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April 2009 Final Report 

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4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

The Aerodynamic Effects of Passing Trains to Surrounding Objects and People 

BB049/RR93 

6. AUTHOR(S) 

Harvey Shui-Hong Lee 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION 

REPORT NUMBER

U.S. Department of Transportation 

Research and Special Programs Administration DOT-VNTSC-FRA-04-05 John A. Volpe National Transportation Systems Center 

Cambridge, MA 02142-1093 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING 

 AGENCY REPORT NUMBER

U.S. Department of Transportation 

Federal Railroad Administration DOT/FRA/ORD/09-07 Office of Research and Development 

1200 New Jersey Ave., SE 

Washington, D.C. 20590 

11. SUPPLEMENTARY NOTES 

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE 

This document is available to the public through the National Technical Information Service, 

Springfield, Virginia 22161. 

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

13. ABSTRACT (Maximum 200 words)

Two safety issues are raised on the aerodynamic effects of a passing train on its surroundings. First, a high-speed train passing 

other trains on an adjacent track exerts aerodynamic pressure that can affect the structural integrity of window mount and glazing, 

and the stability of the railroad car being passed. Second, as a high-speed train passes train stations immediately adjacent to the 

platform without stopping, people and objects on these station platforms are exposed to strong airflow causing debris and objects 

to be blown about and people to potentially lose their balance. This safety issue also extends to railroad workers on trackside as a 

high-speed train passes. 

The objective of the research was to obtain aerodynamic data on passing trains, and to assess its effects on other trains being

passed, as well as on people in proximity to the passing trains. The study entailed both numerical simulation and experimentation. 

Numerical simulation included both simple single degree-of-freedom dynamics models, and more complex computational fluid 

dynamics and multi-body simulation models. Experimentation involved full-scale testing of a rail car passed by a high-speed 

train on an adjacent track, and measurement of train-induced airflow and forces on cylindrical dummies from a passing train. 

14. SUBJECT TERMS 15. NUMBER OF PAGES

high-speed trains, window mount, window glazing, double-stacked containers, station platform, 257 

aerodynamic interactions, aerodynamic loads, transient loads, double-stacked well car, induced 16. PRICE CODE

airflow, slipstream, passing train, aerodynamic effect, railroad and railway aerodynamics, 

trackside 

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT 

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1 foot (ft) = 30 centimeters (cm) 1 centimeter (cm) = 0.4 inch (in) 

1 yard (yd) = 0.9 meter (m) 1 meter (m) = 3.3 feet (ft) 

1 mile (mi) = 1.6 kilometers (km) 1 meter (m) = 1.1 yards (yd) 

 1 kilometer (km) = 0.6 mile (mi)

AREA (APPROXIMATE) AREA (APPROXIMATE) 

1 square inch (sq in, in2

) = 6.5 square centimeters (cm2) 1 square centimeter (cm2) = 0.16 square inch (sq in, in2) 

1 square foot (sq ft, ft2

) = 0.09 square meter (m2) 1 square meter (m2) = 1.2 square yards (sq yd, yd2) 

1 square yard (sq yd, yd2

) = 0.8 square meter (m2) 1 square kilometer (km2) = 0.4 square mile (sq mi, mi2) 

1 square mile (sq mi, mi2

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) 

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1 ounce (oz) = 28 grams (gm) 1 gram (gm) = 0.036 ounce (oz) 

1 pound (lb) = 0.45 kilogram (kg) 1 kilogram (kg) = 2.2 pounds (lb) 

1 short ton = 2,000 pounds = 0.9 tonne (t) 1 tonne (t) = 1,000 kilograms (kg) 

(lb) = 1.1 short tons

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1 teaspoon (tsp) = 5 milliliters (ml) 1 milliliter (ml) = 0.03 fluid ounce (fl oz) 

1 tablespoon (tbsp) = 15 milliliters (ml) 1 liter (l) = 2.1 pints (pt) 

1 fluid ounce (fl oz) = 30 milliliters (ml) 1 liter (l) = 1.06 quarts (qt) 

1 cup (c) = 0.24 liter (l) 1 liter (l) = 0.26 gallon (gal) 

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 meter (m3) = 36 cubic feet (cu ft, ft3) 

1 cubic yard (cu yd, yd3

) = 0.76 cubic meter (m3) 1 cubic meter (m3) = 1.3 cubic yards (cu yd, yd3)

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11 13
iii

Acknowledgement 

The success of this project was due to numerous organizations and individuals including 

the United States Department of Transportation’s (USDOT) Federal Railroad 

Administration (FRA) and the Volpe National Transportation Systems Center (Volpe), 

the National Railroad Passenger Corporation (Amtrak), and support contractors. These 

support contractors include: 

(1) Parsons Brinckerhoff Quade and Douglas, Inc. (PB), 

(2) Applied Research Associates, Inc. (ARA), 

(3) Transportation Technology Center, Inc. (TTCI), 

(4) GEOCOMP Corporation, 

(5) SYSTRA Consulting, Inc., and 

(6) French National Railways (Société Nationale des Chemins de Fer Français or 

SNCF) 

I want to acknowledge the many people from various organizations that participated in 

this research. 

This work was performed as part of the Railroad Systems Safety Program sponsored by 

the FRA’s Office of Research and Development. I would like to thank the following 

people for their support: 

Claire Orth, Division Chief, Equipment and Operating Practices Research Division, 

Office of Research and Development, FRA. 

Tom Tsai, Program Manager, Equipment and Operating Practices Research Division, 

Office of Research and Development, FRA. 

I would like to thank the following colleagues at the Volpe Center: 

Robert Dorer, Acting Deputy Director of the Office of Safety and Security, for his 

extensive support in this research endeavor. 

James Lamond, Project Manager of the Railroad Systems Division, and manager of 

the aerodynamics program, for his steady support throughout this research effort. 

Kenny William, Mechanical Engineer of the Structures and Dynamics Division, for 

his computer programming expertise in processing the massive quantity of data. 
iv

The following individuals are acknowledged for their participation in this research: 

Samuel Holmes, Principal Engineer at ARA, performed the computational fluid 

dynamics modeling study and generated the aerodynamic forces on double-stack 

well cars from a passing train. 

Martin Schroeder, Senior Engineer at TTCI, performed the rail dynamics modeling 

study on the dynamic response of double-stack well cars from the aerodynamic 

forces of a passing train. 

Robert MacNeill, Project Engineer at ARA, performed the full-scale experimental 

study on the aerodynamic interaction of a double-stack well car with a passing 

train. 

Sam Liao, Senior Professional Associate at PB, provided project management support 

on the study of aerodynamic effects from trains passing station platforms. 

William Kennedy, Vice President at PB, performed the study on train-induced airflow 

on station platforms. 

Martin Hawkes, Project Manager at GEOCOMP Corporation, performed the pitotstatic tube airflow measurements and data processing. 

Christophe Jehannin, Project Manger at SYSTRA Consulting, Inc., and Jean-Michel 

Pissot, Direction de l’Ingénierie at SNCF, conducted a test to measure 

aerodynamic forces on cylindrical dummies from passing trains. 

George Binns and David Warner of Amtrak for their support and cooperation in 

conducting the test along Amtrak’s right-of-way. 

Thanks should also be extended to the individuals of the test crew for their responses on 

their experiences to passing trains. 
v

Table of Contents 

iii

Executive Summary............................................................................ xxv

1 Introduction.................................................................... 1

PART 1 

DIGEST OF RESEARCH 

2 Progress Review............................................................. 5

2.1 Literature Survey and Assessment..............................................

2.2 Rails-with-Trails...........................................................................

2.3 Compendium of Reports..............................................................

2.4 Information Exchange................................................................. 8

3 Train Passing Well Car with Double-Stacked 

Containers...................................................................................... 13

3.1 Mathematical Modeling of Double-Stack Well Car Aerodynamic 

Interaction and Response.................................................. 13

3.1.1 Train/Track Interaction of Double-Stack Well Car......... 14

3.1.2 Stability of Container........................................................ 19

3.2 Full-Scale Test of Aerodynamic Loading on Double-Stack Well 

Car................................................................................................ 19

3.2.1 Pressure Measurement.................................................... 23

3.2.2 Rail Car Response........................................................... 30

3.2.3 Comparison of Test with Numerical Simulation............ 30

5

6

7
vi

4 Effect of Passing Train on Window Mount and 

Glazing.............................................................................. 33

4.1 Glazing Impact Strength.................................................... 33

4.2 Aerodynamic Pressure Impulse on Glazing........................... 34

5 People in Proximity to Passing Train............................. 36

5.1 Effect of Wind on People................................................... 36

5.1.1 Equivalent Wind Effect............................................ 37

5.1.2 Wind Speed Criterion............................................. 38

5.2 Station Survey................................................................ 43

5.3 Safety Measure............................................................... 44

6 Airflow Induced by a Passing Train............................... 52

6.1 Mathematical Modeling of Train-Induced Airflow..................... 53

6.1.1 Acela Trainset........................................................ 53

6.1.2 Amfleet Train......................................................... 55

6.1.3 Comparison of Results............................................. 57

6.2 Full-Scale Test Measurement of Induced Airflow..................... 58

6.2.1 Test of September 1998 in New Jersey and Delaware.... 60

6.2.2 Test of February 2000 in Maryland.............................. 60

6.2.3 Test of July 2000 in Massachusetts and Rhode Island.... 61

6.2.4 Test of September to October 2002 in Massachusetts.... 65

7 Measurement of Force on Object from Passing 

Train.................................................................................. 70

7.1 Test Configuration and Instrumentation................................. 71

7.2 Aerodynamic Loading on a Cylindrical Instrumented Dummy.... 79
vii

Part 2 

Analysis and Evaluation 

8 Numerical Simulation of Rail Car Roll Response to Aerodynamic 

Loading...................................................... 98

8.1 Modeling Pressure Variation of a Passing Train...................... 98

8.2 Single Degree-of-Freedom Carbody Roll Model..................... 104

8.2.1 Equation of Motion................................................ 104

8.2.2 Model Parameter.................................................... 110

8.2.3 Comparison of Simulation with Full-Scale Test............. 114

8.3 Simulation Results with Headwind and on Curved Track........... 122

8.3.1 Train Passing with Headwind.................................... 122

8.3.2 Train Passing on Curved Track................................. 124

9 Measurements of Airflow and Aerodynamic Load from Full-Scale Test of 

Passing Train.......................... 130

9.1 Processing Test Data........................................................ 130

9.1.1 Time History of Aerodynamic Data............................. 131

9.1.2 Airflow Velocity from Pitot-Static Tube........................ 132

9.1.3 Data Filtering......................................................... 133

9.1.4 Force on a Circular Cylinder..................................... 134
viii

9.2 Characterization of Airflow.................................................. 136

9.2.1 Time History Examples............................................ 136

9.2.2 Airflow Strength and Distance................................... 141

9.3 Force on a Body............................................................... 145

9.4 Human Exposure Limit to Train-Induced Airflow Referenced to Wind 

Speed Criterion........................................................ 157

9.4.1 Example Time History of Formulated Wind Speed......... 157

9.4.2 Minimum Distance from Passing Train........................ 162

10 Human Response in Proximity to Passing TTrain............ 170

10.1 Property of Human Body.................................................... 171

10.2 Destabilizing Force to Human Body from Horizontal Acceleration 176

10.3 Modeling Mannequin Stability............................................. 177

10.3.1 Defining Stability Boundary....................................... 178

10.3.2 Relating Airflow to Mannequin Stability....................... 181

10.3.3 Rotational Load Factor for Inertia and Drag................. 182

10.3.4 Stance................................................................. 182

10.4 Single Degree-of-Freedom Mannequin Stability Model............. 184

10.4.1 Equation of Motion................................................. 184

10.4.2 Stability Boundary.................................................. 188

10.5 Mannequin Stability to Train-Induced Airflow......................... 199

10.6 Subjective Reaction to Passing Train................................... 205

10.6.1 Study by Swedish National Rail Administration............ 205

10.6.2 Observation from Test Crew.................................... 206
ix

11 Conclusion....................................................................... 210

11.1 Response of Double-Stack Well Car to Aerodynamic Load....... 210

11.2 Window Integrity from Aerodynamic Load............................. 212

11.3 Aerodynamic Characterization of Passing Train..................... 212

11.4 People on Trackside and Platform....................................... 215

12 Recommendations............................................................ 218

12.1 Aerodynamic Interaction Between Passing Trains.................. 218

12.2 Safety Limit for People from the Aerodynamic Effects of Passing 

Train............................................................................. 219

Appendix A: Nomenclature and Glossary......................... 222

A-1 Nomenclature............................................................ 222

A-2 Glossary.................................................................... 225

Appendix B: Aerodynamic Quantity..................................... 226

B-1 Fluid Property.................................................................. 226

B-2 Quantitative Relation......................................................... 227

B-3 Circular Cylinder............................................................... 228

B-3.1 Curve Fit for Drag Coefficient of a Circular Cylinder.......... 228

B-3.2 Drag of a Circular Cylinder.......................................... 228

B-3.3 Drag of CID.............................................................. 228
x

Appendix C: Characterization of Locomotive and Rail 

Car..................................................................... 234

C-1 Dimension and Dynamic Property........................................ 234

C-2 Roll Response of a Stationary Empty Double-Stack Well Car.... 235

Appendix D: Instrumentation and Measurement............... 238

D-1 Measurement on Double-Stack Well Car.............................. 238

D-1.1 Aerodynamic Pressure............................................... 238

D-1.2 Carbody Roll Response............................................ 238

D-1.3 Data Acquisition and Processing.................................. 238

D-2 Airflow Velocity Measurement............................................. 239

D-2.1 Single Peak Value Airflow Velocity Measurement............ 239

D-2.2 Time History Airflow Velocity Measurement.................... 239

D-2.3 Yaw Misalignment of Pitot-Static Tube........................... 239

D-3 Force Measurement on CID................................................ 240

D-3.1 CID........................................................................ 240

D-3.2 Weather Station........................................................ 240

D-3.3 Data Acquisition and Processing.................................. 240

D-4 Moving Average............................................................... 241

Appendix E: Modeling Computation.................................... 244

E-1 Impulse and Momentum in Shock Impact............................... 244

E-2 Numerical Solution to Differential Equation by State Transition 

Method........................................................................... 245
xi

E-3 Single Degree-of-Freedom Carbody Roll Model..................... 246

E-4 Mannequin Stability Model................................................. 247

E-4.1 Geometric and Inertial Properties................................. 247

E-4.2 Gust Profile............................................................. 247

E-4.3 Statically Unstable Equilibrium Position......................... 248

References............................................................................ 252
xii
xiii

List of Figures 

Figure 1. Acela Express Train..................................................... 1

Figure 2. Computed Pressure Coefficient on Double-Stack Well Car from 

Aerodynamic Interaction with a Passing Acela Express 

Train......................................................................... 16

Figure 3. Double-Stack Well Car and TEL Train on Adjacent Track.... 19

Figure 4. Test Configuration of a Passing Train and a Stationary DoubleStack Well Car.................................................. 21

Figure 5. Locations of Pressure Transducers on Containers of a Well 

Car........................................................................... 22

Figure 6. Pressure Coefficients on Near Side at Bottom Row of Double-Stack 

Well Car.................................................. 24

Figure 7. Pressure Coefficients on Near Side at Middle Row of Double-Stack 

Well Car............................................................ 26

Figure 8. Pressure Coefficients on Far Side at Middle Row of Double-Stack 

Well Car............................................................ 27

Figure 9. Pressure Coefficients on Near Side at Top Row of Double-Stack 

Well Car............................................................ 28

Figure 10. Variation in Pressure Coefficients with Height on Near Side of 

Double-Stack Well Car.................................................. 29

Figure 11. Dimensions and Clearances of Station Platform................. 46

Figure 12. Computed Maximum Airflow Velocities at 0.762 m (2.5 ft) above 

Top of Rail......................................................... 56

Figure 13. Pitot-Static Tube System for Measuring Airflow Velocity and 

Support Frame Arrangement.......................................... 59

Figure 14. Maximum Airflow Velocities from Passing Trains Measured at 

Train Station in Maryland............................................... 61
xiv

Figure 15. Pitot-Static Tubes for Measuring Longitudinal and Lateral Airflow 

Velocities Induced by a Passing Train with Cylindrical 

Instrumented Dummy in the Background........................... 65

Figure 16. Cylindrical Instrumented Dummy for Measuring Force from 

Aerodynamic Interaction with a Passing Train.................... 71

Figure 17. SNCF Circular Cylindrical Instrumented Dummy for Measuring 

Force from Aerodynamic Interaction with a Passing 

Train.............................................................. 73

Figure 18. Coordinate Frames for a CID.......................................... 74

Figure 19. Test Layout on Train Station Platform at Mansfield, Massachusetts 

Showing (a) Top View and (b) Rear View..... 75

Figure 20. Types of Passing Trains Tested...................................... 78

Figure 21. Description of Airflow around a Passing Train.................... 80

Figure 22. Maximum Forces on CIDs at 1.20 m (47.4 in) from Passing Acela 

Express Trains................................................... 82

Figure 23. Maximum Forces on CIDs at 1.20 m (47.4 in) from Passing Amfleet 

Trains with AEM-7 locomotives............................ 83

Figure 24. Maximum Forces on CIDs at 1.20 m (47.4 in) from Passing Amfleet 

Trains with HHP-8 Locomotives........................... 84

Figure 25. Maximum Forces on CIDs at 1.20 m (47.4 in) from Passing Trains 

and Locations Along the Passing Trains where Maximum Forces 

Occurred............................................ 85

Figure 26. Maximum Forces on CIDs at 1.20 m (47.4 in) from Passing Trains 

Categorized by Types of Trains and Flow Field 

Regions..................................................................... 87

Figure 27. Maximum Forces on CIDs at 1.46 m (57.7 in) from Passing Acela 

Express Trains.................................................... 91

Figure 28. Maximum Forces on CIDs at 1.46 m (57.7 in) from Passing Amfleet 

Trains with AEM-7 Locomotives........................... 92

Figure 29. Maximum Forces on CIDs at 1.46 m (57.7 in) from Passing Amfleet 

Trains with HHP-8 Locomotives........................... 93
xv

Figure 30. Maximum Forces on CIDs at 1.46 m (57.7 in) from Passing Trains 

Categorized by Types of Trains Flow Field Regions... 94

Figure 31. Modeling Aerodynamic Pressure Variation by Mathematical 

Functions................................................................... 99

Figure 32. Aerodynamic Interaction Between an Observer Car and a Train 

Passing on an Adjacent Track................................. 100

Figure 33. Modeling Aerodynamic Pressure Pulse Produced by Head 

Perturbation of a Passing Train....................................... 102

Figure 34. Freight Car and Single Degree-of-Freedom Model.............. 105

Figure 35. Moment and Wheel Load of Carbody Roll at Equilibrium.... 107

Figure 36. Single Degree-of-Freedom Mathematical Model for Carbody 

Roll........................................................................... 108

Figure 37. Modeling Airflow Relative to a Passing Train..................... 109

Figure 38. Dimensions of a Double-Stack Well Car........................... 112

Figure 39. Pressure Coefficients from Test Measurement and Modeled from 

Piecewise Mathematical Functions........................... 115

Figure 40. Pressure Coefficients from Test Measurement and Modeled from 

Piecewise Mathematical Functions of Pressure Pulses from the 

Nose and Tail of a Passing Train........................ 116

Figure 41. Time History Roll Response of a Double-Stack Well Car from 

Numerical Simulation and Full-Scale Test......................... 117

Figure 42. Maximum Carbody Roll Angles of a Double-Stack Well Car from 

Numerical Simulation and Full-Scale Test.................. 118

Figure 43. Time Histories of Applied Force and Roll Response of a DoubleStack Well Car.................................................. 120

Figure 44. Time Histories of Applied Moments to a Double-Stack Well 

Car........................................................................... 121

Figure 45. Maximum Roll Angles of a Double-Stack Well Car when Passed by 

a Train with Headwind.................................... 123
xvi

Figure 46. Train Speed and Unbalanced Track Cant......................... 125

Figure 47. Maximum Roll Angles to the Inside and to the Outside of the Curve 

for a Double-Stack Well Car Passed by a Train on Curved 

Track............................................................... 127

Figure 48. Maximum Roll Angles of a Double-Stack Well Car Passed by a 

Train on Tangent and Curved Tracks............................ 128

Figure 49. Time Histories of Airflow Velocities Measured from Pitot-Static 

Tubes for a Passing Acela Express Train.................. 138

Figure 50. Time Histories of Airflow Velocities Measured from Pitot-Static 

Tubes for a Passing Amfleet Train with AEM-7 

Locomotive................................................................. 139

Figure 51. Time Histories of Airflow Velocities Measured from Pitot-Static 

Tubes for a Passing Amfleet Train with HHP-8 

Locomotive................................................................. 140

Figure 52. Maximum Airflow Velocities from Passing Acela Express 

Trains........................................................................ 142

Figure 53. Maximum Airflow Velocities from Passing Amfleet Trains with 

AEM-7 Locomotives..................................................... 143

Figure 54. Maximum Airflow Velocities from Passing Amfleet Trains with 

HHP-8 Locomotives..................................................... 144

Figure 55. Time Histories of Forces on a CID from a Passing Acela Express 

Train.............................................................. 146

Figure 56. Time Histories of Forces on a CID from a Passing Amfleet Train 

with AEM-7 Locomotive......................................... 147

Figure 57. Time Histories of Forces on a CID from a Passing Amfleet Train 

with HHP-8 Locomotive......................................... 148

Figure 58. Time Histories of Single Quadrant Forces Measured on a CID and 

Computed from Airflow Velocity from a Passing Acela Express 

Train............................................................. 150
xvii

Figure 59. Time Histories of Single Quadrant Forces Measured on a CID and 

Computed from Airflow Velocity from a Passing Amfleet Train 

with AEM-7 Locomotive......................................... 151

Figure 60. Time Histories of Single Quadrant Forces Measured on a CID and 

Computed from Airflow Velocity from a Passing Amfleet Train 

with HHP-8 Locomotive......................................... 152

Figure 61. Time Histories of Single Quadrant Forces Measured on a CID and 

Computed with Constant Drag Coefficient from a Passing Acela 

Express Train..................................................... 154

Figure 62. Time Histories of Single Quadrant Forces Measured on a CID and 

Computed with Constant Drag Coefficient from a Passing Amfleet 

Train with AEM-7 Locomotive.............................. 155

Figure 63. Time Histories of Single Quadrant Forces Measured on a CID and 

Computed with Constant Drag Coefficient from a Passing Amfleet 

Train with HHP-8 Locomotive.............................. 156

Figure 64. Time Histories of Single Quadrant Airflows Characterizing 

Turbulence from a Passing Acela Express Train................. 159

Figure 65. Time Histories of Single Quadrant Airflows Characterizing 

Turbulence from a Passing Amfleet Train with AEM-7 

Locomotive................................................................. 160

Figure 66. Time Histories of Single Quadrant Airflows Characterizing 

Turbulence from a Passing Amfleet Train with HHP-8 

Locomotive................................................................. 161

Figure 67. Train-Induced Airflow Velocity Data Measured at 0.97 m (38 in) 

above Top of Rail with Formulated Velocity Curves... 163

Figure 68. Train-Induced Airflow Velocity Data Measured at 1.73 m (68 in) 

above Top of Rail with Formulated Velocity Curves... 164

Figure 69. Interpolated Train-Induced Airflow Velocity Data at 1.35 m (53 in) 

above Top of Rail with Formulated Velocity Curves... 168

Figure 70. Human Body Modeled as Geometric Solids....................... 174

Figure 71. States of Stability for a Mannequin................................... 179

Figure 72. Waveforms for Modeling a Gust Profile............................. 180
xviii

Figure 73. Mathematical Model of a Mannequin................................. 185

Figure 74. Time Histories of Force and Moment on a Mannequin from a 

Square Wave Airflow Velocity Pulse................................. 189

Figure 75. Time Histories of Angular Displacement and Velocity of a 

Mannequin from a Square Wave Airflow Velocity Pulse....... 190

Figure 76. Time Histories of Force and Moment on a Mannequin from a 

Versine Wave Airflow Velocity Pulse................................ 192

Figure 77. Time Histories of Angular Displacement and Velocity of a 

Mannequin from a Versine Wave Airflow Velocity Pulse....... 193

Figure 78. Stability Boundaries as Load Factor Limits for a Mannequin 

Responding to an Airflow Velocity Pulse........................... 194

Figure 79. Stability Boundaries as Airflow Velocity Limits for a Mannequin 

Responding to an Airflow Velocity Pulse........... 195

Figure 80. Synthesized Piecewise Stability Boundary for a Mannequin.. 197

Figure 81. Synthesized Piecewise Stability Boundary for a Mannequin at 

Various Breakout Rotational Load Factors........................ 198

Figure 82. Mannequin Stability Relative to Airflow Velocity Data at 0.97 m 

(38 in) above Top of Rail..................................... 202

Figure 83. Mannequin Stability Relative to Airflow Velocity Data at 1.73 m 

(68 in) above Top of Rail..................................... 203

Figure 84. Mannequin Stability Relative to Interpolated Airflow Velocity Data 

at 1.35 m (53 in) above Top of Rail.......................... 204

Figure 85. Drag Coefficients for a Circular Cylinder with (a) Two Dimensional 

Flow (Schlichting and Gersten 2000) and (b) Different Aspect 

Ratios (Horner 1958).............................. 230

Figure 86. Comparison between Data and Curve Fit of Drag Coefficients for a 

Circular Cylinder................................................... 231
xix

Figure 87. Comparison between Data and Curve Fit of Drag Coefficients for a 

Circular Cylinder over the Critical Flow Regime........... 232

Figure 88. Roll Response of a Stationary Empty Double-Stack Well Car from 

Aerodynamic Interaction with a Passing TEL Train...... 236

Figure 89. Effect of Angular Misalignment of a Pitot-Static Tube on (a) 

Differential Pressure (Ower and Pankhurst 1977) and (b) Airflow 

Measurement (Devenport 2001)............................ 242

Figure 90. Geometric Solids Superimposed over the Profile of a Human 

Body......................................................................... 249

Figure 91 Locations of the Center of Masses for Segments of the Human Body 

(Diffrient, Tilley, and Bardagjy 1974)............... 250
xx
xxi

List of Tables 

Table 1. Organizations Performing Research in Railway 

Aerodynamics............................................................. 10

Table 2. Dynamic Response of Five-Unit Articulated Double-Stack Well Car 

Not Meeting AAR Chapter XI Performance 

Specifications*............................................................ 18

Table 3. Peak-To-Peak Differences in Pressure Coefficients on a Well Car 

Averaged over All Speeds of the Passing Train............ 25

Table 4. Maximum Carbody Roll Response of Double-Stack Well Car from 

a Passing Train.................................................... 30

Table 5. Walking Speeds Against the Wind Computed Based on the Same 

Expenditure of Energy as Walking in Still Air (Penwarden 

1973).................................. ..................... 38

Table 6. Wind Speeds Against a Person Walking on Level Ground and 

Equivalent Slopes for a Person Walking Up a Hill Computed Based 

on the Same Metabolic Heat Requirement (Penwarden 

1973)............................................... ........ 38

Table 7. Effects of Wind in Terms of Beaufort Numbers (Penwarden 

1973)....................................... ................................. 40

Table 8. Wind Effect on People Categorized by Wind Conditions (Hunt, 

Poulton, and Mumford 1976)................................. 42

Table 9. Acceptance Criteria Based on Tests of Subject in Wind Tunnel and 

Pedestrians Exposed to Outdoor Wind Averaged over 3 s 

(Murakami and Deguchi 1981)............................ 43

Table 10. Recommended Distances from Passing Trains in Various 

Countries................................................................... 47

Table 11. Maximum Longitudinal Airflow Velocities and Exposure Times 

from an Acela Express Train Passing a Low-Level 

Platform..................................................................... 54

Table 12. Maximum Longitudinal Airflow Velocities at 0.762 m (2.5 ft) 

above Low-Level Platform Induced by an Acela Express Train 

Passing at 241 km/h (150 mph)...................................... 55
xxii

Table 13. Maximum Longitudinal Airflow Velocities at 0.762 m (2.5 ft) 

above Low-Level Platform Induced by an Amfleet Train with 

AEM-7 Locomotive Passing at 201 km/h 

(125 mph)........................... ....................................... 57

Table 14. Maximum Longitudinal Airflow Velocities from Passing Trains at 

0.762 m (2.5 ft) above Low-Level Platform..................... 58

Table 15. Maximum Longitudinal Airflow Velocities from Passing Amfleet 

Trains at about 1.7 m (5.5 ft) above Top of Rail from September 

1998 Test................................................... 60

Table 16. Maximum Longitudinal Airflow Velocities from Passing Trains 

from July 2000 Test...................................................... 63

Table 17. Changes in Maximum Induced Longitudinal Airflow Velocities 

from Changes in Positions............................................. 64

Table 18. Configurations for Airflow Velocity Measurement at Heights 

Z1=0.866 m (34 in) and Z2=1.628 m (64 in) above Top of 

Rail........................................................................... 67

Table 19. Number of Passing Trains............................................. 68

Table 20. Positions of CIDs and the Number of Passing Trains 

Measured................................................................... 76

Table 21. Normalized Resultant Forces on CID-4 and CID-5 at Position 1 

with Cylindrical Axes at 1.20 m (47.4 in) from Side of Passing 

Trains............................................................ 88

Table 22. Drag Indicators on CIDs for Trains Passing at Their Nominal 

Operational Speeds...................................................... 89

Table 23. Normalized Resultant Forces on CID-4 and CID-5 at Position 2 

with Cylindrical Axes at 1.46 m (57.7 in) from Side of Passing 

Trains............................................................ 90

Table 24. Physical Properties of a Well Car with Double-Stacked 

Containers.................................................................. 113

Table 25. Example Cases in Time History Plots............................... 131
xxiii

Table 26. Positions of Pitot-Static Tube and CID in Example Time History 

Plots............................................................... 132

Table 27. Drag Coefficients for a Two-Dimensional Circular Cylinder and 

Corresponding Airflow Velocity for the CID.................. 135

Table 28. Ranges of Airflow Velocities Induced by Different Trains for all 

Lateral Positions...................................................... 141

Table 29. Maximum Train-Induced Airflow Velocities Derived from 

Different Processes...................................................... 158

Table 30. Constants to the Formulated Velocity Regression Power Curve 

Fitted to Data for the Maximum Longitudinal Airflow Velocity over 

a 3 s Moving Average Window..................... 165

Table 31. Formulated Longitudinal Airflow Velocities from 3 s Moving 

Average Window Corresponding to CID Positions............... 166

Table 32. Minimum Distances from a Passing Train for a Person Exposed to 

Train-Induced Airflow Velocity........................ 169

Table 33. Properties of Nude Human Bodies (Diffrient, Tilley, and Bardagjy 

1974)............................................................ 171

Table 34 Human Body Drag Characterization from Wind Tunnel 

Measurement at a Wind Speed of 8.5 m/s (19 mph) (Penwarden, 

Grigg, and Rayment 1976)........................... 173

Table 35. Properties of the Mannequin for Simulation Based on an Average 

50 Percentile Adult Male Wearing Light Clothing.... 175

Table 36. Equilibrium Distribution of Standing Subjects Facing Forward for 

Rate of Change of Acceleration of 3.048 m/s3 (10 ft/s3) (Hirshfeld 

1932)........................................................... 177

Table 37. Mean and Root-Mean-Square for Waveforms of Unit 

Amplitude................................................................... 181

Table 38. Stance Distances and Dynamic Values of a Mannequin at 

Rotational Breakout...................................................... 184

Table 39. Comparison between Maximum Airflow Velocities from a 3 s 

Moving Average and Uniform Airflow Velocities at Breakout from 

Stability Boundary on a Mathematical Mannequin........ 200
xxiv

Table 40. Six Most Frequently Mentioned Sources of Discomfort from 

Passing Trains Listed in Order of Decreasing Frequency Mentioned 

(Lindberg 1994)............................................. 206

Table 41. Observations from Test Participants on their Experiences in 

Proximity to Passing Trains Listed in Order of Decreasing 

Frequency Mentioned................................................... 207

Table 42. Recommended Minimum Distances for People Exposed to the 

Aerodynamic Effects of a Passing Train....................... 219

Table 43. Empirical Equations for Drag Coefficients.......................... 228

Table 44. Drag on a CID as Function of Flow Velocity....................... 229

Table 45. Dimensions of Rail Cars and Locomotives........................ 234

Table 46. Dimensions and Dynamic Properties One Unit of an Articulated 

Double-Stack Well Car................................... 235

Table 47. Periods and Logarithmic Decrements of Carbody Roll Decay of the 

Double-Stack Well Car after Tail Passage of a Passing 

Train......................................................................... 237

Table 48. Dynamic Properties of the Double-Stack Well Car from Measured 

Roll Response.............................................. 237

Table 49. Properties of a Human Body for an Average Adult Male...... 247
xxv

Executive Summary 

As train speed increases, the train’s aerodynamic force on people and objects becomes 

stronger. This force can have an adverse effect on adjacent trains and equipment, and 

might jeopardize the safety of people in proximity to the passing train. Consequently, 

with the inception of high-speed train operation in the United States, a safety evaluation 

was undertaken by the Federal Railroad Administration (FRA) of the United States 

Department of Transportation to determine the effects that the aerodynamic force 

generated by a passing high-speed train have on other trains on an adjacent track, and on 

people in proximity to a passing train. 

Two safety issues are raised on the aerodynamic effects of a passing train on its 

surroundings. First, a high-speed train passing other trains on an adjacent track exerts 

aerodynamic pressure that can affect the structural integrity of window mount and 

glazing, and the stability of the railroad car being passed. Second, as a high-speed train 

passes train stations immediately adjacent to the platform without stopping, people and 

objects on these station platforms are exposed to strong airflow causing debris and 

objects to be blown and people to lose their balance. This safety issue also extends to 

railroad workers on trackside as a high-speed train passes. 

The objective of the research was to obtain aerodynamic data on passing trains, and to 

assess its effects on other trains being passed, as well as on people in proximity to the 

passing trains. The study entailed both numerical simulation and experimentation. 

Numerical simulation included both simple single degree-of-freedom dynamics models, 

and more complex computational fluid dynamics and multi-body simulation models. 

Experimentation involved full-scale testing of a rail car passed by a high-speed train on 

an adjacent track, and measurement of train-induced airflow and forces on cylindrical 

dummies from a passing train. 

Part 1: Digest of Research 

The digest of research is a review on the work that has been completed with the details 

having been described in a number of reports. This includes studies sponsored by FRA 

since 1995 on the aerodynamic effects from passing trains. 
xxvi

Train Passing Well Car with Double-Stacked Containers

Numerical simulation was performed to compute the response of a double-stack well car 

from aerodynamic interaction with a passing high-speed passenger train. The results 

were examined for the potential of derailment and the stability of the containers. The 

five-unit articulated double-stack well car with empty containers produced strong 

dynamic response leading to wheel unloading or high lateral wheel force. The lateral to 

vertical wheel force ratio was much lower reducing the potential of derailment when all 

the containers were loaded. Results from this study found that the containers should not 

become dislodged. 

A full-scale test was performed to measure the aerodynamic pressure and roll response on 

a stationary double-stack well car as a high-speed turbine-electric locomotive pulling two 

passenger cars passes by on an adjacent track. The comparison between computed and 

measured pressures is generally very good. None of the roll angles were very large, with 

the maximum zero-to-peak roll angle of 0.312°, producing a maximum change in lateral 

displacement of 30.1 mm (1.184 in) at the top of the container, when the train passed by 

at 177 km/h (110 mph). 

Passing Train on Window Mount and Glazing

The potential for damage to the window was considered by mathematical modeling of an 

Acela Express train passing a bi-level Kawasaki passenger car. An Acela Express train 

traveling at 241 km/h (150 mph) with a headwind of 80 km/h (50 mph) passing a 

Kawasaki car traveling in the opposite direction at 129 km/h (80 mph), does not appear to 

have sufficient force to dislodge the window glazing on the passenger car. Sufficient 

data does not exist to arrive at a conclusion when the Acela Express train overtakes the 

Kawasaki car. 

Airflow Induced by a Passing Train

An Acela Express train and an Amfleet train were modeled to obtain the induced airflow 

velocity as the train passes a station platform. A numerical simulation of an Acela 

Express train traveling at 241 km/h (150 mph) and an Amfleet train at 201 km/h (125 

mph) induced about the same maximum longitudinal airflow velocities. The Amfleet 

train produced the strongest airflow from the boundary layer, while the strongest airflow 

for the Acela Express train came from the wake. The induced airflow from the Acela 

Express train was lower on a high-level than on a low-level platform. 

A full-scale test was conducted using pitot-static tubes to measure airflow velocities 

induced from a passing Acela Express train, and Amfleet train. Airflow measured from 

the Acela Express train was higher than from the Amfleet train when they passed by at 

their operating speeds. The airflow velocity decreases with increased lateral distance 

from the train, or with increased height from the track. The maximum value of airflow 

for the Acela Express train occurs usually at the tail of the train, whereas the maximum 
xxvii

value of airflow for the Amfleet train is usually at the head of the train. The main 

features between test data and results of numerical simulation are generally in good 

agreement. 

Test Measurement of Force on Object from Passing Train

A full-scale test was conducted on a low-level train station platform in Mansfield, 

Massachusetts to measure the force on two circular cylindrical instrumented dummies 

(CIDs) from the aerodynamic interaction with a passing train. When the mean force on 

the CIDs is normalized with respect to the square of the train speed, the Acela Express 

train produced the lowest force while the Amfleet/AEM-7 train produced the highest 

force. The Amfleet/AEM-7 train produced an aerodynamic force on the CIDs that is a 

factor of 2.4 higher than the Acela Express train, and the Amfleet/HHP-8 train is a factor 

of 1.8 higher than the Acela Express train. When the trains are scaled to the train’s 

maximum nominal operating speed, the Acela Express train passing at a speed of 

241 km/h (150 mph) produced a lower force on the CIDs than the passing Amfleet train 

at the lower speed of 201 km/h (125 mph). 

Part 2: Analysis and Evaluation 

Studies were conducted by the Volpe National Transportation Systems Center to provide 

a more comprehensive analysis and evaluation of the results presented in the digest of 

research. 

Numerical Simulation of Rail Car Roll Response to Aerodynamic Loading

A single degree-of-freedom mathematical carbody roll model was created to simulate the 

dynamic roll response of a rail car from transient aerodynamic force input. This study 

extended the previous research results by including a broader range of train passing 

conditions. The responses of carbody roll from the effects of altitude, ambient wind, 

passing train speed and closing speed, and unbalanced speed on curved track were 

studied. A comparison of the carbody roll angle for a stationary double-stack well car 

from aerodynamic force input between simulation and test data is in very good 

agreement. 

Measurements of Airflow and Aerodynamic Load from Full-Scale Test of Passing Train

The airflow measured from pitot-static tubes and forces measured on CIDs from the test 

at Mansfield, Massachusetts were further processed and analyzed in detail. Based on this 

data, the aerodynamic effects on people are assessed from the wind speed criteria of 

Murakami and Deguchi with an indicated minimum distance from a passing train as 

follows: 
xxviii

Recommended Minimum Distances for People Exposed to the Aerodynamic 

Effects of a Passing Train 

Human Response in Proximity to Passing Train

A single degree-of-freedom mathematical model of a mannequin was created as an 

instrument to map the stability boundary for a simple standing object that can be applied 

to evaluate the aerodynamic data produced from a passing train. A method to assess the 

strength of the airflow data is to relate it to the stability boundaries of the mathematical 

mannequin. The stability boundaries are interpreted in terms of the Beaufort scale where 

the effects on people can be assessed. A comparison is made between the effects on 

people based on the dynamic response of a mathematical mannequin, with the wind 

speed criteria of Murakami and Deguchi based on wind speed averaged over 3 s. Both 

methods predict similar effects on people. 

Minimum Lateral Distance* 

 Distance from Distance from Nominal 

Centerline of Outer Edge of Distance from 

Nearest Track Nearest Rail Side of Train 

Member of Public 3.12 m 2.33 m 1.6 m 

on (123 in) (92 in) (63 in) 

Low-Level Passenger 

Platform 

Worker on 2.72 m 1.93 m 1.2 m 

Trackside at Low- (107 in) (76 in) (47 in) 

Level Platform Height 

*Amfleet/AEM-7 and Amfleet/HHP-8 trains passing at a speed no greater than 201 km/h (125 mph); 

Acela Express train passing at a speed no greater than 241 km/h (150 mph).
1

1. Introduction 

A moving train causes a disturbance to the surrounding air whose effects are insignificant 

at low train speeds. As train speed increases, the train’s aerodynamic force on people 

and objects becomes stronger, and its effect on people and objects becomes more 

significant. This force can have an adverse effect on adjacent trains and equipment, and 

might jeopardize the safety of people in proximity to the passing train. Consequently, 

with the inception of high-speed train operation in the United States, a safety evaluation 

was undertaken by the Federal Railroad Administration (FRA) to determine the effects 

that the aerodynamic force generated by a passing high-speed train has on other trains on 

an adjacent track, and on people in proximity to a passing train. 

In the United States, high-speed 

passenger trains such as Amtrak’s 

Acela Express trains have been 

operating in the Northeast Corridor. 

Figure 1 shows an Acela Express 

train passing a train station. Two 

safety issues have been raised on the 

aerodynamic effects of a passing train 

on its surroundings. First, a highspeed train passing other trains on an 

adjacent track will exert aerodynamic 

pressures on the other trains, with the 

pressures being strong at high speeds 

and close track center spacing (the Figure 1. Acela Express Train 

track center distance along parts of 

the Northeast Corridor is at 3.962 m 

(13 ft) center distance but as close as 3.658 m (12 ft) at best fit areas). The aerodynamic 

interactions of a high-speed train passing other trains can have effects on the structures of 

the trains being passed. The structural integrity of window mounts and glazings, and the 

stability of the railroad cars being passed may be affected. Second, as a high-speed train 

passes some train stations immediately adjacent to the platform without stopping, people 

and objects on these station platforms can be exposed to strong airflow causing debris 

and objects to be blown and people to lose their balance. This safety issue also extends 

to railroad workers on the trackside as a high-speed train passes. 

These two issues, the aerodynamic interaction between passing trains, and the 

aerodynamic effects of trains passing people on station platforms, have been the focus of 

research. The research was to obtain aerodynamic data on passing trains, and to assess 

its effects on other trains being passed, and on people in proximity to the passing trains. 

This entailed both numerical simulation and experimentation. Numerical simulation 

included both simple single degree-of-freedom dynamics models, and more complex 

computational fluid dynamics (CFD) and multi-body simulation models. 
2

Experimentation involved full-scale testing of a rail car passed by a high-speed train on 

an adjacent track, and measurement of train-induced airflow and forces on cylindrical 

dummies from a passing train. 

This report discusses the research performed by the Volpe National Transportation 

Systems Center (Volpe) and by organizations contracted for this research, to support the 

FRA’s Railroad Systems Safety program. The scope of this report includes the studies 

performed since the FRA initiated this research in 1995 to address safety issues related to 

the aerodynamic effects of high-speed trains, particularly with the commencement of 

high-speed Acela Express train service in the Northeast Corridor. 

This report is organized in two parts. Part 1 provides a digest of research that reviews the 

work that has been completed, the details having been described in a number of reports. 

The research review of Part 1 brings together all the studies sponsored by FRA since 

1995 on the aerodynamic effects from passing trains. A progress review is presented that 

includes a description of organizations outside of the United States that are engaged in 

similar research, and a description of reports produced for FRA. The remainder of Part 1 

is a review of the work that has been completed under the FRA program with a summary 

of results. Part 2 provides an analysis and evaluation with detailed studies that extend the 

results found in Part 1. In addition to contractor studies, Volpe also conducted studies, 

which are reported in Part 2. Volpe studies were conducted to provide a more 

comprehensive analysis of the results in Part 1, and to better understand the aerodynamic 

interactions, and its effects of a passing train on other trains, and on people. An 

evaluation is provided of the research along with conclusions and recommendations. 
Part 1: Digest of Research 

3

PART 1 

DIGEST OF RESEARCH 
Part 1: Digest of Research 

4
Part 1: Digest of Research 

5

2. Progress Review 

This progress review covers work that was performed in support of the FRA’s research 

that began in 1995 on the aerodynamic effects of high-speed trains as it impacts safety. 

This research was related to the approaching inception of high-speed passenger train 

operation in the Northeast Corridor of the United States. 

Some of the problems that were addressed in this research are: 

• Derailment potential of a double-stack well car and the stability of containers when 

passed by a high-speed train. 

• Strength of window mount and glazing integrity on a passenger car when passed by 

a high-speed train. 

• Safety of people on station platforms when passed by a high-speed train. 

Following the assessment based on the literature review, organizations were contracted 

by Volpe to perform mathematical modeling and experimentation to acquire data on the 

aerodynamic effects of conventional trains, and on high-speed Acela Express trains, 

which that were to be operational in the Northeast Corridor. 

2.1. Literature Survey and Assessment 

The program on the aerodynamic effects of passing trains began with a literature study by 

Volpe (Lee 1999). The study identified relevant sources of information and data 

available to assess the aerodynamic effects of a train traveling at high speeds passing 

another train on an adjacent track, and a train passing a station at high speeds and its 

effects on people on the station platform. 

The following conclusions were drawn from this study: 

The aerodynamic forces exerted on the window glazing during train passage were 

determined. For trains passing each other at speeds of 150 mph [241 km/h], it is 

unlikely that these forces will cause the glazing to crack. An assessment of the 

strength of the glazing attachment will depend on specific, detailed design of the 

windows. 

The aerodynamic forces experienced by a person from pressures and induced 

airflow of a passing train were determined. For persons situated within 6.6 ft [2 m] 

from the side of a train passing a station platform at a speed of 150 mph 

[241 km/h], the effects of pressure and induced airflow are high enough to be a 

safety issue. The distance of 6.6 ft [2 m] does not represent a safety limit, but it 
Part 1: Digest of Research 

6

does indicate that when people are situated within that distance to a passing train, 

this can be a safety issue. 

When a train is passing a station platform at high speeds, the wake effect of the 

train with its turbulent fluctuations and buffeting in the air, along with any dust and 

debris that is blown or propelled, is a serious issue regarding the comfort and safety 

of people on the platform. (Lee 1999) 

From these conclusions, Volpe recommendations included: 

Identify the equipment and fixtures on trains, and on structures along the wayside 

that are a safety issue when exposed to the aerodynamic effects of pressure and 

airflow generated from a passing train. 

Identify rail cars that are not designed for high-speed operation, particularly cars 

with large windows, or loosely fitted windows such as those that are designed to be 

opened. Obtain design information and data on the windows and glazing for these 

cars to perform a structural integrity assessment on the window glazing to 

determine if cracking or dislodgement will occur from the aerodynamic pressure 

acting on the glazing, also factoring in the effects of material fatigue. The 

assessment should consider the different types of glazing and glazing systems 

(frames and gaskets) used throughout the industry. 

Identify conditions that will impact the magnitude of the data in this study, such as 

natural wind components, and structures along the track, such as the presence of 

steep embankments, overpasses, tunnels, and assess their effects on the results. 

Confirm the boundaries on passing train speed and distance from the train in terms 

of human comfort tolerance levels as they impact the safety of people on station 

platforms. A realistic limiting boundary should include the effects on people when 

they are exposed to the combined actions of pressure, wind, noise, and blown 

debris, particularly from the turbulent actions of the wake produced by the passing 

train. (Lee 1999) 

2.2. Rails-with-Trails 

Increasing development has occurred of pedestrian pathways constructed on or adjacent 

to active railroad right-of-way referred to as rails-with-trails (RWT). As RWTs are 

planned or situated adjacent to high-speed rail lines, the aerodynamic effects from a 

passing high-speed train can be a safety issue. The research results on the aerodynamic 

effects from passing trains have been applied to address the safety concern of RWT 

development (Birk et al 2002; Birk 2003). 

Certain considerations that apply to RWT may not be included to a station platform. 

Different requirements may be recognized in establishing a safe distance between the 
Part 1: Digest of Research 

7

track and people on a station platform, and a setback distance (distance measured from 

centerline of nearest track to edge of paved trail) between the track and a trail. People in 

RWT can include strollers, people pushing baby carriages, bicyclists, etc. Therefore, 

different expectations other than safety are considered by people using RWT, which 

includes comfort and other quality of life factors (noise, startling effects, etc.). 

2.3. Compendium of Reports 

As part of the research effort, Volpe conducted an assessment based on information 

obtained from a literature survey, and organizations were contracted by Volpe to study 

specific facets of the passing train problem. These studies involved mathematical 

modeling, experimentation, and performing field surveys. The results of this research 

activity are documented in reports that will be described briefly. 

Reference: Liao et al 1999

This study examines the aerodynamic effects that high-speed trains can be expected 

to have on the safety and comfort of people in and around the Northeast Corridor 

stations, focusing on the anticipated induced airflow effects on station facilities in 

the Corridor. This included: 

• Numerical modeling of aerodynamic effects from passing trains using the 

FLUENTTM CFD program. 

• Testing to measure the airflow induced by passing trains. 

• Visual field survey of selected train stations to obtain information for assessing 

the impact of Acela Express trains passing the stations at high speeds. 

Reference: Lee 1999

This study was to assess the potential hazards created from the aerodynamic effects 

of passing high-speed trains at speeds of 241 km/h (150 mph). It specifically 

addresses the hazards to window glazing on passenger trains and to people on 

station platforms. A literature review was conducted, and the results of that review 

served as a base for the studies to follow. 

Reference: Holmes, Schroeder, and Toma 2000; Holmes and Schroeder 2002

This study examines the potential safety hazards to existing rail traffic operating in 

the Northeast Corridor from aerodynamic loads generated by the Acela Express 

high-speed passenger train. It specifically addresses the aerodynamic interaction of 

a high-speed Acela Express passenger train passing a double-stack well car on an 

adjacent track. Results were obtained using the AcusolveTM CFD program, and the 

train dynamics simulation program NUCARSTM. Three scenarios were considered: 
Part 1: Digest of Research 

8

• Derailment of double-stack well car when passed by an Acela Express train. 

