 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

61 
1000 

(a) 500
 Spring

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-16. PSD of Longitudinal Acceleration from Location 12 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

62 
1000 

(a) 500
 Spring 

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-17. PSD of Longitudinal Acceleration from Location 13 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

63 
Figure A-18. PSD of Vertical Acceleration from Location 14 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

3000 

2000 

/Hz) 

(a) 

2 (g

Spring 

1000 

PSD 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

2000 

/Hz) 

(b) 

2 (g

Stick-Slip 

1000 

PSD 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

2000 

/Hz) 

(c) 

2 (g

Solid 

1000 

PSD 

0 

0 100 200 300 400 500 600 700 

frequency (Hz) 

64 
1000 

(a) 500
 Spring

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-19. PSD of Longitudinal Acceleration from Location 14 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

65 
1000 

(a) 500
 Spring

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-20. PSD of Longitudinal Acceleration from Location 16 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

66 
Figure A-21. PSD of Vertical Acceleration from Location 17 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

3000 

2000 

/Hz) 

(a) 

2 (g

Spring 

1000 

PSD 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(b) 

1000 

2000 

PSD (g2 /Hz) 

Stick-Slip 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

2000 

/Hz) 

(c) 

PSD (g2

Solid 

1000 

0 

0 100 200 300 400 500 600 700 

frequency (Hz) 

67 
Figure A22. PSD of Vertical Acceleration from Location 18 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

3000 

(a) 

1000 

2000 

PSD (g2 /Hz) 

Spring 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(b) 

1000 

2000 

PSD (g2 /Hz) 

Stick-Slip 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(c) 

1000 

2000 

PSD (g2 /Hz) 

Solid 

0 

0 100 200 300 400 500 600 700 

frequency (Hz) 

68 
1000 

(a) 500 Spring 

0
 

frequency (Hz)
 1000 

(b) 500 Stick-Slip

0
 

frequency (Hz)
 1000 

(c) 500 Solid

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure A-23. PSD of Longitudinal Acceleration from Location 18 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Empty Tank Car 

69 

Appendix B. 

PSD Results of Full Car Impact Tests PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

3000 

2000 

1000 

0 

0 100 200 300 400 500 600 700
 

frequency (Hz) 3000 

2000 

1000 

0 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

frequency (Hz) 

frequency (Hz) 3000 

2000 

1000 

0 

Figure B-1. PSD of Vertical Acceleration from Location 1 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

71 
1000 

(a) 500
 Spring 

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure B-2. PSD of Longitudinal Acceleration from Location 1 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

72 
3000 

2000 

(a) 

1000 

0 

3000 

2000 

(b) 

1000 

0 

3000 

2000 

(c) 

1000 

0 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

Spring 

frequency (Hz) 

0 100 200 300 400 500 600 700
 

Stick-Slip 

frequency (Hz) 

0 100 200 300 400 500 600 700
 

frequency (Hz) 

Solid 

Figure B-3. PSD of Vertical Acceleration from Location 1A for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

73 
1000 

(a) 500
 Spring 

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure B-4. PSD of Longitudinal Acceleration from Location 1A for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

74 
3000 

2000 

(a) 

1000 

0 

3000 

2000 

(b) 

1000 

0 

3000 

2000 

(c) 

1000 

0 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

Spring 

frequency (Hz) 

0 100 200 300 400 500 600 700
 

Stick-Slip 

frequency (Hz) 

0 100 200 300 400 500 600 700
 

frequency (Hz) 

Solid 

Figure B-5. PSD of Vertical Acceleration from Location 5 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

75 
1000 

(a) 500
 Spring

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure B-6. PSD of Longitudinal Acceleration from Location 5 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

76 
Figure B-7. PSD of Vertical Acceleration from Location 6 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

3000 

(a) 

1000 

2000 

PSD (g2 /Hz) 

Spring 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(b) 

1000 

2000 

PSD (g2 /Hz) 

Stick-Slip 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(c) 

1000 

2000 

PSD (g2 /Hz) 

Solid 

0 

0 100 200 300 400 500 600 700 

frequency (Hz) 

77 
1000 

(a) 500
 Spring 

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure B-8. PSD of Longitudinal Acceleration from Location 6 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

78 
Figure B-9. PSD of Vertical Acceleration from Location 9 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

3000 

(a) 

1000 

2000 

PSD (g2 /Hz) 

Spring 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(b) 

1000 

2000 

PSD (g2 /Hz) 

Stick-Slip 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(c) 

1000 

2000 

PSD (g2 /Hz) 

Solid 

0 

0 100 200 300 400 500 600 700 

frequency (Hz) 

79 
1000 

(a) 500 Spring 

0
 

frequency (Hz)
 1000 

(b) 500 Stick-Slip 

0
 

frequency (Hz)
 1000 

(c) 500 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure B-10. PSD of Longitudinal Acceleration from Location 9 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

80 
Figure B-11. PSD of Vertical Aceleration from Location 10 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

3000 

(a) 

1000 

2000 

PSD (g2 /Hz) 

Spring 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(b) 

1000 

2000 

PSD (g2 /Hz) 

Stick-Slip 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(c) 

1000 

2000 

PSD (g2 /Hz) 

Solid 

0 

0 100 200 300 400 500 600 700 

frequency (Hz) 

81 
1000 

(a) 500
 Spring 

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid 

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure B-12. PSD of Longitudinal Acceleration from Location 10 for (a) Spring, (b) StickSlip, and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

82 
Figure B-13. PSD of Vertical Acceleration from Location 18 for (a) Spring, (b) Stick-Slip, 

and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

3000 

(a) 

1000 

2000 

PSD (g2 /Hz) 

Spring 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(b) 

1000 

2000 

PSD (g2 /Hz) 

Stick-Slip 

0 

0 100 200 300 400 500 600 700 

3000 frequency (Hz) 

(c) 

1000 

2000 

PSD (g2 /Hz) 

Solid 

0 

0 100 200 300 400 500 600 700 

frequency (Hz) 

83 
1000 

(a) 500
 Spring 

0
 

frequency (Hz)
 1000
 

(b) 500
 Stick-Slip 

0
 

frequency (Hz)
 1000
 

(c) 500
 Solid

0
 

frequency (Hz)
 

PSD (g2/Hz) PSD (g2/Hz) PSD (g2/Hz) 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

0 100 200 300 400 500 600 700
 

Figure B-14. PSD of Longitudinal Acceleration from Location 18 for (a) Spring, (b) Stickslip, and (c) Solid Load Transfer Mechanisms for the Loaded Tank Car 

84 
Acronyms 

AAR Association of American Railroads 

ACF American Car and Foundry 

FRA Federal Railroad Administration 

MPH miles per hour 

PSD power spectral density 

SRS shock response spectrum 

85