• Breaking loose or dislodgement of shipping containers from the double-stack 

well car when passed by an Acela Express train. 

• Breaking or blow-out of windows in a passenger train when passed by an Acela 

Express train. 

Reference: MacNeill, Holmes, and Lee 2002

A full-scale test was performed to measure the aerodynamic pressure and roll angle 

on a well car with double-stacked containers as a high-speed passenger train passes 

by on an adjacent track. 

Reference: Tsai, Lamond, and Lee 2003

A review of studies conducted by the FRA and the Volpe Center on the 

aerodynamic effects of trains passing double-stack well cars and station platforms. 

Initial results are presented on train-induced airflow velocity and forces on 

cylindrical dummies from trains passing the station platform. 

2.4. Information Exchange 

Many countries outside of the United States have been conducting research on the 

aerodynamic effects of passing high-speed trains, including Japan, France, and other 

European countries. 

In Japan, the Railway Technical Research Institute (RTRI) (1998) conducts railway 

research with aerodynamics being a topic of study as the need arises. The RTRI's LargeScale Low-Noise Wind tunnel for studying railway aerodynamics was opened in June of 

1996 at Maihara-cho in Shiga prefecture. A large belt is used in the wind tunnel to 

simulate the airflow between the train model and the ground. 

In Europe, a research program was formed in January of 1996 called Transient 

Aerodynamics for Railway System Optimisation (TRANSAERO) to study the problems 

of transient aerodynamics in railway operations (Gregoire, Eckl, and Malfattti n.d.). This 

program is a partnership of various institutions, and of three railways (originally together 

with BR Research) from France, Germany, and Italy: Société Nationale des Chemins de 

Fer Français (SNCF), Deutsche Bahn A.G. (DB AG), and Ferrovie dello Stato 

 (FS) respectively (Table 1). Some of the problems studied include effects of side-wind 

gusts on high-speed trains, forces generated from passing of train nose, and generation of 

pressure waves from train tunnel entry. This was a 3 year program that ended in May of 

1999. 
Part 1: Digest of Research 

9

Complementing the earlier research from TRANSAERO is a European research project 

called Railway Aerodynamics of Passing Interactions with Dynamic Effects (RAPIDE). 

This is a consortium organized as a collaborative research effort by European railway and 

industrial partners to investigate transient aerodynamic phenomena associated with highspeed trains (RAPIDE 2001). The consortium consists of: AEA Technology Rail, DB 

AG, SNCF, Bombardier Transportation, FS, Motor Industries Research Association 

(MIRA), and RUAG Aerospace (Table 1). In this project, it specifically addressed the 

periodic and oscillatory airflow from the wake of a passing train, and its effects on people 

and objects on the wayside and on the dynamic and structural behavior of trains. 
Part 1: Digest of Research 

10

Table 1. Organizations Performing Research in Railway Aerodynamics

Country

Japan 

Great Britain 

Germany 

France 

Sweden 

 Organization Resource

Railway Technical Research Institute 

(RTRI)

Railway research center established in 

1986 (includes former Railway Technical 

Research Institute and Railway Labor 

Science Institute) to: 

• develop basic technology and research 

applications 

• promote technology transfer to Japan 

Railways (JR) companies 

• promote the Maglev (magnetic 

levitation) system 

• study safety measures 

Capabilities include Large-Scale LowNoise Wind tunnel. 

AEA Technology Rail

(Formerly as BR Research) Commercial 

company that performs research, testing, 

and consultant service for railway 

companies. 

Capabilities include full-scale site 

testing, on-site wind tunnel testing, 

reduced scale tests on moving model rig 

(MMR), CFD modeling, and subjective 

pressure comfort tests in transient 

pressure chamber facility. 

Deutsche Bahn A.G. (DB AG: German 

Rail)

German Rail Transport company. 

Research performed by aerodynamics 

and air conditioning department TZF 

102. 

Société Nationale des Chemins de Fer 

Français (SNCF: French National 

Railways)

National Rail Transport company. 

Capabilities include full-scale site 

testing, Laser Doppler velocimetry, CFD 

software (STAR-CD, START, TG-FLO)

Bombardier Transportation

Railway industry company, acquired 

Adtranz (ABB Daimler-Benz 

Transportation) in 2001, that does 

research, development, design, and 

manufacturing. 

Research performed by NEG2 

department. 

Continue 
Part 1: Digest of Research 

11

Table 1: Organizations Performing Research in Railway Aerodynamics

(Continued) 

Country Organization Resource

Italy Trenitalia (FS: Italian Railways)

(Formerly Ferrovie dello Stato S.p.A.) 

Italian National Railway company 

Capabilities include surveys of human 

response, full-scale testing, and model 

simulation. 

United Kingdom Motor Industries Research Association 

(MIRA)

Provides engineering development and 

research services to automotive industry. 

Capabilities include full-scale wind 

tunnel, model wind tunnel (up to 40% 

scale) with moving ground plane, 

climatic wind tunnel, fluids engineering 

center, CFD software (EXA Power 

Flow, Star CD, Fluent, ICEM CFD, 

Altair Hypermesh, EnSight, Flowmaster, 

I DEAS). 

Switzerland RUAG Aerospace

(Formerly as SF Emmen) Aerospace 

company that is part of RUAG that does 

development, manufacturing, assembly, 

maintenance and upgrade of aircraft, 

helicopter, drones, missile, C31, and air 

defense systems. 

Performs research in experimental and 

theoretical aerodynamics by the 

Aerodynamics and Flight Mechanics 

Department. 

Capabilities include three wind tunnels, 

moving belt facility, CFD, ICEMCFD 

software for mesh generation, Cray 

computers at Swiss Federal Institute of 

Technology (EPFL). 
Part 1: Digest of Research 

12
Part 1: Digest of Research 

13

3. Train Passing Well Car with Double-Stacked Containers 

An operational hazard that the railroads have known about is the stability of certain 

railroad cars when exposed to an unbalanced side force due to high wind. For this 

reason, railroads impose operational restrictions during high wind conditions.1 In 

addition to wind, railroad cars are also exposed to unbalanced side forces from 

aerodynamic pressure produced when being passed by another train on an adjacent track. 

An interest exists in the aerodynamic interaction of a passenger train traveling at a high 

speed passing another train on adjacent track, especially when high speed passenger train 

service operates at speeds of 241 km/h (150 mph) in mixed traffic with freight trains. 

Well cars with empty double-stack containers are of particular interest when passed by a 

high-speed train, because the resultant side force on the containers can be significant due 

to its great height and large vertical surface area. This aerodynamic side force applied to 

the light carbody, in addition to any wind that might be present, can lead to the possibility 

of containers dislodging and falling over, or to an adverse dynamic response of the 

double-stack well car with a risk of derailment. 

The aerodynamic interaction between passing trains and the dynamic train/track response 

of the train from the transient aerodynamic force input was the subject of study in the 

European RAPIDE project. The aerodynamic load on the train did not cause significant 

track force, and the force was found to be within the same range as input from track 

irregularity (RAPIDE 2001). It was found that the high-speed Inter-City Express 2 

 (ICE2) train traveling at 350 km/h (217 mph) passing another ICE2 train and a slower 

train remained within a safe limit from derailment (Minnis and Denti 2001). 

A study was conducted to determine the response of a double-stack well car from 

aerodynamic interaction with a passing high-speed passenger train. Numerical 

simulation was performed to compute the response of a double-stack well car, and the 

results were examined for the potential of derailment and the stability of the containers 

(Holmes, Schroeder, and Toma 2000; Holmes and Schroeder 2002). A full-scale test was 

performed to measure the aerodynamic loading on a stationary double-stack well car as a 

train passes on an adjacent track, and the test data was compared with modeling results 

(MacNeill, Lynch, and Schroeder 2001; MacNeill, Holmes, and Lee 2002). 

3.1. Mathematical Modeling of Double-Stack Well Car Aerodynamic Interaction 

and Response 

Computer models were created in this study to simulate a high-speed passenger train 

passing a freight train with double-stack well cars. The approach was to first compute 

the aerodynamic pressures on a double-stack well car as the two trains pass each other 

 

1

Steven E. Forsberg (BNSF Railway). Letter to the author, November 20, 2000. 
Part 1: Digest of Research 

14

using the CFD program called AcusolveTM for solving incompressible flow problems. 

The pressure is integrated over the surface of the double-stack well car to obtain the force 

and moment. These aerodynamic loads are then used as applied force and moment inputs 

to the rail car multibody dynamic simulation program NUCARSTM to obtain its dynamic 

response. In NUCARSTM where the double-stack well cars are modeled, the 

aerodynamic loads are applied to each double-stack well car sequentially to simulate the 

effects of being passed by another train. Fifteen cases were evaluated with varying train 

consist types, speeds, and directions, as well as ambient wind speeds and directions. 

Some of these were worst-case scenarios that may not necessarily represent normal 

railroad operating conditions. 

Two trains were modeled: an Acela Express passenger train, and a freight train with well 

cars carrying double-stacked containers (Table 45 and Table 46 of the Appendix). The 

model of the freight train is a five-unit articulated well car where each connected unit 

shares the same two-axle truck. In contrast to freight cars connected by independent 

couplers that transmit principally a longitudinal force between cars, in the articulated 

well car, the units with shared trucks are joined to transmit forces in longitudinal, lateral, 

and vertical directions. Consequently, the units in the articulated well car are 

dynamically coupled to a greater extent than independently coupled freight cars, creating 

a potential for strong dynamic interaction between the units. At the nonarticulated ends 

of the unit (the end trucks on the first and fifth unit), the trucks are not shared, so that 

both axles of the truck are supporting the same unit. This is significant because each axle 

on those non-shared trucks is more lightly loaded than those on the shared trucks. 

In modeling the two trains passing each other, only the pressures generated from the 

head-end segment or the tail-end segment of the Acela Express train are applied to the 

double-stack well cars to simulate the passage of the Acela Express train. Therefore, 

when the Acela Express train meets a double-stack well car, it is modeled with the Acela 

Express nose passing, but without the passage of the tail end of the Acela Express. In an 

analogous fashion, to simulate the passage of the tail end of the Acela Express train, the 

passage of the head end of the Acela Express train is not included. Only two cases were 

simulated with the passage of the tail end of the Acela Express train. 

The dynamic response of the double-stack well car is influenced by the strength and 

duration of the pressure pulse from the passing train. Factors that affect the strength of 

the pressure pulse from the passing train include: train speed, train cross-sectional area, 

lateral clearance between trains, ground clearance, nose geometry, and environmental 

conditions such as wind and other nearby structures. The duration of the pressure pulse 

is governed by the closing speed of the two trains, which is determined by the speed of 

each train, and whether the trains are passing each other in opposite directions, or 

whether one train is overtaking the other train. 

3.1.1. Train/Track Interaction of Double-Stack Well Car 
Part 1: Digest of Research 

15

The two passing trains were modeled with a track center distance of 3.7 m (12 ft). The 

simulation included variations in the speed and direction of each train, and the speed and 

direction of the wind. A lateral side force is produced on the double-stack well car 

generated by the aerodynamic pressures of the passing Acela Express train, most 

significantly by the strong pressure pulse at the nose. This causes an initial push on the 

double-stack well car away from the Acela Express train and is followed immediately by 

a pulling force. This results in a roll and yaw moment exerted on each double-stack well 

car, as the pressure pulse from the passing Acela Express train travels from one end of 

the container freight train to the other end. 

Pressure coefficient from CFD model simulation was computed for the case where an 

Acela Express train traveling at 241 km/h (150 mph) passes a stationary double-stack 

well car. The pressure was computed at the center of the stationary double-stack well 

car, at 1.96 m (77.2 in) from the top of the rail, and at a nominal distance of 0.79 m 

(31.1 in) between the side of the double-stack well car and the side of the Acela Express 

train. Figure 2 is a plot of the computed pressure coefficients on the double-stack well 

car, with the maximum to minimum peaks in pressure coefficients from 0.34 to -0.36, for 

a maximum peak-to-peak pressure coefficient of ΔCp = -0.70. 

Simulations were performed for three aerodynamic loading conditions on the doublestack well car from a passing train including maximum peak-to-peak difference in lateral 

force, maximum lateral impulse, and synchronized resonance loading. The speeds of the 

two passing trains and ambient wind speed were selected to represent some worst-case 

scenarios. Maximum peak-to-peak difference in aerodynamic force was created when 

the Acela Express train traveling at the highest speed, and with the greatest headwind, 

passes the double-stack well car in the opposite direction. This results in a pressure pulse 

of very short duration exerted on the double-stack well car where the dynamic response is 

minimal because the short duration of the aerodynamic load is out of its resonance 

frequency range. When the Acela Express train passes the double-stack well car in the 

same direction, this leads to either an aerodynamic loading on the well car that creates 

maximum aerodynamic impulse (maximum product of force and duration), or a load 

duration that synchronizes with the articulated car resonance mode. These two loading 

conditions are the ones where the double-stack well car dynamic response exceeds the 

derailment criteria as defined in the Association of American Railroads (AAR) 

performance specifications for wheel unloading and wheel/rail lateral to vertical force 

ratio (L/V). 
Part 1: Digest of Research 

16

Pressure Coefficient on Double-Stack Well Car from Aerodynamic Interaction with

Head Perturbation of Acela Express Train Passing at 241 km/h (150 mph)

Computed Pressure Coefficient on Double-Stack Well Car at

1.96 m (77.2 in) above Top of Rail and 2.375 m (93.5 in) from

Longitudinal Centerline of Passing Acela Express Train

Source: Applied Research Associates and

Transportation Technology Center

Figure 2. Computed Pressure Coefficient on Double-Stack Well Car from Aerodynamic Interaction 

with a Passing Acela Express Train 
Part 1: Digest of Research 

17

The five-unit articulated double-stack well car with empty containers produced the 

strongest response when passed by an Acela Express train traveling in the same direction. 

The lateral aerodynamic loading applied to the double-stack well car did not produce 

significant carbody roll, but it did produce strong dynamic response leading to wheel 

unloading or high lateral wheel force. In maximum lateral impulse interaction, the lateral 

load can produce significant wheel unloading on the empty double-stack well car at the 

end unit. During interaction with synchronized resonance loading, the lateral 

aerodynamic loading applied to the double-stack well car produced strong dynamic 

response in the form of lateral displacement to the wheels. This interaction results in the 

wheel flanging with high L/V, or large wheel unloading or wheel lift on the wheel 

opposite the flanging wheel. Five cases are shown with a variety of loading conditions in 

Table 2 where the five-unit articulated double-stack well car produced either large or 

total wheel unloading, or with high L/V, initiated by the passing of the Acela Express 

train. The worst response for the articulated double-stack well car occurs for the 

nonshared trucks on the first and last units where each axle on those trucks is more 

lightly loaded than those on the shared trucks. When the Acela Express train passes the 

articulated double-stack well car with both trains moving in the same direction, the 

double-stack well car was more likely to be in the frequency range of either the roll or 

yaw carbody vibration modes, or the lateral resonance modes of the articulated doublestack well car. This operating condition produces the strongest dynamic response to the 

articulated double-stack well car. 

For the cases studied, the greatest potential for derailment on the five-unit articulated 

double-stack well car was when all the containers are empty, and with the presence of a 

strong headwind on the Acela Express train or a strong crosswind. The worst response 

occurred on the non-shared trucks of the first and last cars where each axle on those 

trucks is more lightly loaded than those on the shared trucks. The conditions improved in 

a partially loaded configuration, where only the containers at the end units are loaded. 

With all the containers loaded, vertical wheel load increased and the wheel/rail L/V was 

much lower, which met performance specification. The only exception was for case 9 

(Table 2) when the Acela Express train passed in the opposite direction to the loaded 

double-stack well car with a crosswind, that significant wheel unloading occurred. 
Part 1: Digest of Research 

18

Table 2. Dynamic Response of Five-Unit Articulated Double-Stack Well Car Not Meeting AAR 

Chapter XI Performance Specifications*

Case 

Train Velocity Wind Velocity*** 

Acela 

Express Train 

Double-Stack 

Well Car 

Ux

(Head or Tail 

Winds on 

Passing 

Train) 

Uy

(Crosswind) Response Failing Performance 

Specification** 

Maximum Lateral Impulse

8 241 km/h 

(150 mph) 

80 km/h 

(50 mph) 

-80 km/h 

(-50 mph) 

0 Coincident Pass with 

Headwind 

• low vertical wheel load (E) 

Opposing Pass with Crosswind 

9 241 km/h 

(150 mph) 

-80 km/h 

(-50 mph) 

0 -80 km/h 

(-50 mph) 

• wheel lift (E),(EL) 

• low vertical wheel load (L) 

• high L/V (E), (EL) 

Synchronized Phased Loading

12 241 km/h 

(150 mph) 

48 km/h 

(30 mph) 

-80 km/h 

(-50 mph) 

0 Coincident Pass with 

Headwind 

• wheel lift (E) 

• high L/V (E) 

Coincident Pass with 

14 241 km/h 

(150 mph) 

80 km/h 

(50 mph) 

-80 km/h 

(-50 mph) 

-80 km/h 

(-50 mph) 

Headwind and Crosswind 

• wheel lift (E) 

• low vertical wheel load (EL) 

• high L/V (E), (EL) 

Synchronized Phased Loading

15 193 km/h 

(120 mph) 

80 km/h 

(50 mph) 

-80 km/h 

(-50 mph) 

0 Coincident Pass with 

Headwind 

• wheel lift (E), (EL) 

• high L/V (E), (EL) 

*AAR Chapter XI performance specifications require the wheel force not fall below 10 percent of static wheel load for 50 ms, and the 

lateral to vertical wheel load not to exceed 1.0 for 50 ms. 

**(E): all units empty; (L): all units loaded; (EL): first and last units loaded, intermediate units empty. 

***+Ux: tailwind on passing train; +Uy: crosswind pushing double-stack well car away from passing train. 

Other results from the simulation are as follows: 

• Highest lateral load on the double-stack well car occurs when the passing Acela 

Express train faces a headwind. 

• Speed of the Acela Express train is more important than the speed of the doublestack well car for producing peak loads. 
Part 1: Digest of Research 

19

• The duration of the load on the double-stack well car and therefore its response 

depends on both the speed of the two passing trains and the directions in which 

they are traveling (passing in opposite directions or in the same direction). 

3.1.2. Stability of Container 

The stability of the containers is a factor to consider when another train passes a doublestack well car. Well cars can carry containers stacked with one on top of another with the 

two containers secured to each other by container restraints at each corner. With the 

container being held in place by its weight and container restraints, it must resist the 

aerodynamic forces in the longitudinal, lateral, and vertical directions. Critical to 

stability is the top container, particularly when empty. Results from this study found that 

the containers should not become dislodged. 

3.2. Full-Scale Test of Aerodynamic Loading on Double-Stack Well Car 

On August 17, 2001, a full-scale test was 

performed at FRA’s Transportation 

Technology Center2 (TTC) in Pueblo, 

Colorado, to measure the aerodynamic 

pressure and roll response on a stationary 

freight car when a train passes by on an 

adjacent track. The stationary freight car 

was a well car with empty double-stack 

containers that were instrumented to 

measure the aerodynamic pressures 

applied to the containers, and the roll 

response of the well car. The passing train 

consisted of a high-speed turbine-electric 

locomotive (TEL) pulling two passenger Figure 3. Double-Stack Well Car and TEL 

cars. The geometry of the locomotive Train on Adjacent Track 

body is very similar to the Acela Express 

power car (Table 45 of the Appendix). The test was conducted at an elevation higher 

than sea level, therefore at a reduced air density, and the force applied to the double-stack 

well car was lower than if the test was performed at or near sea level. Figure 3 shows the 

double-stack well car with the TEL train on an adjacent track. 

The test was performed with the high-speed TEL train running from north to south as it 

passed the stationary double-stack well car on an adjacent track. The track center 

spacing was 3.658 m (12 ft) with a nominal gap distance between the sides of the 

containers and the passing train of 0.813 m (32 in). Figure 4 shows the test configuration 

between the well car and passing train. 

 

2

TTC is owned by FRA and operated by AAR. 
Part 1: Digest of Research 

20

Pressure measurements were obtained on the near side of the container that faced the 

passing train, and on the far side that faced away from the passing train. On the near side 

of the containers, there were nine pressure transducer locations (one location had two 

different types of pressure transducers for comparison purposes for a total of ten pressure 

transducers on the near side). The pressure transducers were mounted as three rows and 

three columns. The location of the pressure transducers will be referred to as row 

position (bottom, middle, and top), and column position (north, middle, and south). Only 

two pressure transducers were on the far side, which were located on the middle row of 

the north and south columns. The height of each row of pressure transducers measured 

from the top of the rail was: bottom row at 2.743 m (108 in), middle row at 4.039 m 

(159 in), and top row at 5.334 m (210 in). Figure 5 shows the locations of the pressure 

transducers on the containers. 

Another measurement obtained was the carbody roll. String potentiometers were 

installed on the double-stack well car between the carbody and its truck frame to measure 

the vertical displacements due to the rocking motion of the well car from the 

aerodynamic loading. The two string potentiometers were attached on either side of the 

well car, each positioned 0.930 m (36.625 in) from the car longitudinal centerline. 

Carbody roll angle was computed from the difference in the vertical displacements 

relative to the right and left truck frames. 
Part 1: Digest of Research 

21

----- (b) -----

Strain Gauge Positions

Optical Beam

Time

3.658 m

(12 ft)

North

----- (a) -----

2.591 m

(8 ft 6 in)

0.813 m

(32 in)

Nominal

2.743 m

(9 ft)

1.676 m

(5 ft 6 in)

5.944 m

(19 ft 6 in)

Rear View

Passing Train

Well Car with

Containers

Near Side

Far Side

0

Container

0.508 m

(20 in)

Nominal

3.200 m

(10 ft 6 in)

Passing

Train

Well

Car

TRAIN PASSING STATIONARY WELL CAR

DURING TEST AT TRANSPORTATION TEST CENTER

DOUBLE-STACK

z

M y

Top View of Test Configuration

Figure 4. Test Configuration of a Passing Train and a Stationary Double-Stack Well Car 
Part 1: Digest of Research 

22

----- (b) -----

----- (a) -----

Car: TTX 456013

1.791 m

(70.5 in)

1.676 m

(66 in)

Train Passing

in Front of

Containers

North

Train Passing Near Side of Well Car

2.743 m

(108 in)

4.039 m

(159 in)

5.334 m

(210 in)

PRESSURE TRANSDUCER ON CONTAINER OF WELL CAR

DURING TEST AT TRANSPORTATION TEST CENTER

1.734 m

(68.25 in)

North

Far Side of Well Car

4.039 m

(159 in)

10.389 m

(409 in)

Near Side Pressure

Transducer

Far Side Pressure

Transducer

12.179 m

(39 ft 11.5 in)

5.944 m

(19 ft 6 in)

Train Passing Near Side of Well Car Viewed from the Far Side

6.134 m

(241.5 in)

10.446 m

(411.25 in)

6.109 m

(240.5 in)

10.573 m

(416.25 in)

Near Side of Well Car

Train Passing

Behind

Containers

Figure 5. Locations of Pressure Transducers on Containers of a Well Car 
Part 1: Digest of Research 

23

3.2.1. Pressure Measurement 

The aerodynamic pressures on the double-stack well car were measured for speeds of the 

passing train ranging from 97 km/h (60 mph) to 209 km/h (130 mph). A maximum peakto-peak difference in pressures from the passing train was obtained from the 

measurements for each pressure transducer location, and a difference in pressure 

coefficients was computed. These maximum pressure changes occurred at the nose of the 

passing train due to the head perturbation of air around the moving train. 

The graph in Figure 6 shows the plots of the maximum peak-to-peak pressure coefficients 

obtained on the near side at the bottom row of pressure transducers for various passing 

train speeds. In comparing the peak-to-peak pressure coefficients on the container, little 

variation occurs in pressure coefficients with passing train speeds from the north column 

location, which is closest to where the passing train first meets the well car. However, 

some variability occurs in the pressure coefficients from the middle and south column 

locations at the lower passing train speeds. At the train speeds that were being tested, 

compressibility is not expected to be a factor on the pressure coefficients. At the lower 

speed and reduced Reynolds number, and with the small gap distance between the 

passing train and the well car being passed, some influence of the viscous boundary layer 

on the pressure coefficient may occur. Perhaps as the passing train drives the flow 

downstream along the container side, turbulence may have developed affecting the 

consistency of the pressure measurements from the middle and south column locations. 

Despite these variations, when the pressure coefficients are averaged over all speeds of 

the passing train, the maximum peak-to-peak pressure coefficients for the north and 

middle columns are both -0.50, while the south column is -0.63. 

Also shown plotted in Figure 6 is a single value maximum peak-to-peak pressure 

coefficient computed from CFD model simulation. The pressure coefficient obtained 

from the simulation is -0.7, which is higher than the test data. A higher pressure was 

expected from the model simulation. The pressure coefficient from the simulation was 

computed at a location that was lower in the container (1.96 m (77 in) from top of the 

rail) as opposed to the test measurement, which at the lowest position was at 2.74 m 

(108 in) from the top of the rail. 
Part 1: Digest of Research 

24

PRESSURE COEFFICIENT ON DOUBLE-STACK WELL CAR PASSED BY A TRAIN

WITH TURBINE-ELECTRIC LOCOMOTIVE

Test Conducted at Transportation Test Center, Railroad Test Track, on AD 2001 August 17

Track Center Spacing: 3.658 m (12 ft)

Bottom Row: 2.743 m (108 in) from Top of Rail

Pressure on Near Side at Bottom Row of Containers on Well Car

Head Pulse Peak-to-Peak Pressure Coefficient Difference, CΔ P

Passing Train Speed, (km/h)

(mph)

40 60 80 100 120 140

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

50 70 90 110 130 150 170 190 210 230 250

Channel 07 (Near Side, Bottom Row, South Column)

Channel 08 (Near Side, Bottom Row, Middle Column)

Channel 09 (Near Side, Bottom Row, North Column)

CFD Model Simulation at 1.96 m from Top of Rail

Figure 6. Pressure Coefficients on Near Side at Bottom Row of Double-Stack Well Car 
Part 1: Digest of Research 

25

At the next height which corresponds to the middle row, pressures were measured both at 

the near and far sides of the well car. The maximum peak-to-peak pressure coefficients 

from the near side at the middle row of the container are shown plotted in Figure 7 for 

various passing train speeds. Measurements from the pressure transducer at the south 

end location (channel 4) were not included because of a transducer defect that was 

discovered after the test. Not much variation occurs in the pressure coefficients with 

changes in speed; with the average maximum peak-to-peak pressure coefficients very 

close in value, at -0.45 and -0.46 for the north and middle columns respectively. Figure 8 

shows the peak-to-peak pressure coefficients from the far side location, which is very low 

and varying little with speed, resulting in average maximum peak-to-peak pressure 

coefficients of -0.050 and -0.037 for the north and south ends respectively. 

Finally, Figure 9 shows plots of the maximum peak-to-peak pressure coefficients from 

the top row of the container for various speeds of the passing train. All the pressure 

coefficients show a relatively consistent value with the exception of one value from the 

south column at 99 km/h (61.5 mph). The average maximum peak-to-peak pressure 

coefficients for the north, middle, and south columns are -0.27, -0.29, and -0.27 

respectively. A summary of the averages in peak-to-peak difference in pressure 

coefficients computed by averaging the pressure coefficients over all the speeds at each 

location is shown in Table 3. 

Table 3. Peak-To-Peak Differences in Pressure Coefficients on a Well Car Averaged over All 

Speeds of the Passing Train 

Averaged Peak-to-Peak Difference in Pressure Coefficients 

Near Side of Well Car Far Side of Well Car 

Distance From Top 

of Rail 

North Column Middle 

Column 

South Column North End South End 

2.743 m 

(108 in) 

-0.50 -0.50 -0.63 

4.039 m 

(159 in) 

-0.45 -0.46 xxx -0.050 -0.037

5.334 m 

(210 in) 

-0.27 -0.29 -0.27 

One of the variables affecting the magnitude of the aerodynamic pressure produced by a 

passing train is the height from the track. A plot of the average peak-to-peak pressure 

coefficients at three different heights illustrates this effect as shown in Figure 10. As the 

height from the track increases toward the top of the train, the average pressure 

coefficient decreases. 
Part 1: Digest of Research 

26

Test Conducted at Transportation Test Center, Railroad Test Track, on AD 2001 August 17

Track Center Spacing: 3.658 m (12 ft)

Middle Row: 4.039 m (159 in) from Top of Rail

Pressure on Near Side at Middle Row of Containers on Well Car

Passing Train Speed, (km/h)

40 60 80 100 120 140

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

50 70 90 110 130 150 170 190 210 230 250

Channel 05 (Near Side, Middle Row, Middle Column)

Channel 06 (Near Side, Middle Row, North Column)

Head Pulse Peak-to-Peak Pressure Coefficient Difference, CΔ P

(mph)

PRESSURE COEFFICIENT ON DOUBLE-STACK WELL CAR PASSED BY A TRAIN

WITH TURBINE-ELECTRIC LOCOMOTIVE

Figure 7. Pressure Coefficients on Near Side at Middle Row of Double-Stack Well Car 
Part 1: Digest of Research 

27

Test Conducted at Transportation Test Center, Railroad Test Track, on AD 2001 August 17

Track Center Spacing: 3.658 m (12 ft)

Middle Row: 4.039 m (159 in) from Top of Rail

Pressure on Far Side at Middle Row of Containers on Well Car

Passing Train Speed, (km/h)

40 60 80 100 120 140

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

50 70 90 110 130 150 170 190 210 230 250

Channel 11 (Far Side, Middle Row, North End)

Channel 12 (Far Side, Middle Row, South End)

Head Pulse Peak-to-Peak Pressure Coefficient Difference, CΔ P

(mph)

PRESSURE COEFFICIENT ON DOUBLE-STACK WELL CAR PASSED BY A TRAIN

WITH TURBINE-ELECTRIC LOCOMOTIVE

Figure 8. Pressure Coefficients on Far Side at Middle Row of Double-Stack Well Car 
Part 1: Digest of Research 

28

Test Conducted at Transportation Test Center, Railroad Test Track, on AD 2001 August 17

Track Center Spacing: 3.658 m (12 ft)

Top Row: 5.334 m (210 in) from Top of Rail

Pressure on Near Side at Top Row of Containers on Well Car

Passing Train Speed, (km/h)

40 60 80 100 120 140

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

50 70 90 110 130 150 170 190 210 230 250

Channel 01 (Near Side, Top Row, South Column)

Channel 02 (Near Side, Top Row, Middle Column)

Channel 03 (Near Side, Top Row, North Column)

Head Pulse Peak-to-Peak Pressure Coefficient Difference, CΔ P

(mph)

PRESSURE COEFFICIENT ON DOUBLE-STACK WELL CAR PASSED BY A TRAIN

WITH TURBINE-ELECTRIC LOCOMOTIVE

Figure 9. Pressure Coefficients on Near Side at Top Row of Double-Stack Well Car 
Part 1: Digest of Research 

29

Test Conducted at Transportation Test Center, Railroad Test Track, on AD 2001 August 17

Track Center Spacing: 3.658 m (12 ft)

Variation in Average Pressure Coefficient with Height from Track

on Near Side of Containers on Well Car

Head Pulse Peak-to-Peak Average Pressure

Coefficient Difference, CΔ P

Distance from Top of Rail, (m)

(in)

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0123456

Average Cp, North Column

Average Cp, Middle Column

Average Cp, South Column

0 50 100 150 200

PRESSURE COEFFICIENT ON DOUBLE-STACK WELL CAR PASSED BY A TRAIN

WITH TURBINE-ELECTRIC LOCOMOTIVE

Figure 10. Variation in Pressure Coefficients with Height on Near Side of Double-Stack Well Car 
Part 1: Digest of Research 

30

3.2.2. Rail Car Response 

The carbody of the double-stack well car rolls in response to the lateral aerodynamic 

loading from the passing TEL train. The roll angles are small as shown in Table 4, with 

the maximum zero-to-peak roll angle of 0.312° when the TEL train passed at 177 km/h 

(110 mph). At this roll angle, it produced a maximum lateral displacement of 30.1 mm 

(1.184 in) at the top of the container. Since the test was performed at a site with an 

elevation of 1,400 m (4,600 ft), these roll angles are smaller than would be at sea level 

where the air density is higher. 

Table 4. Maximum Carbody Roll Response of Double-Stack Well Car from a Passing Train 

Speed of Passing Maximum Roll Angle of Maximum Lateral Displacement 

TEL Train Double-Stack Well Car, at top 

Zero-to-Peak (deg) of Container, 

Zero-to-Peak 

97 km/h 0.055 5.26 mm

(60 mph) (0.207 in) 

129 km/h -0.117 11.3 mm

(80 mph) (0.444 in) 

161 km/h -0.218 21.1 mm

(100 mph) (0.829 in) 

177 km/h -0.312 30.1 mm 

(110 mph) (highest response) (1.184 in) 

193 km/h -0.281 27.1 mm

(120 mph) (1.065 in) 

209 km/h -0.281 27.1 mm

(130 mph) (1.065 in) 

209 km/h -0.281 27.1 mm

(130 mph) (1.065 in) 

3.2.3. Comparison of Test with Numerical Simulation 

An objective of the test was to provide data to compare with numerical simulation. As 

shown plotted in the graph of Figure 6, the value obtained from the model simulation 

does not correspond to the position of the test measurement. A direct comparison cannot 

be made, because the height where the pressure was computed from the model is outside 

the region where the test data was measured. To further compare results, numerical 

simulation was performed at a speed of 209 km/h (130 mph), which corresponds to one 

of the speeds in the test. The pressures corresponding to each of the pressure transducer 

locations were computed against time during the passage of the head of the train where 
Part 1: Digest of Research 

31

the maximum peak-to-peak pressures occurred. In comparing these results, the following 

observations were made (results not shown): 

The agreement between the measured and calculated pressures is generally very 

good. The peak-to-peak pressure magnitude is very well predicted for most 

transducer locations....However, the measured data consistently exhibits quicker 

pressure recovery past the negative pressure peak. This may be due to the lack of a 

turbulence model in the CFD calculation. (MacNeill, Holmes, and Lee 2002) 
Part 1: Digest of Research 

32
Part 1: Digest of Research 

33

4. Effect of Passing Train on Window Mount and Glazing 

A high-speed train with its attendant aerodynamic pressure pulse at the nose of the train 

can exert a brief but strong pressure to structures in proximity to the passing train. The 

aerodynamic load from the passing train has the potential to damage structures on the 

train being passed. An emerging problem in the United Kingdom has been on soft-sided 

swap body3

 wagons where the transient loads from the aerodynamic interactions with 

passing high-speed trains create the potential for structural damage, especially traveling 

in tunnels of the Channel Tunnel Rail Link (Gawthorpe 1994; Baker and Sterling 2003). 

Consequently, and with some damage to internal supports having been reported on swap 

body wagons with fabric sides, an analytical methodology was developed to simulate the 

response of the swap body to the aerodynamic interaction and structural loading from a 

passing train (RAPIDE 2001; Gregoire 2001; Johnson 2001). No aerodynamic pressure 

limit has been defined from this study, although a pressure limit of 1.44 kPa (0.209 psi) 

has been the criterion for trains passing each other in open air. 

A vulnerable structure on a passenger car is the window where the aerodynamic loading 

of a passing train can cause the glazing to crack or the window to be dislodged from its 

mount. This vulnerability was investigated to provide some indication on the potential 

for damage to the window when two trains pass each other (Holmes and Schroeder 

2002). The study consisted of computing the aerodynamic pressures from CFD 

simulation of two trains passing each other and evaluating the potential for damage to the 

window using data from glazing impact experiment. 

4.1. Glazing Impact Strength 

Experiments were conducted on the impact strength for railroad vehicle glazing to 

develop a new standard for testing (PB 1999). The experiment consisted of a variety of 

impact objects, glazing specimens, and mounting designs. The glazing specimen was 

installed in a frame and held in place with a rubber gasket as on the body of a train, and 

tested as a system. A variety of glazing specimens were tested including glass, glass with 

anti-spall coating, and polycarbonate. 

Although the use of concentrated impact objects to strike the glazing does not relate 

directly to the distributed aerodynamic pressure loading from passing trains, some of the 

results from these tests could provide information that is useful in assessing the structural 

integrity of glazing from aerodynamic interaction as trains pass each other. The impulse 

that results from the impact object striking the window, and the extent that the glazing 

can resist impact, can be used as a measure of structure’s response under aerodynamic 

 

3

Swap body is a freight-carrying unit for intermodal transport and optimized to road vehicle dimensions, 

that was originally not strong enough to be top-lifted or stacked when loaded, but some can now be toplifted or stacked. 
Part 1: Digest of Research 

34

loading, providing that they are impacts of short duations. It was determined from these 

glazing impact strength tests that a 5.4 kg (12 lbm) ball striking the glazing at a speed of 

6.71 m/s (15 mph) did not dislodge the glazing from the window frame. This 

corresponded to an impulse of 71 N•s (16 lb•s). When an 11 kg (24 lbm) ball struck the 

glazing at a speed of 6.71 m/s (15 mph), the glazing was dislodged from the window 

frame. The impulse for this case was 142 N•s (32 lb•s). 

4.2. Aerodynamic Pressure Impulse on Glazing 

The aerodynamic pressure pulse from the nose of a high-speed train can exert a brief but 

strong force on the window of another train on an adjacent track. It was estimated that 

for trains passing each other at a speed of 241 km/h (150 mph), it is unlikely that the 

aerodynamic force will cause the glazing to crack (Lee 1999). That estimate was based 

on an extrapolation of results from a test conducted on a particular type of glazing used in 

railroad cars. An assessment on the strength of the glazing attachment requires further 

details on the window design and its structural properties. 

The dislodging of the glazing from its mount can include a series of events, since it 

involves a deformation of the rubber gasket and bending of the glazing until the glazing 

slips out of the gasket, or the gasket slips out of the frame. When the pressure pulse is 

extremely short, and if certain simplifying assumptions can be made and certain 

dynamical properties are known, the assessment on the structural integrity of the window 

can be related to the initial velocity of the glazing generated by the pulse excitation. The 

impulsive force produces a rapid acceleration of the mass resulting in an almost instant 

rise in velocity. Therefore, the velocity of the mass being impacted is an indication of the 

magnitude of the pulse excitation based on the following assumptions: 

• The glazing is rigid without any bending and is initially at rest. 

• The mass of the rubber gasket is negligible relative to the glazing and its damping 

is small. 

• The pulse duration is short compared to the natural period of the mounted glazing 

(pulse duration of about one tenth or less of the natural period). 

Under these conditions, the effect of the impact on the glazing can be directly related to 

the mass and impulse (see Appendex for derivation), 

1

v

ξ

(ξ ) ≈ ∫ F(t)dt

m 0

where, 

v(ξ ) : velocity of glazing from impulsive force, 
Part 1: Digest of Research 

35

m: mass of the glazing, 

∫

ξ

F(t)dt : impulse from impulsive force F(t). 0

The potential for damage to the window was considered from results of a simulation for 

an Acela Express train passing a bilevel Kawasaki passenger car traveling in the opposite 

and same directions. Assuming that the mass of the glazing from the simulation is the 

same as the mass of the glazing from the impact strength test, the impulse can serve as a 

measure of the magnitude of the pulse excitation. The impulses on the window of a 

Kawasaki passenger car from the aerodynamic pressure of a passing Acela Express train 

with a headwind of 80 km/h (50 mph) against the Acela Express train was obtained by 

CFD simulation. When the Acela Express train traveling at 241 km/h (150 mph) passes 

the Kawasaki car traveling in the opposite direction at 129 km/h (80 mph), an impulse of 

62 N•s (14 lb•s) with a duration of 0.011 s is exerted on the window of the Kawasaki car. 

Therefore, the impulse from the simulation can be assumed to be a safe level since it is 

less than the impulse from the glazing impact strength test, where the window resisted an 

impulse of 71 N•s (16 lb•s). 

In another case, the Acela Express train is traveling at 241 km/h (150 mph) and overtakes 

the Kawasaki car traveling at 129 km/h (80 mph), an impulse of 205 N•s (46 lb•s) with a 

duration of 0.38 s is exerted on the window of the Kawasaki car. In the glazing impact 

strength test, the glazing was dislodged from the frame when an impulse of 142 N•s 

(32 lb•s) was applied. While the impulse exerted on the window of the Kawasaki car is 

205 N•s (46 lb•s), which is greater than the impulse from the window test where the 

glazing was dislodged, it may not be meaningful to directly compare impulses in this 

case. From the information that is available, it is not clear for this case whether or not the 

glazing will be dislodged. To use only the impulse as a direct comparison, the duration 

of the applied pressure pulse must be so short that it is treated as a shock impact. If the 

duration of the pressure pulse is very short (about one tenth of the natural period of 

oscillation of the window), then a direct comparison of the impulse can be made. A high 

impulse can also be obtained with a small force but a long duration, in which case, the 

force applied to the glazing has no damaging effect. Because the duration of the 

aerodynamic pressure pulse is 0.38 s, to directly compare impulses, the natural period of 

the window would have to be at least 3.8 s or longer, or a natural frequency no greater 

than 0.26 Hz. Because of a lack of data on the natural frequency of the window, an 

estimate cannot be made on the ability of the window to resist the aerodynamic force. 

Results from the glazing impact experiment can only provide some indication to the 

potential damage to the window from aerodynamic pressures. The concentrated load of 

an object striking glazing does not represent the distributed loading from aerodynamic 

pressure. There are differences in stress and deformation to the glazing and its supporting 

structure between these two events. 
Part 1: Digest of Research 

36

5. People in Proximity to Passing Train 

Circumstances occur where a train traveling at high speeds passes close to people 

alongside the track (railroad workers on the trackside or people waiting on station 

platforms). The passing train can produce airflow velocity and changes in static pressure 

that are destabilizing to people in proximity to the train. Airflow velocity induced by a 

passing train, particularly the airflow induced from the wake, is considered to be the 

more serious effect in destabilizing people and objects alongside the track (RAPIDE 

2001; Gawthorpe 1978). One simple and obvious approach to reduce these aerodynamic 

effects is for people to be situated at a sufficient distance away from the passing train. 

This approach requires information on the strength of the airflow being produced by a 

passing train, the airflow velocity that could destabilize a person, and whether station 

platforms as they exist have sufficient area to accommodate the necessary safety zone. 

The strength of the airflow velocity produced by passing trains has been the focus of 

research involving both numerical simulation and experimentation that will be addressed 

later in this report. To better understand the problem and the analytical and test results, 

an investigation was conducted that includes: 

• A review of the literature on the effects of wind on people, where studies have been 

performed with application to pedestrians in the vicinity of buildings and built-up 

environments. 

• A survey of conditions that exist in railroad station platforms, centered on stations 

along the Northeast Corridor of the United States. 

• The type of safety measures that exist in the United States and in other countries. 

5.1. Effect of Wind on People 

The aerodynamic effect felt by a person in proximity to a passing train is primarily in the 

form of airflow. The turbulent and unsteady airflow induced by the train is a transient 

event, occurring during the train passage and persisting for a short time afterwards. A 

relationship is required between wind speed and human response, particularly as it affects 

physical stability, to evaluate the effects of airflow on a person. 

Extensive research has been done on the effects of wind on people, with application to 

pedestrians in the vicinity of buildings. The data from these studies were to assist 

architects and planners in their design of tall buildings, where high winds can occur from 

the presence of these structures. While much of the research on the effects of wind on 

people was performed to improve the comfort and safety of pedestrians around the 

outside of buildings, the results from these studies provide a general understanding on a 

person’s response when exposed to a wind force. 
Part 1: Digest of Research 

37

Various wind speed criteria have been proposed with some proposed criteria stemming 

directly from outdoor observations, or from wind tunnel experiments. The Beaufort scale 

is one of the oldest wind scales relating wind speed to observable effects, which has been 

expanded over time. Penwarden (1973) presented the expanded Beaufort scale along 

with some other equivalent wind speed effects. Melbourne and Joubert (1971) observed 

pedestrians in high wind open-air environments resulting in a proposed wind speed 

criteria. Hunt, Poulton, and Mumford (1976) based their wind speed criteria on wind 

tunnel experiments, while Murakami and Deguchi (1981) formed their wind speed 

criteria on both wind tunnel experiments and outdoor observation. Other wind speed 

criteria were proposed by: Gandemer (1977); Penwarden and Wise (1975); Lawson and 

Penwarden (1977). 

The effects of wind on people have been observed as pedestrians move about in windy 

environments. In Australia, people were observed walking in the forecourt of a building 

exposed to very severe wind conditions (Melbourne and Joubert 1971). People had great 

difficulty with balance when exposed to wind at gusts up to 20 m/s (45 mph), particularly 

a gust that caught people sideways. Two girls came down on their hands and knees when 

the recorded maximum gust velocity was 23 m/s (51 mph), rising from about 12 m/s 

(27 mph) in 2 to 3 s. Many of those observed were young, with few carrying anything 

more than a briefcase. 

5.1.1. Equivalent Wind Effect 

The effect of wind blowing against a person is usually measured in terms of discomfort, 

difficulty in walking, or loss of balance. To put these descriptors in perspective, wind 

blowing against a person can be compared to various other activities. Since wind 

blowing against a person creates a force against the person, the comparison to other 

activities is based on the same level of force, or expenditure of energy. Penwarden 

(1973) illustrated these effects in terms of the angle that a person must lean to maintain 

balance, on the reduction in walking speed, and on an equivalent slope of walking up a 

hill. 

In the first example, the effects of wind blowing against a person can be viewed in terms 

of the angle a standing person facing against the wind must lean forward to maintain 

equilibrium. The angle θ that a person must lean forward into the wind can be computed 

Wind Force

as, tanθ = . At a wind speed of 10 m/s (22 mph), the angle that a person Body Weight

must lean against the wind to maintain equilibrium is 5°, while at a Beaufort Wind Force 

Scale number 7, that lean angle is 10°. 
Part 1: Digest of Research 

38

Another example relates walking speed of a 

person facing against the wind, and the speed 

of the wind. The energy required for walking 

at a speed of 1.8 m/s (4 mph) in still air was 

used as a reference. Next, the walking speed 

against the wind was computed for a given 

wind speed based on the same expenditure of 

energy as walking in still air. Table 5 shows 

walking speeds when walking against 

different wind speeds, with a reduction in 

walking speed as wind speed increases. 

A final example is the relation between the 

speed of the wind blowing against a person 

walking on level ground, and the equivalent 

slope for a person walking up a hill. This 

relation was computed based on the same 

metabolic heat requirements between 

walking against the wind, and walking up a 

hill. Table 6 shows the various relative 

wind speeds (sum of the walking speed and 

the ground speed of the wind), and walking 

up the hill with the corresponding slopes. 

Also shown is the ground speed of the wind 

if a person was assumed walking at a speed 

of 1.0 m/s (2.2 mph). In either case, as the 

wind blowing against a person increases, it 

is equivalent in energy to walking at up an 

increasingly steep slope. These examples 

provide a tangible sense to the description 

of wind effects when compared to other 

activities. 

Wind Speed Walking Speed 

0 m/s 1.8 m/s 

(4.0 mph) 

9 m/s 

(20 mph) 

1.35 m/s 

(3.0 mph) 

14 m/s 

(31 mph) 

0.9 m/s 

(2.0 mph) 

21 m/s 

(47 mph) 

0.45 m/s 

(1.0 mph) 

Table 5. Walking Speeds Against 

the Wind Computed 

Based on the Same 

Expenditure of Energy 

as Walking in Still Air 

(Penwarden 1973) 

Table 6. Wind Speeds Against a Person 

Walking on Level Ground and 

Equivalent Slopes for a Person 

Walking Up a Hill Computed 

Based on the Same Metabolic Heat 

Requirement (Penwarden 1973) 

Relative Wind 

Speed 

(Walking + 

Headwind)

Wind Speed for 

Walking Speed of 

1.0 m/s 

(2.2 mph)

Slope

10 m/s

(22 mph)

9 

(20 mph)

1/20

14 m/s

(31 mph)

13

(29 mph)

1/10

16.5 m/s

(37 mph)

15.5

(35 mph)

1/7

19.5 m/s

(44 mph)

18.5

(41 mph)

1/5

22 m/s

(49 mph)

21

(47 mph)

1/4

25 m/s

(56 mph)

24

(54 mph)

1/3

5.1.2. Wind Speed Criterion 

One of the earliest efforts to characterize the effects of wind as it applies to sailing ships 

was by Admiral Sir Francis Beaufort, FRS, in 1806. The basis of that scale, known as the 

Beaufort Wind Force Scale, is still used today. Penwarden (1973) presented an extended 
Part 1: Digest of Research 

39

and revised Beaufort scale compiled from various sources for estimating wind speeds on 

land as shown in Table 7. However, the Beaufort scale does not specify the duration at 

which the wind speeds are measured, 

In comparing the descriptions with other information it is important to know the 

time scale involved; whether gusts or long-term average speed are involved. The 

Beaufort scale is not explicit on this point, but it would seem that the speeds quoted 

are fairly long-term averages, perhaps over a period of 10 min to one hour. 

(Penwarden 1973) 

The Beaufort scale is a useful indicator on the relationship between wind speed and the 

expected effect that it could have on a person’s ability to perform certain tasks when 

exposed to that wind. However, it is a scale based on sustained wind speeds, whereas 

wind induced by a passing train will contain fluctuating or nonsteady components that 

will be transient in nature: 

While trains passing stations at high speed do not generate sustained winds, the 

transient induced airflows produced can reach significant velocities, with effects 

not unlike those described in the Beaufort Scale. Nevertheless, it is important to 

note that the transient induced airflows may not have as large an effect as a 

sustained wind of the same velocity. (Liao et al 1999) 

A narrative description on the effects of wind on people over some ranges of wind speeds 

is as follows: 

...discomfort begins at mean wind speed of 5 m/s [11 mph], with hair and clothing 

flapping and dust and loose paper blowing about. Speeds of 8 to 10 m/s [18 to 

22 mph] are unpleasant, with the wind exerting a considerable force on the human 

body; and speeds of 15 to 20 m/s [34 to 45 mph] or more are likely to be 

dangerous. (Penwarden and Wise 1975) 
Part 1: Digest of Research 

40

Table 7. Effects of Wind in Terms of Beaufort Numbers (Penwarden 1973) 

Beaufort 

Number 

Wind Speed Effect Source

(see 

bottom 

of table) 

(m/s) km/h 

(mph) 

0, 1 0 – 1.5 0 – 5.4 km/h 

(0 – 3.4 mph) 

• Calm, no noticeable wind. A, B 

2 1.6 – 3.3 5.8 – 11.9 km/h 

(3.6 – 7.4 mph) 

• Wind felt on face. A 

3 3.4 – 5.4 12.2 – 19.4 km/h 

(7.6 – 12.1 mph) 

•

•

•

Wind extends light flag. 

Hair is disturbed. 

 Clothing flaps. 

A 

B 

4 5.5 – 7.9 19.8 – 28.4 km/h 

(12.3 – 17.7 mph) 

• Raises dust, dry soil, and loose 

paper. 

A, C 

• Hair disarranged. B 

5 8.0 – 10.7 28.8 – 38.5 km/h 

(17.9 – 23.9 mph) 

•

•

Force of wind felt on body. 

Drifting snow becomes airborne. 

B 

D 

• Limit of agreeable wind on land. E 

6 10.8 – 13.8 38.9 – 49.7 km/h 

(24.2 – 30.9 mph) 

•

•

•

•

Umbrellas used with difficulty. 

Hair blown straight. 

Difficult to walk steadily. 

Wind noise on ears unpleasant. 

A 

B 

• Windborne snow above head height 

(blizzard). 

D 

7 13.9 – 17.1 50.0 – 61.6 km/h 

(31.1 – 38.3 mph) 

• Inconvenience felt when walking. A 

8 17.2 – 20.7 61.9 – 74.5 km/h 

(38.5 – 46.3 mph) 

•

•

Generally impedes progress. 

Great difficulty with balance in 

gusts. 

A 

F 

9 20.8 – 24.4 74.9 – 87.8 km/h 

(46.6 – 54.6 mph) 

• People blown over by gusts. F 

ABeaufort land scale. 

B

BRS observations. 

C

Chepil. 

DNewburg. 

E

Shaw. 

F

Melbourne and Joubert.

Specifying the wind speed for steady wind is straightforward, but when wind speeds are 

not steady, such as the presence of gust or turbulence, the method of specifying the 

overall wind speed is less obvious. The wind speed criteria must account for the effects 

of unsteady conditions. Lawson and Penwarden (1977) described the effect of the 
Part 1: Digest of Research 

41

unsteady wind conditions as it relates to the Beaufort scale. It was shown that at a given 

Beaufort force level, the average wind speed corresponding for that force level increased 

as averaging time became shorter, and suggested that it is a function of the turbulence 

intensity. In a case with turbulence intensity of 28 percent, the average wind speed did 

not change at a given Beaufort force level for averaging durations from 1 hour down to 

10 minutes. However, as averaging duration became shorter, the velocity increased at a 

given Beaufort force level. 

Various approaches to establishing wind speed criteria that accounts for fluctuating wind 

speeds exist. Hunt and Poulton suggest that gusts with durations of 0.1 to 0.5 s are likely 

to cause the most difficulty with balance (Penwarden 1973). In some cases, wind criteria 

are based on the frequency of occurrence, where it is unacceptable if induced wind gust 

velocity is likely to exceed 23 m/s (51 mph) in one year for reasons of safety, and 15 m/s 

(34 mph) for 1 percent of total time for comfort (Melbourne and Joubert 1971). A similar 

statement is that the mean hourly wind speed of 5 m/s (11 mph) is the maximum for 

comfort, and the frequency with which this is exceeded is used as a comfort criterion 

(Lawson and Penwarden 1977). Another criterion cites wind speeds that include a 

quantity called the turbulence intensity that accounts for wind turbulence. Gandemer 

(1977) suggested a criterion based on local mean speed and the corresponding root mean 

square of the turbulent fluctuation. 

Wind tunnel experiments have been conducted to quantify the relation between 

fluctuating wind speeds and its effects on people. Hunt, Poulton, and Mumford (1976) 

described wind tunnel experiments and developed quantitative values of wind speeds as it 

relates to its effects on people. The experiments were performed in a wind tunnel at the 

National Physical Laboratory in the United Kingdom, which included a gust generator to 

simulate both steady and turbulent wind. The test subjects were measured for (1) their 

performance of simple tasks, (2) their steadiness, direction, and the force acting on them 

while walking, and (3) their subjective assessments of different wind conditions. It was 

found that, “Our experiments have shown that in gusty winds it is not sufficient to use 

criteria developed for steady winds and then assume that the effect of a gusty wind is the 

same as a steady wind with a speed equal to some peak gust” (Hunt, Poulton, and 

Mumford 1976). The results of these experiments relating the effects of wind on people 

are summarized in Table 8. 
Part 1: Digest of Research 

42

Table 8. Wind Effect on People Categorized by Wind Conditions (Hunt, Poulton, and Mumford 

1976) 

Wind Condition Wind Speed, u Effect on People 

Steady Uniform Wind u < 6 m/s For comfort and little effect on 

< (13 mph) performance. 

u < 13-15 m/s For ease of walking. 

< (29-34 mph) 

u < 20-30 m/s For safety of walking. 

< (45-67 mph) 

Non-Uniform Wind u < 9 m/s To avoid momentary loss of balance and 

< (20 mph) to be able to walk straight. 

Wind speed varies by 70% over a 

distance less than 2 m (79 in). u < 13-20 m/s 

< (29-45 mph) 

For safety (for elderly people, this 

criterion may be to high). 

Gusty Wind ue < 6 m/s For comfort and little effect on 

u : estimated equivalent steady wind e

speed, 

u = u[1+ 3(u ′ u )] e rms

u : average wind speed. 

u′ u : turbulence Intensity.* rms

< (13 mph) performance. 

ue < 9 m/s 

< (20 mph) 

Most performance unaffected. 

ue < 15 m/s 

< (34 mph) 

Control of walking. 

ue < 20 m/s 

< (45 mph) 

Safety of walking. 

* u′ ( )2 ( )2

rms = u′

Xrms + uYrms ′ , where u′

Xrms and uYrms ′ are root mean square turbulent velocity 

components in the horizontal plane. 
Part 1: Digest of Research 

43

In a final study conducted in Japan, 

Murakami and Deguchi (1981) 

described experiments both in a 

wind tunnel and in open air. The 

wind tunnel experiments were 

performed at the Japan Automobile 

Institute where the subjects were 

exposed to both uniform and 

nonuniform wind flow. To create 

nonuniform wind flow, fences were 

erected to block the wind, but with 

openings between the fences to 

produce a rush of wind as the 

subject walked pass. The 

experiments had subjects walk on a 

predetermined path in the wind 

tunnel at various directions to the 

wind while carrying various items. 

Instrument recordings, visual 

assessment by experimenters, and 

verbal assessments by subjects were 

analyzed to determine the wind 

effects on the subjects. The open-air 

experiment was conducted at the 

base of a high-rise building where 

windy conditions were common. 

The first part of the open-air experiment had test subjects walk along a predetermined 

line outside the base of the building where their movements were recorded by a video 

camera. The results were analyzed based on visual assessments from the experimenters 

and verbal assessments from the subjects. The second part of the experiment involved 

analyzing photographs from video recordings to determine the wind effects of over 2,100 

pedestrians walking by the base of a building. Acceptance criteria were developed from 

the results of these experiments as shown in Table 9. The criteria are based on an 

average wind speed with an averaging duration of 3 s. 

5.2. Station Survey 

A survey was conducted of railroad stations along the Northeast Corridor of the United 

States to provide the information necessary for assessing the impact of Acela Express 

trains passing stations at high speeds (Liao et al 1999). The survey was on 57 of the 101 

existing stations along the Northeast Corridor between Union Station in Washington, DC, 

and South Station in Boston, Massachusetts. Stations selected for the survey were those 

where the Acela Express trains will not stop and at which the current maximum 

authorized speeds was greater than 161 km/h (100 mph). The survey did not include 

Table 9. Acceptance Criteria Based on Tests of 

Subject in Wind Tunnel and 

Pedestrians Exposed to Outdoor 

Wind Averaged over 3 s (Murakami 

and Deguchi 1981) 

Wind Speed 

(Averaged over 

3 s) 

Effect on People 

Under 5 m/s 

(11 mph) 

No Effect 

• minor effect on hair and skirt 

for females 

5 – 10 m/s Some Effect 

(11 – 22 mph) • footsteps sometimes irregular 

• hair and skirt considerably 

disturbed 

10 – 15 m/s Serious Effect 

(22 – 34 mph) • walking irregular 

• walking difficult to control 

• upper body bends windward 

Over 15 m/s Very Serious Effect 

(34 mph) • dangerous for elderly person 

• walking impossible to control 

• body blown sideways or 

leeward 
Part 1: Digest of Research 

44

stations where the Acela Express trains will stop, or where they will be moving at slow 

speeds. 

The survey of the selected stations involved observing the station surroundings, the 

general movement of people and trains, and station measurements. The observations 

were physical presence and condition of platforms and structures, presence and 

operational state of public address systems, the actions of passengers boarding and 

disembarking trains, and the period of time between passing and stopping trains. In 

addition, train movements were observed and experienced from an aerodynamic 

perspective, and measurements were made of platform dimensions and platform edge 

safety zone. 

Whereas the scope of information obtained in the station surveys was broad, certain 

information was considered most relevant with respect to aerodynamic effects of passing 

trains. The physical conditions considered most relevant were platform type (side or 

island), platform height (high- or low-level), platform dimensions, presence and 

dimensions of platform-edge safety zones, distance of track for nonexpress-stop trains 

from platform, presence and condition of platform passenger shelters, presence and 

legibility of safety signs, presence and type of safety systems, presence and type of 

platform appurtenances (benches, trash receptacles, billboards, newspaper vending 

machines, etc.), and the existence of a back wall near the platform. 

In addition to the on-site surveys, basic information was collected from Amtrak and other 

agencies on all 101 stations. The information collected from each station included: 

station name and location, maximum authorized speeds (MAS) passing each station, 

name of railroads providing passenger service, ownership of right-of-way, operator 

responsible for dispatching trains, type of passenger trains stopping at each station, 

number of stations within each jurisdiction, operator maintaining the stations, presence of 

safety systems and their accessibility to the disabled, and the station’s historical landmark 

status. 

It was found from this survey that the conditions of the stations varied greatly from each 

other. 

5.3. Safety Measure 

The strength of the airflow induced by a passing train is dependent on the location 

relative to the train. Therefore, the lateral distance from the side of the train and the 

vertical distance from the track, are two significant distances that affect the strength of 

the airflow experienced by a person in proximity to a passing train. Two dimensions that 

are established by design but affect the position of a person relative to a passing train are 

the width of the train and the height of the station platform. The actual or nominal 

dimensions for trains (AAR 1984) and station platforms (AREMA 1999) are shown in 

Figure 11. 
Part 1: Digest of Research 

45

Safety measures to limit people’s exposure to the aerodynamic effects of passing trains 

vary with railways in different countries. Temple and Johnson (2003) conducted a 

detailed review of research on airflow effects from passing trains in the United Kingdom 

and internationally. Baker and Sterling (2003) reviewed recent and current international 

work and identified specific problems to be addressed relating to train-induced airflow in 

urban environments. 

A common approach practiced by railways in various countries to address the safety of 

people from the aerodynamic effects of a passing train is to specify a minimum distance 

from a passing train. Workers are to stay at a certain distance from the track when a train 

passes, whereas markings are used on station platforms to warn passengers from reaching 

too close to the edge of the platform. The recommended safe distance from a passing 

train, as well as the maximum speed of the passing train, varies with railways in different 

countries as shown in Table 10. 

No safety requirements exist in the United States (as of 2005) for people on station 

platforms as it relates to the aerodynamic effects of passing trains. A survey of stations 

in the Northeast Corridor has found that, 

Platform-edge safety zones ranged from none, to those denoted by a single yellow 

stripe, to those well marked and equipped with truncated-dome strips or tiles. In 

width measured from edge of the platform, the zones ranged from less than 

[0.61 m] 2 ft to over [1.2 m] 4 ft. Conditions of the markings ranged from very 

conspicuous to very inconspicuous, due to weathering. (Liao et al 1999) 

Amtrak has been installing yellow markings on the edge of station platforms in the 

Northeast Corridor that are 0.965 m (38 in) wide. 

In Britain, British Railway has suggested criteria for exposure to wind speed induced by 

a passing train to be limited to 11 m/s (25 mph) or a Beaufort scale of 5 for members of 

the public, and limited to 17 m/s (38 mph) or a Beaufort scale of 7 for railroad workers 

(Gawthorpe 1972). Their recommended distances from a passing train are as follows: 
Part 1: Digest of Research 

46

DIMENSION AND CLEARANCE OF STATION PLATFORM RELATIVE TO

PASSENGER RAIL CAR AND TRACK

` x

y

Train

Station Platform

Top View

Nominal Rail Width: 0.0762 m (3.0 in)

Standard Track Gauge: 1.435 m (56.5 in)

Nominal Train Width: 3.048 m* (120 in)*

Nominal Track Width: 1.511 m (59.5 in)

*AAR Manual of Standards and Recommended Practices, 1984

**AREMA Manual for Railway Engineering, 1999

Rear View

Passenger Station Platform z

M y

Low Level

High Level

Passenger Train

3.048 m*

(120 in)*

1.511 m

(59.5 in)

0.203 m**

(8 in)**

1.219 m**

(48 in)**

1.702 m**

(67 in)**

1.549 m**

(61 in)**

Figure 11. Dimensions and Clearances of Station Platform 
Part 1: Digest of Research 

47

Table 10. Recommended Distances from Passing Trains in Various Countries 

Country Railway and Application at Train 

Speed (V) 

Distance to Outer 

Edge of Nearest Rail 

Distance to Edge of 

Station Platform or to 

Side of Train 

United States (non recommended) (non recommended) 

Britain Staff: V ≤ 201 km/h (125 mph). • 2.0 m (79 in) 

Public: 

V ≤ 201 km/h (125 mph). 

• 1.5 m (59 in) 

France SNCF worker on classic line: 

V ≤ 160 km/h (99 mph). 

• 1.5 m (59 in) 

SNCF worker on classic or highspeed line: 

V > 160 km/h (99 mph). 

• 2.0 m (79 in) 

SNCF public on classic line: 

V ≤ 160 km/h (99 mph). 

• 1.8 m (71 in) 

SNCF public on classic line: 

V ≤ 200 km/h (124 mph). 

• 2.5 m (98 in) 

Germany Worker: V ≤ 40 km/h (25 mph). • 1.10 m (43 in) 

Worker:

V ≤ 300 km/h (186 mph). 

• varies up to 

2.55 m (100 in) 

Public: V ≤ 160 km/h (99 mph). •

•

•

1.0 m (39 in) 

1.5 m (59 in) 

2.2 m (87 in) 

Public:

V ≤ 200 km/h (124 mph). 

Public:

V ≤ 230 km/h (143 mph). 

China Employee: 

V ≤ 160 km/h (99 mph). 

• 3.6 m (142 in) 

Public on existing line: 

V ≤ 160 km/h (99 mph). 

•

•

1.5 m (59 in) 

Public on new line: 1.7 m (67 in) 

V ≤ 160 km/h (99 mph). 

Japan Public: V ≤ 95 km/h (59 mph). •

•

0.8 m (31 in) 

Public: 2.5 m (98 in) 

V ≤ 250 km/h (155 mph). 

Russia Public: 

V ≤ 200 km/h (124 mph). 

• 2.0 m (79 in) 
Part 1: Digest of Research 

48

...trains passing through stations at up to 200 km/h (125 mph), the public are 

recommended to keep 1.5 m [59 in] from the platform edge; for staff working at the 

trackside on high-speed routes, a 2 m [79 in] clearance from the nearest running 

edge should be maintained.... 

These clearances are largely the result of combined tests involving measurements 

of the slipstream velocities together with actual subjective assessments. The latter 

are considered a vital part of the investigation of clearances for people, as the 

response of the human body to the type of turbulent flows produced by trains is 

insufficiently understood. Tests have been undertaken in France and Japan with 

instrumented dummies but it is not clear how the results are related to a maximum 

allowable gust condition. (Gawthorpe 1978) 

A comprehensive long-term development strategy was suggested for improving the 

railway network in Britain. In planning for an increase in train speed to 225 km/h 

(140 mph), suggestions were made to upgrade the existing main lines. One of the 

suggestions relates to the track arrangements at stations: 

In an age when absolute safety has become an obsession in the UK, reinforced with 

all the vigour of the law, it is inexplicable that speeding trains are still allowed to 

pass platforms occupied by waiting passengers. All intermediate stations should 

therefore have a pair of ‘through’ tracks away from platforms. (Phillips 2000) 

In France, no platforms are directly adjacent to a direct line high-speed track. A train that 

is to stop at a station is routed away from the direct line track onto a siding that runs 

along the station platform. This off-line track allows at least one track that separates the 

passing track and the station platform. France based their safety requirement from forces 

measured on cylindrical dummies, with safety gauged relative to current operations 

(Temple and Johnson 2003). In the French high-speed train line (Train à Grande Vitesse 

or TGV), the maximum train speed passing a station platform that is not a direct line 

high-speed track is 160 km/h (99 mph); while on a classic line, the maximum train speed 

passing a station platform is 200 km/h (124 mph). No trains are permitted to travel above 

a speed of 201 km/h (125 mph) when passing people on a station platform.4,5

The rules from the SNCF6

 are: 

• For workers: 

o On classic lines, the person must be at least 1.5 m (59 in) from the nearest 

edge of the rail for trains passing by at speeds less than 160 km/h (99 mph). 

 

4

Tom Tsai ( FRA). Trip report to the French National Railroads, December 6–8, 2000. 5

Marcel Fumey (SNCF). Meeting with the author December 17, 2001. 6

Laurent Guccia (SNCF). Notes from “Aerodynamic-Aeroacoustics-Aeraulics.”
Part 1: Digest of Research 

49

o On classic or high-speed TGV lines, the person must be at least 2 m (79 in) 

from the nearest edge of the rail for trains passing by at speeds greater than 

160 km/h (99 mph). 

• For people on station platforms: 

o On classic lines, the person must be at least 1.8 m (71 in) from the nearest 

edge of rail for trains passing by at speeds less than 160 km/h (99 mph). 

o On classic lines, the person must be at least 2.5 m (98 in) from the nearest 

edge of rail for trains passing by at speeds less than 200 km/h (124 mph). 

The safe standing distance from a passing train is defined for railways in Germany with 

safety gauged relative to current operations (Temple and Johnson 2003). Distance for 

workers on trackside varies according to the train passing speed, ranging from 1.10 m 

(43 in) for a train passing up to 40 km/h (25 mph) to 2.55 m (100 in) for a train passing 

up to 300 km/h (186 mph) with the distance measured from the outer edge of the nearest 

rail. The minimum distances from the edge of the platform for the public are 1.0 m 

(39 in) for a train passing up to 160 km/h (99 mph), 1.5 m (59 in) for a speed up to 

200 km/h (124 mph), and 2.2 m (87 in) for a speed up to 230 km/h (143 mph). 

Japan sets its safety distance from a passing train using a limiting airflow velocity of 

9 m/s (20 mph) (Tanemoto and Kajiyama 2003). The standard location was set at 0.8 m 

(31 in) from the platform edge for local trains passing at a maximum speed of 95 km/h 

(59 mph). This was based on a Beaufort wind scale of 4 to 5, or an airflow velocity of 6 

to 9 m/s (13 to 20 mph). A minimum distance was set at 2.5 m (98 in) from the edge of 

the platform for the high-speed Shinkansen train passing at 250 km/h (155 mph). 

Although markings on the edge of the platform are a simple method of warning people 

from being too close to the track, in some cases, a more elaborate technique is 

implemented. On the Tokaido Shinkansen railway line in Atami, Japan, the station does 

not have off-line tracks for nonstop trains where trains pass by at 200 km/h (124 mph) 

adjacent to the passenger platform.7

 In the Atami station, a protective fence prevents 

people from wandering too close to the edge of the platform. An attendant is present to 

operate the gates to allow passengers to pass when a train is stopped at the station. 

Railways in China based their recommended safety distance for higher passing train 

speed from the force measured on a mannequin in a test, and compared it to existing 

service (Heshou, Dezhao, and Houxiong 1996). A train passing on an existing rail line is 

limited to a force of 110 N (24.7 lb) on the mannequin, while a new high-speed line is 

limited to a force of 100 N (22.5 lb). Based on these permissible forces, the 

recommended distance for employees on the trackside is 3.6 m (142 in) from the outer 

edge of the nearest rail for a train passing by at a speed of 160 km/h (99 mph). The 

 

7

John Harding (FRA). Letter to the author, January 24, 2001. 
Part 1: Digest of Research 

50

recommended distances from the edge of a station platform for trains passing at 160 km/h 

(99 mph) is 1.5 m (59 in) for existing lines, and 1.7 m (67 in) for new lines. 

Russia sets their safety distance at 2.0 m (79 in) from the edge of the platform for trains 

passing at 200 km/h (124 mph) (Heshou, Dezhao, and Houxiong 1996). 

The separation distance between people and the passing train can be specified from 

different reference locations. For workers, the distance is generally given relative to the 

outer edge of the nearest rail, because no platform exists, and therefore no platform edge 

can be referenced. Where a station platform exists, a convenient reference is the distance 

to the edge of the platform. Distance from the edge of the platform can be assumed to be 

approximately the same as to the side of the train. Another reference location is from the 

track centerline, but this is a less practical location from which to measure for a person 

on the trackside or platform. The separation distances between people and passing trains 

as specified by various railways are shown in Table 10. 

Certain factors should be considered when comparing distances from a passing train 

between railroads, especially between railroads from different countries. The reason is 

that when distances from a passing train are referenced with respect to the edge of the 

nearest rail or from the edge of the platform, the distance to the side of the train is 

ambiguous. The distance from the side of the train depends on the train width, platform 

clearance from the train, and track gauge. These factors affect the actual distance from 

the side of the train. The ground or platform height relative to the track is also significant 

as the airflow strength is affected by the height. Even specifying the distance directly 

from the side of the train is only a nominal distance because the side of a train is not a 

straight vertical surface from top to bottom. Therefore, these factors must be taken into 

account when comparing their recommended distances with each other. 
Part 1: Digest of Research 

51
Part 1: Digest of Research 

52

6. Airflow Induced by a Passing Train 

A moving train produces a disturbance to the surrounding air that induces an airflow, or 

slipstream,8

 along the train. The train-induced airflow is a complex phenomenon 

influenced by train speed, train geometry, distance from the train, and ambient wind. The 

characteristic of the induced airflow in the presence of ambient wind can be described as 

follows: 

The flow around a train is characterized by strong vorticity on its leeside generated 

by the shedding of the train boundary layers, by wakes and eddies from the train 

nose and discontinuities in the train profile. Compounded with this general nonuniformity of flow along the train are the additional unsteady effects due to the 

continuous variations in the ambient wind meeting the train. This whole unsteady 

flow field is then given a longitudinal component of motion, relative to a trackside 

observer, by the viscous action of the train dragging the slipstream along with it. 

(Gawthorpe 1978) 

Consequently, with trains traveling at high speeds passing some train stations without 

stopping, the airflow from the passing train can affect the safety of people waiting on the 

platform. An incident reportedly occurred in Ventura, California, where an empty 

stroller on a train station platform was propelled toward the track, presumably by the 

airflow induced by the passing train, crushing the stroller under the train’s wheels 

(Freedenberg 2003). Numerous incidents have occurred on station platforms in Britain 

caused by train-induced airflow that included: a luggage barrow and children’s 

pushchairs being set into motion and hitting the train, and people almost losing their 

balance from a passing train (Gawthorpe 1994; Johnson, Dalley, and Temple 2002). 

Passing freight trains have caused most of the incidents in Britain (Temple and Johnson 

2003). In addition to station platforms, safety issues have been raised in the United 

States on the aerodynamic effects from passing trains on people using RWT where 

shared-use trails (trails for pedestrians and bicyclists) are developed and located adjacent 

to active rail lines. 

Safety concerns exist for people on station platforms as trains pass stations faster and the 

aerodynamic effects become stronger. The incidents described above illustrate some of 

the hazards. As a result, a need exists for airflow data to assess its effect on people in 

proximity to passing trains. Although airflow data are reported in the literature, the 

results are very much dependent on train geometry and measurement position relative to 

the train. 

 

8

According to Professor Christopher Baker of the University of Birmingham in the United Kingdom, the 

term slipstream is also used to refer to the boundary layer flow around the train, which may or may not 

include the wake. 
Part 1: Digest of Research 

53

Recent studies have been conducted to obtain aerodynamic characteristics specific to 

current high-speed train designs, and to further understand the airflow around the train. 

As part of Europe’s RAPIDE project, CFD simulation and experiments with full-scale 

and model tests of 1/25 scale were conducted to measure the airflow velocity induced by 

a passing German high-speed ICE passenger train (Johnson, Dalley, and Temple 2002; 

Baker et al 2001). One notable result is the lack of repeatability in the data due to the 

chaotic nature of the airflow, where there was large variation in airflow velocity at a 

given location during repeat runs at the same ambient condition and train speed. 

Therefore, for proper analysis, it is necessary to have sufficient quantity of data on the 

types of trains that are operating, with data measured from known and consistent 

positions. 

With the high-speed Acela Express train being placed into service in the United States, 

numerical simulation and full-scale testing were conducted to determine the strength and 

characteristic of the airflow induced by a train passing a station platform (Liao et al 1999; 

PB 2000; GEOCOMP 2002; Duffell 2000). Results computed from numerical simulation 

were compared with test data. Computed and measured airflows from passing highspeed Acela Express and conventional Amfleet trains provided a relative measure of 

airflow velocity between the two types of trains. By comparing the airflow induced by 

Acela Express trains with the airflow from the existing operation of Amfleet trains, it 

provided a gauge for assessing the aerodynamic effects of a passing Acela Express train 

on people on station platforms. This collection of airflow velocity data measured at 

various lateral distances from passing trains provided the necessary relation to assess the 

aerodynamic effects on people from wind speed criteria. 

6.1. Mathematical Modeling of Train-Induced Airflow 

The FLUENTTM CFD program was used to simulate the airflow induced by a train 

passing a station platform. An Acela Express train and an Amfleet train were modeled to 

obtain the induced airflow velocity for low- and high-level platforms, and for various 

heights from the platform and distances from the passing trains. The train-induced 

airflow velocity obtained from the CFD was for the longitudinal component along the 

direction of the passing train. 

6.1.1. Acela Trainset 

The Acela Express train was modeled as six coaches with two tapered nose power cars 

(one power car at each end). It was found that the induced airflow from the bow wave 

and boundary layer effects were not significant, but wake effects are important with the 

wake from a low level platform being stronger than from a high level platform. The 

maximum airflow velocities and exposure times at various distances from the side of the 

passing train are shown in Table 11. 
Part 1: Digest of Research 

54

Table 11. Maximum Longitudinal Airflow Velocities and Exposure Times from an Acela Express 

Train Passing a Low-Level Platform 

Train Speed Distance above 

Top of Rail 

Distance from Side 

of Train 

Airflow Velocity Exposure Time 

177 km/h 

(110 mph) 

0.762 m 

(2.5 ft) 

0.6096 m 

(2 ft) 

17.9 m/s 

(40 mph) 

0.5 to 1 s 

177 km/h 

(110 mph) 

0.762 m 

(2.5 ft) 

2.7432 m 

(9 ft) 

11.2 m/s 

(25 mph) 

3 s 

177 km/h 

(110 mph) 

1.524 m 

(5 ft) 

1.2192 m 

(4 ft) 

11.2 m/s 

(25 mph) 

2 s 

241 km/h 

(150 mph) 

0.762 m 

(2.5 ft) 

0.9144 to 

1.8288 m 

(3 to 6 ft) 

17.9 m/s 

(40 mph) 

1 s 

241 km/h 

(150 mph) 

0.762 m 

(2.5 ft) 

3.676 m 

(12 ft) 

11.2 m/s 

(25 mph) 

2 to 3 s 

241 km/h 

(150 mph) 

1.524 m 

(5 ft) 

2.4384 m 

(8 ft) 

11.2 m/s 

(25 mph) 

2 s 

The maximum longitudinal airflow velocities (mean plus maximum fluctuating 

velocities) that are induced along various areas of the train, the bow wave, boundary 

layer, and wake, are shown in Table 12 and plotted in Figure 12(a). At a lateral distance 

closest to the side of the train, the maximum longitudinal airflow velocity is 0.27 of the 

train speed occurring at the wake, whereas the airflows from the bow wave and boundary 

layer are lower (Figure 12(a)). Shown with the longitudinal airflow velocity (Table 12) 

is the corresponding Beaufort number. While some very high velocities are reached, 

reference to the Beaufort scale must be qualified: 

Mitigating these concerns, however, is that the air velocities have relatively short 

durations and are transient in nature. Related to this factor, these exposure limits 

are based to some extent on the Beaufort scale, which was originally developed for 

sustained wind rather than transient air velocity effects. (Liao et al 1999) 
Part 1: Digest of Research 

55

Table 12. Maximum Longitudinal Airflow Velocities at 0.762 m (2.5 ft) above Low-Level Platform 

Induced by an Acela Express Train Passing at 241 km/h (150 mph)

Distance 

from Side of 

Train 

Bow Wave 

Element 

Boundary Layer 

Element 

Wake 

Element 

Airflow 

Velocity, U 

Beaufort 

Number 

Airflow 

Velocity, U 

Beaufort 

Number 

Airflow 

Velocity, U 

Beaufort 

Number 

0.9144 m 5.8 to 11.2 4 to 6 5.8 to 11.2 4 to 6 U>17.9 m/s above 8 

m/s m/s 

(3 ft) (13 to 25 

mph) 

(13 to 25 

mph) 

(U>40 mph) 

1.822 m U<5.8 m/s 3 U<5.8 m/s 3 11.2 to 17.9 6 to 8 

m/s 

(6 ft) (U<13 mph) (U<13 mph) (25 to 40 

mph) 

2.7432 m U<5.8 m/s 3 U<5.8 m/s 3 5.8 to 11.2 4 to 6 

m/s 

(9 ft) (<13 mph) (U<13 mph) (13 to 25 

mph) 

3.6576 m U<5.8 m/s 3 U<5.8 m/s 3 5.8 to 11.2 4 to 6 

m/s 

(12 ft) (U<13 mph) (U<13 mph) (13 to 25 

mph) 

6.1.2. Amfleet Train 

The second model that was simulated is an Amfleet train that consisted of an AEM-7 

bluff nose electric locomotive with six coaches. The maximum airflow velocities that 

were induced along various areas of the train, the bow wave, boundary layer, and wake, 

are shown in Table 13 and plotted in Figure 12(b). At the closest lateral distance to the 

train side, the maximum longitudinal airflow velocity from the boundary layer and wake 

is 0.32 of the train speed (Figure 12(b)). The bow wave does not reach as high a value, 

but this is the longitudinal component of airflow, while the lateral component would be 

expected to be significant for the bow wave as the head of the train pushes the air aside in 

the lateral direction. 
Part 1: Digest of Research 

56

MAXIMUM LONGITUDINAL AIRFLOW VELOCITY AT 0.762 m (2.5 ft) ABOVE TOP OF RAIL

FROM NUMERICAL SIMULATION OF AIRFLOW INDUCED BY A PASSING TRAIN 

----- (b) -----

----- (a) -----

Data Grouped at the Same Lateral Distance from the Side of Train

(Some Data are Plotted at a Distance from the Side of the Train that Slightly

Deviates from the Actual Distance to Improve Readability)

Dimensionless 

Normalized with respect

to Train Speed

Airflow Velocity

Acela Express Train with Six Coaches and Two Power Cars

Lateral Distance from Side of Train, (m)

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

(in)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3 3.5 4

Bow Wave

Boundary Layer

Wake

Amfleet Train with AEM-7 Locomotive and Six Coaches

Lateral Distance from Side of Train, (m)

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

(in)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3 3.5 4

Bow Wave

Boundary Layer

Wake

Dimensionless 

Normalized with respect

to Train Speed

Airflow Velocity

Figure 12. Computed Maximum Airflow Velocities at 0.762 m (2.5 ft) above Top of Rail
Part 1: Digest of Research 

57

Table 13. Maximum Longitudinal Airflow Velocities at 0.762 m (2.5 ft) above Low-Level 

Platform Induced by an Amfleet Train with AEM-7 Locomotive Passing at 201 km/h 

(125 mph)

Distance 

from Side of 

Train 

Bow Wave 

Element 

Boundary Layer 

Element 

Wake 

Element 

Airflow 

Velocity, U 

Beaufort 

Number 

Airflow 

Velocity, U 

Beaufort 

Number 

Airflow 

Velocity, U 

Beaufort 

Number 

0.9144 m 5.8 to 11.2 4 to 6 U>17.9 m/s above 8 11.2 to 17.9 6 to 8 

m/s m/s 

(3 ft) (13 to 25 

mph) 

(U>40 mph) (25 to 40 

mph) 

1.822 m 5.8 to 11.2 4 to 6 11.2 to 17.9 6 to 8 5.8 to 11.2 4 to 6 

m/s m/s m/s 

(6 ft) (13 to 25 

mph) 

(25 to 40 

mph) 

(13 to 25 

mph) 

2.7432 m U<5.8 m/s 3 5.8 to 11.2 4 to 6 5.8 to 11.2 4 to 6 

m/s m/s 

(9 ft) (U<13 mph) (13 to 25 

mph) 

(13 to 25 

mph) 

3.6576 m U<5.8 m/s 3 U<5.8 m/s 3 U<5.8 m/s 3 

(12 ft) (U<13 mph) (U<13 mph) (U<13 mph) 

6.1.3. Comparison of Results 

Numerical simulations were performed for an Acela Express train traveling at 241 km/h 

(150 mph) and an Amfleet at 201 km/h (125 mph). At these operating speeds, both trains 

induced about the same maximum longitudinal airflow velocities as shown in Table 14, 

with the Amfleet train producing the strongest airflow from the boundary layer, while the 

strongest airflow for the Acela Express train was coming from the wake (Table 12 and 

Table 13). At the furthest distance from the train, the wake from the Acela Express train 

produced a stronger airflow than the overall airflow from the Amfleet train. Relative to 

platform height, induced airflow from the Acela Express train was lower on a high-level 

than on a low-level platform. 

A comparison between the results from this CFD model with data reported from the 

literature indicates some differences: 

...there may be assumptions that limit the absolute predictive accuracy of the CFD 

models. However, the comparative accuracy of the CFD models has more validity 
Part 1: Digest of Research 

58

than the absolute accuracy, e.g., comparison of the relative wind velocities, due to 

different cars are more valid than absolute values of the calculated velocities 

themselves. (Liao et al 1999) 

Table 14. Maximum Longitudinal Airflow Velocities from Passing Trains at 0.762 m (2.5 ft) 

above Low-Level Platform 

Distance from Side 

of Train 

Acela Express 

at 

241 km/h (150 mph) 

Amfleet Train with AEM-7 Locomotive 

at 

201 km/h (125 mph) 

Airflow Velocity, 

U 

Beaufort Number Airflow Velocity, 

U 

Beaufort Number 

0.9144 m 

(3 ft) 

U>17.9 m/s 

(U>40 mph) 

above 8 U>17.9 m/s 

(U>40 mph) 

above 8 

1.822 m 

(6 ft) 

11.2 to 17.9 m/s 

(25 to 40 mph) 

6 to 8 11.2 to 17.9 m/s 

(25 to 40 mph) 

6 to 8 

2.7432 m 

(9 ft) 

5.8 to 11.2 m/s 

(13 to 25 mph) 

4 to 6 5.8 to 11.2 m/s 

(13 to 25 mph) 

4 to 6 

3.6576 m 

(12 ft) 

5.8 to 11.2 m/s 

(13 to 25 mph) 

4 to 6 U<5.8 m/s 

(U<13 mph) 

3 

6.2. Full-Scale Test Measurement of Induced Airflow 

Full-scale tests were conducted to measure the airflow induced by a passing train. A 

series of tests were conducted over a span of time at various locations along the 

Northeast Corridor route, whose locations were selected based on factors such as speed 

of passing trains, station configuration, and ease of testing. Airflow velocity was 

measured by pitot-static tube as illustrated in Figure 13(a), and unless otherwise 

specified, measurements were for the longitudinal airflow velocity, which was the airflow 

parallel to the track and flowing in the direction of the passing train (with the pitot tube 

nose facing the approaching train). In earlier tests, only a single peak airflow velocity 

value was obtained, whereas later tests used a more sophisticated measurement 

arrangement in which a time history of the data was recorded during the entire passage 

of a train. 
Part 1: Digest of Research 

59

PITOT-STATIC TUBE CONFIGURATION FOR MEASURING AIRFLOW VELOCITY

Support Frame for Four-Position Pitot-Static Tubes

Position YA-Z2

(Spacing Adjustable)

----- (b) -----

Pitot-Static Tube Measuring System

----- (a) -----

Position YA-Z1

Position YB-Z2

Position YB-Z1

z

M

y

0.914 m

(36 in)

Maximum

0.762 m

(30 in)

1.524 m

(60 in)

Rear View with Train Moving

Away from Observer

Airflow

Pressure

Indicating

Device Wind Speed

Pitot-Static Tube

Figure 13. Pitot-Static Tube System for Measuring Airflow Velocity and Support Frame 

Arrangement 
Part 1: Digest of Research 

60

6.2.1. Test of September 1998 in New Jersey and Delaware 

The initial test was performed on the train stations at Princeton Junction, New Jersey, and 

at Newark, Delaware, during September 1998 (Liao et al 1999). The train-induced 

airflow velocity was measured with a pitot tube positioned parallel to the track at about 

1.7 m (5.5 ft) above the platform level, with the pitot tube nose facing the approaching 

train. Measurements were obtained at high- and low-level platforms. 

These measurements demonstrate the effect of position on the strength of the airflow. 

The airflow velocity, as shown in Table 15, normalized with respect to train speed, 

decreases with increased lateral distance from the train, or with increased height in the 

platform. Whereas only longitudinal airflow velocity along the direction of the moving 

train was measured, a perceived airflow occurred in the lateral direction. Comparison 

between the full-scale test and CFD results shows some differences with the test results 

being either within the range or slightly higher than the CFD results. 

Table 15. Maximum Longitudinal Airflow Velocities from Passing Amfleet Trains at about 1.7 m 

(5.5 ft) above Top of Rail from September 1998 Test

Location Platform Distance from Train Speed, Airflow Velocity 

& 

Date 

(Year-Month-Day)

Height Side of Train Vtrain Uair Uair/Vtrain

Princeton Junction, Low 2.74 m 201 km/h 27 km/h 0.136 

NJ (9.0 ft) (125 mph) (17 mph) 

1998-09-01 

Princeton Junction, High 1.68 m 177 km/h 16 km/h 0.091 

NJ 

1998-09-08 

(5.5 ft) (110 mph) (10 mph) 

5.49 m 

(18 ft) 

201 km/h 

(125 mph) 

13 km/h 

(8 mph) 

0.064 

Newark, DE Low 1.68 m 198 km/h 45 km/h 0.23 

(5.5 ft) (123 mph) (28 mph) 

1998-09-17 5.18 m 183 km/h 3 km/h 0.018 

(17.0 ft) (114 mph) (2 mph) 

6.2.2. Test of February 2000 in Maryland 

A second test was performed during February 20 and 21, 2000, on a low-level platform 

train station in Edgewood, Maryland (Duffell 2000). It was similar to the first test, with a 

single pitot tube positioned parallel to the track with the pitot tube nose facing the 

approaching train. The pitot tube was at a distance of about 0.6 m (2 ft) from the edge of 

the platform and at a height of about 1.5 m (5 ft) above the platform. 
Part 1: Digest of Research 

61

Longitudinal airflow velocities were 

measured for a number of different types of 

passing trains, including Acela Express, 

Amfleet, and freight trains. All the 

passenger trains passed at speeds ranging 

from 179 to 240 km/h (111 to 149 mph). 

The Amfleet trains consisted of eight cars 

pulled by two locomotives. The freight 

trains were estimated at over 1.6 km 

(1 mile) long consisting of a mixture of 

different types of cars pulled by dieselelectric locomotives. In Figure 14 a plot 

shows the maximum airflow velocity 

normalized with respect to train speed. The 

Acela Express train induced the lowest 

airflow with a mean airflow velocity of 0.25 

and a maximum of 0.28 of the train speed. 

Amfleet trains induced a slightly higher 

airflow with a mean of 0.33 and a maximum 

of 0.37. Only two measurements were 

MAXIMUM LONGITUDINAL AIRFLOW VELOCITY

INDUCED BY TRAIN PASSING

LOW-LEVEL PLATFORM

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

123

Acela Express X

Train

Amfleet 

Train

Freight 

Train

Distance from Platform Edge: 0.6 m (2 ft)

Height Above Platform: 1.5 m (5 ft)

Test at Edgewood, Maryland on February 20-21, 2000.

Nondimensional Airflow Velocity Normalized

with respect to Train Speed

recorded for the freight train; which passed at a speed of 48 km/h (30 mph) producing a 

velocity ratio of 0.7. The strong airflow produced by a freight train is consistent to other 

observations where the aerodynamically rough geometries of the different freight cars 

induced airflow that is much greater than the smoother profile on a passenger train 

(Gawthorpe 1978; Temple and Johnson 2003; Johnson, Dalley, and Temple 2002; 

Andersson, Aronsson, and Pettersson 1994). 

6.2.3. Test of July 2000 in Massachusetts and Rhode Island 

In the third July 2000 test series, the measurements were obtained on low-level station 

platforms at Mansfield and Sharon, Massachusetts, and at Kingston, Rhode Island during 

July 2000 (PB 2000). The design for this test was more sophisticated than in the 

previous tests. Simultaneous measurements of longitudinal airflow velocities were 

obtained from pitot-static tubes at four different positions. Each pitot-static tube was 

positioned parallel to the track with the pitot-static tube nose facing the approaching 

train. The measurement was recorded over the duration of the passing train to obtain a 

velocity-time history of the data. A photoelectric sensor and a light beam that spans 

across the tracks were used to detect the presence of a train. As a train passes, the light 

beam is interrupted, therefore providing an indication on the head and tail ends of the 

train as it passes by the location of the pitot-static tubes. 

The four pitot-static tubes were mounted on a frame with two pitot-static tubes on each of 

the two horizontal arms of the frame as shown in Figure 13(b). This provided 

measurements at two different lateral distances from the side of the train and at two 

4

Figure 14. Maximum Airflow Velocities from 

Passing Trains Measured at Train 

Station in Maryland 
Part 1: Digest of Research 

62

different heights. The lateral positions of the two pitot-static tubes on each arm were 

spaced at a distance of 0.914 m (36 in) relative to each other, with the heights of the 

lower pitot-static tubes at 0.762 m (30 in) and the upper pitot-static tubes at 1.524 m 

(60 in) above the platform. 

Numerous measurements were made from the passage of Amfleet and Acela Express 

trains, but because of some test difficulties, only two of the best measurements were 

selected for detailed analysis as shown in Table 16. The maximum speed of the induced 

airflow for the Acela Express train traveling at 233 km/h (145 mph) is in most cases 

slightly lower than the Amfleet train traveling at 154 km/h (96 mph). When the airflow 

velocity is normalized with respect to train speed, it is apparent that the airflow induced 

by the Acela Express train is less than the Amfleet train, ranging from 16 to 49 percent 

less in the strength of the airflow, depending on the location of the measurement. 

One of the motivations of the full-scale test was to compare the test data with the results 

from the CFD simulation. The following observations were made when the results were 

examined (results not shown): 

...it is seen that the major features of the data and the CFD calculations agree quite 

well. In particular, it should be noted that the maximum value of airflow for the 

Acela [Express] occurs usually at the tail of the train, whereas the maximum value 

of airflow for the Amfleet train is usually at the head of the train, or shortly 

thereafter, especially for positions closer to the side of the train. This is evident in 

both the CFD calculations and the measurements. This difference in when the 

maximum occurs reflects the fact that the Acela [Express] is much more 

streamlined, whereas the Amfleet engine has a blunt front end that tends to cause 

more disturbance and tends to push the air ahead of it, causing a more pronounced 

bow wave effect. (PB 2000) 
Part 1: Digest of Research 

63

Table 16. Maximum Longitudinal Airflow Velocities from Passing Trains from July 2000 Test

Location Train Type Lateral Height above Airflow Airflow 

& & Distance from Rail Velocity, Uair Velocity, 

Date Train Speed, Side of Train Uair/Vtrain 

(Year-Month-Day) Vtrain 

Mansfield, MA Amfleet 0.603 m 0.914 m 116 km/h 0.75 

at (23.8 in) (36 in) (72 mph) 

2000-07-07 154 km/h 

(96 mph) 1.676 m 

(66 in) 

116 km/h 

(72 mph) 

0.75 

1.52 m 0.914 m 88 km/h 0.57 

(59.8 in) (36 in) (55 mph) 

1.676 m 50 km/h 0.32 

(66 in) (31 mph) 

Kingston, RI Acela Express 0.616 m 0.914 m 114 km/h 0.49 

at (24.3 in) (36 in) (71 mph) 

2000-07-19 233 km/h 

(145 mph) 1.676 m 

(66 in) 

93 km/h 

(58 mph) 

0.40 

1.53 m 0.914 m 68 km/h 0.29 

(60.3 in) (36 in) (42 mph) 

1.676 m 63 km/h 0.27 

(66 in) (39 mph) 

The results from the measurements listed in Table 16 illustrate the effect of location on 

the strength of the airflow velocity. Because the pitot-static tubes were located at four 

corners of the frame, this provided measurements at two different distances from the train 

and at two different heights. A reduction occurs in maximum airflow velocity from 

either an increase in lateral distance from the train, or from an increase in height from the 

track, as shown in Table 17. 

Attention will be focused on the measurements from the pitot-static tubes located either 

at the bottom or the one nearest the train, because these locations will generally have the 

strongest airflow. An increase in lateral distance from the train by a factor of 2.73 for the 

bottom measurements reduces the airflow by 40 percent for the passing Acela Express 

train, and by 24 percent for the Amfleet train. Therefore, increasing the height by a 

factor of 1.83 for the measurements nearest the train reduces the airflow by 18 percent for 

the passing Acela Express train, but with no change in the strength of the airflow for the 

Amfleet train. 
Part 1: Digest of Research 

64

All airflow velocities that have been 

presented are raw data as measured 

without any additional processing. 

However, the data contained a high 

frequency component, which was 

suspected to be electrical noise (PB 

2000). By applying a moving average 

to the data with a minimum averaging 

duration of 0.032 s, this acts as a lowpass filter which removes the high 

frequency noise. 

In addition to noise removal, there is 

another purpose of applying an 

averaging process to the data. The 

averaging of the data removes the 

rapid changes and short duration 

peaks. The results of which can be 

useful to assessing human response: 

The high frequency components 

of the airflow, even if they were 

actual turbulence effects (and not noise in the signal), could likely not be felt or 

experienced by people. It is unlikely that the human senses can detect rapid 

changes and short duration peaks. Thus a spike of [113 km/h] 70 mph for less than 

0.1 second may not have any practical effect; it would likely be felt as an 

equivalently lower velocity gust of air....The moving average smoothing technique 

thus provides an indication of the sustained effects of the airflow as a train passes, 

over realistic periods (say 0.5 to 2 seconds) that are within the range of human 

experience. (PB 2000) 

To illustrate this effect, a moving average is applied to the data from the bottom pitotstatic tube closest to the train. By performing this process on the airflow data from the 

passing Acela Express train, the maximum induced airflow velocity dropped from a high 

of 114 km/h (71 mph), with no filtering, to 68 km/h (42 mph), and 64 km/h (40 mph) 

corresponding to moving average intervals of 1.0 s and 2.0 s respectively. The results 

suggest that these values “...may reflect the equivalent values of the airflow that could be 

compared to some extent to such measures as the Beaufort scale, though smoothing at 

even longer intervals may be appropriate for a direct comparison” (PB 2000). 

One of the considerations in applying the moving averages is the effect of averaging 

duration. Because the disturbance to the surrounding air by a passing train is transient, a 

very long averaging duration that extends excessively beyond the period of the passing 

train will approach the condition for the ambient undisturbed air. Also, while smoothing 

of the data over a certain averaging duration is applicable to human response, a shorter 

averaging duration is necessary when evaluating the effect of airflow to particles with 

Table 17. Changes in Maximum Induced 

Longitudinal Airflow Velocities from 

Changes in Positions 

Passing 

Train 

Increase 

Factor in 

Lateral 

Distance 

Increase 

Factor in 

Height 

Reduction in 

Airflow 

Velocity 

Acela 

Express 

2.73 0 40% (Z1*)

2.73 0 32% (Z2*)

0 1.83 18% (YA*)

0 1.83 7% (YB*)

Amfleet 2.73 0 24% (Z1*)

2.73 0 57% (Z2*)

0 1.83 0 (YA*)

0 1.83 43% (YB*)

*Pitot-static tubes located near (YA) or far (YB) from 

the train, or at the bottom (Z1) or top (Z2) positions. 
Part 1: Digest of Research 

65

low mass. Particles with low mass, and therefore low inertia, can respond much more 

readily to the rapid changes in the airflow: 

...small particulate matter, such as loose debris, soil particles, snow or ice, on the 

track or platforms, would respond to higher frequency peak airflow values....In the 

limit as the particulate mass and density approaches the mass and density of the air 

(e.g.[,] a mist of rain or snowflakes), the particles may respond at high frequencies 

to be nearly the same values as the peaks of airflow velocity record. The moving 

average smoothing technique may thus not [be] as representative of what the 

buffeting effects of turbulent airflow would be on very small particulate matter. 

(PB 2000) 

6.2.4. Test of September to October 2002 in Massachusetts 

In this final test, airflows were 

measured on a station platform 

alongside another test where forces 

were measured from instrumented Cylindrical Instrumented

Dummy

dummies (Chapter 7 provides 

information on the instrumented 

dummies with test configuration 

related to the airflow measurement) 

(GEOCOMP 2002). The test was 

performed on a train station with a Pitot-Static Tubes

low-level platform in Mansfield, 

Massachusetts, from September 29 to 

October 3, 2002. Measurements were 

obtained from three different types of 

trains as distinguished by its head- and Figure 15. Pitot-Static Tubes for Measuring 

Longitudinal and Lateral Airflow tail-end geometries. In many cases Velocities Induced by a Passing Train data was obtained for multiple passes with Cylindrical Instrumented Dummy 

of the same type of train. Also, the in the Background 

airflow was measured at various 

distances from the train and with 

different orientations of the pitot-static tubes, as shown in Figure 15. 

Four pitot-static tubes mounted on a frame at two different heights, and at two different 

lateral positions or orientations, simultaneously measured the airflow velocities as a 

velocity-time history data (Figure 13). Except for some reference measurements, each 

pitot-static tube was either oriented to measure longitudinal (+x) airflow parallel to the 

track along the direction of the passing train, or oriented to measure lateral (+y) airflow 

perpendicular to the track away from the passing train, as each pitot-static tube can 

measure the component flowing in only one direction. These orientations were expected 

to have the strongest airflow. In some configurations, the pitot-static tubes were oriented 
Part 1: Digest of Research 

66

perpendicular to each other to capture the simultaneous longitudinal and lateral 

components of airflow. 

Airflow velocities were measured for six different configurations of the pitot-static tubes. 

In configuration 1, the pitot-static tubes were arranged with the same alignment to 

previous tests. With configurations 2, 3, and 4, the pitot-static tubes were placed at the 

same lateral distance from the track as the axes of the cylindrical dummies. 

Configurations 5 and 6 were reference measurements to determine the extent of reversed 

airflow (airflow in the -x and -y directions). The details of each of these configurations 

are shown in Table 18. 
Part 1: Digest of Research 

67

Table 18. Configurations for Airflow Velocity Measurement at Heights Z1=0.866 m (34 in) and 

Z2=1.628 m (64 in) above Top of Rail 

Description 

Configuration 

Pitot-Static 

Tube 

Position* 

Lateral 

Distance 

(YA or YB) 

from Side 

of Train 

Direction of Airflow 

 being Measured 

Alignment same as July 

2000 test with pitot-static 

tubes parallel to track. 

1 YA-Z1 

YA-Z2 

0.603 m 

(23.8 in) 

•

•

parallel to track 

in direction of moving train (+x) 

YB-Z1 

YB-Z2 

1.442 m 

(59.8 in) 

•

•

parallel to track 

in direction of moving train (+x) 

YA-Z1 & YA-Z2 aligned 

with cylinder axes of 

cylindrical dummies at 

position 1 with pitot-static 

tubes parallel to track. 

2 YA-Z1 

YA-Z2 

1.17 m 

(46.3 in) 

•

•

parallel to track 

in direction of moving train (+x) 

YB-Z1 

YB-Z2 

2.09 m 

(82.3 in) 

•

•

parallel to track 

in direction of moving train (+x) 

YA-Z1 & YA-Z2 aligned 

with cylinder axes of 

cylindrical dummies at 

position 1 with pitot-static 

tubes parallel & 

perpendicular to track. 

3 YA-Z1 

YA-Z2 

1.17 m 

(46.3 in) 

•

•

parallel to track 

in direction of moving train (+x) 

YB-Z1 

YB-Z2 

0.933 m 

(36.8 in) 

•

•

perpendicular to track 

away from train (+y) 

YA-Z1 & YA-Z2 aligned 

with cylinder axes of 

cylindrical dummies at 

position 2 with pitot-static 

tubes parallel & 

perpendicular to track. 

4 YA-Z1 

YA-Z2 

1.43 m 

(56.3 in) 

•

•

parallel to track 

in direction of moving train (+x) 

YB-Z1 

YB-Z2 

1.19 m 

(46.8 in) 

•

•

perpendicular to track 

away from train (+y) 

Reversed airflow 

measurement with pitotstatic tubes parallel & 

perpendicular to track. 

5 YA-Z1 

YA-Z2 

1.63 m 

(64.3 in) 

•

•

perpendicular to track 

toward train (-y) 

YB-Z1 

YB-Z2 

1.39 m 

(54.8 in) 

•

•

parallel to track 

opposite direction of moving train (-x) 

YA-Z1 & YA-Z2 aligned 

with cylinder axes of 

cylindrical dummies at 

position 1 for reversed 

airflow measurement with 

pitot-static tubes parallel & 

perpendicular to track. 

6 YA-Z1 

YA-Z2 

0.845 m 

(33.3 in) 

•

•

perpendicular to track 

toward train (-y) 

YB-Z1 

YB-Z2 

0.603 m 

23.8 in) 

•

•

parallel to track 

opposite direction of moving train (-x) 

*Pitot-static tubes located near (YA) or far (YB) from the train, or at the bottom (Z1) or top (Z2) positions. 
Part 1: Digest of Research 

68

The airflow was measured for six 

different test configurations of the pitotstatic tubes with one or more passes 

from each of three different types of 

trains. Table 19 shows the number of 

train passes for each test configuration 

for three types of trains: the Acela 

Express train, and the Amfleet trains 

with either an AEM-7 or HHP-8 

locomotive. The greatest number of 

airflow measurements was from the 

Acela Express train, whereas the 

Amfleet trains generally had only one or 

two passes for each type of locomotive. 

The results of these measurements are discussed in Part 2 of this report. 

Table 19. Number of Passing Trains 

Train Type Number Passing Trains for each 

Test Configuration 

1 2 3 4 5 6 

Acela Express 6 1 6 6 0 1 

Trainset 

Amfleet with 0 2 2 1 0 1 

AEM-7 

Amfleet with 3 1 2 2 1 0 

HHP-8 
Part 1: Digest of Research 

69
Part 1: Digest of Research 

70

7. Measurement of Force on Object from Passing Train 

A moving train displaces the air around it and causes a disturbance in the surrounding air 

that is reflected as a flow field around the train of varying static pressure and flow 

velocity. When a person is near a passing train, an interaction will occur with the flow 

field creating a pressure distribution on the person that can result in an unbalanced force. 

A measurement of airflow velocity captures one component of the disturbance, and while 

the dynamic pressure from the airflow can be related to a force on a person, yet another 

method is by a direct measurement of the force on the body. 

Forces have been measured using circular cylinders to represent a human body. Horner 

(1958) indicated that the human body is similar in aerodynamic shape to a circular 

cylinder with a height to diameter ratio of between 4 and 7. SNCF uses forces measured 

from instrumented circular cylinders to base their trackside and platform safety distances. 

However, for the range of airflow velocity of interest, the drag coefficient of a circular 

cylinder varies by a factor of three, as the airflow occurs in Reynolds numbers that are in 

the critical regime. The results from these tests indicate that the cylinder responded 

strongly to static pressure effects, but not to the dynamic wake velocity that is considered 

significant to the stability of people and objects (RAPIDE 2001). 

Because the characteristics of a circular cylinder may not be representative of a human 

body, tests have been directed to measure the force on a human-shaped mannequin whose 

geometric and physical properties closely resemble that of a human being. A test was 

conducted in Sweden to measure forces on simple bodies in the form of a semicircular 

cylinder that simulated a person standing on a station platform exposed to the wind 

effects of the following passing trains: Inter-City trains (Swedish express trains), freight 

trains, and Swedish X2 modern high-speed trains (Andersson, Aronsson, and Pettersson 

1994). As part of the European RAPIDE project, a full-scale test was conducted in 

Germany to measure the forces on instrumented mannequins placed alongside the track 

as an ICE high-speed train passes (Johnson, Dalley, and Temple 2002; Prevezer 2001). 

China also performed similar full-scale tests on instrumented mannequins from which the 

data was used to arrive at recommended trackside and platform safety distances (Heshou, 

Dezhao, and Houxiong 1996). 

Although the circular cylinder may not fully simulate a human body over its full range of 

airflow velocity, it provides a means of gauging the relative force levels from its 

aerodynamic interaction with different trains. A circular cylinder’s symmetry simplifies 

the testing, because the response characteristic is the same independent of its orientation. 

The interaction of fluid flow over a circular cylinder has been extensively studied with an 

abundance of data available for computation and analysis. Therefore, a test was 

conducted using instrumented circular cylinders stationed alongside the track to gain a 

better understanding on the load applied to a body from the aerodynamic interaction with 

a passing train (SNCF 2002). 
Part 1: Digest of Research 

71

7.1. Test Configuration and Instrumentation 

In a research program conducted in France by the SNCF, both theoretical and 

experimental results were obtained on the force that would be experienced by a person in 

proximity to a passing train (Marty, Coulmy, and Luu 1978). During the early stages of 

their research, a series of detector pins were placed at various distances from the track. 

These detector pin were designed to fall at a defined wind speed of 17 m/s (38 mph) 

generated by a passing train. In the 1970s, SNCF developed a dummy that was 

instrumented to measure the force from the aerodynamic interaction between the dummy 

and a passing train. The dummy was designed as a circular cylinder that geometrically 

represents the trunk of a person and accounts for the muscular reaction time of a human. 

Both theoretical calculations and experimental measurements were made to determine the 

force on the cylindrical object from the induced airflow generated by the head of a 

passing TGV 001 train. The maximum force measured from the dummy can be related to 

the airflow velocity from the safety distance found during the test with the detector pins. 

This establishes the maximum force that is applied to a person (the trunk segment) when 

situated at a distance from the track where the maximum air velocity is attained. 

Using cylindrical dummies similar to those used in 

France, a full-scale test was conducted by SNCF 

personnel to measure the forces on the dummies 

from the aerodynamic interaction with a passing 

train. The circular cylindrical instrumented dummy 

(CID) was a SNCF/VR Model 1993 which consisted 

of a cylinder with a diameter of 0.39 m (15.4 in) and 

an axial length of 0.92 m (36.2 in) as shown in 

Figure 16 and illustrated in Figure 17. The cylinder 

was supported on a post with strain gauges attached 

to the post to measure the unbalanced force acting on 

the cylinder along a horizontal plane. Any bending 

to the post is related to the unbalanced force applied 

to the cylinder. Data from the CID was measured at 

1200 samples per second and was processed through 

a Bessel second order 15 Hz low-pass digital filter to 

account for the muscular reaction time of a human 

being. The resultant force is expressed as two time- Figure 16. Cylindrical Instrumented varying force components, Fx(t) and Fy(t), with the Dummy for Measuring Force coordinate frame shown in Figure 18. Relative to an from Aerodynamic 

observer facing the same direction of travel as the Interaction with a Passing 

passing train, the positive longitudinal axis (+x) is in Train 

the direction of the facing observer, and the positive 

lateral axis (+y) is to the right. Zero time occurs 

when the nose of the train reaches each CID, with time increasing as the train passes. 
Part 1: Digest of Research 

72

The test was performed on a low-level train station platform in Mansfield, Massachusetts, 

from September 29 to October 3, 2002. Two CIDs referred to as CID-4 and CID-5, were 

placed on the platform (platform height was about 0.1 m (4 in) from the top of the rail) 

with both CIDs at the same distance away from the track for simultaneous measurements 

as shown in Figure 19. Forces on the CIDs were measured for two different lateral 

positions from the track. In the first location, the nominal distance from the side of the 

train to the axis of the cylindrical body was 1.20 m (47.4 in). At this distance, the nearest 

surface of the cylinder facing the track was at the edge of the 0.965 m (38 in) wide 

platform safety line. In the second location, the nominal distance from the side of the 

train to the axis of the cylindrical body was 1.46 m (57.7 in). This distance corresponded 

to the safety distance used in France for railroad personnel next to a high-speed track 

(with TGV trains running faster than 209 km/h (130 mph) and conventional trains 

running faster than 161 km/h (100 mph)). The lateral distances measured from various 

locations are shown in Table 20. 
Part 1: Digest of Research 

73

SNCF CIRCULAR CYLINDRICAL INSTRUMENTED DUMMY (CID) SIMULATING THE REACTION

FORCE ON THE TRUNK OF A HUMAN BODY WITH MUSCULAR REACTION TIME

Total Weight: 1,177 N (265 lb)

Fluid Pressure

Gaging Unit 15 Hz

Low-Pass Filter Force

Strain

Gauges

Damping System

(Suspended Weights)

Aluminum Measuring Stand

* Tube diameter: 90 mm (3.5 in)

* Wall thickness: 5 mm (0.197 in)

SNCF/VR Model 1993

Carbon Fiber Cylinder 0.92 m (36.2 in)

0.39 m

(15.4 in)

1.00 m

(39.4 in)

Figure 17. SNCF Circular Cylindrical Instrumented Dummy for Measuring Force from 

Aerodynamic Interaction with a Passing Train 
Part 1: Digest of Research 

74

CYLINDRICAL INSTRUMENTED DUMMY WITH SPATIAL AND TEMPORAL COORDINATE FRAMES

Top View

Time

0

Train

x

y

Dummy

Figure 18. Coordinate Frames for a CID 
Part 1: Digest of Research 

75

Dummy

CID-4

Dummy

CID-5

TEST LAYOUT FOR MEASURING AIRFLOW VELOCITY AND FORCE ON CID

ON STATION PLATFORM AT MANSFIELD IN MASSACHUSETTS

Providence, Rhode Island Boston, Massachusetts

22.25 m

(73 ft)

Train Direction

Pitot-Static Tubes

Strain Gauges Beam and Photoelectric Sensor

Top View

----- (b) -----

----- (a) -----

Rear View with Train Moving Away from Observer

Lateral Distance to Nearest

Cylindrical Body Surface

Facing Train

Lateral Distance to Axis of

Cylindrical Body

Height to Center of Pressure

CID

Quadrant

1

ψ x

y

z

φ y

Figure 19. Test Layout on Train Station Platform at Mansfield, Massachusetts Showing (a) Top 

View and (b) Rear View 
Part 1: Digest of Research 

76

Table 20. Positions of CIDs and the Number of Passing Trains Measured 

Location Position 1 Position 2 

CID-4 CID-5 CID-4 CID-5

Lateral distance (y) from nearest cylindrical 

body surface to outer edge of nearest rail. 

1.74 m 

(65.50 in) 

1.74 m 

(65.50 in) 

2.00 m 

(78.74 in) 

2.00 m 

(78.74 in) 

Nominal lateral distance (y) from axis of 

cylindrical body to side of train. 

1.20 m 

(47.4 in) 

1.20 m 

(47.4 in) 

1.46 m 

(57.7 in) 

1.46 m 

(57.7 in) 

Nominal lateral distance (y) from nearest 

cylindrical body surface to side of train. 

1.01 m 

(39.8 in) 

1.01 m 

(39.8 in) 

1.27 m 

(49.9 in) 

1.27 m 

(49.9 in) 

Height (z) from center of pressure of 

cylindrical body to top of rail. 

1.25 m 

(49.21 in) 

1.24 m 

(48.82 in) 

1.25 m 

(49.21 in) 

1.24 m 

(48.82 in) 

Type of Train Number of Passing Trains at 

Position 1 

Number of Passing Trains at 

Position 2 

Acela Express Trainset 14 (28 samples) 12 (24 samples) 

Amfleet Train with AEM-7 Locomotive 8 (16 samples) 9 (18 samples) 

Amfleet Train with HHP-8 Locomotive 7 (14 samples) 3 (6 samples) 

At the location of each cylindrical dummy, strain gauges were installed on the rail to 

detect the axles of the passing trains. A weather station was present for measuring wind 

speed, wind direction, air temperature, barometric pressure, and relative humidity. Wind 

direction is referenced to positive rotation about the z-axis (+z down) with 0° wind 

direction along (+x), and 90° wind direction along (+y) (Figure 19). 

Measurements were made from three different types of trains passing the test site. The 

significant features that distinguish each type of train are the geometries of the nose and 

tail with the nose shape generally having the greatest aerodynamic effect. The three 

types of trains tested that represent the various geometries are: 

• High-speed Acela Express trainset with a tapered nose power car at each end 

(Acela Express train). 

• Conventional train with flat end Amfleet cars pulled by bluff nose AEM-7 

locomotive (Amfleet/AEM-7 train). 

• Conventional train with flat end Amfleet cars pulled by slant nose HHP-8 

locomotive (Amfleet/ HHP-8 train). 

The geometric profiles for these trains and the number of locomotives and cars for the 

consist in the test are shown in Figure 20. From the geometric profiles, the Acela 

Express train represents one end of the geometric spectrum with a tapered nose and tail, 
Part 1: Digest of Research 

77

whereas the Amfleet/AEM-7 train represents the other geometric extreme with a bluff 

nose and flat tail end at the last car. The Amfleet/HHP-8 train is a geometric hybrid with 

a slant nose and a flat tail end. No trains with the F40PH locomotive were in this test, 

but this locomotive pulled trains in previous tests. 

Many passes of each type of train were measured. To obtain a valid statistical 

measurement, the test required a minimum of 20 samples (SNCF 2002). Since two CIDs 

were used, the test required 10 passes for each type of train. Only measurements from 

the Acela Express train fulfilled the minimum of 20 samples (Table 20). Only six 

samples were obtained for the Amfleet/HHP-8 train with the CIDs placed at position 2. 
Part 1: Digest of Research 

78

GEOMETRIC PROFILE AND CONSIST OF PASSING TRAIN

Acela Express Trainset

Number of power cars: 2 at each end.

Number of passenger cars: 6.

Amfleet Train with AEM-7 Locomotive

Number of locomotives: 1 (2 in one case).

Number of Amfleet cars: 3 to 8.

Amfleet Train with HHP-8 Locomotive

Number of locomotives: 1.

Number of Amfleet cars: 7 to 10.

Amfleet Train with F40PH Locomotive

Number of locomotives: 1.

Number of cars: number varies with mixed Amfleet and other cars.

Figure 20. Types of Passing Trains Tested 
Part 1: Digest of Research 

79

7.2. Aerodynamic Loading on a Cylindrical Instrumented Dummy 

The force measured from each CID was processed to provide a statistical description of 

the data. First, the raw data representing the force was processed by a digital Bessel 

second order 15 Hz low-pass filter to account for the muscular response time of a human 

being as established by SNCF. After the filtering, maximum forces were obtained for 

various zones along the length of the train. 

A train moving through the atmosphere creates peak disturbances to the air in certain 

defined zones along the length of the train. Generally, these peak changes in static air 

pressure from the inviscid flow field occur at the head and tail ends of the train, as well 

as from the gaps between cars or other discontinuities. In addition, regions where airflow 

velocity from the viscous effects can reach significant levels exist, which are largely 

influenced by the geometry of the train. Therefore, for purposes of data analysis, the 

flow field from a passing train is divided into regions of aerodynamic disturbance along 

the length of the train as shown in Figure 21 and described as follows: 

• Head region, from ahead of the nose to the passage of the head of the train, 

• Tail region, from the passage behind the head to the tail end of the train including 

the wake, 

• Wake region, from the passage of the tail end behind the base of the train, and 

• Train region, the entire flow field surrounding the passing train. 

The maximum force from the CID was obtained for each train pass over each flow field. 

For a given train type and position of the CIDs, the mean and its standard deviations of 

all the maximum forces are computed for all the train passes. Because trains passed at 

various speeds, the force on the CID for each train pass is normalized by the square of the 

train speed from which a drag indicator9

 can be obtained for comparing the aerodynamic 

force from the different types of trains (SNCF 2002). Train speed is the normalizing 

parameter because the force on the CID is a drag produced by its interaction with the 

flow field around the passing train. The drag is proportional to the square of the airflow 

velocity, and if the assumption is that the airflow velocity on the CID is proportional to 

the speed of the train, the force on the CID is then proportional to the square of the train 

speed. 

 

9

SNCF defines the drag indicator as a force obtained by multiplying the normalized statistical force (mean 

plus two standard deviation) by the square of the desired train speed for comparing the different types of 

trains at the desired speed. 
Part 1: Digest of Research 

80

FLOW FIELD AROUND A PASSING TRAIN

Nose

Train Direction

Tail Pulse Head Pulse

Boundary Layer

Base

Wake Region

Tail Region

Flow Field from Tail Passage

(Train Passage Excluding Head)

Tail End Head End

Train Region

Flow Field from Train Passage

(Complete Passage of Train Including Wake)

Head Region

Flow Field from Head Passage

Figure 21. Description of Airflow around a Passing Train 
Part 1: Digest of Research 

81

The maximum force per train speed square on the CIDs, with the cylindrical axis at 

1.20 m (47.4 in) from the side of the train (position 1), are plotted for each passing train 

as shown in Figure 22, Figure 23, and Figure 24 for the Acela Express train, 

Amfleet/AEM-7 train, and Amfleet/HHP-8 train respectively. Each graph is a triptych 

showing the maximum normalized forces from the passing head and tail of the train for 

each CID, and the maximum forces from the passage of the entire train from both CIDs. 

From the first two panels of each graph, the normalized forces on the CID from the head 

pulse of the Acela Express train and the Amfleet/HHP-8 train are clustered in a narrow 

range indicating a relatively smooth inviscid flow from the slender nose geometry. This 

is in contrast to the large scatter in the forces from the head pulse of the AEM-7 

locomotive and in the tails of the Acela Express and Amfleet trains. In the last panel of 

each graph is the maximum normalized force from the passage of the entire train, either 

from the head or tail, for both CIDs. A horizontal line indicates the mean value of the 

maximum normalized forces for all the train passes. The Acela Express train produced 

the lowest mean normalized force whereas the Amfleet/AEM-7 train produced the 

highest force, and the mean force from the Amfleet/HHP-8 train is between the other two 

types of trains. When compared with the French TGV train at the same speed and 

distance away, the head perturbation from the Acela Express train produces a force that is 

about 15 percent higher (SNCF 2002). The cross sectional area of the Acela Express 

train is also slightly greater than the TGV train. 

The geometry of the train can also influence the location along the train where the 

maximum force on the CID occurred. Figure 25 shows the plots of the maximum 

normalized forces on the CIDs and its location of occurrence along the trains. Each 

dimensionless location is normalized by the length of the passing train, so that the head 

end of the train is zero, the tail end is one, and locations along the wake of the train will 

be greater than one. As these plots show, the maximum force for the Acela Express train 

occurred largely at the wake of the train (Figure 25(a)). This differs from the 

Amfleet/AEM-7 train where the maximum force was generally from the head of the train 

(Figure 25(b)), whereas with the HHP-8 locomotive, the maximum force all occurred 

somewhere between the head and tail ends (Figure 25(c)). None of the Amfleet trains 

with a flat-tail base create a large wake force. 
Part 1: Digest of Research 

82

MAXIMUM NORMALIZED RESULTANT FORCE ON CID WITH 

CYLINDER AXIS AT 1.20 m (47.4 in) FROM SIDE OF PASSING 

ACELA EXPRESS TRAIN

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

4.50E-03

5.00E-03

123

Data Set: 1.x (M5), 2.x (M4), 3.x (M5+M4)

Force per Train Speed Square, (N)/(km/h)**2

CID-5 Force from Passing Head of Train

CID-5 Force from Passing Tail of Train

CID-4 Force from Passing Head of Train

CID-4 Force from Passing Tail of Train

CID-5 and CID-4 Force from Complete Train Passage

Mean Force from CID-5 and CID-4

CID-5 CID-4 CID-5 & CID-4

Raw Data Filtered by Bessel Second Order 15 Hz Low-Pass Digital Filter

CID: Cylindrical Instrumented Dummy

4

Figure 22. Maximum Forces on CIDs at 1.20 m (47.4 in) from Passing Acela Express Trains 
Part 1: Digest of Research 

83

MAXIMUM NORMALIZED RESULTANT FORCE ON CID WITH 

CYLINDER AXIS AT 1.20 m (47.4 in) FROM SIDE OF PASSING 

AMFLEET TRAIN WITH AEM-7 LOCOMOTIVE

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

4.50E-03

5.00E-03

123

Data Set: 1.x (M5), 2.x (M4), 3.x (M5+M4)

Force per Train Speed Square, (N)/(km/h)**2

CID-5 Force from Passing Head of Train

CID-5 Force from Passing Tail of Train

CID-4 Force from Passing Head of Train

CID-4 Force from Passing Tail of Train

CID-5 and CID-4 Force from Complete Train Passage

Mean Force from CID-5 and CID-4

CID-5 CID-4 CID-5 & CID-4

Raw Data Filtered by Bessel Second Order 15 Hz Low-Pass Digital Filter

CID: Cylindrical Instrumented Dummy

4

Figure 23. Maximum Forces on CIDs at 1.20 m (47.4 in) from Passing Amfleet Trains with 

AEM-7 locomotives 
Part 1: Digest of Research 

84

MAXIMUM NORMALIZED RESULTANT FORCE ON CID WITH 

CYLINDER AXIS AT 1.20 m (47.4 in) FROM SIDE OF PASSING 

AMFLEET TRAIN WITH HHP-8 LOCOMOTIVE

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

4.50E-03

5.00E-03

123

Data Set: 1.x (M5), 2.x (M4), 3.x (M5+M4)

Force per Train Speed Square, (N)/(km/h)**2

CID-5 Force from Passing Head of Train

CID-5 Force from Passing Tail of Train

CID-4 Force from Passing Head of Train

CID-4 Force from Passing Tail of Train

CID-5 and CID-4 Force from Complete Train Passage

Mean Force from CID-5 and CID-4

CID-5 CID-4 CID-5 & CID-4

Raw Data Filtered by Bessel Second Order 15 Hz Low-Pass Digital Filter

CID: Cylindrical Instrumented Dummy

4

Figure 24. Maximum Forces on CIDs at 1.20 m (47.4 in) from Passing Amfleet Trains with HHP-8 

Locomotives 
Part 1: Digest of Research 

85

MAXIMUM NORMALIZED RESULTANT FORCE ON CID AND LOCATION OF

MAXIMUM FORCE RELATIVE TO PASSING TRAIN

----- (c) -----

----- (a) -----

----- (b) -----

Cylinder Axis of CID at a Nominal Distance of 1.20 m (47.4 in) from Side of Train

0

0.001

0.002

0.003

0.004

0.005

0 1

(head) Train (tail)

Normalized Force,

(N/(km/h) )2

Dimensionless Distance Normalized by Train Length

Acela Express Train

CID-5

CID-4

CID: Cylindrical Instrumented Dummy

0

0.001

0.002

0.003

0.004

0.005

0 1

(head) Train (tail)

Amfleet Train with AEM-7 Locomotive

Normalized Force,

(N/(km/h) )2

CID-5

CID-4

Dimensionless Distance Normalized by Train Length

0

0.001

0.002

0.003

0.004

0.005

0 1

(head) Train (tail)

Amfleet Train with HHP-8 Locomotive

Normalized Force,

(N/(km/h) )2

CID-5

CID-4

Dimensionless Distance Normalized by Train Length

Figure 25. Maximum Forces on CIDs at 1.20 m (47.4 in) from Passing Trains and Locations Along 

the Passing Trains where Maximum Forces Occurred 
Part 1: Digest of Research 

86

These results can be summarized by plotting a bar graph of the mean plus two standard 

deviations of the maximum normalized forces on the CIDs at various flow fields around 

the passing trains. Figure 26 shows the plots of the normalized forces comparing the 

three types of trains along the different flow fields created by the passage of the head, 

tail, wake, and entire train. Treating each flow field individually (Figure 26(a)), the 

largest force from the head flow field is from the Amfleet/AEM-7 train, whereas at the 

wake, it is the Acela Express train that produced the largest force. At the tail flow field, 

the greatest force is from the Amfleet/HHP-8 train, which occurs before the tail end of 

the train (Figure 25(c)). These same effects at different flow fields are also shown for 

each train individually (Figure 26(b)). The maximum force from the Acela Express train 

is at or near the wake, the maximum force from Amfleet/AEM-7 train is at head flow 

field, and diminishes toward the wake, whereas the maximum force from Amfleet/HHP-8 

train reaches its maximum toward the tail end of the train but before the wake. 

Overall, for the passage of the entire train, the Acela Express train produced the lowest 

normalized force on the CIDs, and the Amfleet/AEM-7 train produced the strongest 

force. In terms of relative strength with the CID at position 1, the Amfleet/AEM-7 train 

produced an aerodynamic force on the CIDs that is a factor of 2.4 higher than the Acela 

Express train, and the Amfleet/HHP-8 train is a factor of 1.8 higher than the Acela 

Express train. The maximum normalized forces, means, standard deviations, and means 

plus two standard deviations are all listed in Table 21 for the different trains and flow 

field regions. 

From these results, the geometry of the train, particularly at the head end, has a 

significant influence on the flow field that is created around the train, and therefore, on 

the aerodynamic effects to its surroundings. This phenomenon and its relation to the 

head end geometry can be described as follows: 
Part 1: Digest of Research 

87

----- (b) -----

----- (a) -----

Acela Express Train

Amfleet Train with AEM-7 Locomotive

Amfleet Train with HHP-8 Locomotive

Head Tail Wake Train

NORMALIZED RESULTANT FORCE ON CID AS A MEAN PLUS 2 STANDARD DEVIATIONS

OF THE MAXIMUM FORCES

CID: Cylindrical Instrumented Dummy Normalized Force, x10 (N/(km/h) ) -4 2

Flow Field Region

Comparison of Forces between Different Types of Trains

0

10

20

30

40

50

Head Tail Wake Train

Train Type

Comparison of Forces between Flow Field Regions

0

10

20

30

40

50

Acela Express Train Amfleet Train with AEM-7

Locomotive

Amfleet Train with HHP-8

Locomotive

Normalized Force,

x10 (N/(km/h) ) -4 2 Cylinder Axis of CID at a Nominal Distance of 1.20 m (47.4 in) from Side of Train

Figure 26. Maximum Forces on CIDs at 1.20 m (47.4 in) from Passing Trains Categorized by 

Types of Trains and Flow Field Regions 
Part 1: Digest of Research 

88

Table 21. Normalized Resultant Forces on CID-4 and CID-5 at Position 1 with Cylindrical Axes 

at 1.20 m (47.4 in) from Side of Passing Trains 

Train Type Flow Field Maximum, 

10-4

(N/(km/h)2

) 

Mean 

10-4

(N/(km/h)2

) 

Standard 

Deviation 

10-4

(N/(km/h)2

) 

Mean + 

2 Standard 

Deviations 

10-4

(N/(km/h)2

) 

9.5

18.4

Acela Express 

Trainset 

Head 

Tail 

9.8 

22.9 

8.2 

11.0 

0.7 

3.7 

Wake 22.9 10.7 3.9 18.5

18.2

43.2

25.1

12.5

43.1

13.5

32.0

10.1

32.0

Train 22.9 11.3 3.5 

Amfleet Train 

with AEM-7 

Locomotive 

Head 

Tail 

Wake 

43.5 

25.2 

13.7 

23.6 

17.9 

8.0 

9.8 

3.6 

2.3 

Train 43.5 25.0 9.1 

Amfleet Train 

with HHP-8 

Locomotive 

Head 

Tail 

Wake 

14.2 

31.3 

9.8 

10.9 

20.8 

7.7 

1.3 

5.6 

1.2 

Train 31.3 20.8 5.6 

Firstly, the perturbation to the air caused by the head of the train as it passes is 

transmitted through the surrounding air for some distance before it dies away.... 

Although this first phenomenon is an inviscid effect, there may be associated with 

it, particularly for trains with blunter head shapes, a viscous effect caused by a local 

separated flow just behind the head, due to the fluid close to surface being unable 

to negotiate the adverse pressure gradient of the sharp corner around the head. The 

separation bubble is effectively dragged along with the train and the mean axial 

velocity of the fluid contained in it is moving at approximately the train speed. Its 

effect therefore on a stationary body in its path can be significant. In addition, the 

far-field pressure effects of the head perturbation will be increased due to the 

enlarged effective train head cross-section caused by the displacement surface 

representing the separated flow region. However, for well streamlined nose/head 

shapes, there will be no separated flow region...and these secondary effects will 

not be present. (Gawthorpe 1972) 

The tail end geometry also has its influence on the flow, where a rear-facing power car as 

in the Acela Express train with its tapered tail end can have the following effect: “For 

slender-nosed trains, the gust associated with the train nose and the mean level of 

slipstream speed is much reduced but the gusts in the wake are more pronounced due to 
Part 1: Digest of Research 

89

the improved tail-end shapes, which cause a narrower and more concentrated wake” 

(Gawthorpe 1978). 

The relative aerodynamic forces on the CIDs from the different trains are compared, with 

the mean force plus two standard deviations scaled to the train’s maximum nominal 

operating speed. For trains passing at a speed of 201 km/h (125 mph), the Acela Express 

train produces a force on the CIDs of 74 N (17 lb), while the Amfleet/AEM-7 train 

generates a force of 174 N (39 lb). When the Acela Express train is increased to a speed 

of 241 km/h (150 mph), it produces a force on the CIDs of 106 N (24 lb), which is still a 

lower force than the force generated from a passing Amfleet train at the lower speed of 

201 km/h (125 mph). These results are shown in Table 22. 

Table 22. Drag Indicators on CIDs for Trains Passing at Their Nominal Operational Speeds 

Train Type Resultant Force Mean + 2 Standard Deviation 

Position 1 Position 2 

Cylindrical Axis at 1.20 m Cylindrical Axis at 1.46 m 

(47.4 in) from Side of Train (57.7 in) from Side of Train 

201 km/h 241 km/h 201 km/h 241 km/h 

(125 mph) (150 mph) (125 mph) (150 mph) 

Acela Express Trainset 74 N 106 N 63 N 91 N 

(17 lb) (24 lb) (14 lb) (20 lb) 

Amfleet Train with AEM-7 174 N 119 N 

Locomotive (39 lb) (27 lb) 

Amfleet Train with HHP-8 129 N 129 N 

Locomotive (29 lb) (29 lb) 

The CIDs were also tested at position 2 that was further away from the passing train, with 

the cylindrical axis at 1.46 m (57.7 in) away from the side of the train. Results for 

position 2 are shown plotted in Figure 27, Figure 28, Figure 29, and Figure 30 and listed 

in Table 22 and Table 23. There were only six samples (three train passes) of force 

measurements from the Amfleet/HHP-8 train (Figure 29), which were insufficient for a 

valid characterization of this train according to the SNCF criterion (SNCF 2002). The 

results for this train are listed in Table 22 and Table 23 for completeness, and should not 

be used for comparison with the other trains. Comparing the relative force level, the 

Amfleet/AEM-7 train produced an aerodynamic force on the CIDs that is a factor of 1.9 

higher than the Acela Express train. An increase in lateral distance from the side of the 

train by 22 percent reduced the mean force plus 2 standard deviations by 14 percent for 

the passage of Acela Express train and reduced the force by 32 percent for the 

Amfleet/AEM-7 train. The trend on the forces for the various flow fields at position 2 is 

the same as in position 1 (Figure 30) except for a general reduction in the strength of the 

force. 
Part 1: Digest of Research 

90

Table 23. Normalized Resultant Forces on CID-4 and CID-5 at Position 2 with Cylindrical Axes 

at 1.46 m (57.7 in) from Side of Passing Trains 

Train Type Flow Field Maximum, 

10-4

(N/(km/h)2

) 

Mean 

10-4

(N/(km/h)2

) 

Standard 

Deviation 

10-4

(N/(km/h)2

) 

Mean + 

2 Standard 

Deviations 

10-4

(N/(km/h)2

) 

Acela Express 

Trainset 

Head 

Tail 

9.8 

15.8 

7.2 

9.7 

1.0 

3.1 

9.2

15.9

Wake 15.8 9.6 3.2 16.1

Train 15.8 10.1 2.7 15.6

Amfleet Train 

with AEM-7 

Locomotive 

Head 

Tail 

Wake 

31.0 

22.7 

9.4 

16.7 

14.1 

6.5 

6.2 

3.8 

1.1 

29.2

21.8

8.8

Train 31.0 17.8 5.8 29.4

Amfleet Train 

with HHP-8 

Locomotive 

Head 

Tail 

Wake 

11.5* 

27.8* 

15.8* 

9.4* 

23.2* 

9.3* 

1.5* 

4.4* 

3.3* 

12.3*

32.0*

15.9*

Train 27.8* 23.2* 4.4* 32.0*

*The number of samples was insufficient for a valid characterization of this train according to SNCF criterion but the values were 

computed and listed for completeness and should not be used for comparison with the other trains. 
Part 1: Digest of Research 

91

MAXIMUM NORMALIZED RESULTANT FORCE ON CID WITH 

CYLINDER AXIS AT 1.46 m (57.7 in) FROM SIDE OF PASSING 

ACELA EXPRESS TRAIN

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

4.50E-03

5.00E-03

123

Data Set: 1.x (M5), 2.x (M4), 3.x (M5+M4)

Force per Train Speed Square, (N)/(km/h)**2

CID-5 Force from Passing Head of Train

CID-5 Force from Passing Tail of Train

CID-4 Force from Passing Head of Train

CID-4 Force from Passing Tail of Train

CID-5 and CID-4 Force from Complete Train Passage

Mean Force from CID-5 and CID-4

CID-5 CID-4 CID-5 & CID-4

Raw Data Filtered by Bessel Second Order 15 Hz Low-Pass Digital Filter

CID: Cylindrical Instrumented Dummy

4

Figure 27. Maximum Forces on CIDs at 1.46 m (57.7 in) from Passing Acela Express Trains 
Part 1: Digest of Research 

92

MAXIMUM NORMALIZED RESULTANT FORCE ON CID WITH 

CYLINDER AXIS AT 1.46 m (57.7 in) FROM SIDE OF PASSING 

AMFLEET TRAIN WITH AEM-7 LOCOMOTIVE

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

4.50E-03

5.00E-03

123

Data Set: 1.x (M5), 2.x (M4), 3.x (M5+M4)

Force per Train Speed Square, (N)/(km/h)**2

CID-5 Force from Passing Head of Train

CID-5 Force from Passing Tail of Train

CID-4 Force from Passing Head of Train

CID-4 Force from Passing Tail of Train

CID-5 and CID-4 Force from Complete Train Passage

Mean Force from CID-5 and CID-4

CID-5 CID-4 CID-5 & CID-4

Raw Data Filtered by Bessel Second Order 15 Hz Low-Pass Digital Filter

CID: Cylindrical Instrumented Dummy

4

Figure 28. Maximum Forces on CIDs at 1.46 m (57.7 in) from Passing Amfleet Trains with 

AEM-7 Locomotives 
Part 1: Digest of Research 

93

MAXIMUM NORMALIZED RESULTANT FORCE ON CID WITH 

CYLINDER AXIS AT 1.46 m (57.7 in) FROM SIDE OF PASSING 

AMFLEET TRAIN WITH HHP-8 LOCOMOTIVE

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

4.50E-03

5.00E-03

123

Data Set: 1.x (M5), 2.x (M4), 3.x (M5+M4)

Force per Train Speed Square, (N)/(km/h)**2

CID-5 Force from Passing Head of Train

CID-5 Force from Passing Tail of Train

CID-4 Force from Passing Head of Train

CID-4 Force from Passing Tail of Train

CID-5 and CID-4 Force from Complete Train Passage

Mean Force from CID-5 and CID-4

CID-5 CID-4 CID-5 & CID-4

Raw Data Filtered by Bessel Second Order 15 Hz Low-Pass Digital Filter

CID: Cylindrical Instrumented Dummy

4

Figure 29. Maximum Forces on CIDs at 1.46 m (57.7 in) from Passing Amfleet Trains with HHP-8 

Locomotives 
Part 1: Digest of Research 

94

----- (b) -----

----- (a) -----

Head Tail Wake Train

NORMALIZED RESULTANT FORCE ON CID AS A MEAN PLUS 2 STANDARD DEVIATIONS

OF THE MAXIMUM FORCES

CID: Cylindrical Instrumented Dummy

Acela Express Train

Amfleet Train with AEM-7 Locomotive

Amfleet Train with HHP-8 Locomotive*

Normalized Force,

x10 (N/(km/h) ) -4 2

Flow Field Region

Comparison of Forces between Different Types of Trains

0

10

20

30

40

50

Head Tail Wake Train

0

10

20

30

40

50

Acela Express Train Amfleet Train with AEM-7

Locomotive

Amfleet Train with HHP-8

Locomotive

Train Type

Comparison of Forces between Flow Field Regions

Normalized Force,

x10 (N/(km/h) ) -4 2

The number of samples

was insufficient for a

valid characterization

of this train.

Cylinder Axis of CID at a Nominal Distance of 1.46 m (57.7 in) from Side of Train

Figure 30. Maximum Forces on CIDs at 1.46 m (57.7 in) from Passing Trains Categorized by 

Types of Trains Flow Field Regions 
Part 2: Analysis and Evaluation 

95
Part 2: Analysis and Evaluation 

96

Part 2 

Analysis and Evaluation 
Part 2: Analysis and Evaluation 

97
Part 2: Analysis and Evaluation 

98

8. Numerical Simulation of Rail Car Roll Response to Aerodynamic 

Loading 

Part 1 of this report described a study to address the issue of dynamic response of a well 

car carrying empty double-stacked containers from aerodynamic interaction with a 

passing train. The aerodynamic side force applied to a light carbody can lead to the 

possibility of containers dislodging and falling over, or to an adverse dynamic response 

with a risk of derailment. The study involved CFD modeling of a high-speed passenger 

train passing a double-stack well car on tangent track that included the presence of 

ambient wind. A multi-body simulation model was used to obtain the dynamic response 

of the well car. A full-scale test was performed to measure the aerodynamic pressure on 

the surface of the containers as a high-speed train passes the double-stack well car on an 

adjacent track to obtain data to compare with modeling results. 

This chapter describes a single degree-of-freedom mathematical carbody roll model 

created to simulate the dynamic roll response of a rail car from transient aerodynamic 

force input produced by a train passing on an adjacent track. Force input to the doublestack well car was modeled from the aerodynamic pressure variation measured from a 

full-scale test. The roll response from the model was compared with test data to validate 

the model. Because the test was conducted at an altitude with a low air density 

environment, the carbody roll model was used to obtain roll response at sea level, where 

the force on the double-stack well car would be higher. 

The objective of this study was to extend the previous research results by including a 

broader range of train passing conditions. The responses of carbody roll from the effects 

of altitude, ambient wind, passing train speed, closing speed, and unbalanced speed on 

curved track were studied. In the first case, the double-stack well car was modeled 

traveling at different speeds as another train with different headwinds passes it. A second 

case was to study the effect on the response of a double-stack well car while negotiating a 

curved track with excessive cant as another train passes it. The results of this study also 

demonstrated the capability of using a single degree-of-freedom carbody roll model to 

predict the roll response of a rail car to aerodynamic interactions with a passing train, and 

with potential applications to other types of cars and trains. 

8.1. Modeling Pressure Variation of a Passing Train 

When a train moves through the air, a variation occurs in air pressure produced by the 

moving train, with the strength and shape of the variations depending on such factors as 

the speed and geometry of the train in addition to the presence and proximity of 

surrounding objects. With respect to an observer alongside the track, an increase in 

aerodynamic pressure occurs immediately before the head of the approaching train. The 

pressure rises to a positive peak, with the peak corresponding to approximately the nose 

of the train. As the head of the train passes, the pressure rapidly drops to a negative peak 
Part 2: Analysis and Evaluation 

99

and rises again to near ambient value. While the train is passing, any perturbations, such 

as gaps between cars, will produce additional pressure pulses. At the tail end of the train, 

another pressure pulse is produced, similar to the nose, but with a pressure dropping to a 

negative peak first and then quickly rising to a positive peak before a gradual recovery to 

ambient condition. These pressure variations are shown in Figure 31. 

AERODYNAMIC PRESSURE VARIATION PRODUCED BY A PASSING TRAIN MODELED BY

MATHEMATICAL FUNCTIONS AS PIECEWISE SECTIONS

OF STRAIGHT LINES AND SINUSOIDS

Pressure, (P)

t1

WAVE NUMBER

0 1 32 4 8

t0 t2 t3 t4 t5 t6 t7 t8 t9

Nose Pulse Tail Pulse

x0 x1 x2 x3 x4 x5 x6x7 x8 x9

Time, (t)

Distance, (x)

x = (V )(t) RELATIVE TRAIN SPEEDS

5 6 7

Figure 31. Modeling Aerodynamic Pressure Variation by Mathematical Functions 

As the train passes a rail car (a rail car being passed is referred to as the observer car) on 

an adjacent track, a load is exerted on the observer car from the aerodynamic pressures 

produced by the passing train. This load creates a lateral force and a roll moment on the 

observer car as shown in Figure 32. The largest aerodynamic pressure exerted on the 

observer car appears from the nose and tail of the passing train—with the pressures being 

highest near the ground—and diminishing toward the top of the train. 
Part 2: Analysis and Evaluation 

100

PRESSURE VARIATION ON OBSERVER CAR FROM AERODYNAMIC INTERACTION

WITH A TRAIN PASSING ON AN ADJACENT TRACK

----- (c) -----

----- (a) -----

Pressure, P

ΔP

Passing Train

(A) vA

Observer Car

(B) vB

----- (b) -----

Rear View of Train (A) Passing Observer Car (B)

with Side Force on Observer Car

(A)

LA

v VB LC A

(B)

Side View of Train (A) Passing Behind Car (B)

Top View of Train (A) Passing Observer Car (B)

Figure 32. Aerodynamic Interaction Between an Observer Car and a Train Passing on an Adjacent 

Track 
Part 2: Analysis and Evaluation 

101

The aerodynamic pressure variations for the entire train were modeled by dividing the 

variations into nine sections as wave numbers 0 to 8, with each section being modeled as 

a straight line or sinusoid, as shown in Figure 31. Wave numbers 0, 4, and 8 are modeled 

as straight lines, and the remaining waves are modeled as sine waves. A detailed 

description follows for wave number 0, and the nose pressure pulse composed of wave 

numbers 1, 2, and 3. 

Prior to the nose pressure pulse, the pressure variation for wave number 0 is represented 

by the straight-line equation, 

⎛ P − P ⎞ Equation 1

x0 ≤ x < x P P ⎜ x x1 x

1

x

0 = x x ⎟ 0 + = = 0

= ( ) x − x ⎜ ⎟ ⎝ x

1

1 − x0 ⎠

The nose and tail pressure pulses are modeled as a series of sinusoidal waves. Since 

these pressure pulses from the passing train are a significant contribution to the 

aerodynamic load exerted on the car being passed, it is necessary to have an accurate 

representation to these pressure variations. Figure 33 shows the aerodynamic nose 

pressure modeled by a series of three sinusoidal waves as follows: 

⎡1 ⎤⎧ ⎡2π ⎤⎫ E

x1 ≤ x < x2

P1 = ΔP1 + ⎢ ( ) quation 2a PAO − ΔP1 ⎥⎨1− cos⎢ ( ) x − x ⎥⎬ ⎣2 ⎦⎩ ⎣ λ 1

1 ⎦⎭

⎛ 1 ⎞ ⎡2πx ( )⎤ Equation 2b 

x ≤ x < x P2 = PAB − ⎜ ΔPAB ⎟ cos⎢ x − x2 ⎥ 2 3 ⎝ 2 ⎠ ⎣ λ2 ⎦

⎡1 ⎧ ⎫

x3 ≤ x < x4

P3 = ΔP3 − ⎢ ( )⎤⎪ ⎡2π ⎛ λ ⎞⎤⎪ Equation 2c ΔP 3

⎣2 3 − PBO ⎨ cos⎢ x − x ⎟ ⎥ 1− ⎜ + ⎥⎬ ⎦⎩

⎪ ⎣ λ3 ⎝ 3 2 ⎠⎦⎭

⎪

1 The peak-to-peak pressure pulse is ΔPAB = ( ) PBO − PAO , and its average value is 2

1 PAB = ( ) PAO + P

2 BO . The pressures for wave numbers 4 to 8 can be found in a similar 

fashion by changing the indices to correspond to that wave number and substituting the 

values for that particular section. 
Part 2: Analysis and Evaluation 

102

AERODYNAMIC PRESSURE PULSE FROM NOSE OF A PASSING TRAIN

MODELED BY PIECEWISE SECTIONS OF SINUSOIDS

ΔP1

PAO

PBO

λ1/2 λ3 λ /2 2/2

PAB

ΔP4

P1= P + [1⁄2(P - P)]{1 - cos[(2 / )(x - x)]} ΔΔ π 1 AO 1 λ1 1

PAB = 1⁄2(P + P ) AO BO

ΔPAB = (P - P ) BO AO

P2 = P + (1⁄2 P )cos[(2 / )(x - x)] AB Δ πλ AB 2 2

t2 t3 t4

P3= P - [1⁄2( P - P )]{1 - cos[(2 / )(x - x + /2)]} Δ Δ 4 4BO πλ λ 3 33

ΔPAB

Wave 1 Wave 2 Wave 3

t1

Pressure, (P)

Time, (t)

x = (V )(t) TRAIN SPEED

Distance, (x)

x1 x2 x3 x4

Figure 33. Modeling Aerodynamic Pressure Pulse Produced by Head Perturbation of a Passing 

Train 
Part 2: Analysis and Evaluation 

103

When a train passes a flat surface such as a wall besides the track or a rail car on an 

adjacent track, a force will be exerted on the surface from the aerodynamic pressures of 

the passing train. The aerodynamic force applied over an area on one side of the surface 

is, F = ∫∫ p(x,z)dzdx , 

A

where, 

x: longitudinal distance, 

z: vertical distance, and 

p: aerodynamic pressure. 

Assuming that the pressure varies only along the longitudinal (x) direction over the 

length LA, but is a uniform average pressure in the vertical (z) direction over the height 

LC, the force on the surface is, F = LC ∫ p(x)dx . This represents the force exerted on 

LA

only one side of the wall. 

Integrating the pressure variations represented by the linear and sinusoidal functions 

provides the force exerted on only one side of the wall facing the passing train. 

However, pressure variation measured on the far side of the well car were very small 

(Table 3 and Figure 8) and therefore, only the pressure variation exerted on the near side 

of the wall needs to be considered. 

From Equation 1 and Equation 2(a to b) for the nose pressure pulse (wave numbers 0, 1, 

2, and 3), the forces on the wall are derived as follows: 

⎧⎡ ⎛ P − P ⎞⎤ ⎫ ⎪⎢P = 0

1 − ⎜ x=x1 x x

x=x ⎟⎥( ) x − x ⎜ ⎟ x

1 ⎪

x0 ≤ < x1 ⎪⎢⎣ ⎝ x1 − x0 ⎠⎥⎦ ⎪ F0 = LC ⎨ ⎬ Equation 3

⎪ 1 ⎛ P − P ⎞ ⎪ + ⎜ x=x x x ⎟ ⎪ x − ⎜ 1 = 0

x x ⎟

( ) 2

x

2

1 ⎪ ⎩ 2 ⎝ 1 − 0 ⎠ ⎭

⎧⎡ 1 Equation 4a P ( )⎤ Δ 1 PAO P1 − ⎥( ⎫ ⎪ + − Δ ⎢ x x ⎣ 2 ⎦ 1 ) ⎪ ⎪ ⎪ x1 ≤ x < x2 F1 = LC ⎨ ⎬ ⎡⎛ λ1 ⎤ π ⎤ ⎪ ⎞

( ) ⎡2 P P ( ) x x ⎪ − ⎢⎜ ⎟ − Δ sin⎢ ⎪ 4 1 ⎥⎪ ⎩ ⎝ ⎠ AO ⎥ −

⎣ π

1

⎦ ⎣ λ1 ⎦⎭
Part 2: Analysis and Evaluation 

104

⎧ ( ) ⎛ λ2 ⎞ ⎡2π ⎤⎫ Equation 4b 

x ≤ x < x F2 = LC ⎨PAB x − x2 + ⎜ ⎟ΔPAB sin x − x2 2 3 ⎢ ( )⎥⎬ ⎩ ⎝ 4π ⎠ ⎣ λ2 ⎦⎭

⎧⎡ 1

⎪ ΔP3 + ⎢ ( )⎤

( ⎫ P quati Δ 3 − PBO x − x ) E on 4c ⎥ 3 ⎪ ⎪⎣ 2 ⎦ ⎪ x3 ≤ x < x4 F3 = LC ⎨ ⎬ ⎡ ⎪ ⎛ λ3 ⎞

( )⎤ ⎡2π ⎛ λ ⎤⎪ + ⎢⎜ ⎟ ΔP P 3 ⎞

⎪ 4π

3 − ⎝ ⎠ BO ⎥sin⎢ ⎜ x − x3 + ⎟⎥⎪ ⎩ ⎣ ⎦ ⎣ λ3 ⎝ 2 ⎠⎦⎭

Finally, to evaluate the pressure equations requires the values or amplitudes of the 

pressures at specified points and the range or wavelengths of the pressure variations. The 

magnitudes of these parameters are obtained either from results of CFD simulation, or 

from test data. 

8.2. Single Degree-of-Freedom Carbody Roll Model 

A single degree-of-freedom mathematical model was created to simulate the carbody roll 

response of the observer car from a transient aerodynamic side force input of a train 

passing on an adjacent track. The loads applied to the observer car include (1) the 

aerodynamic pressure variation of the passing train with the effects of ambient wind 

along the longitudinal direction (head or tail winds) on the passing train, and (2) the 

unbalanced force on the observer car as it negotiates a curve at unbalanced speed. 

8.2.1. Equation of Motion 

A freight car consists of a carbody, which is commonly suspended by two trucks. Each 

truck is composed of a bolster, two side frames, and two wheelsets (two wheels and an 

axle). The carbody rests on the bolster through the center plate, and the bolster is 

suspended by springs attached to the left and right side frames. The side frames are 

supported by the wheelsets. These components are shown in Figure 34(a). 
Part 2: Analysis and Evaluation 

105

ROLL MOTION OF FREIGHT CAR AND SINGLE DEGREE-OF-FREEDOM

MODEL OF CAR-BODY ROLL

Single Degree-of-Freedom Car-Body Roll Model with Car-Body and

Bolster Rolling together as a Single Body on the Suspension Springs

----- (a) -----

Freight Car Roll Motion with Bolster Deflecting Suspension Springs

and Car-Body Lifting off the Center Plate

Wheelset and Truck Frames

Car-Body

Bolster

Side Bearing

Vertical Suspension

Spring and Damper

Center Plate

Car-Body and Bolster

Torque

Torque

----- (b) -----

Figure 34. Freight Car and Single Degree-of-Freedom Model 
Part 2: Analysis and Evaluation 

106

The roll motion of a freight car is highly nonlinear during large roll angles. The roll 

moment is computed by applying a pure torque to the carbody (Figure 34(a)), as shown 

by the moment/roll angle plot in Figure 35(a). At small roll angles, the carbody and 

bolster roll as a unit deflecting the springs where it is relatively linear. At larger roll 

angles, the center plate has only partial contact with the carbody as the carbody rolls 

pivoting about the edge of the center plate. For even larger roll motion, the carbody 

completely lifts off the center plate and pivots about the side bearing. 

The significance of the carbody roll as it relates to the potential for derailment can be 

seen from the wheel loading. Carbody roll during static equilibrium redistributes the 

reaction forces at the wheel/rail contacts so that the reaction force on one wheel 

increases, while the reaction force on the other wheel decreases. Figure 35(b) shows the 

plots of the wheel loads on the unloading wheel for three different cases of applied 

torque. A pure torque applied to the carbody will not cause any wheel lift, with the 

minimum wheel load at 4.7 percent. However, a lateral force producing the equivalent 

applied torque either at the center-of-mass or at the center-of-pressure will cause the 

wheel to lose contact with the rail at about 0.85 deg. While these wheel loads are for 

static equilibrium, and do not account for the dynamic response, the wheel load to an 

initial lateral aerodynamic load to the carbody can be approximated from the static 

loading. 

The single degree-of-freedom mathematical model consists of a single mass that 

represents the carbody and bolster, with both always rolling as a unit (Figure 34(b)). It is 

suspended by a single set of linear springs and viscous dampers on each side. Figure 

36(a) shows the lateral forces acting on the model that consist of aerodynamic force and 

inertia forces from track superelevation and curvature. The free body diagram of the 

model with the suspension forces and the forces acting at the center-of-mass and centerof-pressure are shown in Figure 36(b). The roll moment for the linear single degree-offreedom model is shown in Figure 35(a), where the roll moment is valid until it reaches a 

carbody roll angle of about 0.3°. Therefore, when this roll angle is exceeded in the 

simulation, the results should be regarded as qualitative trends. 

Another parameter included in this model is ambient wind that is either a headwind or 

tailwind to the passing train. The wind speed is an additive or subtractive component to 

the airflow velocity relative to the passing train. The assumption is that the end effects of 

the observer car do not disrupt the airflow as if the passing train is running along side an 

infinitely long smooth wall as shown in Figure 37. 
Part 2: Analysis and Evaluation 

107

STATIC EQUILIBRIUM OF CAR-BODY ROLL AND WHEEL LOAD FROM

TORQUE APPLIED TO AN EMPTY DOUBLE-STACK WELL CAR

----- (b) -----

----- (a) -----

Car-Body Roll Angle, (deg)

Roll Moment, (N m) •

(lb in) •

0

10x105

5x105

Car-Body Roll Moment

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

5x104

10x104

15x104

Single Degree-of-Freedom Car-Body Roll Model

Force on the Unloading Wheel

Car-Body Roll Angle, (deg)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

10

20

30

40

50

60

70

80

90

100

Wheel/Rail Load, (Percent of Static Load)

Wheel Load from Pure Torque

Wheel Load from Lateral Force

 at Center-of-Mass

Wheel Load from Lateral Force

 at Center-of-Pressure

X

Figure 35. Moment and Wheel Load of Carbody Roll at Equilibrium 
Part 2: Analysis and Evaluation 

108

mg

zT

MT

yT

SINGLE DEGREE-OF-FREEDOM MATHEMATICAL MODEL OF CAR-BODY ROLL

FROM LATERAL FORCE WITH TRACK SUPERELEVATION AND CURVATURE

----- (b) -----

FyCP

φ

FyCM

kLS SB BSφ + c L (d /dt) S φ

k: SS pring Constant per Car Side

c : Coefficient of Viscous Damping

 per Car Side S

kLS SB BSφ S + c L (d /dt) φ

FyCP: Force Applied to

 Center-of-Pressure

FyCM: Force Applied to

 Center-of-Mass

Free Body Diagram

----- (a) -----

Rear View

2LBS

Track Plane

Center of Curvature

Horizontal Plane RT

Parallel to Track Plane

mg

Car-Body

Center of Mass

Fy

LCCM

LCCP

2LBS

LCCM: Vertical Distance to

 Center-of-Mass

LCCP: Vertical Distance to

 Center-of-Pressure

z

y

φ

Figure 36. Single Degree-of-Freedom Mathematical Model for Carbody Roll 
Part 2: Analysis and Evaluation 

109

AIRFLOW ON PASSING TRAIN AND OBSERVER CAR WITH AMBIENT WIND

----- (b) -----

` x

y

Passing Train (A)

U = V - U A A windX

----- (a) -----

Longitudinal Airflow on Passing Train Modeled as a Train

Passing an Infinitely Long Wall

UwindX

Wind Velocity

Infinitely Long Wall

Passing Train and Observer Car with Longitudinal Wind

Passing Train

(A) vA

Observer Car

(B) vB

Airflow Velocity U Relative to Passing T A rain

Observer Car

Figure 37. Modeling Airflow Relative to a Passing Train 
Part 2: Analysis and Evaluation 

110

By summing moments about the roll axis at the base of the truck bolster, and assuming 

small roll angles, the equation of motion for the single degree-of-freedom model is: 

d 2

φ ⎛ 2c L2

S BS ⎞ dφ ⎛ 2k L2 ⎞ F (t)L F (t)L Equation 5a + ⎜ ⎟ 2 + ⎜ S BS ⎟φ = YCM CCM + YCP CCP ⎜ ⎟ ⎜ ⎟ dt ⎝ I XXCB ⎠ dt ⎝ I XXCB ⎠ I XXCB I XXCB

or in terms of damping ratio ζ, and natural frequency ωn (Thomson 1988): 

d 2

φ ( ) dφ ( ) 2 LCCM FYCM (t) LCCP F

ω YCP (t) 2 quati

2 + ζω + E on 5b

dt n = +

dt n φ I XXCB I XXCB

where, 

2cS L2

2ζω BS

n = I XXCB

2

ω2 2k n = S LBS

I XXCB

The differential equation was solved numerically using a state transition method. 

Two lateral forces are applied to the car. One of the forces, FyCP(t), is from the 

aerodynamic pressures of a train passing on adjacent track and acting at the center of 

pressure of the observer car. The other is the unbalanced force, FyCM(t), which acts at the 

center of mass and occurs during curve negotiation when the observer car is not running 

at balanced speed, either due to excessive track superelevation (cant excess), or an 

insufficient track superelevation (cant deficiency). In this simulation, it was assumed the 

observer car was negotiating a track with constant curvature and superelevation in a 

steady-state condition, and therefore the unbalanced force, FyCM, did not vary with time. 

8.2.2. Model Parameter 

The parameters for the simulation were to be the same as those in the test that was 

conducted at TTC and described in Part 1 of this report. This included duplicating the 

values for the physical properties of the observer car, and the aerodynamic pressure from 

the passing train. In that test, the observer car was a stationary well car carrying empty 

double-stacked containers, which was passed by a high-speed passenger train pulled by a 

TEL locomotive. 
Part 2: Analysis and Evaluation 

111

The physical properties of the car were modeled to represent the car in the test, which 

included reproducing its mass, inertia, dimensions, and values for stiffness and damping 

of the suspension elements. The dimensions for a double-stack well car are shown in 

Figure 38. The double-stack well car was suspended by three-piece freight trucks with 

nonlinear elements in the suspension such as clearances, stops, sliding friction, and 

different regions of roll motion (rolling about the truck springs, or rocking about the 

center plate and side bearings). However, the model consists of linear springs and 

viscous dampers for the suspension elements, which is a good approximation for small 

roll angles where the roll motion of carbody is from the deflection of the spring groups 

that are relatively linear. Values of the parameters were obtained from the literature 

(Holmes and Schroeder 2002; Przybylinski and Anderson 1980; R.E.R. 1997), except the 

damping ratio for the roll mode of the carbody, which was measured from the roll 

response in the test (Figure 88, Table 47, and Table 48 in the Appendix). Specifications 

for a freight truck with a 70-ton capacity were assumed because information on the 

freight truck used in the test was not available, and the carbody roll response from this 

truck compares best with the test data. Values of the parameters for the model are shown 

in Table 24. 
Part 2: Analysis and Evaluation 

112

DIMENSION OF DOUBLE-STACK WELL CAR IN FULL-SCALE TEST OF

AERODYNAMIC INTERACTION WITH A PASSING TRAIN

----- (b) -----

----- (a) -----

2.591 m

(8’ 6”)

21.87 m

(71’ 9”)

Car: TTX 456013

12.18 m

(39’ 11.5”)

14.63 m

(48’)

3.200 m

(10’ 6”)

2.743 m

(9’)

1.651 m

(5’ 5”)

5.944 m

(19.5’)

0.4572 m

(18”)

0.3048 m

(12”)

End View

Side View

1.981 m

(78”)

1.511 m

(59.5”)

Top Container

Bottom Container

Figure 38. Dimensions of a Double-Stack Well Car 
Part 2: Analysis and Evaluation 

113

Table 24. Physical Properties of a Well Car with Double-Stacked Containers 

Description Symbol Value

Mass of Carbody (with Empty Containers) mCB 21,420 kg

(122.3 lb•sec2

/in) 

Mass of a 70-Ton 3-Piece Freight Car Truck mT 3,695 kg

(21.1 lb•sec2

/in) 

Mass of a Wheelset (Axle and 2 Wheels) mW 981 kg

(5.6 lb•sec2

/in) 

Roll Moment of Inertia of Carbody about Center of 

Mass (with Empty Containers) 

IXXCB 2 110,000 kg•m 

(970,000 lb•in•sec2

) 

Spring Constant per Truck (same as per Car Side kS 8.252x106

 N/m 

for Two Trucks) (47,130 lb/in) 

Half Width between Suspension Springs LBS 0.991 m

(39 in) 

Height of Car Center of Mass (From Top of Rail) 1.81 m 

(71.3 in) 

LCCM 1.35 m 

(From Top of Spring) (53.3 in) 

Height of Car Center of Pressure (From Top of Rail) 2.68 m 

(105 in) 

LCCP 2.22 m 

(From Top of Spring) (87.4 in) 

Damping Ratio for Carbody Roll  0.03 

Diameter of Center Plate 0.356 m

(14 in) 

Lateral Distance of Side Bearing from Center of 0.635 m

Car (25 in) 

Diameter of Wheel 0.838 m

(33 in) 

Vertical Clearance of Side Bearing 6.35 mm

(0.25 in) 

The second test condition reproduced for the model was aerodynamic pressure, which 

provides the input force to the car. The pressure waves for the model are in the forms of 

linear and sinusoidal shapes, and were adjusted to match the pressure variations 

measured from the test. While the actual pressure exerted on the side of the car is a 

distributed load that varies both longitudinally and vertically, the pressure only varied 

longitudinally in the model and remained uniform in the vertical direction. Therefore, 

the distributed aerodynamic load in the vertical direction is reduced to a single force 

acting at the center of pressure on the side of the car. 
Part 2: Analysis and Evaluation 

114

The pressure variation was measured from the test of a TEL passenger train passing a 

double-stacked well car. The maximum and minimum peak pressures and its 

wavelengths of the various wave sections can be fitted based on the test data. Expressing 

the pressure variation from a passing train in terms of pressure coefficient, the results 

between the modeled and test measurement are compared as shown in Figure 39. 

Accurate modeling of the pressure pulses is important at the nose and tail, because it is 

these pressure pulses that provide the significant loading to the car being passed. Figure 

40 shows in greater detail a comparison of the nose and tail pressure pulses between the 

model results and test data, where the model achieved a very good fit. The pressure 

variation on the far side of the well car is assumed to be at ambient condition. As the test 

data indicate, the changes in pressure on the well car at the far side of the passing train 

are small compared to the changes in pressure at near side of the car. 

8.2.3. Comparison of Simulation with Full-Scale Test 

The roll response of the stationary well car with empty double-stack containers was 

computed from the single degree-of-freedom roll model for a speed of 177 km/h 

(110 mph). A comparison of the time history in the response of the carbody roll angles 

between simulation and test data is in very good agreement, as shown in Figure 41. The 

maximum zero-to-peak roll angle from the model is computed to be 0.301°, while the 

maximum zero-to-peak roll angle measured from the test is 0.312°. Based on the roll 

response from the test, the natural frequency in roll is about 1.6 Hz, and the damping 

ratio is about 0.03. The roll natural frequency computed from the car parameters is 

1.64 Hz, which agrees with the measured value. A skewing can be observed in the test 

data, where the roll motion of the carbody initially oscillates with the average roll angle 

centering about zero, but it gradually drifts to a negative average roll angle (Figure 88 in 

the Appendix). Thus, an apparent divergence exists between the computed roll angles 

and those from test data because of the skewing effect in the test data with increasing 

time. 

The maximum roll angles of the double-stack well car from model simulation and test are 

compared for the entire tested speed range of the passing train. An excellent agreement 

exists between the roll angles obtained from simulation and measured from the test, as 

shown in Figure 42. The simulation result predicts the maximum roll angle as it reaches 

a peak at about 177 km/h (110 mph), and drops above that speed, as in the test data. The 

simulation shows the maximum roll angle increasing again above a train passing speed of 

209 km/h (130 mph), which is beyond the speed range of the test, and therefore no test 

data are available. 
Part 2: Analysis and Evaluation 

115

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

-50.00 0.00 50.00 100.00 150.00

Distance, (m)

Pressure Coefficient, Cp

Test Data for Train Passing Speed of 209 km/h (130 mph)

Modeled from Mathematical Function

(ft)

-100 0 100 200 300 400

COMPARISON OF PRESSURE COEFFICIENTS BETWEEN TEST MEASUREMENT AND MATHEMATICAL

REPRESENTATION FOR TRAIN PASSING DOUBLE-STACK WELL CAR

Pressure Measured from Channel 8 Transducer at Bottom and Mid-Length

of Container from Passage of Turbine-Electric Locomotive with 2 Horizon

Passenger Cars

Front End of Locomotive at

Mid-Length of Container

Rear End of Last Car at

Mid-Length of Container

Intercar Gaps

Figure 39. Pressure Coefficients from Test Measurement and Modeled from Piecewise 

Mathematical Functions 
Part 2: Analysis and Evaluation 

116

(ft)

260240220200 280 300 320 340 360 380

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

60.00 70.00 80.00 90.00 100.00 110.00 120.00

Distance, (m)

Pressure Coefficient, Cp

-80 -60 -20-40 0 20 40 60 80

(ft)

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

-30.00 -20.00 -10.00 0.00 10.00 20.00 30.00

Distance, (m)

Pressure Coefficient, Cp

COMPARISON OF PRESSURE COEFFICIENTS BETWEEN TEST MEASUREMENT AND MATHEMATICAL

REPRESENTATION FROM NOSE AND TAIL OF TRAIN PASSING DOUBLE-STACK WELL CAR

----- (b) -----

----- (a) -----

Rear End of Last Car at

Mid-Length of Container

Pressure Pulse from Head of Train

Pressure Pulse from Tail of Train

Nose of Locomotive at

Mid-Length of Container

Rear End of Locomotive

Test Data for Train Passing Speed of 209 km/h (130 mph)

Modeled from Mathematical Function

Figure 40. Pressure Coefficients from Test Measurement and Modeled from Piecewise 

Mathematical Functions of Pressure Pulses from the Nose and Tail of a Passing Train 
Part 2: Analysis and Evaluation 

117

COMPARISON OF ROLL ANGLES BETWEEN NUMERICAL 

SIMULATION AND FULL-SCALE TEST FOR A DOUBLE-STACK WELL 

CAR FROM AERODYNAMIC INTERACTION WITH A PASSING TRAIN

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

-1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0

Time, (s)

Car-Body Roll Angle (Positive when Well Car Rotates Away from Passing Train), (deg)

Test Data: Channel 15 East String Potentiometer

Simulation

Turbine-Electric Locomotive Pulling Two Horizon Passenger Cars at 177 

km/h (110 mph) Passing a Stationary Well Car with Empty Double Stacked 

Containers

Figure 41. Time History Roll Response of a Double-Stack Well Car from Numerical Simulation and 

Full-Scale Test 
Part 2: Analysis and Evaluation 

118

0

0.1

0.2

0.3

0.4

0.5

0.6

0 50 100 150 200 250 300

Speed of Passenger Train with Turbine-Electric Locomotive, (km/h)

Maximum Car-Body Roll Angle Relative to Track Plane, Zero-to-Peak (deg)

Test Data from Pueblo, CO

Simulation for Pueblo, CO

Simulation for Sea Level

(mph)

0 1 20 40 60 80 00 120 140 160 180

COMPARISON BETWEEN NUMERICAL SIMULATION AND

FULL-SCALE TEST ON A STATIONARY DOUBLE-STACK WELL CAR FROM

AERODYNAMIC INTERACTION WITH A PASSING TRAIN

OF MAXIMUM ROLL ANGLES

Turbine-Electric Locomotive Pulling Two Horizon Passenger Cars Passing

a Stationary Well Car with Empty Double Stacked Containers.

Track Geometry

 Tangent Track

 Track Center Spacing: 3.658 m (12 ft)

Air Density

 1.225 kg/m at Sea Level 3

 1.01 kg/m at Pueblo, CO 3

Speed Range

of Test

Figure 42. Maximum Carbody Roll Angles of a Double-Stack Well Car from Numerical Simulation 

and Full-Scale Test 
Part 2: Analysis and Evaluation 

119

The previous results compared model simulation with a full-scale test for conditions at 

Pueblo, Colorado, where the altitude is significantly above sea level. The simulation was 

repeated to determine the roll response of the double-stack well car at sea level since the 

air density would be noticeably higher. Carbody roll angles for air density at sea level 

were computed and are plotted along with those for Pueblo (Figure 42), where the 

maximum carbody roll angle at sea level is higher than for Pueblo, but the trend is 

otherwise similar. 

` 

Two factors influence the roll response of the double-stack well car, which are related to 

the speed of the passing train. As the passing train increases in speed, the aerodynamic 

pressure around the train increases as the square of its velocity, resulting in a higher force 

applied to the double-stack well car, and therefore a greater roll response. The second 

factor is the relation between the passing train speed and the natural frequency of the 

carbody roll. A pressure pulse that sweeps by at a speed that matches the carbody roll 

natural frequency can amplify the carbody response. Besides the frequency content of 

the pressure pulse, a period exists between the passage of the head pulse and the arrival 

of the tail pulse. If the tail pulse arrives to produce a net force on the double-stack well 

car that is in phase with the carbody roll motion, the carbody roll angle is further 

amplified. This phenomenon is shown in Figure 43, where the lateral aerodynamic force 

of the passing train and the roll response of the double-stack well car are plotted for the 

case of a train passing at a speed of 177 km/h (110 mph). The roll response of the 

double-stack well car is further magnified from the passage of the tail pulse. If the 

passing train is long, the roll motion of the double-stack well car can decay sufficiently, 

so that the passage of the tail pulse will have a lesser effect. 

These results demonstrate that the simple single degree-of-freedom roll model can 

provide good predictions of carbody roll from transient aerodynamic force input 

produced by a passing train. Besides the roll motion to the carbody, a dynamic 

vehicle/track interaction occurs as a result of the aerodynamic force applied to the 

double-stack well car. The time-varying aerodynamic pressure sweeping along the side 

of the double-stack well car produces both roll and yaw moments to the car. The roll 

moment about the longitudinal axis at the track plane (from the top of the rail), and the 

yaw moment about the vertical axis at the center of the car, applied to the stationary 

double-stack well car from a train passing at a speed of 177 km/h (110 mph), are shown 

plotted in Figure 44. Although roll is the only degree-of-freedom in the carbody roll 

model, the aerodynamic force along with the computed roll and yaw moments complete 

the forcing inputs to a more complex multi-body simulation model for dynamic response 

from vehicle/track interaction. 
Part 2: Analysis and Evaluation 

120

NUMERICAL SIMULATION OF ROLL RESPONSE FOR A STATIONARY DOUBLE-STACK WELL CAR FROM

AERODYNAMIC INTERACTION WITH A TRAIN PASSING AT 177 km/h (110 mph)

-10123456

-0.4

-0.2

0

0.2

0.4

----- (b) -----

Time, (s)

Car-Body Roll on Double-Stack Well Car

Roll Angle, (deg)

Head

Tail

Train

End of Last Car

Completely

Passes Container

----- (a) -----

Time, (s)

Lateral Aerodynamic Force on Side of Double-Stack Well Car

1 0.5 0 0.5 1 1.5 2 2.5 3

2 .

104

1 .104

0

1 .104

2 .104

Force, (N)

(lb)

0

2x103

4x103

-2x103

-4x103

End of Last Car

Completely

Passes Container

Head Tail

Train

Turbine-Electric Locomotive Pulling Two Horizon Passenger Cars Passing

a Stationary Well Car with Empty Double Stacked Containers.

Track Center Spacing: 3.658 m (12 ft)

Air Density: 1.225 kg/m (Sea Level) 3

Figure 43. Time Histories of Applied Force and Roll Response of a Double-Stack Well Car 
Part 2: Analysis and Evaluation 

121

NUMERICAL SIMULATION OF MOMENT ON A STATIONARY DOUBLE-STACK WELL CAR

FROM AERODYNAMIC FORCE OF A PASSING TRAIN AT 177 km/h (110 mph)

----- (a) -----

Time, (s)

Roll Moment

1 0.5 0 0.5 1 1.5 2 2.5 3

6 .104

4 .104

2 .104

0

2 .104

4 .104

6 .104

Moment about X-Axis at

Track Plane, (N-m)

(lb-ft)

0

2x104

1x104

-1x104

3x104

4x104

-2x104

-3x104

-4x104

End of Last Car

Completely

Passes Container

Train

Head Tail

----- (b) -----

Time, (s)

Yaw Moment

1 0.5 0 0.5 1 1.5 2 2.5 3

4 .105

2 .105

0

2 .105

4 .105

6 .105

Moment about Z-Axis at

Center of Car, (N-m)

(lb-ft)

0

2x104

1x104

-1x104

3x104

4x104

-2x104

-3x104

End of Last Car

Completely

Passes Container

Train

Head Tail

Turbine-Electric Locomotive Pulling Two Horizon Passenger Cars Passing

a Stationary Well Car with Empty Double Stacked Containers.

Track Center Spacing: 3.658 m (12 ft)

Air Density: 1.225 kg/m (Sea Level) 3

Figure 44. Time Histories of Applied Moments to a Double-Stack Well Car 
Part 2: Analysis and Evaluation 

122

8.3. Simulation Results with Headwind and on Curved Track 

A parametric study of roll response was conducted for a well car with empty doublestacked containers as a TEL train with two passenger cars passes by on an adjacent track 

(consist in this simulation corresponds to the consist in the full scale test (see Section 

3.2)). Simulations were performed using the single degree-of-freedom carbody roll 

model for the following conditions: (1) a double-stack well car traveling over a range of 

speeds being passed by a train traveling against various headwind speeds, and (2) a 

double-stack well car traveling over a range of speeds on a curved track being passed by 

a train on the inside and outside tracks of the curve. The double-stack well car traveled 

over a speed range both in the same and in opposite directions to the passing train. 

8.3.1. Train Passing with Headwind 

The strength of the aerodynamic pressure generated by the passing train is dependent on 

the speed of the airflow relative to the train. With a headwind, the airflow velocity 

relative to the passing train is the speed of the headwind added to the speed of the train. 

The roll response for the observer car was for passing train encounters in the same and 

opposite directions with the observer car traveling over a speed range of 0 to 129 km/h (0 

to 80 mph) in both directions passed by a train traveling in one direction at 241 km/h 

(150 mph) with and without headwind. Four headwind speeds were included in the 

simulation from 24 km/h (15 mph) to 80 km/h (50 mph). 

Maximum carbody roll angles were obtained for the observer car traveling at various 

speeds passed by a train against various headwind speeds. The roll angle on the observer 

car is lowest when the passing train has no headwind, with higher roll angle as the 

passing train encounters higher headwind, as shown in Figure 45. The speeds of the 

passing train and observer car simulated in this study produced a relative, or closing 

speed ranging from 370 km/h (230 mph) to 113 km/h (70 mph). For any given ambient 

wind speed, the trend of the observer car response is a relatively consistent increase in 

roll angle, as the relative speeds between the observer car and passing train decrease (or 

with the observer car traveling at 129 km/h (80 mph) in the opposite direction to the 

passing train, to 129 km/h (80 mph) in the same direction as the passing train). At a 

decreasing closing speed, the aerodynamic pressure pulse from the passing train sweeps 

by the observer car approaching that of its roll natural frequency. As the observer car 

increases in speed opposite to the passing train direction, the pressure pulse sweeps by 

increasingly beyond its roll natural frequency and resulting in a reduced roll angle. 
Part 2: Analysis and Evaluation 

123

NUMERICAL SIMULATION FOR MAXIMUM ROLL ANGLE OF A DOUBLE-STACK WELL CAR FROM

AERODYNAMIC INTERACTION WITH A TRAIN PASSING AT 241 km/h (150 mph)

WITH HEADWIND AGAINST THE PASSING TRAIN

Turbine-Electric Locomotive Pulling Two Horizon Passenger Cars Passing

a Well Car with Empty Double Stacked Containers

Track Geometry

 Tangent Track

 Track Center Spacing: 3.658 m (12 ft)

Air Density: 1.225 kg/m (Sea Level) 3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

-150 -100 -50 0 50 100 150

Speed of Double-Stack Well Car, (km/h)

Car-Body Roll Angle Relative to Track Plane, Zero-to-Peak (deg)

(mph)

-80 -60 -40 -20 0 20 40 60 80

Double-Stack Well Car

Traveling in Opposite

Direction to Passing Train

Double-Stack Well Car

Traveling in Same

Direction to Passing Train

No Wind

Headwind of 24 km/h (15 mph)

Headwind of 48 km/h (30 mph)

Headwind of 80 km/h (50 mph)

Figure 45. Maximum Roll Angles of a Double-Stack Well Car when Passed by a Train with 

Headwind 
Part 2: Analysis and Evaluation 

124

Another characteristic, when the train passes the observer car, is periodic peaks in the 

maximum roll angles of the observer car at certain relative speeds (Figure 45). This 

occurs when the observer car is traveling at speeds of 64.4 km/h (40 mph) and 113 km/h 

(70 mph) in the same direction as the passing train, and when the observer car is traveling 

at 32.2 km/h (20 mph) in the opposite direction to the passing train. In each of these 

speeds, the observer car reaches its highest roll angle following the passage of the last car 

of the passing train. The roll motion of the observer car from the initial pressure pulse is 

further amplified when the tail pulse arrives to produce a net force on the observer car 

that is in phase with the carbody roll motion. This corresponds to relative speeds 

between the passing train and observer car of 177 km/h (110 mph), 129 km/h (80 mph), 

and 274 km/h (170 mph). 

When the passing train overtakes the observer car, the peak maximum roll angle on the 

observer car traveling at 64.4 km/h (40 mph) is greater than the peak maximum roll angle 

when traveling at 113 km/h (70 mph). As the closing speed between the observer car and 

passing train continues to be reduced, the pressure pulse will sweep along the observer 

car further away from its roll natural frequency. Moreover, it takes the passing train a 

longer time to pass a faster moving observer car traveling in the same direction, resulting 

in a longer time lapse between the arrival of the nose and tail pressure pulses from the 

passing train. In that extra time, the observer car rolls an extra cycle with a further decay 

in roll motion. Therefore, a lower peak roll angle is attained on the observer car since it 

has a reduced roll angle when it encounters the tail pressure pulse of the passing train. 

8.3.2. Train Passing on Curved Track 

When a rail car is traveling on curved track at balanced speed, no net lateral force occurs 

on the rail car from negotiating the curve, and the response of the car from a passing train 

is similar to traveling on tangent track. However, when it is negotiating a curve at a 

speed that is not balanced, a net lateral force acts on the rail car. If it is traveling below 

the balanced speed, or at a cant excess, the net lateral force applied to the car is inward 

toward the center of the curve (toward the inside of the curve). If the car is traveling 

above the balanced speed, or at a cant deficiency, the net lateral force applied to the car is 

outward away from the center of the curve (toward the outside of the curve). The 

relationship between train speed and unbalanced track cant is shown in Figure 46 for a 

track with a 1 deg curve and a 152 mm (6.0 in) superelevation. Balanced speed occurs 

when the cant unbalance is zero, which for a 1-degree curve is at a speed of 150 km/h 

(93 mph). 
Part 2: Analysis and Evaluation 

125

-150 -100 -50 0 50 100 150

0

20

40

60

80

100

120

140

160

180

200

220

Train Speed, (km/h)

Unbalanced Track Cant, (mm)

0

10

20

30

40

50

60

70

80

90

100

110

120

130

(mph)

(inch)

-1-2-3-4-5 012345

TRAIN SPEED AND UNBALANCE IN TERMS OF EXCESS OR DEFICIENCY IN TRACK CANT

IN A 1.0 DEGREE CURVE AT 152 mm (6.0 in) SUPERELEVATION

Cant Deficiency Cant Excess

Figure 46. Train Speed and Unbalanced Track Cant 
Part 2: Analysis and Evaluation 

126

A simulation was performed with the observer car traveling at various below balanced 

speeds (cant excess) on a 1-degree curve with a 152 mm (6.0 in) superelevation while a 

train passes on an adjacent track. The observer car traveled over a speed range of 0 to 

129 km/h (0 to 80 mph) in both directions, while the passing train traveled at 184 km/h 

(114.5 mph) in one direction, providing for passing train encounters in the same and 

opposite directions. The train passed the observer car on an adjacent track that is on the 

inside, and on the outside tracks of the curve. The observer car responds to the 

aerodynamic force of the passing train with a roll motion oscillating toward the inside 

and outside of the curve as shown plotted in Figure 47. Highest maximum roll angle is 

when the observer car rolls toward the inside of the curve, which is especially noticeable 

with high cant excess (stationary car). This is the case whether the train is passing the 

observer car on the inside or outside of the curved tracks. 

Also shown in the Figure 47 is a plot of the maximum roll angle due only to the lateral 

force from unbalanced speed with no trains passing. Because the observer car is 

traveling below balanced speed, a bias exists in the roll angle where the carbody is rolled 

toward the inside curve. This additional constant bias in the roll angle contributes to the 

perturbed roll angle of the observer car to be greater toward the inside of the curve than 

toward the outside. As the car increases toward the balanced speed, the roll angle 

becomes smaller and approaches zero, and will roll toward the outside curve as it 

traverses the curve above the balanced speed (not shown in the graph). 

The maximum roll angle of the observer car is dependent on if a train passes it on an 

adjacent track that is on the inside or outside curve. The observer car traveling at below 

balanced speed produces a greater maximum roll angle of oscillation when it is passed by 

a train on the inside than on the outside of the curved track as shown plotted in Figure 48 

(carbody roll angle measured relative to steady-state carbody roll as zero reference). The 

reason is that these two passing situations are not equivalent when the observer car is 

traveling at an unbalanced speed, where a constant bias occurs in the roll angle. The 

initial pressure pulse from the passing train is always a positive to negative pressure, 

producing a push and then a pull on the observer car. When the train is passing the 

observer car on the outside curve, it first pushes the car toward the inside of the curve; 

while when passing the observer car on the inside curve, it first pushes the car to the 

outside of the curve. However, as the observer car approaches balanced speed, the roll 

angles become the same whether the passing train on the adjacent track is on the inside or 

outside of the curve. When the carbody roll angle is measured as a deviation from its 

steady-state roll, a train passing the observer car on the inside curve produces the same 

maximum carbody roll angle as a train passing the observer car on tangent track (Figure 

48). 
Part 2: Analysis and Evaluation 

127

Roll Angle from Unbalanced Curving Speed

Passing Train on Outside Curve of the Car Being Passed

Passing Train on Inside Curve of the Car Being Passed

NUMERICAL 

PASSED

BY A TRAIN AT 184 km/h (114.5 mph) 

SIMULATION FOR MAXIMUM ANGLES ON A DOUBLE-STACK WELL CAR

ROLLING TO THE INSIDE AND TO THE OUTSIDE OF THE CURVE WHEN 

ON 1.0 DEGREE CURVED TRACK 

Track Geometry

 Curved Track

 Curvature: 1.0 deg with Superelevation of 152 mm (6 in)

 Balanced Speed: 150 km/h (93 mph)

 Track Center Spacing: 3.658 m (12 ft).

Air Density: 1.225 kg/m (Sea Level) 3

Turbine-Electric Locomotive Pulling Two Horizon Passenger Cars

R

Passing a

unning on Curved Track at 76 mm (3 in) Cant Deficiency

 Well Car with Empty Double-Stacked Containers

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-150 -100 -50 0 50 100 150

Roll Towards Inside of Curve

Roll Towards Outside of Curve

Double-Stack Well Car

Traveling in Opposite

Direction to Passing Train

Double-Stack Well Car

Traveling in Same

Direction as Passing Train

(mph)

-80 -60 -40 -20 0 20 40 60 80

Speed of Double-Stack Well Car, (km/h)

Car-Body Roll Angle Relative to Track Plane, Zero-to-Peak (deg)

Figure 47. Maximum Roll Angles to the Inside and to the Outside of the Curve for a Double-Stack 

Well Car Passed by a Train on Curved Track 
Part 2: Analysis and Evaluation 

128

Tangent Track

Passing Train on Outside Curve of the Car Being Passed

Passing Train on Inside Curve of the Car Being Passed

NUMERICAL SIMULATION FOR MAXIMUM ROLL ANGLE ON A DOUBLE-STACK WELL CAR

WHEN PASSED BY A TRAIN AT 184 km/h (114.5 mph) ON

TANGENT AND 1.0 DEGREE CURVED TRACKS

Track Geometry

 Tangent Track

 Curved Track

 Curvature: 1.0 deg with Superelevation of 152 mm (6 in)

 Balanced Speed: 150 km/h (93 mph)

 Track Center Spacing: 3.658 m (12 ft).

Air Density: 1.225 kg/m (Sea Level) 3

Turbine-Electric Locomotive Pulling Two Horizon Passenger Cars

R

Passing a

unning on Tangent Track and Curved Track at 76 mm (3 in) Cant

Deficiency Well Car with Empty Double-Stacked Containers

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

-150 -100 -50 0 50 100 150

(mph)

-80 -60 -40 -20 0 20 40 60 80

Speed of Double-Stack Well Car, (km/h)

Car-Body Roll Angle Towards Inside of Curve Relative

to Steady-State Car-Body Roll as Zero Reference,

Zero-to-Peak (deg)

Double-Stack Well Car

Traveling in Opposite

Direction to Passing Train

Double-Stack Well Car

Traveling in Same

Direction as Passing Train

Tangent Track and Curved Track

for Passing Train on Inside Curve

Figure 48. Maximum Roll Angles of a Double-Stack Well Car Passed by a Train on Tangent and 

Curved Tracks 
Part 2: Analysis and Evaluation 

129
Part 2: Analysis and Evaluation 

130

9. Measurements of Airflow and Aerodynamic Load from Full-Scale 

Test of Passing Train 

Part 1 of this report presented a digest on the mathematical and full-scale test results of 

the effects to people and objects alongside the track from the airflow and aerodynamic 

pressure created by a passing train. In this chapter, the data obtained from the test 

conducted in Mansfield, Massachusetts from September to October of 2002, is further 

processed and analyzed in detail. In that test, airflow velocities were measured using 

pitot-static tubes, and forces were measured on CIDs. Also, some of the airflow velocity 

data from previous tests are included in the analysis. 

Two methods were used to characterize the aerodynamic effects of passing trains with the 

purpose of assessing safety of people alongside the track. One method was to measure 

the airflow velocity, which characterized the fluid property in the flow field surrounding 

the passing train. The drag on a body can then be computed from the airflow velocity. 

This measurement is significant because the airflow velocity induced by a passing train is 

considered to be the more serious effect in destabilizing people and objects (RAPIDE 

2001; Gawthorpe 1978). The second method was to directly measure the force on a 

cylindrical object situated beside a passing train. This method measures the effect on an 

object instead of the property of the fluid. The airflow velocity measured by a pitot-static 

tube, and the load on the cylindrical object, represent two different methods of arriving at 

the force on an object. 

In this chapter, the aerodynamic data are processed and analyzed, and then applied to 

relate the distance from a passing train with the strength of airflow. First, the airflow 

velocity and force on the CID are analyzed to characterize the aerodynamic signatures 

associated with the different trains. Also, the force measured on the CID is compared 

with computed drag on other bodies. Next, a relationship is established between induced 

airflow velocity and lateral distance from the train. Finally, the aerodynamic effects on 

people are assessed from wind speed criteria with an indicated minimum distance from a 

passing train. 

9.1. Processing Test Data 

Data were measured as time histories of airflow velocities from pitot-static tubes and of 

forces on the CIDs. One of the processing procedures involves filtering out certain 

frequencies in the data, which in almost all cases was performed to remove noise in the 

signal. However, the filtering process was also performed so that the data conforms to 

proper conditions for analysis. Another processing involves computing drag on a 

cylinder from airflow velocity. Because the drag coefficient for a cylinder varies with 

Reynolds number, a mathematical function is required to be derived for the drag 

coefficient. The other processing procedure includes extracting maximum values in the 

data and obtaining statistical quantities. 
Part 2: Analysis and Evaluation 

131

9.1.1. Time History of Aerodynamic Data 

The geometry of the train, particularly the head end, has a strong influence on the 

aerodynamic effect as the train passes by. Aerodynamic data was obtained from passing 

trains of different head and tail end geometries. These trains consisted of four train styles 

with distinctive geometric appearance, which are: 

• Acela Express trainset, 

• Amfleet train with AEM-7 locomotive, 

• Amfleet train with HHP-8 locomotive, and 

• Amfleet train with F40PH locomotive. 

An example of the aerodynamic data 

is presented as time history plots for 

each of these trains except the 

Amfleet/F40PH train. The time 

history data includes airflow 

velocities measured from pitot-static 

tubes and the force on one of the 

two CIDs. Only one of the train 

passes from each of the three styles 

of trains is included as an example. 

Table 25 describes the example 

cases. 

Table 25. Example Cases in Time History Plots 

Train Speed Length* Designation

Acela Express 239 km/h 202 m B02J01- 

(149 mph) (663 ft) 1012 

1L+6C 

+1L 

Amfleet with 184 km/h 224 m B02J01- 

AEM-7 (114 mph) (735 ft) 1825 

Locomotive 1L+8C 

Amfleet with 201 km/h 228 m B02J01- 

HHP-8 (125 mph) (748 ft) 1101 

Locomotive 1L+8C 

* L: locomotive or power car; C: passenger car 
Part 2: Analysis and Evaluation 

132

The data of the time history plots 

are measurements from the CID 

at the location closest to the 

track, and from pitot-static tubes 

that are placed to correspond 

with the cylinder axis of the 

CID. Data, from the lower or in 

some cases the average value 

from data that is measured from 

the top and bottom pitot-static 

tubes, are plotted. The positions 

of the pitot-static tubes and CID 

for the example plots are shown 

in Table 26. 

9.1.2. Airflow Velocity from Pitot-Static Tube 

Time histories of airflow velocities were measured from four pitot-static tubes at two 

different heights and at various lateral distances from the train (Figure 13 and Table 18). 

In configurations 1 and 2, the pitot-static tubes were oriented to measure longitudinal 

airflow (+x airflow in the direction of the passing train) for two different lateral distances 

from the passing train. In configurations 3 and 4, pitot-static tubes were oriented 

perpendicular to each other, and at the same two nominal lateral distances from the track 

as the cylindrical axes of the CIDs. These orientations of the pitot-static tubes measured 

the airflow velocities on the horizontal plane along two directions to obtain simultaneous 

measurements of the longitudinal (+x) and lateral airflow (+y airflow in the direction 

away from the side of the train) velocity components. A single quadrant resultant airflow 

velocity is computed as a vector sum from the two perpendicular components in the 

positive longitudinal and positive lateral directions (any negative velocity was set to 

zero), and is referred to as the quadrant 1 resultant airflow velocity (coordinate axes 

shown in Figure 19). 

One significant source of error in these measurements is in the misalignment of the pitotstatic tube with the direction of airflow. The misalignment error depends on the nose 

shape of the pitot tube (Ower and Pankhurst 1977). With the hemispherical nose pitot 

tube that was used, the manufacturer specifies that it has low sensitivity to misalignment, 

and gives accurate reading even when the tube is misaligned up to 15°. However, airflow 

velocity from a passing train can be from any direction, although the expected flow is 

primarily on a horizontal plane and longitudinal in the direction of the passing train. It 

was also assumed that some significant lateral airflow component occurs away from the 

side of the train. In these conditions, the pitot-static tube can be greatly misaligned 

because the airflow can be in any direction along the horizontal plane, with a significant 

flow between 0 to 90° (0-degree positive longitudinal and 90-degree positive lateral). No 

Table 26. Positions of Pitot-Static Tube and CID in Example 

Time History Plots 

Measurement Nominal Lateral Nominal Vertical 

Distance from Side of Distance from Top of 

Train Rail 

Pitot-Static Tube 1.17 m 0.97 m 

(46 in) (38 in) 

Pitot-Static Tube 1.17 m 1.25 m 

for Computing (46 in) (49 in) 

Cylinder Force* 

CID-5 1.20 m 1.24 m 

(47 in) (49 in) 

Cylinder Axis Center of Pressure 

* Airflow velocity was averaged from values measured at two other heights. 
Part 2: Analysis and Evaluation 

133

single orientation of the pitot tube can measure the airflow over its full range of flow 

directions. 

To obtain the two orthogonal components of airflow velocities, two pitot-static tubes 

were placed perpendicular to each other to measure the airflow in the positive 

longitudinal and lateral directions. However, a significant error can exist in computing 

the resultant airflow as the vector sum of the two components. A correct resultant 

airflow velocity from a vector sum of its components requires that the velocity due to 

misalignment error varies according to the cosine of the misalignment angle (or that the 

differential pressure from the pitot-static tube vary according to the cosine square of the 

misalignment angle). However, the error of misalignment does not vary according to 

these relationships (Figure 89 in the Appendix) (Ower and Pankhurst 1977; Devenport 

2001). When the airflow is at 45 deg, the error is estimated to be 17 percent. If the 

airflow is primarily along the longitudinal direction, and if the lateral airflow component 

is small relative to the longitudinal component, then the impact of this error is not 

expected to be significant. 

Two pitot-static tubes at one location were arranged perpendicular to each other to 

measure horizontal airflow along the two directions. Because each pitot tube can only 

measure airflow in one direction, no reverse airflow (flow away from the pitot tube 

orifice) was measured at any one time. Therefore, any airflow that was parallel to the 

track flowing opposite to the direction of train travel, and perpendicular to the track 

flowing toward the train, was not included in computing the resultant velocity. Some test 

cases were performed where the pitot-static tubes were place facing the opposite 

direction to its normal orientation to determine the extent of reverse airflow. A 

noticeable reverse flow was found, particularly in the lateral direction back toward the 

direction of the track. 

When two pitot-static tubes were placed perpendicular to each other, the pitot-static tube 

in the lateral orientation was at least 0.241 m (9.5 in) closer to the track than the nominal 

distance. The reason is that due to mounting limitation on the support rack, it was 

difficult to position the two pitot-static tubes to measure the airflow at exactly the same 

position. Therefore, the two pitot-static tubes measured airflow that was at a distance of 

0.341 m (13.4 in) from each other. The nominal distance was always referenced to the 

location of the pitot-static tube in the longitudinal orientation to be consistent with 

reference to other measurements. 

Airflow data were measured at various lateral distances from the train. In some cases, the 

pitot-static tubes were configured to measure simultaneous airflows at two different 

lateral positions. Generally, that was not the case, and the airflows measured at different 

lateral distances were from different passing trains. 

9.1.3. Data Filtering 
Part 2: Analysis and Evaluation 

134

The forces measured from the CIDs have been processed by a Bessel second order 15 Hz 

low-pass digital filter to account for the muscular-response time of a human being. 

Airflow velocity data measured from the pitot-static tube was processed either by a 

moving average or a Bessel filtering depending on the application of the data. All 

airflow data that was not treated to Bessel filtering was processed by a moving average 

filtering with a minimum of 0.032 s duration window to remove the 60 Hz noise that was 

present in the data. Airflow velocity data that was used to compute the cylinder force 

was processed by a Bessel second order 15 Hz low-pass digital filter to maintain 

consistency when comparing with forces measured from the CIDs. 

9.1.4. Force on a Circular Cylinder 

The force on the CID is created by the pressure distribution around the cylindrical body 

from its aerodynamic interaction with a passing train. The unbalanced force along the 

horizontal plane of the CID can be computed from the airflow velocity and the drag 

coefficient for a cylinder. The drag is computed from the drag coefficient measured for 

airflow to an isolated cylinder, which does not account for the effect of static pressure 

variation around the cylinder due to the presence of a passing train. The drag on an 

object is computed as, 

⎛ 1 F = ⎜ ρ v

2 ⎞

D ∞ ∞ ⎟CD A ⎝ 2 ⎠ P

Equation 6

where, 

ρ∞: free stream density 

v∞: free stream flow velocity 

CD: drag coefficient 

AP: projected area 

The drag on a circular cylinder situated with its axis perpendicular to the airflow, with AP

= DCLC, is computed as, 

1 F = ρ 2

D−cyl ∞v∞DC L Equation 7 CC (Re) 2 D

where, 

DC: diameter of the cylinder 

LC: Axial Length of the cylinder 
Part 2: Analysis and Evaluation 

135

Re: Reynolds number 

The drag coefficient CD(Re) for a circular cylinder is a function of the Reynolds number, 

and airflow over a cylinder can occur in different flow regimes depending on the 

Reynolds number. The CID consists of a cylindrical body that is smooth and rigid and 

similar to a two-dimensional circular cylinder (cylinder of infinite or very long axial 

length) where drag coefficient data has been measured (Figure 85(a) in the Appendix). If 

the cylinder dimensions, fluid density, and viscosity remain constant, then the drag 

coefficient for the cylinder depends only on the speed of the air flowing toward the 

cylinder (Table 44 in the Appendix). The Reynolds number and airflow velocity where 

the flow regime changes for the CID are shown in Table 27 (Schlichting and Gersten 

2000). Much of the train-induced airflow velocities to the CID are at the critical 

Reynolds number. 

Table 27. Drag Coefficients for a Two-Dimensional Circular Cylinder and Corresponding 

Airflow Velocity for the CID 

Reynolds number Drag Coefficient Airflow Velocity CID* 

300 to 1x105

subcritical regime 

≈1.2 0.011 to 3.7m/s 

(0.025 to 8.4 mph) 

1x105

 to 1x106

critical regime 

0.2 to 1.2 3.7 to 37 m/s 

(8.4 to 84 mph) 

1x106

 to 3.5x106

critical regime 

0.2 to 0.5 37 to 131 m/s 

(84 to 293 mph) 

*Standard atmosphere at sea level 

When a cylinder has a short axial length, the flow that is induced around the side edges to 

the rear of the cylinder will contribute to a reduction in drag coefficient from that of a 

two-dimensional body (Horner 1958). The flow over a short cylinder must be treated as 

flow over a three-dimensional body. For a short cylinder, the drag coefficient will be 

⎛ C ⎞ reduced from a two-dimensional body by a factor ⎜ D ⎟ ⎜ ⎟, where C C D is the drag 

⎝ D2 ⎠

coefficient for a cylinder that is a three-dimensional body, and CD2 is the drag coefficient 

for a cylinder that is a two-dimensional body. 

An indication on the character of the flow can be obtained from the aspect ratio, or the 

ratio of the span (axial length) to the diameter of the cylinder (Figure 85(b) in the 

Appendix). Studies have found that for the same profile shape, the drag coefficient for a 

two-dimensional shape is higher than for a three-dimensional shape by a factor of about 
Part 2: Analysis and Evaluation 

136

1.8 (McCormick 1979). For the CID, the span is LC=0.92 m (36.22 in), the diameter is 

DC=0.39 m (15.35 in), and aspect ratio ARC=LC/DC is ARC=2.36. With an aspect ratio of 

approximately 5 or less, the drag coefficient is nearly constant at a value corresponding 

to a three-dimensional shape (Horner 1958; McCormick 1979). Therefore, the drag for 

⎛ C the CID can be corrected for three-dimensional effects as approximately ⎜ D ⎞

⎟ ⎜ ⎟ = 0.56 . 

⎝ CD2 ⎠

The drag coefficient for a circular cylinder varies with Reynolds number, particularly 

when the Reynolds numbers are very low and at high Reynolds numbers over the critical 

flow regime. Application of the drag equation for the CID (Equation 7) requires a 

functional relationship between the drag coefficient and Reynolds number. A series of 

piecewise linear functions for the drag coefficient of a circular cylinder were fitted to the 

data over the Reynolds numbers of interest (Table 43, Figure 86, and Figure 87 in the 

Appendix). 

9.2. Characterization of Airflow 

Airflows induced by passing trains are characterized for three different types of trains as 

distinguished by their nose and tail base geometries. Frequently, the maximum airflow 

velocity is required. Therefore, the relative strength between longitudinal and lateral 

airflow components is compared to determine if a measurement of the longitudinal 

airflow component alone is sufficient to obtain the maximum airflow velocity of the 

passing train. 

9.2.1. Time History Examples 

The example plots illustrate the characteristic aerodynamic signature of these different 

trains and the influence of train geometry on the signature. Some of the significant 

characteristics are the trends in the aerodynamic signature along the positions of the 

passing train, and the magnitudes of the head and tail perturbations, and the wake, 

relative to the total trace. The local variations in aerodynamic signature from any one of 

these example time history plots are not expected to be the same as other examples of the 

same type of train because of the random nature of the turbulent airflow. Measurements 

from the different types of trains were generally at different train speeds so any 

comparison of magnitudes in the data between trains must account for the speed 

difference. 

The relative magnitudes between the longitudinal and lateral airflow velocity components 

are compared for the three different trains (Figure 49(a), Figure 50(a), and Figure 51(a)). 

Generally, the lateral airflow velocity component is very small relative to the longitudinal 

component. The exception is at the head of the train where the lateral airflow velocity 

component is higher than the longitudinal component, and is especially strong for the 

Amfleet train with the bluff nose AEM-7 locomotive (Figure 50(a)). However, the 
Part 2: Analysis and Evaluation 

137

signature and magnitude of the resultant airflow at quadrant 1 (Figure 49(b), Figure 

50(b), and Figure 51(b)) appeared almost identical to the longitudinal component except 

for the higher resultant airflow at the head end, especially for the Amfleet/AEM-7 train 

(Figure 50(b)). 

Each of the three trains, with its different nose and tail base geometries, produced a 

distinctive time history signature for the resultant airflow at quadrant 1. The Acela 

Express train with its tapered nose produced a weak head perturbation, with the resultant 

airflow gradually increasing in strength toward the tail end of the train (Figure 49(b)). 

The airflow velocity is highest near the tail end, continues to be strong after the last 

power car with its rearward facing tapered nose has passed and is only slowly reduced far 

into the wake. The Amfleet/AEM-7 train produced a very different airflow signature 

(Figure 50(b)). Its bluff nose locomotive creates a strong initial gust, with the airflow 

reaching a high level immediately behind the head of the train, and remains high along 

the length of the train. A drop in airflow does occur toward the flat-tail base with a weak 

airflow at the wake. The Amfleet/HHP-8 train with its slant nose and flat-tail base 

produced an airflow signature similar to the other two types of geometries. Its slant nose 

is similar to the Acela Express. It is reflected by a similar signature (Figure 51(b)), 

except for a more rapid decrease in airflow at the tail end, similar to the signature of the 

Amfleet/AEM-7 train that also has a flat tail base. These results illustrate the influence 

of train geometry on airflow signature, especially the nose and tail-base geometries. 

The strength of the airflow is derived mainly in the longitudinal component. The lateral 

airflow component does not appear to contribute significantly to the resultant airflow, 

except in the case of a bluff nose head end where a very strong lateral gust is 

encountered. These results are limited to the longitudinal airflow in the direction of the 

passing train and to the lateral airflow away from the side of the train, where these 

airflow directions were expected to be the strongest. 
Part 2: Analysis and Evaluation 

138

COMPONENT AND SINGLE QUADRANT RESULTANT AIRFLOW VELOCITIES INDUCED BY A PASSING

ACELA EXPRESS TRAIN AT 239 km/h (149 mph)

Train Detector

Nominal Lateral Distance of Pitot-Static Tube from Side of Train:

Distance of Pitot-Static Tube from Top of Rail: 0.97 m (38 in)

 1.17 m (46 in)

Nominal Vertical 

Data: B02J01-1012

Airflow Velocity Data Processed by 0.032 s Moving Average Window

----- (a) -----

Time, (s)

Components of Longitudinal and Lateral Airflow Velocities

Longitudinal (+x) Component

Lateral (+y) Component

1 012345678

0

5

10

15

20

25

30

35

40

Airflow Velocity, (m/s)

(mph)

0

40

10

20

30

50

60

70

80 Train Head

Tail

----- (b) -----

Time, (s)

Quadrant 1 Resultant Airflow Velocity

1 012345678

0

5

10

15

20

25

30

35

40

Airflow Velocity, (m/s)

(mph)

0

40

10

20

30

50

60

70

80 Train Head

Tail

Figure 49. Time Histories of Airflow Velocities Measured from Pitot-Static Tubes for a Passing 

Acela Express Train 
Part 2: Analysis and Evaluation 

139

COMPONENT AND SINGLE QUADRANT RESULTANT AIRFLOW VELOCITIES INDUCED BY A PASSING

AMFLEET TRAIN WITH AEM-7 LOCOMOTIVE AT 184 km/h (114 mph)

Train Detector

Nominal Lateral Distance of Pitot-Static Tube from Side of Train:

Distance of Pitot-Static Tube from Top of Rail: 0.97 m (38 in)

 1.17 m (46 in)

Nominal Vertical 

Data: B02J01-1825

Airflow Velocity Data Processed by 0.032 s Moving Average Window

----- (b) -----

Time, (s)

Quadrant 1 Resultant Airflow Velocity

Airflow Velocity, (m/s)

(mph)

0

40

10

20

30

50

60

70

80

1 0123 45678

0

5

10

15

20

25

30

35

40

Train

Head

Tail

----- (a) -----

Time, (s)

Components of Longitudinal and Lateral Airflow Velocities

Airflow Velocity, (m/s)

(mph)

0

40

10

20

30

50

60

70

80

1 012345678

0

5

10

15

20

25

30

35

40

Longitudinal (+x) Component

Lateral (+y) Component

Train

Head

Tail

Figure 50. Time Histories of Airflow Velocities Measured from Pitot-Static Tubes for a Passing 

Amfleet Train with AEM-7 Locomotive 
Part 2: Analysis and Evaluation 

140

COMPONENT AND SINGLE QUADRANT RESULTANT AIRFLOW VELOCITIES INDUCED BY A PASSING

AMFLEET TRAIN WITH HHP-8 LOCOMOTIVE AT 201 km/h (125 mph)

Train Detector

Nominal Lateral Distance of Pitot-Static Tube from Side of Train:

Distance of Pitot-Static Tube from Top of Rail: 0.97 m (38 in)

 1.17 m (46 in)

Nominal Vertical 

Data: B02J01-1101

Airflow Velocity Data Processed by 0.032 s Moving Average Window

----- (a) -----

Time, (s)

Components of Longitudinal and Lateral Airflow Velocities

Airflow Velocity, (m/s)

(mph)

0

40

10

20

30

50

60

70

80

1 012345678

0

5

10

15

20

25

30

35

40

Longitudinal (+x) Component

Lateral (+y) Component

Train

Head

Tail

----- (b) -----

Time, (s)

Quadrant 1 Resultant Airflow Velocity

Airflow Velocity, (m/s)

(mph)

0

40

10

20

30

50

60

70

80

1 012345678

0

5

10

15

20

25

30

35

40

Train

Head

Tail

Figure 51. Time Histories of Airflow Velocities Measured from Pitot-Static Tubes for a Passing 

Amfleet Train with HHP-8 Locomotive 
Part 2: Analysis and Evaluation 

141

9.2.2. Airflow Strength and Distance 

Both lateral distance from the train and height above the track are factors affecting the 

strength of the airflow. The maximum airflow velocities at two heights for the three 

different types of train are shown plotted in Figure 52, Figure 53, and Figure 54. If both 

the longitudinal and lateral airflow velocities were measured, then the maximum 

longitudinal and the resultant airflows at quadrant 1 were plotted on the same graph for 

comparison. This comparison shows that the maximum resultant airflow velocity over 

the entire length of the passing train is not noticeably greater than the maximum 

longitudinal component. 

The airflow velocity measured at the 

same location from different passes of the Table 28. Ranges of Airflow Velocities Induced 

same type of trains is not very repeatable, by Different Trains for all Lateral 

Positions as evident by the considerable scatter in 

the data. This is consistent with Train Range of Airflow Velocity as 

observation from other studies on the Percent of Train Speed 

lack of repeatability in the data due to the Height above Top of Rail chaotic nature of the airflow (Johnson, 

Dalley, and Temple 2002). However, the 0.97 m (38 in) 1.73 m (68 in) 

trend in the data is a reduction in airflow Acela Express 24 to 49% 18 to 41% 

velocity at increased distance from the Amfleet with 32 to 62% 20 to 39% 

train or at increased height from the AEM-7 

track. The influence of train geometry is Amfleet with 46 to 65% 27 to 60% apparent with the Acela Express train HHP-8 

inducing a lower airflow velocity than the 

Amfleet trains with either locomotive. 

These results are summarized in Table 28. 
Part 2: Analysis and Evaluation 

142

MAXIMUM NORMALIZED AIRFLOW VELOCITY INDUCED BY A PASSING ACELA EXPRESS TRAIN

Longitudinal (+x) Airflow

+ Resultant Airflow in Quadrant 1

Airflow Velocity Measured from Pitot-Static Tube and

 Processed by 0.032 s Moving Average Window

----- (a) -----

Dimensionless Airflow Velocity,

(Airflow Velocity/Train Speed)

Nominal Vertical Distance at 0.97 m (38 in) from Top of Rail

Dimensionless Lateral Distance from Side of Train,

(Lateral Distance/Width of Train)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

----- (b) -----

Nominal Vertical Distance at 1.73 m (68 in) from Top of Rail

Dimensionless Lateral Distance from Side of Train,

(Lateral Distance/Width of Train)

Dimensionless Airflow Velocity,

(Airflow Velocity/Train Speed)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Figure 52. Maximum Airflow Velocities from Passing Acela Express Trains 
Part 2: Analysis and Evaluation 

143

MAXIMUM NORMALIZED AIRFLOW VELOCITY INDUCED BY A PASSING

AMFLEET TRAIN WITH AEM-7 LOCOMOTIVE

Longitudinal (+x) Airflow

+ Resultant Airflow in Quadrant 1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Train with F-40PH Locomotive

----- (a) -----

Dimensionless Airflow Velocity,

(Airflow Velocity/Train Speed)

Nominal Vertical Distance at 0.97 m (38 in) from Top of Rail

Dimensionless Lateral Distance from Side of Train,

(Lateral Distance/Width of Train)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Train with F-40PH Locomotive

----- (b) -----

Dimensionless Airflow Velocity,

(Airflow Velocity/Train Speed)

Nominal Vertical Distance at 1.73 m (68 in) from Top of Rail

Dimensionless Lateral Distance from Side of Train,

(Lateral Distance/Width of Train)

Airflow Velocity Measured from Pitot-Static Tube and

 Processed by 0.032 s Moving Average Window

Figure 53. Maximum Airflow Velocities from Passing Amfleet Trains with AEM-7 Locomotives 
Part 2: Analysis and Evaluation 

144

MAXIMUM NORMALIZED AIRFLOW VELOCITY INDUCED BY A PASSING

AMFLEET TRAIN WITH HHP-8 LOCOMOTIVE

Longitudinal (+x) Airflow

+ Resultant Airflow in Quadrant 1

----- (a) -----

Dimensionless Airflow Velocity,

(Airflow Velocity/Train Speed)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Nominal Vertical Distance at 0.97 m (38 in) from Top of Rail

Dimensionless Lateral Distance from Side of Train,

(Lateral Distance/Width of Train)

----- (b) -----

Dimensionless Airflow Velocity,

(Airflow Velocity/Train Speed)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Nominal Vertical Distance at 1.73 m (68 in) from Top of Rail

Dimensionless Lateral Distance from Side of Train,

(Lateral Distance/Width of Train)

Airflow Velocity Measured from Pitot-Static Tube and

 Processed by 0.032 s Moving Average Window

Figure 54. Maximum Airflow Velocities from Passing Amfleet Trains with HHP-8 Locomotives 
Part 2: Analysis and Evaluation 

145

9.3. Force on a Body 

Another method to characterize the effect of aerodynamic interaction with a passing train 

is to measure the force on a cylindrical body alongside the track. Examples of forces on 

CID-5 as time history plots are illustrated for the three types of trains. Drag on a circular 

cylinder was also computed from airflow velocity data and compared with the force 

measured directly on the CID. Also, the drag was computed for a body with the same 

projected area as the cylinder but with constant drag coefficient. This provides an 

estimate on the extent that the force from a circular cylinder can represent the drag on a 

human body. 

The forces applied to the CID in the longitudinal and lateral directions share certain 

similar characteristics between the different trains as shown in Figure 55(a), Figure 56(a), 

and Figure 57(a). As the head of the train passes, the longitudinal component of force 

pushes the CID in the same direction as the passing train and is immediately followed by 

a pull in the reverse direction. After the head of the train passes and for the remainder of 

the passing train, the CID is primarily being pushed in the same direction as the passing 

train. In the lateral direction, the force initially pushes the CID away from the train 

immediately followed by a pull toward the train, as the head of the train passes by. 

Afterwards, the CID is pushed and pulled oscillating about zero for the remaining train 

passage. 

Whereas certain characteristics in the force are similar to all the passing trains tested, 

distinctive signatures between the different trains also exist. This is illustrated by the 

resultant forces on the CID shown in Figure 55(b), Figure 56(b), and Figure 57(b). For 

the passing Acela Express train, the force on the CID increases to a peak toward the tail 

of the train and remains high beyond the tail end, only slowly decreasing further into the 

wake. This is in contrast to the force on the CID from the passage of the Amfleet/AEM-7 

train where the force rises immediately from the head of the train, and remains at a high 

level until at the tail end where it decreases, then dropping to a very small level at the 

wake. The signature of the force on the CID from the Amfleet/HHP-8 train has 

similarities with both of the other two trains. The force increases from the head toward 

the tail, begins to drop before the tail end, and generates a very low force at the wake. In 

all these trains, very prominent peak forces occur, especially at the head end and toward 

the tail end, with the highest peak force produced at the tail end by the tapered base Acela 

Express train (rearward-facing tapered nose) and at the head end by the bluff nose 

AEM-7 locomotive. 
Part 2: Analysis and Evaluation 

146

FORCE ON CID-5 FROM AERODYNAMIC INTERATION WITH A PASSING

ACELA EXPRESS TRAIN AT 239 km/h (149 mph)

Train Detector

Nominal Lateral Distance of from Side of Train:

Vertical Distance of Center of Pressure from Top of Rail: 1.24 m (49 in)

Raw Data Processed by Bessel Second Order 15 Hz Low-Pass Digital Filter

Cylinder Axis 1.20 m (47 in)

Data: B02J01-1012

CID: Cylindrical Instrumented Dummy

----- (a) -----

Time, (s)

Components of Longitudinal and Lateral Forces

Force, (N)

(lb) -5

0

5

10

Longitudinal (x) Component

Lateral (y) Component

1 012345678

40

20

0

20

40

60

Train

Head

Tail

----- (b) -----

Time, (s)

Resultant Force

0

5

10

Force, (N)

(lb)

1 012345678

0

20

40

60

Train

Head

Tail

Figure 55. Time Histories of Forces on a CID from a Passing Acela Express Train 
Part 2: Analysis and Evaluation 

147

FORCE ON CID-5 FROM AERODYNAMIC INTERACTION WITH A PASSING

AMFLEET TRAIN WITH AEM-7 LOCOMOTIVE AT 184 km/h (114 mph)

Train Detector

Data: B02J01-1825

CID: Cylindrical Instrumented Dummy

Nominal Lateral Distance of from Side of Train:

Vertical Distance of Center of Pressure from Top of Rail: 1.24 m (49 in)

Raw Data Processed by Bessel Second Order 15 Hz Low-Pass Digital Filter

Cylinder Axis 1.20 m (47 in)

----- (a) -----

1 012345678

80

60

40

20

0

20

40

60

80

Time, (s)

Components of Longitudinal and Lateral Forces

Force, (N)

(lb)

0

-5

-10

-15

5

10

15

Longitudinal (x) Component

Lateral (y) Component

Train

Head

Tail

1 012345678

0

20

40

60

80

----- (b) -----

Time, (s)

Resultant Force

0

5

10

15

Force, (N)

(lb)

Train

Head

Tail

Figure 56. Time Histories of Forces on a CID from a Passing Amfleet Train with AEM-7 Locomotive 
Part 2: Analysis and Evaluation 

148

FORCE ON CID-5 FROM AERODYNAMIC INTERACTION WITH A PASSING

AMFLEET TRAIN WITH HHP-8 LOCOMOTIVE AT 201 km/h (125 mph)

Train Detector

Data: B02J01-1101

CID: Cylindrical Instrumented Dummy

Nominal Lateral Distance of from Side of Train:

Vertical Distance of Center of Pressure from Top of Rail: 1.24 m (49 in)

Raw Data Processed by Bessel Second Order 15 Hz Low-Pass Digital Filter

Cylinder Axis 1.20 m (47 in)

1 012345678

80

60

40

20

0

20

40

60

80

100

120

----- (a) -----

Time, (s)

Components of Longitudinal and Lateral Forces

Force, (N)

(lb)

0

-5

-10

-15

5

10

15

20

25

Longitudinal (x) Component

Lateral (y) Component

Train

Head

Tail

1 012345678

0

20

40

60

80

100

120

----- (b) -----

Time, (s)

Resultant Force

0

5

10

15

20

25

Force, (N)

(lb)

Train

Head

Tail

Figure 57. Time Histories of Forces on a CID from a Passing Amfleet Train with HHP-8 

Locomotive 
Part 2: Analysis and Evaluation 

149

The force measured on the CID is compared with the computed drag on a circular 

cylinder with the same dimensions as the CID. The drag on a cylinder was computed 

from the resultant airflow velocity at quadrant 1 with the airflow velocity measured at the 

same nominal location as the CID. To make corresponding comparisons between the 

measured force on the CID and the drag computed on a cylinder, both are processed by a 

Bessel second order 15 Hz low-pass filter, and only the resultant force from the CID that 

belongs to quadrant 1 was retained. The force measured from the CID and the drag 

computed on a cylinder are shown plotted in Figure 58(a), Figure 59(a), and Figure 60(a) 

for the three types of trains. The CID-measured force is higher in magnitude and 

frequency and with greater peak-to-peak fluctuations, than from the computed cylinder 

drag. Next, the forces were processed by a 1 s moving average window to filter out the 

lower frequencies, which provided a clearer trend as shown in Figure 58(b), Figure 59(b), 

and Figure 60(b). These results show the CID force is generally higher than the 

computed cylinder drag. Although in some locations, mostly in the wake region, the 

computed cylinder drag does exceed the CID force. 

The CID was designed to be representative of the trunk of a human being. Below the 

critical Reynolds number, the drag coefficient on a circular cylinder is about the same as 

for a human body, which is about 1.2 based on projected frontal area. Once the critical 

Reynolds number is reached, the drag coefficient is reduced to about 0.3, and the drag on 

a circular cylinder may not be a good representation of a human body. To determine this 

effect, the force measured from the CID is compared to the drag computed for a body 

with the same projected area as the CID but with a constant drag coefficient of 1.1, which 

is more representative of a human body. The body with a constant drag coefficient will 

be referred to as a flat body, and approximates the drag on a human trunk (scaled to the 

size of the CID) assuming that the drag coefficient on a human body remains constant 

over the range of Reynolds numbers. 
Part 2: Analysis and Evaluation 

150

SINGLE QUADRANT FORCE ON CID-5 FROM AERODYNAMIC INTERACTION WITH A PASSING

ACELA EXPRESS TRAIN AT 239 km/h (149 mph)

Force Measured from CID

Cylinder Drag Force Computed from Airflow Velocity

 Measured by Pitot-Static Tube

Train Detector

Data: B02J01-1012

CID: Cylindrical Instrumented Dummy

Nominal Lateral Distance of from Side of Train:

Vertical Distance of Center of Pressure from Top of Rail: 1.24 m (49 in)

Raw Data Processed by Bessel Second Order 15 Hz Low-Pass Digital Filter

Cylinder Axis 1.20 m (47 in)

----- (a) -----

Time, (s)

Resultant Force in Quadrant 1

1 012345678

0

20

40

60

0

5

10

Forcer, (N)

(lb)

Train

Head

Tail

1 012345678

0

20

40

60

----- (b) -----

Time, (s)

0

5

10

Force, (N)

(lb)

Moving Average Window of 1 s on Resultant Force in Quadrant 1

Train

Head

Tail

Figure 58. Time Histories of Single Quadrant Forces Measured on a CID and Computed from 

Airflow Velocity from a Passing Acela Express Train 
Part 2: Analysis and Evaluation 

151

SINGLE QUADRANT FORCE ON CID-5 FROM AERODYNAMIC INTERACTION WITH A PASSING

AMFLEET TRAIN WITH AEM-7 LOCOMOTIVE AT 184 km/h (114 mph)

Force Measured from CID

Cylinder Drag Force Computed from Airflow Velocity

 Measured by Pitot-Static Tube

Train Detector

Data: B02J01-1825

CID: Cylindrical Instrumented Dummy

Nominal Lateral Distance of from Side of Train:

Vertical Distance of Center of Pressure from Top of Rail: 1.24 m (49 in)

Raw Data Processed by Bessel Second Order 15 Hz Low-Pass Digital Filter

Cylinder Axis 1.20 m (47 in)

1 012345678

0

20

40

60

80

----- (a) -----

Time, (s)

Resultant Force in Quadrant 1

0

5

10

15

Force, (N)

(lb)

Train

Head

Tail

1 012345678

0

20

40

60

80

----- (b) -----

Time, (s)

Moving Average Window of 1 s on Resultant Force in Quadrant 1

0

5

10

15

Force, (N)

(lb)

Train

Head

Tail

Figure 59. Time Histories of Single Quadrant Forces Measured on a CID and Computed from 

Airflow Velocity from a Passing Amfleet Train with AEM-7 Locomotive 
Part 2: Analysis and Evaluation 

152

SINGLE QUADRANT FORCE ON CID-5 FROM AERODYNAMIC INTERACTION WITH A

PASSING AMFLEET TRAIN WITH HHP-8 LOCOMOTIVE AT 201 km/h (125 mph)

Force Measured from CID

Cylinder Drag Force Computed from Airflow Velocity

 Measured by Pitot-Static Tube

Train Detector

Data: B02J01-1101

CID: Cylindrical Instrumented Dummy

Nominal Lateral Distance of from Side of Train:

Vertical Distance of Center of Pressure from Top of Rail: 1.24 m (49 in)

Raw Data Processed by Bessel Second Order 15 Hz Low-Pass Digital Filter

Cylinder Axis 1.20 m (47 in)

1 012345678

0

20

40

60

80

100

120

----- (a) -----

Time, (s)

Resultant Force in Quadrant 1

Force, (N)

(lb)

0

5

10

15

20

25

Train

Head

Tail

1 012345678

0

20

40

60

80

100

120

----- (b) -----

Time, (s)

0

5

10

15

20

25

Force, (N)

(lb)

Moving Average Window of 1 s on Resultant Force in Quadrant 1

Train

Head

Tail

Figure 60. Time Histories of Single Quadrant Forces Measured on a CID and Computed from 

Airflow Velocity from a Passing Amfleet Train with HHP-8 Locomotive 
Part 2: Analysis and Evaluation 

153

The single quadrant force measured from the CID is compared with the drag on a flatbody computed from measured airflow velocity. For the three types of passing trains, the 

computed drag on the flat-body is in general considerably higher than those computed for 

a circular cylinder, and is also generally higher than the force measured from the CID 

(Figure 61(a), Figure 62(a), and Figure 63(a)). Next, the forces were processed by a 1 s 

moving average window to remove the higher frequencies to better view the trend as 

shown in Figure 61(b), Figure 62(b), and Figure 63(b). Although the flat-body drag is 

generally higher than the measured CID force along the length of the train, forces from 

both bodies diminished to about the same level in the wake region for the 

Amfleet/AEM-7 train. However, the flat-body drag remains consistently higher than the 

CID force in the wake region of the Acela Express train. This is likely due to the high 

airflow velocity in the wake of the Acela Express train, which is at the critical Reynolds 

number for a circular cylinder where the variable drag coefficient remains low. 

Therefore, the circular cylinder produces a lower drag on the CID than on a flat body 

where the drag was computed with a constant higher drag coefficient. Finally, the flatbody drag and CID force from the Amfleet/HHP-8 train share similar characteristics with 

the other two trains. 

These results are consistent with those from the RAPIDE study, which states that, 

Comparison between and instrumented cylinder and an instrumented mannequin 

showed extremely different results, both in magnitude of response and in response 

to different slipstream events. 

...a cylinder is not a very good representation for a person. Its drag coefficient 

varies by a factor of three over the wind speed range of interest...Its symmetry 

about the vertical axis generates a larger pressure differential between the front and 

back surfaces than does that of the more elliptical cylinder-shape of a human. This 

causes a larger difference in force due to the train pressure field.... 

...The cylinder that was tested only responded strongly to the static pressure effects 

of the train passing. It did not react significantly to the dynamic wake 

velocity....The results suggest that it is effectively measuring a pressure 

phenomenon. (RAPIDE 2001) 
Part 2: Analysis and Evaluation 

154

SINGLE QUADRANT FORCE ON CID-5 AND ON BODY WITH CONSTANT DRAG COEFFICIENT

FROM AERODYNAMIC INTERACTION WITH A PASSING

ACELA EXPRESS TRAIN AT 239 km/h (149 mph)

Force Measured from CID

Drag Computed for Constant Drag Coefficient C = 1.1

 from Airflow VelocitY Measured by Pitot-Static Tube

Train Detector

D

Data: B02J01-1012

CID: Cylindrical Instrumented Dummy

Nominal Lateral Distance of from Side of Train:

Vertical Distance of Center of Pressure from Top of Rail: 1.24 m (49 in)

Raw Data Processed by Bessel Second Order 15 Hz Low-Pass Digital Filter

Cylinder Axis 1.20 m (47 in)

1 012345678

0

20

40

60

80

----- (a) -----

Time, (s)

Resultant Force in Quadrant 1

0

5

10

15

Force, (N)

(lb)

Train

Head

Tail

1 012345678

0

20

40

60

80

----- (b) -----

Time, (s)

0

5

10

15

Force, (N)

(lb)

Moving Average Window of 1 s on Resultant Force in Quadrant 1

Train

Head

Tail

Figure 61. Time Histories of Single Quadrant Forces Measured on a CID and Computed with 

Constant Drag Coefficient from a Passing Acela Express Train 
Part 2: Analysis and Evaluation 

155

SINGLE QUADRANT FORCE ON CID-5 AND ON BODY WITH CONSTANT DRAG

COEFFICIENT FROM AERODYNAMIC INTERACTION WITH A PASSING

AMFLEET TRAIN WITH AEM-7 LOCOMOTIVE AT 184 km/h (114 mph)

Force Measured from CID

Drag Computed for Constant Drag Coefficient C = 1.1

 from Airflow Velocity Measured by Pitot-Static Tube

Train Detector

D

Data: B02J01-1825

CID: Cylindrical Instrumented Dummy

Nominal Lateral Distance of from Side of Train:

Vertical Distance of Center of Pressure from Top of Rail: 1.24 m (49 in)

Raw Data Processed by Bessel Second Order 15 Hz Low-Pass Digital Filter

Cylinder Axis 1.20 m (47 in)

1 012345678

0

20

40

60

80

100

120

140

160

180

----- (a) -----

Time, (s)

Resultant Force in Quadrant 1

Force, (N)

(lb)

0

10

20

30

40

Train

Head

Tail

1 012345678

0

20

40

60

80

100

120

140

160

180

----- (b) -----

Time, (s)

Force, (N)

(lb)

0

10

20

30

40

Moving Average Window of 1 s on Resultant Force in Quadrant 1

Train

Head

Tail

Figure 62. Time Histories of Single Quadrant Forces Measured on a CID and Computed with 

Constant Drag Coefficient from a Passing Amfleet Train with AEM-7 Locomotive 
Part 2: Analysis and Evaluation 

156

SINGLE QUADRANT FORCE ON CID-5 AND ON BODY WITH CONSTANT DRAG

COEFFICIENT FROM AERODYNAMIC INTERACTION WITH A PASSING

AMFLEET TRAIN WITH HHP-8 LOCOMOTIVE AT 201 km/h (125 mph)

Force Measured from CID

Drag Computed for Constant Drag Coefficient C = 1.1

 from Airflow Velocity Measured by Pitot-Static Tube

Train Detector

D

Data: B02J01-1101

CID: Cylindrical Instrumented Dummy

Nominal Lateral Distance of from Side of Train:

Vertical Distance of Center of Pressure from Top of Rail: 1.24 m (49 in)

Raw Data Processed by Bessel Second Order 15 Hz Low-Pass Digital Filter

Cylinder Axis 1.20 m (47 in)

1 012345678

0

20

40

60

80

100

120

140

160

180

----- (a) -----

Time, (s)

Resultant Force in Quadrant 1

Force, (N)

(lb)

0

10

20

30

40

Train

Head

Tail

1 012345678

0

20

40

60

80

100

120

140

160

180

----- (b) -----

Time, (s)

Force, (N)

(lb)

0

10

20

30

40

Moving Average Window of 1 s on Resultant Force in Quadrant 1

Train

Head

Tail

Figure 63. Time Histories of Single Quadrant Forces Measured on a CID and Computed with 

Constant Drag Coefficient from a Passing Amfleet Train with HHP-8 Locomotive 
Part 2: Analysis and Evaluation 

157

Although differences exist in relative magnitudes between the drag computed on a 

circular cylinder from the train-induced airflow velocity and the force measured on a CID 

from its aerodynamic interaction with the passing train, the general trend is the same. 

The time history signatures from airflow velocity and CID force for the different passing 

trains are similar. Both types of measurements indicate that the dominant airflow and 

force on the cylinder is primarily the longitudinal component in the direction of the 

passing train. 

9.4. Human Exposure Limit to Train-Induced Airflow Referenced to Wind Speed 

Criterion 

Airflow velocity referenced directly to a wind speed criterion is one approach to 

determine the aerodynamic effects of a passing train on people alongside the track. 

Another method based on the effects of airflow velocity on the stability of a 

mathematical mannequin will be discussed in the next chapter. In this section, wind 

speed criteria obtained from two different processes were applied to determine their 

suitability for evaluating the effect of train-induced airflow velocity on people. 

9.4.1. Example Time History of Formulated Wind Speed 

Airflow generated from a passing train is both transient and highly turbulent, and this 

factor must be considered in comparing the airflow velocity with any criterion relating 

wind speed to its effect on people. Two different wind speed criteria that were discussed 

in Part 1 were applied to the airflow induced by a passing train. One of the criteria that 

accounts for gusty wind was proposed by Hunt, Poulton, and Mumford (1976). They 

calculated an estimated equivalent steady wind speed for gusty wind conditions based on 

both an average wind speed and its turbulence intensity (Table 8). The duration window 

over which the average and fluctuating values are computed must be large enough to 

average the fluctuations effectively, but small compared to the time during which 

significant variations occur in the average value (Whitaker 1968). The turbulent 

fluctuation was computed as a deviation from a mean airflow velocity that was averaged 

over a 30 m (98 ft) averaging window. The other criteria were by Murakami and 

Deguchi(1981), which are based on the wind speed averaged over a 3 s averaging 

window (Table 9). 
Part 2: Analysis and Evaluation 

158

The two different wind speed criteria are applied to the three example types of trains and 

their results are compared (Figure 64(a), Figure 65(a), and Figure 66(a)). All the data 

were scaled so that the time and airflow velocity for the Acela Express train corresponds 

to a train speed of 241 km/h (150 mph). In the case of the Amfleet train, the data was 

scaled to correspond to a train speed of 201 km/h (125 mph). Two of the curves were 

processed from moving averages with averaging windows of 0.032 s and 3 s, while the 

third curve was computed from Hunt’s formulation on the equivalent steady airflow 

velocity for gusty conditions. The airflow velocity processed from the moving average 

window of 0.032 s serves as the baseline for the raw data. The maximum airflow 

velocities for these three processes and the three different trains are shown in Table 29. 

Hunt’s criteria predict that the airflow velocity for all three trains in these examples 

exceed the safe walking speed of 20 m/s (45 mph). By applying the Murakami and 

Deguchi criteria, both the Acela Express and the Amfleet/HHP-8 train induced airflow 

velocities between 10 to 15 m/s (22 to 34 mph) in which walking is difficult to control. 

The airflow velocity induced by the Amfleet/AEM-7 train is over 15 m/s (34 mph), 

which makes walking impossible to control. 

Table 29. Maximum Train-Induced Airflow Velocities Derived from Different Processes 

Train Scaled Train Airflow Velocity 

Speed Moving Equivalent Moving 

Average Steady Wind for Average 

Window of Gusty Window 

0.032 s Conditions* of 3 s** 

Acela Express train 241 km/h 22.6 m/s 23.7 m/s 12.5 m/s 

(B02J01-1012) (150 mph) (51 mph) (53 mph) (28 mph) 

Amfleet train with AEM-7 201 km/h 34.5 m/s 31.7 m/s 16.2 m/s 

locomotive (125 mph) (77 mph) (71 mph) (36 mph) 

(B02J01-1825) 

Amfleet train with HHP-8 201 km/h 31.6 m/s 35.3 m/s 14.5 m/s 

locomotive (125 mph) (71 mph) (79 mph) (32 mph) 

(B02J01-1101) 

*Formulation of equivalent airflow velocity for wind speed criteria of Hunt, Poulton, and Mumford. 

**Average airflow velocity over 3 s for wind speed criteria of Murakami and Deguchi.
Part 2: Analysis and Evaluation 

159

CHARACTERIZING TURBULENCE OF SINGLE QUADRANT AIRFLOW VELOCITY FROM A PASSING

ACELA EXPRESS TRAIN SCALED TO 241 km/h (150 mph)

Data: B02J01-1012

*Formulation of Hunt, Poulton, and Mumford

Nominal Lateral Distance of Pitot-Static Tube from Side of Train:

Distance of Pitot-Static Tube from Top of Rail: 0.97 m (38 in)

 1.17 m (46 in)

Nominal Vertical 

Train Detector

-1 0 1 2 3 4 5 6 7 8

0

5

10

15

20

25

30

35

40

----- (a) -----

Equivalent Steady Airflow Velocity for Gusty Conditions*

Average Airflow Velocity from 3 s Moving Average Window

Average Airflow Velocity from 0.032 s Moving Average Window

Time, (s)

Airflow Velocity, (m/s)

(mph)

0

20

40

60

80

Head

Tail

Train

Average and Equivalent Steady Resultant Airflows in Quadrant 1

----- (b) -----

Time, (s)

Intensity of Turbulence for Resultant Airflow in Quadrant 1

Turbulence Intensity

-1 0 1 2 3 4 5 6 7 8

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Head

Tail

Train

Figure 64. Time Histories of Single Quadrant Airflows Characterizing Turbulence from a Passing 

Acela Express Train 
Part 2: Analysis and Evaluation 

160

Data: B02J01-1825

*Formulation of Hunt, Poulton, and Mumford

Nominal Lateral Distance of Pitot-Static Tube from Side of Train:

Distance of Pitot-Static Tube from Top of Rail: 0.97 m (38 in)

 1.17 m (46 in)

Nominal Vertical 

CHARACTERIZING TURBULENCE OF SINGLE QUADRANT AIRFLOW VELOCITY FROM A PASSING

AMFLEET TRAIN WITH AEM-7 LOCOMOTIVE SCALED TO 201 km/h (125 mph)

Train Detector

-1 0 1 2 3 4 5 6 7 8

0

5

10

15

20

25

30

35

40

Time, (s)

Airflow Velocity, (m/s)

(mph)

0

20

40

60

80

Head

Tail

Train

Average and Equivalent Steady Resultant Airflows in Quadrant 1

----- (a) -----

Equivalent Steady Airflow Velocity for Gusty Conditions*

Average Airflow Velocity from 3 s Moving Average Window

Average Airflow Velocity from 0.032 s Moving Average Window

-1 0 1 2 3 4 5 6 7 8

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Time, (s)

Turbulence Intensity

Head

Tail

Train

Intensity of Turbulence for Resultant Airflow in Quadrant 1

----- (b) -----

Figure 65. Time Histories of Single Quadrant Airflows Characterizing Turbulence from a Passing 

Amfleet Train with AEM-7 Locomotive 
Part 2: Analysis and Evaluation 

161

Data: B02J01-1101

*Formulation of Hunt, Poulton, and Mumford

Nominal Lateral Distance of Pitot-Static Tube from Side of Train:

Distance of Pitot-Static Tube from Top of Rail: 0.97 m (38 in)

 1.17 m (46 in)

Nominal Vertical 

CHARACTERIZING TURBULENCE OF SINGLE QUADRANT AIRFLOW VELOCITY FROM A PASSING

AMFLEET TRAIN WITH HHP-8 LOCOMOTIVE SCALED TO 201 km/h (125 mph)

Train Detector

Time, (s)

Airflow Velocity, (m/s)

(mph)

0

20

40

60

80

-1 0 1 2 3 4 5 6 7 8

0

5

10

15

20

25

30

35

40

Head

Tail

Train

Average and Equivalent Steady Resultant Airflows in Quadrant 1

----- (a) -----

Equivalent Steady Airflow Velocity for Gusty Conditions*

Average Airflow Velocity from 3 s Moving Average Window

Average Airflow Velocity from 0.032 s Moving Average Window

Time, (s)

Turbulence Intensity

-1 0 1 2 3 4 5 6 7 8

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Head

Tail

Train

Intensity of Turbulence for Resultant Airflow in Quadrant 1

----- (b) -----

Figure 66. Time Histories of Single Quadrant Airflows Characterizing Turbulence from a Passing 

Amfleet Train with HHP-8 Locomotive 
Part 2: Analysis and Evaluation 

162

Whether the equivalent steady wind for gusty conditions computed from Hunt’s 

formulation can be properly related to the airflow induced from a passing train remains 

uncertain. The equivalent steady wind is related to the turbulence intensity, which is 

about 0.14 (about the same amount of energy as in the natural wind) for airflow that was 

generated by the wind tunnel during their experiment (Hunt, Poulton, and Mumford 

1976). However, the transient nature of airflow and the high turbulent fluctuation 

induced from a passing train can result in high turbulence intensity, especially at the nose 

region where the average airflow velocity is small (Figure 64(b), Figure 65(b), and 

Figure 66(b)). It is difficult to select a duration window sufficiently long enough to 

average the fluctuations effectively, but still small compared to the time during which 

significant variations occur in the average value. This is especially true near the head 

and tail ends of the train where rapid changes in average airflow velocities occur. 

9.4.2. Minimum Distance from Passing Train 

A relation between maximum longitudinal airflow velocity and lateral distance from the 

passing train was established from the data that was measured for the different types of 

passing trains. The maximum airflow velocity was computed from a 3 s moving average 

window, and scaled so that the airflow velocity for the Acela Express train corresponded 

to a train speed of 241 km/h (150 mph) and 201 km/h (125 mph) for the Amfleet train. 

The maximum airflow velocity is plotted from a 3 s moving average window at various 

lateral distances from a passing train at a nominal vertical distance of 0.97 m (38 in) from 

the top of the rail (Figure 67). A great deal of scatter occurs in the maximum airflow 

velocity because of the turbulent nature of the airflow as well as the varying types of 

trains. Plotted next is the maximum airflow velocity at a nominal height of 1.73 m 

(68 in) from the top of the rail where the induced airflow velocity is reduced at the 

increased height (Figure 68). 
Part 2: Analysis and Evaluation 

163

MAXIMUM LONGITUDINAL AIRFLOW VELOCITY DATA FROM 3 s MOVING AVERAGE WINDOW

AT NOMINAL VERTICAL DISTANCE OF 0.97 m (38 in) FROM TOP OF RAIL

Longitudinal Airflow Velocity Measured by Pitot-Static Tube

Airflow Data

 Acela Express Train Scaled to 241 km/h (150 mph)

 Amfleet Train Scaled to 201 km/h (125 mph)

Formulated Velocity

Formulated Velocity Plus 2 Standard Deviations

Lateral Position of CID at Cylindrical Axis

Minimum Distance

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

0

2

4

6

8

10

12

14

16

18

20

22

24

Lateral Distance from Side of Train, (m)

(in)

20 30 40 50 60 70 80

Airflow Velocity, (m/s)

(mph)

0

10

20

30

40

50

5

15

25

35

45

Minimum Distance 1

Figure 67. Train-Induced Airflow Velocity Data Measured at 0.97 m (38 in) above Top of Rail with 

Formulated Velocity Curves 
Part 2: Analysis and Evaluation 

164

MAXIMUM LONGITUDINAL AIRFLOW VELOCITY DATA FROM 3 s MOVING AVERAGE WINDOW

AT NOMINAL VERTICAL DISTANCE OF 1.73 m (68 in) FROM TOP OF RAIL

Longitudinal Airflow Velocity Measured by Pitot-Static Tube

Airflow Data

 Acela Express Train Scaled to 241 km/h (150 mph)

 Amfleet Train Scaled to 201 km/h (125 mph)

Formulated Velocity

Formulated Velocity Plus 2 Standard Deviations

Lateral Position of CID at Cylindrical Axis

Minimum Distance

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

0

2

4

6

8

10

12

14

16

18

20

22

24

Lateral Distance from Side of Train, (m)

(in)

20 30 40 50 60 70 80

Airflow Velocity, (m/s)

(mph)

0

10

20

30

40

50

5

15

25

35

45

Minimum Distance 1

Figure 68. Train-Induced Airflow Velocity Data Measured at 1.73 m (68 in) above Top of Rail with 

Formulated Velocity Curves 
Part 2: Analysis and Evaluation 

165

A curve was fitted to the data by regression as a power function to obtain a continuous 

empirical relation between airflow velocity and lateral distance as follows, 

u

~

max−3s = ( ) A yk

O train +UO Equation 8

where, 

u

~

max−3s : is formulated longitudinal airflow velocity. 

ytrain: is the lateral distance from side of a train. 

The function for the formulated 

longitudinal airflow velocity, 

u

~

max−3s , represents the best fit 

to the maximum airflow 

velocity obtained from a 3 s 

moving average window as a 

function of lateral distance 

from the side of a train. Table 

30 shows the values for the 

constants of the function that 

were computed by minimizing 

the error between the function 

and the data measured at the 

two heights of 0.97 m (38 in) 

and 1.73 m (68 in) from the top 

of the rail. These constants are 

valid for the data between the 

limits of lateral distances from the side of train of 0.60 m (24 in) and 2.1 m (83 in). This 

curve for the formulated velocity along with the curve for the formulated velocity plus 2 

standard deviations are plotted with the measured airflow data (Figure 67 and Figure 68). 

Table 30. Constants to the Formulated Velocity Regression 

Power Curve Fitted to Data for the Maximum 

Longitudinal Airflow Velocity over a 3 s Moving 

Average Window 

~umax−3s = k (A y O train )+UO m/s

Nominal Height AO k UO

above Top of Rail 

0.97 m 1.952x102

 -3.661x10-2 -1.810x102

(38 in) 

1.35 m 1.065x106

 -5.978x10-6 -1.065x106

(53) 

1.73 m 1.155x106

 -4.835x10-6 -1.155x106

(68) 
Part 2: Analysis and Evaluation 

166

With the relation between lateral 

distance from the train and airflow 

velocity established, its effect on people 

can be estimated from the wind speed 

criteria of Murakami and Deguchi 

(1981). The effect is based on the wind 

speed averaged over 3 s. The effect of 

airflow on people is described at the two 

lateral positions corresponding to the 

locations of the CIDs. These two 

positions are indicated in Figure 67 and 

Figure 68 at nominal lateral distances of 

1.17 m (46 in) and 1.43 m (56 in) from 

the side of the train. The formulated 

velocity plus 2 standard deviations 

corresponding to the two locations of 

the CIDs and at two heights of 0.97 m 

(38 in) and 1.73 m (68 in) are shown in 

Table 31. While the airflow velocity is 

lower at the CID location further away 

from the train, the magnitudes of the 

airflow velocities at both lateral 

locations are described relative to its 

Nominal 

Height from 

Top of Rail 

Nominal 

Distance from 

Side of Train 

Airflow 

Velocity, ~umax−3s + 2σ

0.97 m 

(38 in) 

1.17 m 

(46 in) 

17.5 m/s 

(39 mph) 

1.43 m 

(56 in) 

16.1 m/s 

(36 mph) 

1.35 m 

(53 in) 

1.17 m* 

(46 in)* 

15.1 m/s* 

(34 mph)* 

1.43 m* 

(56 in)* 

13.8 m/s* 

(31 mph)* 

1.73 m 

(68 in) 

1.17 m 

(46 in) 

13.8 m/s 

(31 mph) 

1.43 m 

(56 in) 

12.7 m/s 

(28 mph) 

effect on people as: walking can be 

impossible to control for airflow close to the ground, and walking can be difficult to 

control for airflow further from the ground. 

The lateral distance from the train set by the limits of airflow velocity also depends on 

the height at which the airflow is referenced since the airflow velocity varies with height 

from the ground. If the airflow velocity is limited to 10 to 15 m/s (22 to 34 mph) where 

walking is difficult to control, based on airflow that is 0.97 m (38 in) above the top of the 

rail, this would require a distance of about 1.7 m (67 in) from the side of the train (Figure 

67). If the requirement is based on airflow 1.73 m (68 in) above the top of the rail, the 

lateral distance is reduced to about 1.1 m (43 in) from the side of the train (Figure 68). 

These lateral distances are referred to as minimum distance 1. 

People vary in height and shape, which affect their center of pressures. Furthermore, the 

height of the platform on which the person is standing can vary. Therefore, the center of 

pressure relative to the track can vary. Given these variations, a nominal height of 

1.35 m (53 in) from the top of the rail is selected as the vertical location that is 

representative of the strength in the airflow that is experienced by an adult standing on a 

low-level passenger platform. This height references the airflow velocity that is slightly 

above the center of pressure of the human body for an average adult male when the 

person is standing on a low-level station platform that is at a height designed according to 

specification. This representative intermediate height also corresponds to the nominal 

location of the center of pressure of the CID. 

Table 31. Formulated Longitudinal Airflow 

Velocities from 3 s Moving 

Average Window Corresponding 

to CID Positions 

*Interpolated values.
Part 2: Analysis and Evaluation 

167

Airflow velocity at 1.35 m (53 in) from top of the rail is estimated by linear interpolation 

from the airflow data measured at 0.97 m (38 in) and at 1.73 m (68 in) from the top of the 

rail (the interpolated airflow is also the average airflow since it is at the midpoint of the 

two measured values). The interpolated maximum airflow velocity at a nominal height 

of 1.35 m (53 in) from the top of the rail is shown plotted in Figure 69 along with the 

curve fitted to this data with new constants for the formulated velocity (Table 30). At 

this middle height, the magnitude of the airflow velocity at the lateral location of the CID 

closest to the train is described relative to its effect on people as walking can be 

impossible to control. Airflow velocity, occurring at the lateral location of the CID and 

further away from the train, has the effect on people described as “walking can be 

difficult to control.” 

Two minimum lateral distances from a passing train are indicated from two ranges of 

airflow velocities. In the first minimum distance (minimum distance 1), the exposure of 

airflow velocity is limited to a range of 10 to 15 m/s (22 to 34 mph), which is described 

relative to its effect on people as walking is irregular and difficult to control. This 

requirement is met at a nominal minimum distance of 1.2 m (47 in) from the side of a 

passing train. At this distance, the formulated velocity and the formulated velocity plus 

two standard deviations are both within the specified limiting airflow velocity range. A 

second minimum distance (minimum distance 2) is to limit the exposure of airflow 

velocity such that the formulated velocity is below 10 m/s (22 mph), which is described 

relative to its effect on people as walking with footsteps that are sometimes irregular. 

This requirement is met at a nominal minimum distance of 1.6 m (63 in) from the side of 

a passing train. At this distance, the formulated velocity is below 10 m/s (22 mph), while 

the formulated velocity plus two standard deviations is between 10 and 15 m/s (22 and 

34 mph). These two minimum distances are shown in the graph of Figure 69. The results 

of all the minimum distances are summarized in Table 32. 
Part 2: Analysis and Evaluation 

168

INTERPOLATED MAXIMUM LONGITUDINAL AIRFLOW VELOCITY FROM 3 s MOVING AVERAGE

WINDOW AT NOMINAL VERTICAL DISTANCE OF 1.35 m (53 in) FROM TOP OF RAIL

Longitudinal Airflow Velocity Linearly Interpolated from Data Measured

 by Pitot-Static Tubes at Two Heights

Interpolated 

Amfleet Train Scaled to 201 km/h (125 mph)

Airflow Data

 Acela Express Train Scaled to 241 km/h (150 mph)

 

Minimum Distance

Lateral Position of CID at Cylindrical Axis

Formulated Velocity

Formulated Velocity Plus 2 Standard Deviations

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

0

2

4

6

8

10

12

14

16

18

20

22

24

Lateral Distance from Side of Train, (m)

(in)

20 30 40 50 60 70 80

Airflow Velocity, (m/s)

(mph)

0

10

20

30

40

50

5

15

25

35

45

Minimum Distance 1Minimum Distance 2

Figure 69. Interpolated Train-Induced Airflow Velocity Data at 1.35 m (53 in) above Top of Rail 

with Formulated Velocity Curves 
Part 2: Analysis and Evaluation 

169

Table 32. Minimum Distances from a Passing Train for a Person Exposed to Train-Induced 

Airflow Velocity 

Nominal Location Lateral Distance Airflow Velocity 

Height from 

Top of Rail 

Number Distance from 

Outer Edge of 

Nearest Rail 

Nominal 

Distance from 

Side of Train 

~umax−3s~umax−3s + 2σ

0.97 m Minimum 2.43 m 1.7 m 10.5 m/s 14.9 m/s 

(38 in) Distance 1 (96 in) (67 in) (23 mph) (33 mph) 

1.35 m Minimum 1.93 m 1.2 m 11.4 m/s 14.9 m/s 

(53 in) Distance 1 (76 in) (47 in) (26 mph) (33 mph) 

Minimum 2.33 m 1.6 m 9.5 m/s 13.1 m/s 

Distance 2 (92 in) (63 in) (21 mph) (29 mph) 

1.73 m Minimum 1.83 m 1.1 m 10.3 m/s 14.1 m/s 

(68 in) Distance 1 (72 in) (43 in) (23 mph) (32 mph) 

No airflow was measured at a height corresponding to an adult standing on a high level 

platform. The greatest height that was measured is 1.73 m (68 in) from the top of the rail. 

This is above the high level platform of 1.219 m (48 in) from the top of the rail, but 

below the center of pressure of an average adult standing on a high level platform. An 

estimate for a minimum lateral distance for a high level platform can be indicated from 

the airflow data measured at the greatest height (Figure 68) and limiting the exposure to a 

formulated velocity below 10 m/s (22 mph), and the formulated velocity plus two 

standard deviations below 15 m/s (34 mph). A minimum distance that satisfies this 

requirement is 1.2 m (47 in) from the side of the train. This estimate does not take into 

account the effect that the presence of the high level platform would have on the 

measurement of the airflow. 
Part 2: Analysis and Evaluation 

170

10. Human Response in Proximity to Passing Train 

A person in proximity to a train passing at high speeds will experience a force from the 

aerodynamic effects of the train’s passage. The person can respond both physically and 

psychologically to this event. There is the physical sensation of a force on the person’s 

body, which the person can sense as a loss of balance if the force is of substantial 

magnitude. A passing train, because of its mass, size, noise, and speed, can also evoke a 

psychological response from a person. From a safety standpoint, the aerodynamic effects 

of a passing train should not cause a person to fall, be drawn closer toward the train, or 

create an unsafe condition such as being struck by propelling debris. The subjective 

experience will also be considered to provide a comprehensive picture of this human 

experience. 

Human response to an external force on the body is complex, particularly when muscular 

action is involved. Many variables exist such as people of different heights, size, weight, 

physical strength, and psychological states. Different people can respond differently to 

the same event. The same person can respond differently to the same event at different 

times, depending on their attentiveness at the moment. Finally, added to the complexity 

of human response is the unsteady nature of the transient turbulent airflow induced by the 

passing train. 

Although a complete human response to an external force is complicated, predictions can 

be made for a short time interval where the human body initially acts as a rigid body. 

Prevezer (2001), and Johnson, Dulley, and Temple (2002) described a mathematical 

model base on mechanical action to simulate human response from the application of a 

short duration force. A single degree-of-freedom mechanical human response model was 

used to predict human response for a period of about 0.35 s after application of force. 

The force applied to the body was a superposition of a mean wind speed and a sinusoidal 

pulse. A time-stepping solution was used to determine when the model would fall over 

from rotation. The mechanical model is appropriate only within about 0.35 s from the 

application of a sudden force. After time, subjective response is assumed to take place, 

and human response cannot be predicted mechanically. 

A mannequin can be a useful tool in assessing the effects of wind on people if its 

dynamic response can be related to the long-established Beaufort scale. A simple single 

degree-of-freedom model can serve to illustrate the methodology, whose principle is 

similar to the previous use of detector pins that falls at a defined wind speed. The 

dynamic response of the mannequin may provide insight on the effects that wind force of 

varying magnitude and duration have on stability, particularly from a single strong gust 

over a short duration. Therefore, the mannequin model, when used in conjunction with 

the wind speed criteria of Murakami and Deguchi, can complement each other to provide 

a more adequate assessment on the effects of wind on human stability. 
Part 2: Analysis and Evaluation 

171

A mathematical model of a mannequin was created as an instrument to map the stability 

boundary for a simple standing object that can be applied to evaluate the aerodynamic 

data produced from a passing train. The mannequin stability model is a rigid body with 

dimensions and mass based on a human body. Impulsive force is applied to the body at 

various durations from which a relationship can be obtained between magnitude of 

impulsive force and duration of applied force to satisfy a given state of stability. The 

mannequin stability model is not intended to replicate the complex behavioral response 

of a human being, but it is a rigid inanimate object with the size and shape of a person. 

As such, it will provide a metric for the measured data that is valid for this rigid 

mannequin. 

10.1. Property of Human Body 

The stability boundaries will be developed for a mannequin based on properties for a 

human. Geometric and dynamic properties required to model a human include the mass, 

moment of inertia, center of mass, center of pressure, projected area, and drag coefficient. 

Some of these values were obtained from reference sources, whereas others had to be 

computed or estimated. Table 33 shows the weights, heights, and center of masses for a 

small, average, and large person (Diffrient, Tilley, and Bardagjy 1974). 

Table 33. Properties of Nude Human Bodies (Diffrient, Tilley, and Bardagjy 1974) 

Property Gender Size (Percentile) 

Small (2.5) Average (50) Large (97.5) 

Weight Male 68.5 kg 

(151 lb) 

78 kg 

(172 lb) 

87.1 kg 

(192 lb) 

Female 60.3 kg 

(133 lb) 

65.8kg 

(145 lb) 

71.2 kg 

(157 lb) 

Height Male 1.615 m 

(63.6 in) 

1.748 m 

(68.8 in) 

1.880 m 

(74 in) 

Female 1.491 m 

(58.7 in) 

1.615 m 

(63.6 in) 

1.74 m 

(68.5 in) 

Center of Mass Male

Female 

 0.879 m 

(34.6 in) 

0.963 m 

(37.9 in) 

1.046 m 

(41.2 in) 

The two properties of a human body that affect the wind force experienced by a person 

are the body’s drag coefficient and the projected area. Penwarden, Grigg, and Rayment 

(1976) described a wind tunnel experiment that measured the wind drag on people, from 

which drag coefficients, and the relationship of their projected area to total surface area 

were obtained. The measurements were performed for a wide range of people wearing 
Part 2: Analysis and Evaluation 

172

different types of clothing. Each person’s weight and height were measured, and grouped 

according to the type of clothes that were worn. Once the ratio of a person’s projected 

areas to total surface areas is established, the projected areas can be estimated from the 

formula of DuBois and DuBois (1916a, 1916b), which relates a person’s total body 

surface area to weight and height as follows (converted to present system of units 

(Penwarden, Grigg, and Rayment 1976)): 

A = 0.0769× ( ) mg

0.425

x(L )

0.725

Du h , 

where, 

ADu: total body surface area, (m), 

mg: weight, (N), and, 

Lh: height, (m), 

The results for a human body’s projected area to total surface area ratios and its drag 

coefficient with various types of clothing are shown in Table 34. Hill (1928) reported a 

wind tunnel test using an unclothed scaled model to measure the air resistance of a man. 

A drag coefficient was computed from the test data to be 0.98 for a nude man in the erect 

position facing the wind (Penwarden, Grigg, and Rayment 1976). These drag 

coefficients are all in the range determined by Horner (1958). The drag coefficients for a 

standing person are between 1.0 and 1.3, and 5 to 10 percent less without clothing. 
Part 2: Analysis and Evaluation 

173

Table 34 Human Body Drag Characterization from Wind Tunnel Measurement at a Wind Speed 

of 8.5 m/s (19 mph) (Penwarden, Grigg, and Rayment 1976) 

Category Frontal Area 

Ratio, Af/ADu

Side Area 

Ratio, As/ADu

Frontal Drag 

Coefficient, 

CDf

Side Drag 

Coefficient, 

CDs

Skirt with shirt, sweater or buttoned 

jacket. 

0.30 0.21 1.08 0.95

Skirt with shirt, sweater or buttoned 

jacket, carrying bag or clothing. 

0.32 0.23 

Skirt with coat or open jacket. 

Trousers with shirt, sweater or buttoned 

jacket. 

0.32 0.22 1.17 1.01

Trousers with shirt, sweater or buttoned 

jacket, carrying bag or clothing. 

0.35 0.23 

Trousers with buttoned coat. 0.35 0.24 

Trousers with open coat. 0.36 0.24 

Trousers with jacket held open. 0.34 0.22 1.23 1.06 

Trousers with flapping coat or carrying 

clothes. 

0.35 0.26 1.33 1.12

Finally, the moment of inertia and the location of the center of pressure were computed 

from a rigid geometric model (no movable joints) representing the human body. The 

human body was modeled by a series of geometric shapes that were superimposed over 

the outline of the human body (Figure 90 in the Appendix). Next, a series of geometric 

solids were used to approximate the human body as shown in Figure 70. Each human 

body segment was modeled by: (1) an ellipsoid for the head (head included the neck), (2) 

a frustum for the shoulder, (3) elliptical cylinders for the trunk, upper arms, forearms, 

thighs, and legs, and (4) rectangular prisms for the hands and feet. In modeling the body 

segments, each geometric solid was assumed to be of uniform density. When the center 

of mass of a body segment was not located at the geometric center, the total mass of that 

segment was redistributed by an addition of a point mass at one end of the geometric 

segment to produce the proper center of mass location. The moment of inertia, center of 

pressure, and projected area were computed for each geometric segment from which the 

moment of inertia and the location of the center of pressure for the human body were 

determined (Table 49 and Figure 91 in the Appendix). 
Part 2: Analysis and Evaluation 

174

HUMAN BODY MODELED BY SEGMENTS OF BASIC GEOMETRIC SOLIDS

φ

y

θ

x

z

ψ

Figure 70. Human Body Modeled as Geometric Solids 
Part 2: Analysis and Evaluation 

175

The stability boundaries were 

developed from a mannequin based on 

the specifications for an average 50 

percentile adult male. Table 35 lists 

the value of the parameters for the 

mannequin. The stability of the 

mathematical mannequin from wind 

force is determined for a frontal facing 

projected area. Whereas a person is 

least stable when pushed sideways, 

wind blowing against the front of a 

person and being pushed backwards is 

expected to create the most instability 

given the greater frontal area being 

presented to the wind (Temple and 

Johnson 2003). The computed centerof-pressure can be compared with the 

dummy used in the experiment 

conducted by China Academy of 

Railway Sciences, which had a center 

of pressure that was 51 percent of the dummy height (Heshou, Dezhao, and Houxiong 

1996). The height to the top of the head of a 50 percentile male is 1.748 m (68.8 in), and 

the computed center of pressure for the mathematical mannequin is 0.894 m (35.2 in), 

which is 51 percent of its height—the same relative height as the physical dummy. 

Table 35. Properties of the Mannequin for 

Simulation Based on an Average 50 

Percentile Adult Male Wearing 

Light Clothing 

Property Value

Mass 

(Diffrient, Tilley, and Bardagjy 1974) 

78 kg 

[0.445 (lb•s2

)/(in)] 

Pitch Moment of Inertia about 

Bottom of Feet 

2 82.1 N•m•s

(727 lb•in•s2

) 

Height to Center of Mass 

(Diffrient, Tilley, and Bardagjy 1974) 

0.963 m 

(37.9 in) 

Height to Center of Pressure 0.894 m 

(35.2 in) 

Frontal Area 

(DuBois Formula) 

0.628 m2

(973 in2

) 

Frontal Drag Coefficient 1.1 
Part 2: Analysis and Evaluation 

176

10.2. Destabilizing Force to Human Body from Horizontal Acceleration 

A critical threshold value needed to interpret the measured train-induced airflow data is 

the relationship between a person’s stability, the force applied to a person, and the 

duration of that force. Two types of studies provide insight to this question. One type of 

study is the stability of people when exposed to the force of wind. The results of these 

studies were discussed previously on the effect of wind on people. The other study 

discussed is the measurements of stability on people that are in a standing position, and 

undergoing control levels of horizontal accelerations. 

An experience that is common to many people is the attempt to maintain balance while 

standing on a train or bus during acceleration or braking. Hirshfeld (1932) conducted an 

experiment to determine the best form of acceleration curve for rapid starting of a 

streetcar that would attain the maximum acceleration and cause the least discomfort to 

standing passengers. The test apparatus was a movable platform where test subjects 

stood. Sensors on the platform detected when the weight of the person shifted due to 

tipping or loss of equilibrium. The person stood with their feet 0.254 m (10 in) apart 

with the heel of one foot 0.203 m (8 in) behind the heel of the other foot. Any loss of 

contact between a foot and the ground was considered a loss of balance. The tests were 

performed for different rates of acceleration, different acceleration curves (linear or 

parabolic acceleration, and dips in acceleration), and different standing configurations 

(facing forward, backward, sideways, and holding on to straps). 
Part 2: Analysis and Evaluation 

177

Of the tests conducted, the method that is of 

interest is the steep rise starting method 

where a very high rate of acceleration of 

3.048 m/s3

 (10 ft/s3) is applied, and the 

equilibrium performance of the test subjects 

was measured. The performance of the test 

subjects as measured by the average 

acceleration attained while maintaining 

equilibrium is shown in Table 36. Almost 

everyone in this test could maintain balance 

at acceleration below 0.305 m/s2

 (1 ft/s2), but 

nobody was able to do so at acceleration of 

1.067 m/s2

 (3.5 ft/s2) or higher. In these 

tests, the acceleration level was obtained 

within 1 s, and the acceleration was 

maintained within the physical limits of the 

length of the platform track. The time it took 

for balance to be lost was not a consideration 

in these tests, and therefore, not specified. 

Three of the results arrived by Hirshfeld 

(1932) from this experiment relating to 

human response are: 

• The ability to withstand acceleration 

force in standing position does not 

appear to be influenced to any marked 

extent by age, sex, occupation, size, or 

build. 

• An individual varies in his ability to maintain equilibrium, which could be affected 

by his physical and mental condition. 

• Performances vary with different individuals for the same conditions. 

10.3. Modeling Mannequin Stability 

When the airflow velocity is relatively steady, or an unsteady airflow velocity is averaged 

over an extended period of time, the Beaufort wind force scale can be used to relate wind 

speed with its effects on a person. However, when a significant gust occurs over a short 

duration, a strong wind force could be imparted to the person. This effect cannot be 

adequately captured by use of the Beaufort wind force scale, which relies on an extended 

averaging duration. Therefore, a mannequin stability model was used as an analytical 

tool to map the stability boundary from an applied force of both short and long durations, 

and to relate these results to the Beaufort scale. 

Table 36. Equilibrium Distribution of 

Standing Subjects Facing Forward 

for Rate of Change of 

Acceleration of 3.048 m/s3

(10 ft/s3

) (Hirshfeld 1932) 

Average 

Acceleration 

Attained 

Acceleration, 

Number of 

Gravity (g)* 

Percentage 

of Test in 

which 

Equilibrium 

was 

Maintained 

--- --- 100

2 0.305 m/s

(1 ft/s2

) 

0.031 98

2 0.457 m/s

(1.5 ft/s2

) 

0.047 87

2 0.610 m/s

(2.0 ft/s2) 

0.062 56

2 0.762 m/s

(2.5 ft/s2

) 

0.078 25

2 0.914 m/s

(3.0 ft/s2

) 

0.093 11

2 1.067 m/s

(3.5 ft/s2

) 

0.11 0

*Number of gravities were computed for this report by dividing 

the average acceleration attained by the acceleration of gravity. 
Part 2: Analysis and Evaluation 

178

10.3.1. Defining Stability Boundary 

A mathematical mannequin model was used to develop the stability boundary that relates 

an applied external force to the duration of applied force. In modeling mannequin 

stability, the assumption is that the body only undergoes rotation as shown in Figure 71 

for the various states of stability. When a force, FCP(t), is applied to the mannequin at the 

center of pressure, the mannequin remains stationary until the moment from the applied 

force balances the moment due to its weight. The moment that is reached at this 

balancing condition will be referred to as the breakout moment. Although the applied 

force is below the breakout moment of the mannequin, the mannequin will remain 

stationary and be statically stable (Figure 71(a)). Once a force of sufficient magnitude is 

applied to the mannequin to exceed the breakout moment, the body will rotate, and 

depending on the strength and duration of the applied force, the body will either be 

dynamically stable and return to its initial position, or continue to rotate and become 

dynamically unstable and fall over (Figure 71(b)). A state exists such that the application 

and then the release of a force will cause the mannequin to rotate, and then the 

mannequin comes to rest when it’s center of mass is immediately above the pivot point, 

or point of center-of-rotation (Figure 71(c)). This position is statically unstable and will 

be referred to as the statically unstable equilibrium (SUE) point. Any greater force or 

duration of applied force will cause the mannequin to continue to rotate and fall; any less 

force or duration of applied force will return the mannequin to a stable standing position. 

The stability boundary for the mannequin is the relationship between the magnitude and 

duration of applied force for the mannequin to reach the SUE point. 

The stability boundary for the mannequin will be developed for an applied force with 

waveforms that are representative of gust profiles that are present during train passages. 

A velocity variation that can be loosely identified as an isolated single pulse is referred to 

as a gust, while a fluctuating airflow velocity that is continuous, such as a series of 

individual gusts, is spoken of as turbulence (Hoblit 1988). Gust profiles for aircraft 

design application were originally modeled as a sharp-edge gust but have evolved to the 

current one-minus-cosine pulse (Hoblit 1988). The stability boundaries for the 

mannequin were developed for three different gust profiles: sharp-edge profile (or square 

wave), a half sine wave, and a one-minus-cosine wave (or versine wave). These three 

gust profiles are shown in Figure 72. For each gust profile, a stability boundary was 

computed for various time durations. 
Part 2: Analysis and Evaluation 

179

FORCE APPLIED TO ST MANNEQUIN AND RESULTING ATE OF STABILITY

----- (c) -----

----- (a) -----

----- (b) -----

F (t) CP

Dynamically Unstable

Statically Stable

(Equilibrium)

Dynamically Stable

Statically Unstable

(Statically Unstable Equilibrium or SUE)

Breakout Moment: mgLCM1

LCM1

mg

LCM3

LCP3

mg

x

z

θ

Figure 71. States of Stability for a Mannequin 
Part 2: Analysis and Evaluation 

180

WAVEFORM OF AIRFLOW VELOCITY PULSE FOR MODELING GUST PROFILE

----- (c) -----

Time, (s)

Unit Amplitude

0.0

0.5

1.0

1.5

0

HALF SINE WAVE

Average

0.6366

Time, (s)

Unit Amplitude

VERSINE WAVE

0.0

0.5

1.0

1.5

0 1.0

Average

0.5

----- (b) -----

----- (a) -----

Time, (s)

Unit Amplitude

SQUARE WAVE

Average

1.0

0.0

0.5

1.0

1.5

0

1.0

1.0

Figure 72. Waveforms for Modeling a Gust Profile 
Part 2: Analysis and Evaluation 

181

10.3.2. Relating Airflow to Mannequin Stability 

Once the stability boundaries are developed, they can be applied to determine the 

stability of the mannequin to the airflow induced by a passing train. However, the 

transient aerodynamic effect created by a passing train is an unsteady fluctuating airflow, 

and this stochastic phenomenon cannot be described by a simple waveform. In contrast, 

the stability boundaries will be based on simple well-defined gust profiles. Therefore, 

the approach was to use the mean as the statistical quantity that relates the stability 

boundaries with the airflow data. The premise is that the average values of the gust 

profiles can be a good description of the airflow data when they are averaged over a 

range of averaging duration windows. 

If it is assumed that the destabilizing force acting on the mannequin is due to the dynamic 

pressure of the airflow, then the force on the mannequin is the aerodynamic drag, 

1 FD = ρu

2

(t)CD AP . The airflow velocity u(t) can be expressed as u(t) = U f (t) 2 O S , 

where UO is the amplitude of the gust, and fS(t) is a shape function, which is a time 

varying waveform of unit amplitude that represents the gust profile. Letting the 

⎛ 1 ⎞ amplitude of the drag be FO, where F 2

O = ⎜ ρC

2 D A ⎝ P ⎟U

⎠ O , the drag can be expressed as an 

amplitude and a time-varying component, F F f 2

D = O S (t) . 

In developing the stability 

boundary, for each gust profile 

that is applied to the mannequin 

over a given period of time, there 

will be a force amplitude and a 

corresponding airflow velocity 

amplitude that will cause the 

mannequin to reach a SUE point. 

The average airflow velocity, or 

the root mean square of the drag, 

forms the stability boundary. On 

the basis of a unit amplitude of 

each gust profile (Figure 72), the 

means and root-mean-squares are 

shown in Table 37. 

To relate the airflow data to the stability boundaries, the average airflow velocities are 

computed from the airflow data at various averaging durations over the entire flow 

disturbance created by the passing train. From this moving average, the maximum 

airflow velocity is obtained for each averaging duration. The duration of the moving 

average is considered to correspond to the duration of the gust force that acts on the 

mannequin. These average airflow velocities are plotted on the same graph as the plots 

Table 37. Mean and Root-Mean-Square for 

Waveforms of Unit Amplitude 

Unit Amplitude Mean Root Mean Square 

Waveform 

Square 1 1 

Half Sine 2

π ≈ 0.6366 2

2 ≈ 0.7071

Versine 0.5 3

8 ≈ 0.6124
Part 2: Analysis and Evaluation 

182

of the stability boundaries to determine the effects of the airflow data on the stability of 

the mannequin. The averaging technique is applied to relate the two sets of results, the 

airflow velocity data from a passing train, and the stability boundaries derived from 

numerical simulation on a mannequin, to a common measurement. 

Simplifications and assumptions exist in this procedure. First is that averages are not 

unique, because different sets of numbers produce the same average value. Therefore, 

the waveforms applied to the mannequin are assumed to approximate the waveform of 

the airflow data. Secondly, the response of the mannequin is from a single isolated 

airflow velocity pulse, and not from a continuous airflow stream that occurs during train 

passage. 

10.3.3. Rotational Load Factor for Inertia and Drag 

The force on a person standing on a platform undergoing acceleration differs from the 

force of air pressure. These differences must be taken into account when comparisons are 

made between data from a moving platform and those from the effects of wind. The 

unbalance that a person senses standing on an accelerated platform is due to the inertia of 

the body as the force acts horizontally at the feet. This inertial reaction, or body force, 

can be considered to act at the center of mass of the body. The force on a body from air 

pressure is a surface force, which acts on the surface of the body and can be considered to 

act at the center of pressure of the body. For a human body, which is composed of many 

movable segments with flexible body surface, the type of force and its point of 

application are significant, in terms of sensation and injury, and its dynamic response. 

However, for a rigid inanimate object, no difference in response between the effect of 

inertia and aerodynamic drag exists, except for the point at which the force acts. 

An index will be defined to relate the wind force acting on a body, with the inertia of an 

accelerated platform. The response of the mathematical mannequin to drag is modeled as 

a pure rotation. Because the body is responding to the moment produced by the drag, the 

drag acting at the center of pressure of the body can be replaced by an effective force 

acting at the center of mass that produce the same moment. A rotational load factor, nα, 

will be defined as the ratio of the effective force acting at the center of mass to the weight 

of the body. The rotational load factor is a dimensionless quantity and is interpreted as 

the ratio of the effective acceleration on the body to the acceleration of gravity, or as the 

number of gravities (g). Using this definition of rotational load factor, a force applied to 

the body causing pure rotation can be compared to the force from ground acceleration. 

10.3.4. Stance 

The ability of the mannequin to resist rotation from an external force depends on the 

stance, or the distance of the moment arm from the center of mass to the center of 

rotation. This distance on the mannequin (Figure 71), LCM1, is analogous to the positions 

of the feet on a standing person, and corresponds to approximately half the distance 
Part 2: Analysis and Evaluation 

183

between the front and rear feet. The stance distance for the mannequin is determined by 

the breakout moment that the mannequin is to resist, which is, 

⎛ F ⎞ L = L ⎜ CPbo

CM1 CP3 ⎟ ⎜ ⎟ Equation 9

⎝ mg ⎠

where FCPbo is the breakout force applied at the center of pressure that causes a state of 

impending rotation on the mannequin. 

The ability of the mannequin to resist rotation depends on the stance, and a stability 

boundary occurs for each stance distance. Corresponding to each stance is a breakout 

moment produced by the wind force acting at the center of pressure of the mannequin. 

Each stability boundary is identified by the rotational breakout load factor at the center of 

mass, which is computed as, 

⎛ F ⎞⎛ L ⎞ Equation 10 nαbo = ⎜ CPbo ⎟⎜ CP3 ⎟ ⎜ ⎟⎜ ⎟ ⎝ mg ⎠⎝ LCM 3 ⎠

The stance distances, forces, and moments of the mannequin for various values of 

rotational load factor at breakout are shown in Table 38. A breakout rotational load 

factor of 0.05 g, which is produced by an airflow velocity of 9.86 m/s (22.1 mph), was 

selected as the lower limit of destabilizing force applied to the mannequin for computing 

the stability boundary. This value corresponded to a small percentage of people losing 

their balance in the Hirshfield (1932) test (Table 36), and where there is only a minimal 

effect of wind speed on a person (Table 7, Table 8, and Table 9). The largest 

destabilizing force applied to the mannequin is a breakout rotational load factor of 0.25 g, 

which is equivalent to an airflow velocity of 22.1 m/s (49.3 mph). This is at or above the 

wind speed limit considered to be safe for walking. 

The purpose of the mannequin stability model is to provide an analytical tool to evaluate 

the aerodynamic effects of a passing train on people. A method to interpret the breakout 

load in terms of its effect on people is to relate it to the Beaufort scale. The rotational 

load factor at breakout is based on a steady uniform force applied to the center of mass of 

the mathematical mannequin. Corresponding to the rotational load factor is an equivalent 

steady uniform airflow velocity acting at the center of pressure of the mannequin. The 

Beaufort scale can now be applied since the airflow velocity at breakout is steady and 

uniform. Table 38 shows the Beaufort number associated with each of the equivalent 

steady uniform airflow velocity. 
Part 2: Analysis and Evaluation 

184

Table 38. Stance Distances and Dynamic Values of a Mannequin at Rotational Breakout 

Rotational 

Breakout Load 

Factor, 

n bo

Stance 

Distance, 

LCM1

Breakout 

Force, 

FCPbo

Breakout 

Moment 

Airflow 

Velocity at 

Breakout 

Beaufort 

Number 

0.05 48.2 mm 

(1.90 in) 

41.2 N 

(9.26 lb) 

36.8 N•m 

(326 lb•in) 

9.86 m/s 

(22.1mph) 

5 

0.10 96.3 mm 

(3.79 in) 

82.4 N 

(18.5 lb) 

73.7 N•m 

(652 lb•in) 

13.9 m/s 

(31.2 mph) 

7 

0.15 144 mm 

(5.67 in) 

124 N 

(27.9 lb) 

110 N•m 

(973 lb•in) 

17.1 m/s 

(38.2 mph) 

7 

0.20 193 mm 

(7.60 in) 

165 N 

(37.1 lb) 

147 N•m 

(1300 lb•in) 

19.7 m/s 

(44.1 mph) 

8 

0.25 241 mm 

(9.49 in) 

206 N 

(46.3 lb) 

184 N•m 

(1628 lb•in) 

22.1 m/s 

(49.3 mph) 

9 

10.4. Single Degree-of-Freedom Mannequin Stability Model 

A mathematical model of a mannequin with a single degree-of-freedom was developed to 

establish the stability boundary from the response to an airflow velocity pulse. It is 

assumed that sufficient friction occurs at the feet of the mannequin so that a horizontal 

force applied to the body will cause it to rotate, but not to slide. 

10.4.1. Equation of Motion 

The mannequin is modeled as a rigid body with an applied force representing the wind 

drag as shown in Figure 73. The dynamics of the standing object subject to an applied 

force F(t) acting at the center of pressure can be determined from the equations of 

motion. 
Part 2: Analysis and Evaluation 

185

SINGLE DEGREE-OF-FREEDOM ROTATIONAL MODEL OF A MANNEQUIN

----- (b) -----

----- (a) -----

Center of Rotation

Ayy

x

z

θ

F(t)

mg

LCP3

LCM3

LCM1

LCP1

RCP

RCM

θCP

θCM

x

z

θ

F(t)

mg

XCM

ZCM

ZCP

θ

XCP

RCP

RCM

θCP+ θ

θCM+ θ

Figure 73. Mathematical Model of a Mannequin 
Part 2: Analysis and Evaluation 

186

Summing the moments about the center of rotation Ayy, ∑ d 2

θ M Ayy = I Ayy dt 2 , the 

equation of motion is, 

( )[ ] d 2

θ F t LCP3 cosθ + LCP1 sinθ − mg[LCM1 cosθ − LCM 3 sinθ ] = I on 11

Ayy

Equati

dt 2

The height to the center of pressure is, 

zCP = LCP3 cosθ + LCP1 sinθ Equation 12

The angle at the SUE point is, 

π θ SUE = −θ

2 CM , or 

θ −1 ⎛ LCM1 ⎞ Equation 13

SUE = tan ⎜ ⎟ ⎜ ⎟ ⎝ LCM 3 ⎠

Generally, the stance distance is small compared to the height of the center-of-pressure, 

L and therefore, (L / L ) is small, CP1

CP1 CP3 << 1, θ

L SUE will be small, and the change in 

CP3

height of the center of pressure, zCP, will be small. Because the equation is applied up to 

the SUE point, the angle, θ, will be small, sinθ ≈ θ , cosθ ≈ 1, and the height in the 

center of pressure can be approximated as, 

⎡ ⎛ LCP ⎞ ⎤

z = θ ⎢ + ⎜ 1

CP LCP3 cos 1 ⎟ θ ⎜ ⎟tan ⎥ ⎣ ⎝ LCP3 ⎠ ⎦

⎡ ⎛ L ⎤ ≈ L + 1

3 ⎢1 ⎜ CP ⎞

CP ⎟θ ⎜ ⎟ ⎥ ⎣ ⎝ LCP3 ⎠ ⎦

The equation of motion for small angle is, 
Part 2: Analysis and Evaluation 

187

d 2

θ 1 ⎧⎪⎡ ⎛ L ⎞ ⎤⎫⎪ 1 Equation 14 

2 − ⎨⎢LCP3F(t)⎜ CP1 ⎟ + mgLCM 3 ⎥⎬θ = [ ] LCP3F(t) − ⎜ ⎟ mgLCM1 dt I Ayy ⎣ ⎝ LCP3 ⎠ ⎦⎪ I ⎩

⎪ ⎭ Ayy

If it is assumed that the height of the center of pressure does not change with rotation, the 

equation of motion can be further simplified as follows: 

d 2

θ ⎛ mgL ⎞ ⎜ CM 3 1 ⎟ Equation 15 

dt 2 − θ = [ ] L 3F(t) − mgL ⎜ ⎟ I CP CM1

⎝ I Ayy ⎠ Ayy

The applied force F(t) depends on the waveform of the airflow velocity pulse, period Tp, 

and frequency Ω. The equations of motion for the three waveforms are as follows: 

Square Wave Airflow Velocity Pulse 

d 2

θ ⎡ 1 ⎤ ⎡ 1 ⎤ Equation 15a

2 − ⎢ ( ) LCP1FO + mgLCM 3 ⎥θ = ⎢ ( ) LCP3FO − mgLCM1 ⎥ dt ⎢⎣I Ayy ⎦⎥ ⎣⎢I Ayy ⎥⎦

F(t) = FO for 0 < t < TP

Half Sine Wave Airflow Velocity Pulse 

d 2

θ ⎛ mgL ⎞ ⎛ CM 3 1 ⎞

2 = ⎜ [ ] Equation 15b

− ⎜ ⎟θ ⎟ L 2

dt ⎜ I ⎟ ⎜ I ⎟ CP3FO ( ) sin Ωt − mgLCM1

⎝ Ayy ⎠ ⎝ Ayy ⎠

⎛T ⎞ F(t) = F ( ) sinΩt 2

 for 0 < t < ⎜ P

O ⎟ ⎝ 2 ⎠

where T 2π

P = Ω
Part 2: Analysis and Evaluation 

188

Versine Wave Airflow Velocity Pulse 

d 2

θ ⎛ mgL ⎞ ⎛ ⎞ Equation 15c

− ⎜ CM 3 1 ⎡⎛ L F ⎞ ⎤ ⎟θ ⎜ ⎟

2 = ⎢⎜ CP3 O ⎟ 1− cosΩt 2 − mgL ⎥ dt ⎜ ( ) ⎝ I ⎟ ⎜⎝ 4 CM

Ayy I ⎟

Ayy ⎣⎝ ⎠ 1

⎠ ⎠ ⎦

⎡1 ⎤

2

F(t) = FO ( ) 1- cosΩt for 0 < < ⎢ ⎥ t T ⎣2 ⎦ P

where T 2

P = π

Ω

10.4.2. Stability Boundary 

A series of stability boundaries were established for a mannequin based on properties for 

a frontal facing average 50 percentile adult male wearing light clothing. The stability 

boundary was computed by solving a set of simultaneous equations to determine the 

amplitude of the drag corresponding to the airflow velocity pulse for a given time 

duration that the pulse is applied to the mannequin. The solution must satisfy the 

equation of motion, the SUE point, and other constraints. Once the force amplitude was 

found, the velocity amplitude, and the average force and velocity were computed. 

In addition to the stability boundary, the time history response of the mannequin was also 

computed. The equation of motion for the mannequin in its simplified form (Equation 

15) is a linear differential equation with constant coefficients, which can be determined 

exactly for the general solution. Once the required force amplitude was determined for a 

given pulse duration, the angular acceleration, velocity, and displacement responses of 

the mannequin can be computed. 

A case will be illustrated with an airflow velocity pulse of 1 s duration applied to the 

mannequin for a rotational breakout load factor of 0.05 g. The angle at the SUE point for 

this stance on the mannequin is 2.86 deg. A square wave airflow velocity pulse was 

applied to the mannequin. The applied force and the corresponding moment are shown in 

Figure 74. The resultant positive moment on the mannequin increases with time to 

destabilize the mannequin, and immediately drops to a negative value pulling the 

mannequin back once the applied force is released. The angular displacement and 

velocity in response to the applied force are shown in Figure 75. The angular 

displacement approaches the SUE angle as the angular velocity approaches zero. The 

maximum angular velocity is reached when the applied force is released. 
Part 2: Analysis and Evaluation 

189

----- (b) -----

----- (a) -----

 Airflow Velocity for Rotational Breakout: 9.86 m/s (22.1 mph)

o Point of Release of Applied Force

FORCE AND MOMENT ON MANNEQUIN FROM SQUARE WAVE AIRFLOW VELOCITY PULSE

OF 1 s DURATION AT A BREAKOUT ROTATIONAL LOAD FACTOR OF 0.05 g

Force Pulse Applied to Mannequin

Time, (s)

Force, (N)

0

2

4

6

8

10

12

14

16

18

(lb)

0 1 2 3 4

0

20

40

60

80

-0.5

0.5

1.0

2.0

0

1.5

0 1 2 3 4

Nondimensionalized Moment

Time, (s)

Nondimensionalized Moment,

Normalized by Breakout Moment

Breakout Moment = 1.0

Resultant Moment on Mannequin

Moment Applied to Mannequin

Figure 74. Time Histories of Force and Moment on a Mannequin from a Square Wave Airflow 

Velocity Pulse 
Part 2: Analysis and Evaluation 

190

----- (b) -----

----- (a) -----

ANGULAR DISPLACEMENT AND VELOCITY OF MANNEQUIN FROM SQUARE WAVE

AIRFLOW VELOCITY PULSE OF 1 s DURATION AT A BREAKOUT

ROTATIONAL LOAD FACTOR OF 0.05 g

Angular Displacement of Mannequin

Time, (s)

Angle, (deg)

0

1

3

2

0 1 2 3 4

Angular Velocity, (rad/s)

Angular Velocity of Mannequin

Time, (s)

0.02

0.04

0.06

0.08

0.10

0.00

-0.02

0 1 2 3 4

 Airflow Velocity for Rotational Breakout: 9.86 m/s (22.1 mph)

o Point of Release of Applied Force

Figure 75. Time Histories of Angular Displacement and Velocity of a Mannequin from a Square 

Wave Airflow Velocity Pulse 
Part 2: Analysis and Evaluation 

191

Another case will be illustrated with a versine wave airflow velocity pulse applied to the 

mannequin with all other conditions being the same as in the previous case. The applied 

force and the corresponding moment are shown in Figure 76. In this case, the resultant 

moment on the mannequin remains at zero while the force is being applied until the 

breakout moment is reached. Once the resultant moment exceeds the breakout moment, 

the mannequin begins to rotate. This is further illustrated in Figure 77 where the angular 

displacement and velocity of the mannequin remains stationary until the applied moment 

is large enough to initiate rotation. The angular displacement approaches the SUE angle 

as the angular velocity approaches zero after the applied force is released. 

These time history responses demonstrate the dynamics of the mannequin as it reaches 

the state of statically unstable equilibrium. For each time duration that an airflow 

velocity pulse is applied, there is a force amplitude of such magnitude that the mannequin 

will rotate and come to rest at the SUE point. The set of all points relating the force or 

velocity with time duration constitute the stability boundary. 

The stability boundaries for the mannequin from the three airflow velocity pulses: the 

square wave, half sine wave, and versine wave, are illustrated for a breakout rotational 

load factor of 0.05 g. A plot of the stability boundary as amplitudes of rotational load 

factors for various durations of airflow velocity pulses is shown in Figure 78(a). For a 

3 s duration, the amplitudes of all three wave shapes approach a rotational load factor of 

0.05 g. As the duration of the pulse is reduced, the amplitude of the pulse required to 

reach the SUE point increases. At a pulse duration of 0.01 s, a load factor amplitude of 

over 1 g is required for all three pulses. The pulse amplitudes for the half sine and 

versine waves are higher than the square wave since for a portion of the time, the 

moments for half sine and versine waves are below the breakout moment. When the 

average rotational load factors are computed, the averages from the half sine and versine 

waves are higher than for the square wave at a short pulse duration, but lower than for the 

square wave at a long pulse duration as shown in Figure 78(b). 

Instead of load factor limit, the stability boundary is also expressed as airflow velocity 

limit, which can be compared directly to airflow data. The limit on amplitude of airflow 

velocity shown in Figure 79(a) has the same trend and a similar characteristic as the limit 

on amplitude of rotational load factor. However, when the average is computed, both the 

averages from the half sine and versine waves are lower than for the square wave for all 

pulse durations as shown in Figure 79(b). Although the amplitude of airflow velocity 

forming the stability boundary is highest for the versine pulse, it is the lowest when 

expressed as an average airflow velocity. 
Part 2: Analysis and Evaluation 

192

----- (b) -----

----- (a) -----

FORCE AND MOMENT ON MANNEQUIN FROM VERSINE WAVE AIRFLOW VELOCITY PULSE

OF 1 s DURATION AT A BREAKOUT ROTATIONAL LOAD FACTOR OF 0.05 g

-0.5

0.5

1.0

2.0

0

1.5

0 1 2 3

Nondimensionalized Moment

Time, (s)

Nondimensionalized Moment,

Normalized by Breakout Moment

Breakout Moment = 1.0

Moment Applied to Mannequin

Resultant Moment on Mannequin

Force Pulse Applied to Mannequin

Time, (s)

Force, (N)

0

2

4

6

8

10

12

14

16

18

(lb)

0 1 2 3

0

20

40

60

80

 Airflow Velocity for Rotational Breakout: 9.86 m/s (22.1 mph)

x Point of Breakout Moment

o Point of Release of Applied Force

4

4

Figure 76. Time Histories of Force and Moment on a Mannequin from a Versine Wave Airflow 

Velocity Pulse 
Part 2: Analysis and Evaluation 

193

----- (b) -----

----- (a) -----

ANGULAR 

OF 1 s DURATION AT A BREAKOUT

ROTATIONAL LOAD FACTOR OF 0.05 g

DISPLACEMENT AND VELOCITY OF MANNEQUIN FROM VERSINE WAVE

AIRFLOW VELOCITY PULSE 

Angular Displacement of Mannequin

Time, (s)

Angle, (deg)

0

1

3

2

0 1 2 3 4

Angular Velocity, (rad/s)

Angular Velocity of Mannequin

Time, (s)

0.02

0.04

0.06

0.08

0.10

0.00

-0.02

0 1 2 3 4

 Airflow Velocity for Rotational Breakout: 9.86 m/s (22.1 mph)

x Point of Breakout Moment

o Point of Release of Applied Force

Figure 77. Time Histories of Angular Displacement and Velocity of a Mannequin from a Versine 

Wave Airflow Velocity Pulse 
Part 2: Analysis and Evaluation 

194

----- (b) -----

----- (a) -----

STABILITY BOUNDARY FOR A MANNEQUIN

RESPONDING TO AIRFLOW VELOCITY PULSE 

AS LOAD FACTOR LIMIT AT THE SUE POINT

AT A BREAKOUT

ROTATIONAL LOAD FACTOR OF 0.05 g

Amplitude of Rotational Load Factor

Duration of Pulse, (s)

Rotational Load Factor,

Effective Force/Weight (g)

0.01 0.1 1 10

0.01

0.1

1

10

Average Rotational Load Factor

Duration of Pulse, (s)

Rotational Load Factor,

Effective Force/Weight (g)

0.01 0.1 1 10

0.01

0.1

1

10

Square Wave

Half Sine 

Versine

 Wave

 Wave

Airflow Velocity Pulse

 Moment: 36.8 N-m (326 lb-in)

 Force at Center of Pressure: 41.2 N (9.26 lb)

 Airflow Velocity: 9.86 m/s (22.1 mph)

Rotational Breakout for Mannequin

Figure 78. Stability Boundaries as Load Factor Limits for a Mannequin Responding to an 

Airflow Velocity Pulse 
Part 2: Analysis and Evaluation 

195

----- (b) -----

----- (a) -----

STABILITY BOUNDARY AS AIRFLOW VELOCITY LIMIT AT THE SUE POINT FOR A MANNEQUIN

RESPONDING TO AIRFLOW VELOCITY PULSE AT A BREAKOUT

ROTATIONAL LOAD FACTOR OF 0.05 g

Square Wave

Half Sine 

Versine

 Wave

 Wave

Airflow Velocity Pulse

 Moment: 36.8 N-m (326 lb-in)

 Force at Center of Pressure: 41.2 N (9.26 lb)

 Airflow Velocity: 9.86 m/s (22.1 mph)

Rotational Breakout on Mannequin

Average Airflow Velocity

Duration of Pulse, (s)

Airflow Velocity, (m/s)

0.01 0.1 1 10

1

10

100

10

100

(mph)

Amplitude of Airflow Velocity

Duration of Pulse, (s)

Airflow Velocity, (m/s)

0.01 0.1 1 10

1

10

100

10

100

(mph)

Figure 79. Stability Boundaries as Airflow Velocity Limits for a Mannequin Responding to an 

Airflow Velocity Pulse 
Part 2: Analysis and Evaluation 

196

Different stability boundaries exist for the different airflow velocity pulses. An 

examination of the airflow velocity data suggest that these three stability boundaries can 

be simplified to a single boundary based on the following assumptions: 

• The airflow velocity data for averages of 1 s duration or longer is best represented 

by a square wave. 

• The airflow velocity data for averages of 0.1 s duration or shorter is best 

represented by a vesine wave. 

On the basis of these assumptions, a synthesized piecewise stability boundary from a 

versine and square wave velocity pulses for a breakout rotational load factor of 0.05 g 

were created as shown plotted in Figure 80. The synthesized boundary line is described 

by a power function of the form uSUE = ( ) A k

syntP +Usyn , 

where, 

uSUE: synthesized piecewise stability boundary for the SUE point, 

Asyn: coefficient that is a function of load factor, 

Usyn: constant that is a function of load factor, 

k: exponent, and 

tP: duration of velocity pulse. 

A series of synthesized piecewise stability boundaries are shown plotted in Figure 81 

with breakout rotational load factors of 0.05 g to 0.25 g as parameters of the curves. 

These curves can be closely fitted by the function uSUE as follows, 

u = [( ) 0.80753 + (13.95173)n − (16.90143)n

2 t

−0.71166

SUE

+ [ α α P Equation 16 m/s, ( ) 4.96272 + (85.65632)nα − (103.55686)n

2

α

within the range of, 

0.01 s ≤ tP ≤ 3 s and,

0.05 g ≤ nα ≤ 0.25 g

]

]
Part 2: Analysis and Evaluation 

197

SYNTHESIZED PIECEWISE STABILITY BOUNDARY AT THE SUE POINT FOR A MANNEQUIN

RESPONDING TO VERSINE OR SQUARE WAVES OF AIRFLOW VELOCITY PULSES

AT A BREAKOUT ROTATIONAL LOAD FACTOR OF 0.05 g

Time Duration, (s)

Airflow Velocity, (m/s)

0.01 0.1 1 10

0

10

20

30

40

50

60

(mph)

0

10

20

30

40

50

60

70

80

90

100

110

120

130

 Moment: 36.8 N-m (326 lb-in)

 Force at Center of Pressure: 41.2 N (9.26 lb)

 Airflow Velocity: 9.86 m/s (22.1 mph)

Rotational Breakout on Mannequin

Boundary of Square Wave

Airflow Velocity Pulse

Boundary of Versine Wave

Airflow Velocity Pulse

Stability Boundary from Versine or Square Wave

 Velocity Pulse

X Synthesized Piece Wise Stability Boundary

Figure 80. Synthesized Piecewise Stability Boundary for a Mannequin 
Part 2: Analysis and Evaluation 

198

SYNTHESIZED PIECEWISE STABILITY BOUNDARY AT THE SUE POINT FOR A MANNEQUIN

RESPONDING TO VERSINE OR SQUARE WAVES OF AIRFLOW VELOCITY PULSES

FOR VARIOUS BREAKOUT ROTATIONAL LOAD FACTORS

Properties of mannequin based on a frontal facing average

50 percentile adult male wearing light clothing.

0.01 0.1 1 10

0

10

20

30

40

50

60

70

80

90

100

110

Duration of Pulse, (s)

Airflow Velocity, (m/s)

(mph)

0

20

40

60

80

100

120

140

160

180

200

220

240

0.20 g

n = 0.25 g αbo

0.15 g

0.10 g

0.05 g

Figure 81. Synthesized Piecewise Stability Boundary for a Mannequin at Various Breakout 

Rotational Load Factors 
Part 2: Analysis and Evaluation 

199

10.5. Mannequin Stability to Train-Induced Airflow 

In the previous chapter, the maximum airflow was determined at various lateral distances 

from the side of a passing train, and a minimum distance was established based on wind 

speed criteria. Another method to assess the airflow strength is to relate the airflow data 

relative to the stability boundary of the mathematical mannequin. The data for the 

assessment is from the resultant airflow velocity at quadrant 1 for nominal lateral 

distances of 1.17 m (46 in) and 1.43 m (56 in) from the side of the train. These two 

lateral distances correspond to the positions of the CIDs as referenced to their cylindrical 

axes. All the data were scaled so that the time and airflow velocity for the Acela Express 

train corresponded to a train speed of 241 km/h (150 mph), and the Amfleet train 

corresponded to a train speed 201 km/h (125 mph). 

The first case analyzed was the airflow data measured from the bottom position at a 

nominal height of 0.97 m (38 in) from the top of the rail. At a nominal lateral distance of 

1.17 m (46 in) from the side of the train (Figure 82(a)), the maximum airflow velocity 

reached a stability boundary of about 0.20 g. For the mathematical mannequin to remain 

stable, its stance distance must be wide enough to withstand a rotational load factor of 

0.20 g when exposed to a steady uniform force applied to its center of mass. By 

increasing the nominal lateral distance to 1.43 m (56 in) from the side of the train (Figure 

82(b)), the maximum airflow velocity reached a stability boundary of about 0.15 g. At 

this lateral distance, the mathematical mannequin can be stable at a narrower stance 

distance. 

The next case is for airflow data measured from the top position at a nominal height of 

1.73 m (68 in) from the top of the rail. At this greater height, the maximum airflow 

velocity reached a stability boundary of about 0.12 g at a nominal lateral distance of 

1.17 m (46 in) from the side of the train (Figure 83(a)), and reduced slightly to 0.11 g 

when the nominal lateral distance is increased to 1.43 m (56 in) (Figure 83(b)). 

Finally, the airflow velocity at a middle height was linearly interpolated from airflows 

measured at two other heights to estimate the value at a nominal height of 1.35 m (53 in) 

from the top of the rail. This intermediate height would be a better representation of the 

airflow at which an adult would be exposed. The interpolated maximum airflow velocity 

reached a stability boundary of about 0.15 g at a nominal lateral distance of 1.17 m 

(46 in) from the side of the train (Figure 84(a)), and reduced to 0.12 g when the nominal 

lateral distance is increased to 1.43 m (56 in) (Figure 84(b)). 

These results lead to several observations. The maximum airflow velocity reaches a 

stability boundary with a lower rotational load factor when the height above the rail or 

the lateral distance from the train is increased, which is consistent with other observed 

trends (Table 31). Each of the cases analyzed was based only a single data point that 

reached the highest rotational load factor on the stability boundary. Other maximum 

airflow velocities are as much as 0.05 to 0.10 g below that single data point. Generally, 
Part 2: Analysis and Evaluation 

200

the maximum airflow velocity reaching the stability boundaries with the highest 

rotational load factor occurs between moving average windows of 0.1 to 1 s. 

The effect on people from train-induced airflow velocity can be related to the dynamic 

response of a mathematical mannequin by interpreting the breakout load in terms of the 

Beaufort scale (Table 38). Now a relationship occurs between the airflow data relative to 

the stability boundary and its effect on people based on the Beaufort scale (Table 7). The 

strongest airflow was measured lowest to the ground at 0.97 m (38 in) above the top of 

the rail, and closest to the train at 1.17 m (46 in) from the side of the train. At this 

location, the mannequin remains statically stable up to a maximum airflow velocity of 

19.7 m/s (44 mph), corresponding to a Beaufort number of 8. A Beaufort number of 8 

will impede progress and cause great difficulty with balance in gusts. The remaining 

airflow corresponds to a Beaufort number of 7, which is described as “inconvenience felt 

when walking.” The results are summarized in Table 39. 

Table 39. Comparison between Maximum Airflow Velocities from a 3 s Moving Average and 

Uniform Airflow Velocities at Breakout from Stability Boundary on a Mathematical 

Mannequin 

Nominal Nominal Maximum Highest Breakout Load on Mannequin Stability 

Height above Distance from Airflow Boundary relative to Airflow Velocity Data

Top of Rail Side of Train Velocity from

3 s Moving 

Average 

Window

Rotational 

Load Factor 

Uniform 

Airflow 

Velocity

Beaufort 

Number 

0.97 m 1.17 m 15.9 m/s 0.20 g 19.7 m/s 8 

(38 in) (46 in) (36 mph) (44 mph) 

1.43 m 14.0 m/s 0.15 g 17.1 m/s 7 

(56 in) (31 mph) (38 mph) 

1.35 m 1.17 m 13.6 m/s 0.15 g 17.1 m/s 7 

(53 in) (46 in) (30 mph) (38 mph) 

1.43 m 13.1 m/s 0.12 g 15.3 m/s 7 

(56 in) (29 mph) (34 mph) 

1.73 m 1.17 m 12.1 m/s 0.12 g 15.3 m/s 7 

(68 in) (46 in) (27 mph) (34 mph) 

1.43 m 12.3 m/s 0.11 g 14.6 m/s 7 

(56 in) (28 mph) (33 mph) 

A comparison is made between the effects on people based on the dynamic response of a 

mathematical mannequin, and the wind speed criteria of Murakami and Deguchi, which 

is based on wind speed averaged over 3 s (Table 9). The maximum airflow velocities 

from a 3 s moving average window are shown in Table 39. The strongest airflow 

velocity is 15.9 m/s (36 mph), measured lowest to the ground at 0.97 m (38 in) above the 

top of the rail, and closest to the train at 1.17 m (46 in) from the side of the train. In the 
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201

Murakami and Deguchi criteria, the effect of this wind speed is described as “walking 

impossible to control with body blown sideways.” This is comparable to Beaufort 

number 8, which will impede progress and cause great difficulty with balance in gusts. 

The maximum airflow velocities for all the remaining locations are between 10 to 15 m/s 

(22 to 34 mph). The Murakami and Deguchi criteria describe the effect of this wind 

speed as “walking becomes irregular and difficult to control.” This is comparable to 

Beaufort number 7, which is described as “inconvenience felt when walking.” Since 

these effects on people are qualitative descriptions, the comparison is to some extent a 

subjective interpretation. Both methods predict similar effects on people amidst 

differences in phraseology between the two criteria. 
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MANNEQUIN STABILITY RELATIVE TO MAXIMUM SINGLE QUADRANT RESULTANT 

MEASURED 

AIRFLOW VELOCITY

DATA AT NOMINAL VERTICAL DISTANCE OF 0.97 m (38 in) FROM TOP OF RAIL

Resultant Airflow Velocity on Quadrant 1 Measured from Pitot-Static Tube

n Breakout Rotational Load Factor αbo

Airflow Data from Acela Express Train Scaled to

 241 km/h (150 mph)

Stability Boundary from Analytical Mannequin Model

Airflow Data from Amfleet Train with AEM-7 Locomotive

 Scaled to 201 km/h (125 mph)

Airflow Data from Amfleet Train with HHP-8 Locomotive

 Scaled to 201 km/h (125 mph)

0

5

10

15

20

25

30

35

40

45

50

0.01 0.1 1 10

Duration Window of Moving Average, (s)

Airflow Velocity, (m/s)

(mph)

0

20

40

60

80

100

----- (a) -----

Nominal Lateral Distance at 1.17 m (46 in) from Side of Train

0.05 g

0.10 g

0.15 g

0.20 g

n = 0.25 g αbo

0

5

10

15

20

25

30

35

40

45

50

0.01 0.1 1 10

Duration Window of Moving Average, (s)

Airflow Velocity, (m/s)

(mph)

0

20

40

60

80

100

----- (b) -----

Nominal Lateral Distance at 1.43 m (56 in) from Side of Train

0.05 g

0.10 g

0.15 g

0.20 g

n = 0.25 g αbo

Figure 82. Mannequin Stability Relative to Airflow Velocity Data at 0.97 m (38 in) above Top of 

Rail 
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MANNEQUIN STABILITY RELATIVE TO MAXIMUM SINGLE QUADRANT RESULTANT AIRFLOW VELOCITY

DATA MEASURED AT NOMINAL VERTICAL DISTANCE OF 1.73 m (68 in) FROM TOP OF RAIL

Resultant Airflow Velocity on Quadrant 1 Measured from Pitot-Static Tube

n Breakout Rotational Load Factor αbo

Airflow Data from Acela Express Train Scaled to

 241 km/h (150 mph)

Stability Boundary from Analytical Mannequin Model

Airflow Data from Amfleet Train with AEM-7 Locomotive

 Scaled to 201 km/h (125 mph)

Airflow Data from Amfleet Train with HHP-8 Locomotive

 Scaled to 201 km/h (125 mph)

0

5

10

15

20

25

30

35

40

45

50

0.01 0.1 1 10

Duration Window of Moving Average, (s)

Airflow Velocity, (m/s)

(mph)

0

20

40

60

80

100

----- (a) -----

Nominal Lateral Distance at 1.17 m (46 in) from Side of Train

0.05 g

0.10 g

0.15 g

0.20 g

n = 0.25 g αbo

0

5

10

15

20

25

30

35

40

45

50

0.01 0.1 1 10

Duration Window of Moving Average, (s)

Airflow Velocity, (m/s)

(mph)

0

20

40

60

80

100

----- (b) -----

Nominal Lateral Distance at 1.43 m (56 in) from Side of Train

0.05 g

0.10 g

0.15 g

0.20 g

n = 0.25 g αbo

Figure 83. Mannequin Stability Relative to Airflow Velocity Data at 1.73 m (68 in) above Top of 

Rail 
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MANNEQUIN STABILITY RELATIVE TO INTERPOLATED MAXIMUM SINGLE QUADRANT RESULTANT

AIRFLOW VELOCITY DATA AT NOMINAL VERTICAL DISTANCE

OF 1.35 m (53 in) FROM TOP OF RAIL

Resultant Airflow Velocity on Quadrant 1 Measured from Pitot-Static Tube

n Breakout Rotational Load Factor αbo

Stability Boundary from Analytical Mannequin Model

Interpolated 

Amfleet Train Scaled to 201 km/h (125 mph)

Airflow Data

 Acela Express Train Scaled to 241 km/h (150 mph)

 

0

5

10

15

20

25

30

35

40

45

50

0.01 0.1 1 10

Duration Window of Moving Average, (s)

Airflow Velocity, (m/s)

(mph)

0

20

40

60

80

100

----- (a) -----

Nominal Lateral Distance at 1.17 m (46 in) from Side of Train

0.05 g

0.10 g

0.15 g

0.20 g

n = 0.25 g αbo

0

5

10

15

20

25

30

35

40

45

50

0.01 0.1 1 10

Duration Window of Moving Average, (s)

Airflow Velocity, (m/s)

(mph)

0

20

40

60

80

100

----- (b) -----

Nominal Lateral Distance at 1.43 m (56 in) from Side of Train

0.05 g

0.10 g

0.15 g

0.20 g

n = 0.25 g αbo

Figure 84. Mannequin Stability Relative to Interpolated Airflow Velocity Data at 1.35 m (53 in) 

above Top of Rail 
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10.6. Subjective Reaction to Passing Train 

A train approaching at high speeds can evoke an emotional response in the form of 

anxiety or excitement from a person on a station platform. Although a person’s 

subjective experience of being in proximity to a passing train is not a safety-related issue, 

a person’s physical response can be influenced by psychological factors. There is value 

in their perception and sensation when it is included along with the quantitative data, 

where their perspective can portend a future problem, reveal a condition that is not easily 

measurable, or corroborate the finding from quantitative data. 

10.6.1. Study by Swedish National Rail Administration 

Lindberg (1994) described a study conducted in Sweden financed by the Swedish 

National Rail Administration on the perception and sensation experienced by travelers 

waiting on train station platforms where trains not scheduled to stop pass the platforms at 

speeds up to 200 km/h (124 mph). About 800 men and women, with ages up to 65 years, 

were interviewed while on the platforms at ten different stations. The platform edge had 

a yellow zigzag line to warn people from reaching too close to the edge of the platform, 

while some stations had either electronic signs or audio warnings of approaching trains 

that do not stop at the station. Forty to 70 percent of interviewees expressed discomfort 

from passing trains, but the proportions expressing discomfort varied with stations. 

Differences in stations that could affect people’s response to passing trains included: 

• Platform layout (platform width, whether trains pass on one or both sides, etc.), 

• Access to shelters on the platform, 

• Proportion of daily travelers (who have ample experience of passing trains) and, 

• Speed of passing trains. 
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Table 40 shows the sources of discomfort and 

the frequency that was mentioned. A strong 

psychological factor appears to be associated 

with the passing train experience. “It may 

seem somewhat surprising that the most 

common reason for discomfort has nothing to 

do with the wind forces generated by the 

passing trains. Rather, the speed of the 

passing train seems to be the primary source 

of discomfort, or as one of the interviewees 

phrased it, ‘the unpleasant feeling that 

something large and heavy is coming straight 

towards you at high speed’” according to 

Lindberg (1994). On the question of hazards, 

18 percent of the interviewees expressed that 

passing trains were a hazard to people on the 

platform, while 10 percent did not think 

passing trains were dangerous to them, but 

might be a hazard to other people (mainly 

children) on the platform. Some respondents 

stating that this is particularly true in crowded 

or slippery conditions. 

Views on the electronic advanced warning were mixed. There were positive responses to 

electronic warning signs and sound indications. However, some interviewed felt that 

they were insufficient. Audio advanced warning received less positive response and 

thought of as being unreliable. At stations with no advance warnings, about half said that 

it should be provided. 

10.6.2. Observation from Test Crew 

Many of the individuals that were involved with the test at the train station in Mansfield, 

Massachusetts, also had the opportunity to be on the platform as trains passed by the 

station at relatively high speeds. These members of the test crew were asked to express 

their views on their experiences of trains passing the station while they were on the 

platform. The views expressed were not a representative distribution of the population or 

a statistically significant sample. Their observations however, do provide a subjective 

perspective to the objective data. 

The Mansfield train station has a low-level platform where commuter trains stop, but not 

intercity trains. The station had a warning area consisting of a yellow strip that was 

0.965 m (38 in) wide along the edge of the platform. In addition, an electronic TrainApproach Monitoring System (TAMS) provided an audio announcement and a sign 

warning of an approaching train. 

Table 40. Six Most Frequently Mentioned 

Sources of Discomfort from 

Passing Trains Listed in Order of 

Decreasing Frequency Mentioned 

(Lindberg 1994) 

Common Source of 

Discomfort 

Frequency 

Mentioned 

Number Percent 

High Speed of the Train 140 37 

Air Turbulence 108 29 

Noise 61 16

Being Startled/Surprised 30 8 

Concerns about the Safety 

of other People (mostly 

Children) on the Platform 

27 7 

Swirling Snow 11 3 

Total 377 100 
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Nine people on the test crew provided 

their observations on their experience of 

being on the station platform while in 

proximity to trains passing by at high 

speeds. They were provided with 

specific questions with allowance for 

general comments. First, they were 

asked to express any concerns or 

discomfort of being on the station 

platform as a train passed. They were 

then asked on their perception of the 

force that was felt due to a passing train. 

The results of these observations are 

listed in Table 41. Two of the top three 

frequently mentioned sources of concern 

or discomfort relates to the size and speed 

of the passing train, whereas the other 

relates to the safety of other people on the 

platform. A small number expressed 

discomfort from noise, debris, and 

experience of instability that could lead 

to physical harm. The psychological 

factor is also a significant source of 

concern or discomfort. The test crew did 

not mention air turbulence as a source of 

Sources of Concern or 

Discomfort 

Frequency 

Mentioned 

Number Percent 

Size of the Train 4 22 

Concerns about the Safety 

of other People (mostly 

Children) on the Platform 

4 22

High Speed of the Train 3 17 

Noise 2 11

Debris 2 11

Experienced Instability* 2 11 

Being Startled/Surprised 1 6 

Total 18 100

discomfort or concern. Since the weather was mostly clear during the test, the effects of 

weather were not a factor on the test crew, but it was mentioned that rain or snow blown 

by a passing train could be an additional source of discomfort. When asked if they 

perceived the passing train as a source of concern or discomfort, seven out of the nine in 

the test crew felt that it was; and when asked if they perceived the passing train to be a 

hazard, four of the test crew responded positively. 

The other observation from the test crew relates to the perception of force felt from the 

passing trains. The crew expressed general agreement from many that they perceived the 

strongest force produced by the Acela Express train at the tail end, while the 

Amfleet/AEM-7 train produced the strongest force at the head end. This is consistent 

with the quantitative data. In one case, the hard hats of two of the test crew were blown 

off by the passage of the Amfleet/AEM-7 train, but that did not occur for the passage of 

the Acela Express train. However, the sense of instability that was mentioned by two of 

the test crew was from the passage of the Acela Express train. A very interesting 

observation from three of the test crew was that not much sensation was perceived from 

the passage of the Amfleet/HHP-8 train. The quantitative data does show the level of 

aerodynamic forces on the CIDs from the Amfleet/HHP-8 train to be between the Acela 

Express train and the Amfleet/AEM-7 train. 

Table 41. Observations from Test 

Participants on their Experiences 

in Proximity to Passing Trains 

Listed in Order of Decreasing 

Frequency Mentioned 

* The sense of instability was not expressed as a source of 

discomfort or concern, but was in specific response to the 

perception of force from a passing train. 
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208

A part of the subjective response to the passing train is the attentiveness of the person on 

the platform to an approaching train. The warning system that alerts people of an 

approaching train in some cases also produced the unintended effect in which a person’s 

response places himself or herself in potential harm. Some of the test crew had claimed 

that people who are waiting on the platform had expected their commuter train to arrive 

at the activation of the warning system, and proceeded to moved toward the edge of the 

platform for boarding, but were not necessarily attentive to the type of train or its speed. 

In certain situations, perhaps due to a train not being on schedule, it was a high-speed 

nonstop train instead of a commuter train slowing to a stop. The person standing close to 

the edge of the platform may be caught unawares by the passage of an unexpected 

nonstop train. The test crew has suggested that the warning system should provide 

information on the type of train approaching. 

As stated earlier, there was no mention by the test crew of air turbulence as a source of 

discomfort, although both air turbulence and swirling snow were mentioned with the 

Swedish study (Table 40). In the test at Mansfield, the weather was generally fair and 

mild with no snow present, and the test crew was asked about only their experience with 

passing trains during the test period. It is possible that in cold weather, as suggested by 

the presence of swirling snow in the Swedish study, that a wind chill factor due to air 

turbulence might be causing a discomfort that would otherwise not be sensed as 

uncomfortable. 

The limited observations from the test crew at Mansfield and the specific questions that 

were asked of them cannot be compared directly with the study in Sweden described by 

Lindberg. It is notable that their subjective responses are so similar in both cases. The 

psychological factor appears to play a common role affecting a person’s subjective 

response both in the Swedish study and Mansfield test crew observation. A natural 

anxiety expressed by many of being close to a large fast moving object exists. In neither 

of these cases were there reports of injuries or falls, but there was legitimate concern for 

the safety of others, particularly children on the platform. Small children, being shorter 

and closer to the ground, could be exposed to greater overall airflow velocity than an 

adult. 
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11. Conclusion 

Numerical simulation and experimentation were conducted on the aerodynamic 

interaction between passing trains and the aerodynamic effects of trains passing people 

on station platforms. Numerical simulation included both simple single degree-offreedom dynamics models and more complex CFD and multibody simulation models. 

Experimentation involved full-scale testing of a rail car passed by a high-speed train on 

an adjacent track, measurement of train-induced airflow velocities, and of forces on CIDs 

from its interaction with the flow field of a passing train. 

11.1. Response of Double-Stack Well Car to Aerodynamic Load 

A study was conducted to determine the response of a double-stack well car from 

aerodynamic interaction with a passing high-speed passenger train. Numerical 

simulation was performed to compute the response of a double-stack well car, and the 

results were examined for the potential of derailment and the stability of the containers. 

A full-scale test was performed to measure the aerodynamic pressure and roll response on 

a stationary double-stack well car when a train passes by on an adjacent track, and the 

test data was compared with modeling results. The possibility of window glazing being 

dislodged from its mount from the aerodynamic force of a passing train was investigated. 

CFD simulation was performed to study the response of a five-unit articulated doublestack well car from the aerodynamic interaction with a passing Acela Express passenger 

train. The lateral aerodynamic loading applied to the double-stack well car did not 

produce significant carbody roll, but it did produce strong dynamic response leading to 

wheel unloading or high lateral wheel force. For the cases studied, the greatest potential 

for derailment on the five-unit articulated double-stack well car was when all containers 

were empty and with the presence of a strong headwind on the Acela Express train or a 

strong crosswind. The worst response occurred on the nonshared trucks of the first and 

last cars where each axle on those trucks is more lightly loaded than those on the shared 

trucks. The condition improved in a partially loaded configuration, when only the 

containers at the end units are loaded. With all the containers loaded, vertical wheel load 

increased and the wheel/rail L/V was much lower, therefore, meeting performance 

specifications. The only exception was when the Acela Express train passed in opposite 

direction to the loaded double-stack well car with a crosswind in which significant wheel 

unloading occurred. 

Other results from the simulation are as follows: 

• Highest lateral load on the double-stack well car occurs when the passing Acela 

Express train faces a headwind. 
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211

• Speed of the Acela Express train is more important than the speed of the doublestack well car for producing peak loads. 

• The duration of the load on the double-stack well car, and therefore its response, 

depends on both the speed of the two passing trains and the directions in which 

they are traveling (passing in opposite directions or in the same direction). It is 

when the Acela Express train overtakes the double-stack well car that it was more 

likely to excite the natural frequency of the double-stack well car producing a 

strong dynamic response. 

The stability of the containers is a factor to consider when another train passes a doublestack well car. Critical to stability is the top container, particularly when emptied. 

Results from this study found that the containers should not become dislodged. 

A test was performed to measure the aerodynamic pressure and carbody roll angle of a 

double-stack well car as a high-speed TEL train passes it on an adjacent track. It was 

found that the measured and computed pressures agreed, except that the measured data 

exhibits a quicker pressure recovery past the negative pressure peak at the nose of the 

passing train. The roll angles on the double-stack well car are small, with the maximum 

zero-to-peak roll angle of 0.312° when the TEL train passed at 177 km/h (110 mph). 

An analytical study was conducted using a single degree-of-freedom mathematical 

carbody roll model to extend the CFD results by including a broader range of train 

passing conditions. Excellent agreement occurs between the roll angles obtained from 

simulation and those measured from the test. The responses of carbody roll from the 

effects of altitude, ambient wind, passing train speed and closing speed, and unbalanced 

speed on curved track were studied. 

Larger carbody roll response occurs on the observer car from the aerodynamic interaction 

with a passing train when any of these conditions exist: 

• Reduced altitude, 

• Presence of a headwind against the passing train, 

• The relative speed between the passing train and observer car is such that the 

aerodynamic pressure variation sweeps past the observer car that corresponds to the 

natural roll frequency of the observer car, and 

• The passing train is short in length and the relative speed between the passing train 

and observer car is such that the pressure variation from the tail pulse of the passing 

train is in phase with the roll motion of observer car. 

The carbody roll response from the aerodynamic interaction with a passing train while 

the observe car is negotiating a curve below its balanced speed is as follows: 
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212

• Highest maximum roll angle is when the observer car rolls toward the inside of the 

curve. 

• The observer car traveling at below balanced speed produces a greater maximum 

roll angle of oscillation when passed by a train on the inside than on the outside of 

the curve. 

• When the carbody roll angle is measured as a deviation from its steady-state roll, a 

train passing the observer car on the inside curve produces the same maximum 

carbody roll angle as a train passing the observer car on tangent track. 

11.2. Window Integrity from Aerodynamic Load 

The aerodynamic force created by a passing train can exert a high force on the window of 

another train. An Acela Express train traveling at 241 km/h (150 mph) passing a 

Kawasaki passenger car traveling in the opposite direction at 129 km/h (80 mph) does not 

appear to have sufficient impulse to dislodge the window glazing on the passenger car, 

when compared with the impulse from an object striking and dislodging a window 

glazing. Sufficient data does not exist to arrive at a conclusion when the Acela Express 

train overtakes the Kawasaki car. 

11.3. Aerodynamic Characterization of Passing Train 

Numerical simulation and full-scale testing were conducted to determine the strength and 

characteristic of the aerodynamic effects from a train passing a station platform. The 

aerodynamic effects were examined from the train-induced airflow velocity and from the 

force on the CID during interaction with a passing train’s flow field that included the 

following trains: Acela Express train, Amfleet/AEM-7 train, Amfleet/HH-8 train, and 

Amfleet/F40PH train. 

A CFD simulation computed the airflow induced by an Acela Express and an 

Amfleet/AEM-7 train to provide a relative measure on the strength of airflow velocity 

between the two types of trains. The simulation revealed the following characteristics: 

• The Acela Express train traveling at 241 km/h (150 mph) and an Amfleet train at 

201 km/h (125 mph) induced about the same maximum longitudinal airflow 

velocities. At the furthest distance from the train, the wake from the Acela Express 

train produced a stronger airflow than the overall airflow from the Amfleet train. 

• The Amfleet train produced the strongest airflow from the boundary layer, whereas 

the strongest airflow for the Acela Express train came from the wake. 

• Induced airflow from the Acela Express train was lower on a high-level than on a 

low-level platform. 
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213

A full-scale test was conducted where train-induced airflow velocities were measured by 

using pitot-static tubes and forces were measured from CIDs’ aerodynamic interaction 

with a passing train. Airflow velocities from CFD calculations were compared with test 

data, where the major features agree, particularly the relative levels of induced airflow 

characteristic between the different trains. 

A passing train causes a disturbance to the surrounding air, which is very turbulent and 

chaotic, with airflow in various directions. However, the dominant airflow and load on 

the CID are primarily in the direction of the passing train. The strength of the airflow is 

derived mainly in the longitudinal component while the lateral component does not 

appear to contribute significantly to the resultant airflow, except in the case of a train 

with a bluff nose head where a strong lateral gust occurs. The force applied to the CID is 

similar for all the trains as follows: 

• Longitudinal Direction: As the head of the train passes, the CID is pushed in the 

same direction as the passing train, immediately followed by a pull in the reverse 

direction. After the head of the train passes and for the remainder of the passing 

train, the CID is primarily being pushed in the same direction as the passing train. 

• Lateral Direction: The CID is initially pushed away from the train immediately 

followed by a pull toward the train, as the head of the train passes by. Afterwards, 

the CID is being pushed and pulled oscillating about zero for the remaining train 

passage. 

One of the characterizations of a passing train is the aerodynamic signature. The 

signature is the time or distance history variation in an aerodynamic variable that is 

caused by a passing train. A passing train produces an aerodynamic time history 

signature that depends on the geometry of the train. When all other factors are the same, 

the exterior geometry of a train and surface continuity play a significant role in its 

aerodynamic effect. An understanding of the relationship between the exterior surface 

geometry of a train, and the aerodynamic strength that it produces, can assist in body 

design to lessen the adverse effect to the surrounding. 

The airflow velocity and the force on the CID are both examined from the perspective of 

its aerodynamic signature. Both exhibited similar time history signatures. The 

aerodynamic signatures for the trains with three different geometries are as follows: 

• Acela Express Train: Both airflow velocity and load on the CID gradually 

increases from the tapered nose head end toward the tail and produces a persistent 

strong wake after the passage of the tapered tail base. The nose produces a minor 

airflow velocity but a relatively strong force on the CID. The airflow velocity at 

the wake retains a steady level with a gradual decrease, while a high initial load 

occurs on the CID from the wake, the load decreases more rapidly. The maximum 

load on the CID was largely from the wake of the train. 
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214

• Amfleet/AEM-7 Train: Both airflow velocity and load on the CID rises 

immediately from the bluff nose head end and remains at a high level until near the 

flat tail base where it rapidly drops, leading to a weak wake. The nose produces a 

relatively strong air gust but the CID has a much more prominent peak load. The 

airflow velocity at the wake is weak, but the CID load from the wake dropped to a 

negligible level. The maximum load on the CID was generally from the head of the 

train. 

• Amfleet/HHP-8 Train: The slant nose and flat tail base share similar characteristics 

with the Acela Express and Amfleet/AEM-7 trains. Both airflow velocity and load 

on the CID produce a noticeable peak at the nose, increasing in strength and 

decreasing toward the tail end,. The airflow velocity at the wake remains relatively 

strong, while the CID load from the wake rapidly drops to a negligible level. The 

maximum load on the CID was somewhere between the head and tail ends of the 

train. 

The airflow strength, either as a train-induced airflow velocity or as a force on the CID, is 

very much influenced by the geometry of the train. Trains with different geometries can 

pass by at different speeds but produce similar airflow strength because the airflow is 

very much dependent on its surface geometry of the train. In general, the head end of a 

train with a slender nose that gradually increases in cross section for a smooth transition 

to the body produces a weaker disturbance to the air than a bluff shape nose. For this 

reason, a tapered nose Acela Express train can travel at a greater speed than a bluff nose 

Amfleet/AEM-7 train without producing greater airflow. The disturbance to the air is 

even stronger for a freight train, which consists of freight cars of irregular geometric 

shapes, with sharp corners and protuberance. 

The relative aerodynamic effects between different trains can be quantified by comparing 

the normalized forces on the CIDs as follows: 

• With the cylindrical axes of the CIDs at 1.20 m (47.4 in) from the side of the train: 

o The Amfleet/AEM-7 train produced a force that is a factor of 2.4 higher 

than the Acela Express train. 

o The Amfleet/HHP-8 train is a factor of 1.8 higher than the Acela Express 

train. 

• With the cylindrical axes of the CIDs at 1.46 m (57.7 in) from the side of the train, 

the Amfleet/AEM-7 train produced an aerodynamic force on the CIDs that is a 

factor of 1.9 higher than the Acela Express train 

When the aerodynamic forces on the CIDs are scaled to the train’s operating speed, the 

forces are as follows: 
Part 2: Analysis and Evaluation 

215

• The Amfleet/AEM-7 train passing at a speed of 201 km/h (125 mph) produced a 

force of 174 N (39 lb). 

• The Acela Express train passing at a speed of 241 km/h (150 mph) produced a 

force of 106 N (24 lb). 

Airflow strength varies with location relative to the passing train. Airflow velocity 

decreases with increased distance from the train and at increased height from the track. 

Airflow velocity is lower on a high-level than on a low-level platform. When the lateral 

distances of the CIDs are increased by 22 percent from the side of the train, the forces on 

the CIDs are: 

• Reduced by 14 percent for the Acela Express train. 

• Reduced by 32 percent for the Amfleet/AEM-7 train. 

There is greater attenuation on the airflow with distance for Amfleet/AEM-7 train than 

for the Acela Express train. This is also the case in the CFD simulation where the wake 

from the Acela Express train produced a stronger airflow than the overall airflow from 

the Amfleet train when measured at the furthest distance from the train. 

The drags on an isolated cylinder and on an isolated flat-body with constant drag 

coefficient were computed from airflow velocity and compared with the load on the CID. 

The force measured from the CID was higher in magnitude than from the drag computed 

from airflow velocity for an isolated cylinder. This is consistent with studies that suggest 

the CID is responding to the effects of static pressure variation from the flow field of the 

passing train. When the drag was computed for a flat-body, it is in general considerably 

higher than the drag computed for a circular cylinder, and is also generally higher than 

the force measured from the CID. This indicates the circular cylinder and the CID are 

not responding very strongly to the airflow velocity. Therefore, a circular cylindrical 

body is not an effective gauge of wind force in the range of airflow velocity induced by a 

passing train. 

11.4. People on Trackside and Platform 

A survey was conducted of railroad stations along the Northeast Corridor of the United 

States to provide the information necessary for assessing the impact of Acela Express 

trains passing the stations at high speeds. The survey of the selected stations involves 

observing the station surroundings, the general movement of people and trains, and 

station measurements. In addition to the on-site surveys, basic information was collected 

from Amtrak and other agencies on all 101 stations. The survey found that the conditions 

of the stations vary greatly from each other. 

A common approach, practiced by railways in various countries to address the safety of 

people from the aerodynamic effects of a passing train, is to specify a minimum distance 
Part 2: Analysis and Evaluation 

216

from a passing train. Workers are to stay at a certain distance from the track when a train 

passes, meanwhile markings are used on station platforms to warn passengers from 

getting too close to the edge of the platform. Recommended distance from the passing 

train varies with railways in different countries, as does the maximum speed of the 

passing train. No safety requirements exist in the United States (as of 2005) for people 

on station platforms as it relates to the aerodynamic effects of passing trains. Amtrak has 

been installing yellow markings on the edge of station platforms in the Northeast 

Corridor that are 0.965 m (38 in) wide. 

A passing train induces airflow that creates a destabilizing force on people in proximity 

to the train. The effects of wind on people have been studied with application to 

pedestrians in the vicinity of buildings and built-up environments. There are different 

wind speed criteria with one of the most common being the Beaufort scale. Various 

attempts have occurred to factor in the unsteady and turbulent airflow in the criteria 

based on experiments conducted in wind tunnel and from outdoor observation. The wind 

speed criteria of Murakami and Deguchi were applied in setting the minimum distance 

for people in proximity to a passing train. 

The effects of wind on people from wind speed criteria were compared with the effects 

on people based on the dynamic response of a single degree-of-freedom mathematical 

mannequin model. The Murakami and Deguchi criteria are based on wind averages over 

a 3 s duration, while the mathematical mannequin provides a dynamic response to a 

transient force of an idealized pulse shape. The stability boundary from the mannequin 

was interpreted relative to the Beaufort scale from which the effects on a person from 

train-induced airflow velocity can be evaluated. Comparison of the effects on people 

from the mannequin stability boundary with the Murakami and Deguchi criteria indicates 

very similar results. 

The criteria for airflow from a passing train were based in part on studies of pedestrian 

response to high wind in the vicinity of buildings. In addition to any differences between 

the dynamics of meteorological wind and the airflow induced by a passing train, 

differences occur between a pedestrian in a street setting, a worker on the trackside, or a 

waiting passenger on a station platform. These differences may affect their expectation 

of some disturbance, and thus their ability to counter any destabilizing effect. 

In many of the studies on a person’s response to wind force, the measure is for the 

stability of a person that is walking. Because of the kinematics of a walking person, their 

stability would presumably be less than that of a stationary person with both feet on the 

ground. Workers on the trackside would be expected to be standing still as a train 

approaches and passes. People on a station platform may be walking while many people 

are generally standing still or with little movement. 

Another factor that enters into a person’s response is their sensory input. A pedestrian in 

the street may be exposed to a strong wind gust without any warning. However, a worker 

on the trackside or a person on a station platform will have the benefit of perceiving an 

approaching train and preparing for its effect. From people’s subjective response on the 
Part 2: Analysis and Evaluation 

217

passing train experience, the wind effect felt by a person is accompanied by an 

intimidation factor of seeing a train approaching at high speed. This factor is not 

applicable to a pedestrian walking on the street. If a person is alert to an approaching 

train, this additional visual sense and the anxiety that it produces could cause the person 

to move away from the approaching train for reasons that might or might not be related to 

the aerodynamic factor. 
Part 2: Analysis and Evaluation 

218

12. Recommendations 

Recommendations are proposed to address safety issues relating to the aerodynamic 

interaction between passing trains, and the aerodynamic effects of trains passing people. 

12.1. Aerodynamic Interaction Between Passing Trains 

A train traveling at high speeds passing another train produces an aerodynamic force on 

the other train that can create the potential for structural damage, cargo being dislodged 

from the rail car, or derailment. 

• Operating conditions and rail cars should be examined to determine if conditions 

exist to create a safety concern. In addition to the high speed of the passing train, 

other conditions that create the potential for adverse response on the observer car 

are: 

o Close track center spacing. 

o High ambient wind. 

o Confined environments such as steep embankments, overpasses, or tunnels. 

o Bluff nose on the high-speed passing train. 

o For the observer car: 

 Structural members susceptible to damage such as window glazing 

or flexible exterior surface material such as cloth. 

 Structural members that contain discontinuity such as attached 

panels, window frames, or doors. 

 Side surface with large vertical area such as double-stack well car. 

 A rail car that is light in weight. 

• The integrity of structures susceptible to damage should be examined for potential 

failure from high aerodynamic loading, or fatigue failure from cyclic aerodynamic 

loading of frequent high-speed train passes. A more complete study should be 

conducted on the structural integrity of window mount and glazing to determine if 

cracking or dislodgement will occur. Further data required includes: 

o Pull out force on window glazing and mounting frame. 
Part 2: Analysis and Evaluation 

219

o Burst pressure for the window glazing. 

o Window mounting design, dimensions, and structural properties. 

• The effects of track geometry variation should be considered in rail vehicle 

response from aerodynamic interaction with a passing train. 

• Maintain a source of aerodynamic data for mathematical modeling. The data 

should include pressure coefficients as it relates to: (1) geometry of the passing 

train, (2) configurations of the train being passed and surrounding structures, (3) 

lateral and vertical distances relative to the passing train, and (4) ambient wind. 

12.2. Safety Limit for People from the Aerodynamic Effects of Passing Train 

A person in proximity to a train passing at high speeds can experience destabilizing 

effects of the aerodynamic force created by the train. Debris can be blown and objects 

and equipment can be pushed onto the passing trains. 

• Members of the public on a station platform and railroad workers on the trackside 

in open calm air should maintain a minimum distance from a passing train, as 

shown in Table 42. 

Table 42. Recommended Minimum Distances for People Exposed to the 

Aerodynamic Effects of a Passing Train 

o Railroad worker is an adult that is of average size, physically fit, standing 

stationary on a stable surface, and alert to an approaching train and the 

sensation of aerodynamic force. 

Minimum Lateral Distance 

 Distance from Distance from Nominal 

Centerline of Outer Edge of Distance from 

Nearest Track Nearest Rail Side of Train 

Member of Public 3.12 m 2.33 m 1.6 m 

on (123 in) (92 in) (63 in) 

Low-Level Passenger 

Platform 

Worker on 2.72 m 1.93 m 1.2 m 

Trackside at Low- (107 in) (76 in) (47 in) 

Level Platform Height 
Part 2: Analysis and Evaluation 

220

o

passing speeds, 

 Amfleet/AEM-7 and Amfleet/HHP-8 trains passing at a speed no 

greater than 201 km/h (125 mph). 

 Acela Express train passing at a speed no greater than 241 km/h 

(150 mph). 

The minimum distances can also apply to other trains with similar geometry 

and corresponding passing speeds. 

o The recommended distances from the passing train were based on data 

measured from a low-level platform at 203 mm (8 in) above the top of the 

rail. If the trackside or platform is at a height that is significantly different 

from this height, these distances may not apply. 

o A warning strip on a low-level platform that is 1.57 m (62 in) wide as 

measured from the edge of the platform would correspond to the 

recommended minimum nominal distance from the side of the train of 1.6 m 

(63 in). 

o Further study on the aerodynamic effects of passing trains should include: 

(1) the presence of ambient wind, (2) freight trains, and (3) locations that 

are more reflective of workers on the trackside or situations where 

pedestrians are on a public pathway adjacent to the track. 

• The effects of people exposed to the aerodynamic force from a passing train were 

based on a person’s physical ability to maintain stability. Human response is also 

influenced by psychological factors that can compromise safety. 

o Announcement of an approaching train should include information on the 

type of train service or whether the train is stopping at the station. 

o Further study should include the role that psychological factors play for 

people on station platforms. 

• The applicability of the stability boundary derived from the mathematical 

mannequin should be confirmed with additional data and further analysis. 

• Maintain a source of aerodynamic data for mathematical modeling. The data 

should include the normalized train-induced airflow velocity as it relates to: (1) 

train geometry, (2) configurations of surrounding structures, (3) lateral and vertical 

distances from the track of passing train, and (4) ambient wind. 

The minimum distances apply to the following passenger trains and their 
Part 2: Analysis and Evaluation 

221

• Platform safety limits were recommended based on the stability of an average adult 

male. Other factors that should be considered are as follows: 

o Train-induced airflow in itself is unlikely to be strong enough to propel a 

solid object such as a rock. However, any particles on the track agitated by 

the turbulent airflow and its buffeting effect, if struck by the train especially 

at the underside of a car, can cause the particle to become a fast moving 

projectile. This would propel it in the direction of the train unless it is 

deflected outward to the platform. A person on the trackside or low-level 

platform would be most vulnerable to this hazard. 

o Rolling objects put into motion by the aerodynamic drag of the traininduced airflow are a safety issue. A light cart can roll into and be struck by 

the train causing it to be propelled back onto the platform. The same risk 

would apply to a baby carriage with potential disastrous consequences if a 

baby should be in the carriage. 

o People on a station platform can be of different heights and different 

degrees of agility and strength. A small child could be exposed to greater 

airflow. People that are frail or the elderly would be less stable than the 

average adult. 
Appendix A 

222

Appendix A: Nomenclature and Glossary 

A-1 Nomenclature 

Symbol Definition

AF fronted area 

AP projected area 

AS side area 

A/D analog-to-digital 

ADC analog-to-digital converter 

Amtrak National Railroad Passenger Corporation 

AAR Association of American Railroads 

APTA American Public Transit Association 

ARA Applied Research Associates, Inc. 

AREMA American Railway Engineering and Maintenance-of-Way Association 

CARS China Academy of Railway Sciences 

CEN European Committee for Standardization 

CFD computational fluid dynamics 

CID cylindrical instrumented dummy 

CD drag coefficient 

CP pressure coefficient 

DC diameter of cylinder 

DB AG Deutsche Bahn A.G. (German Rail) 

FD drag (force) 

FRA Federal Railroad Administration 

FS Trenitalia (Italian Railways) 

ICE Inter-City Express or Inter-City Experimental (German high-speed train) 

ISO International Organization for Standardization 

LC length of cylinder 

L/V ratio of lateral to vertical forces 
Appendix A 

223

Symbol Definition 

MAS Maximum Authorized Speeds 

MIRA Motor Industries Research Association 

nα rotational load factor 

NUCARSTM New and Untried Car Analytic Regime Simulation 

PB Parsons Brinckerhoff Quade and Douglas 

q∞ free stream dynamic pressure 

Re Reynolds number 

RWT rails-with-trails 

RAPIDE Railway Aerodynamics of Passing Interactions with Dynamic Effects 

RSSB Rail Safety and Standards Board 

RTRI Railway Technical Research Institute 

SI Système International d'Unités (International System of Units) 

SNCF Société Nationale des Chemins de Fer Français 

(French National Railways) 

SUE statically unstable equilibrium 

TAMS Train-Approach Monitoring System 

TEL turbine-electric locomotive 

TGV Train à Grande Vitesse (French high-speed train or the system) 

TRANSAERO Transient Aerodynamics for Railway System Optimisation 

TTC Transportation Technology Center 

TTCI Transportation Technology Center, Inc. 

USDOT United States Department of Transportation 

Volpe Volpe National Transportation Systems Center (VNTSC or Volpe Center) 
Appendix A 

224

Mathematical Symbol 

Symbol Definition 

u velocity of fluid 

v velocity of solid body 

x, y, z x, y, z coordinate or translational displacement in the longitudinal, lateral, and 

vertical directions respectively, (length) 

φ, θ, ψ φ, θ, ψ rotation in roll, pitch, and yaw about the longitudinal, lateral, and vertical 

axes respectively, (angle) 

ζ damping ratio 

Λ excitation wavelength, (length) 

λ wavelength, (length) 

λ n natural wavelength, (length) 

 fluid density 

Ω excitation frequency, (rad/time) or (rad/length) 

σ standard deviation 

ω frequency, (rad/time) or (rad/length) 

ωn natural frequency, (rad/time) or (rad/length) 

ωd frequency of damped oscillation, (rad/time) or (rad/length) 

Subscript 

Symbol Definition 

1, 2, 3 longitudinal, lateral, and vertical directions respectively 

bo breakout 

CM center of mass 

CP center of pressure 

cyl cylinder 

ef effective 
Appendix A 

225

A-2 Glossary 

Term Definition 

Acela Express Bombardier/Alstom high-speed trainset for Amtrak passenger train service. 

alongside the track On the trackside or on a station platform. 

Amfleet Budd passenger rail car for Amtrak passenger train service. 

Amfleet/AEM-7 Train with Amfleet cars pulled by GM-ASEA AEM-7 electric locomotive. 

Train 

Amfleet/HHP-8 Train with Amfleet cars pulled by Bombardier/Alstom HHP-8 electric locomotive. 

Train 

Amfleet/ F40PH Train with Amfleet cars pulled by General Motors F40PH diesel-electric locomotive. 

Train 

drag indicator A force obtained by multiplying the normalized statistical force (mean plus 2 

standard deviation) by the square of the desired train speed. 

observer car The observer car is the rail car that is responding to the force produced by the other 

passing train during aerodynamic interaction between passing trains. 

rotational load The ratio of the effective force acting at the center of mass to the weight of the body, 

factor with the effective force producing the same moment as the actual force acting at 

another location. 

Shinkansen New trunk line: the rail line of the Japanese high-speed passenger train. 

slipstream The boundary layer flow around the train, which may or may not include the wake. 

swap body A freight-carrying unit for intermodal transport and optimized to road vehicle 

dimensions, that was originally not strong enough to be top-lifted or stacked when 

loaded, but some can now be top-lifted or stacked. 

trainset A train whose cars are intended to be permanently coupled together. 

turbine-electric Locomotive using a gas turbine engine to generate power to an electric traction 

locomotive motor. Also refers to the prototype FRA/Bombardier turbine-electric locomotive. 
Appendix B 

226

Appendix B: Aerodynamic Quantity 

B-1 Fluid Property 

u: Fluid velocity. 

ρ: Density. 

q: Dynamic pressure. 

μ: Coefficient of viscosity, for air at sea level. 

ν: kinematic viscosity, 

P: Static pressure. 

u∞: Free stream flow velocity. 

ρ∞: Free stream density. 

q∞: Free stream dynamic pressure. 

μ∞: Free stream coefficient of viscosity. 

ν∞: Free stream kinematic viscosity, 

P∞: Free stream static pressure. 

Standard atmosphere at sea level: 

ρ∞ = 1.225 kg/m3

 (0.0023769 slug/ft3). 

μ∞ = 1.7894x10-5 kg/m•s (3.738x10-7 slug/ft•s). 

ν∞ = 1.4607x10-5 m2

/s (1.5723x10-4 in2/s). 

P∞ = 1.01325 x 105

 N/m2 (14.696 lb/in2). 
Appendix B 

227

B-2 Quantitative Relation 

Quantity Definition

Dynamic Pressure (q) 1 2

q = ρu

2

Pressure Coefficient (CP) P − P∞ Cp = q∞

Peak-to-Peak Change in P2 1 − P

Pressure Coefficient (ΔCP) ΔCp = q∞

Average Pressure Coefficient 1 X2

C = C ( )s ds P P (CP ) )∫X (X − X 1 2 1

Averaged over the range X1 to X2. 

Center of Pressure (XCP, YCP) p x( , y xdA ) p x y ydA ( , ) ∫ ∫

A A XCP = YCP = p x( , y dA ) p x y dA ( , ) ∫ ∫

A A

Distributed pressure p(x,y) over the surface area A. 

Reynolds Number (Re) u∞ ∞ ρ L Re = μ ∞

Flow over surface length L. 

Drag Coefficient (CD) P − P∞ CD = q∞

Drag (FD) FD = q C A ∞ D

Turbulence Intensity u ′

rms

u

1 T

Mean flow velocity: u = u t dt ( ) T ∫0

Fluctuation of the flow velocity from its average value: u′ = u − u

1 T

)

2 Root mean square (rms) of the fluctuation: u ′ = (u ′ dt rms T ∫0
Appendix B 

228

B-3 Circular Cylinder 

B-3.1 Curve Fit for Drag Coefficient of a Circular Cylinder 

The drag coefficient for a circular cylinder varies with Reynolds number (Figure 85). 

Empirical equations for the drag coefficient of a two-dimensional circular cylinder were 

derived by least square method of curve fit over a range of Reynolds numbers as follows: 

Table 43. Empirical Equations for Drag Coefficients. 

Reynolds number, Re Drag Coefficient, CD

300 < Re < 2.15×105 CD = 1.2

2.15 10 x

5 < Re < 5.435×105 CD = (− 2.728×10−6 × Re +1.787

5.435×105 < Re < 9.779×105 CD = (1.285×10−7 × Re)+ 0.234

9.779×105 < Re < 3.5×106 CD = (1.6×10−8 ×Re)+ 0.344

3.5×106 < Re < 1.0×107 CD = 0.4

)

Shown in Figure 86 and Figure 87 are comparisons of drag coefficients between data and 

curve fit. 

B-3.2 Drag of a Circular Cylinder 

When the dimensions of the circular cylinder and the fluid properties do not vary, the 

drag coefficient CD is a function only of the flow velocity, and the drag FD is, 

1 F 2

D = ρ u D

2 ∞ ∞ C LCCD (u∞ ) , where DC is the cylinder diameter, and LC is the cylinder 

length. The drag can also be expressed as, 

1 F = ρ u

2 ⎛ C ∞ 2 ( ∞ )⎜ D ⎞

D ∞ DC LCCD u ⎟ ⎜ ⎟, 2 ⎝CD2 ⎠

where CD2 is the drag coefficient for a circular cylinder with long axial length, whose 

fluid flow over the cylinder can be approximated as two-dimensional flow (Figure 85). 

B-3.3 Drag of CID 
Appendix B 

229

The circular cylinder of the CID has a diameter of DC = 0.39 m (15.4 in) and a length of 

LC = 0.92 m (36.2 in), with a Reynolds number of Re = (2.67x104

 u∞) for standard 

atmosphere at sea level. The aspect ratio is LC/DC = 2.36 (reciprocal is 0.42), and 

therefore the drag for the CID can be corrected for three-dimensional effects as 

⎛ C ⎞ approximately ⎜ D ⎟ ⎜ ⎟ = 0.56 . The drag for the CID can be expressed in terms of flow 

⎝ CD2 ⎠

velocity as shown in Table 44. 

Table 44. Drag on a CID as Function of Flow Velocity 

Reynolds number (Re) Drag (FD) as Function of Flow Velocity (U) 

300 < Re < 2.15x105 For 0.011 < U < 8.1 (m / )s

⎟

⎠

⎞ ⎜

⎝

2 ⎛ Cd F = 0.2638U ( D ⎜ ⎟ Cd 2

N)

For 0.025 < U < 18 (mph)

⎟

⎠

⎞ ⎜

⎝

2 ⎛ Cd FD = 0.01185U ⎜ ⎟ Cd 2

(lb)

2.15x105 < Re < 5.435x105 For

⎜

⎝

⎛

8.1 < U < 20 (m / )s

2 Cd FD = [− (0.01601U ) + 0.3928]U ⎜Cd 2

⎟

⎠

⎞

⎟ (N)

For 18 < U < 46 (mph)

⎜

⎝

⎛2 FD = [− (0.0003215U )+ 0.01765U ⎜

Cd

Cd 2

⎟

⎠

⎞

⎟ (lb)

5.435x105 < Re < 1.0x106 For

⎜

⎝

⎛

20 < U < 37 (m / )s

2 FD = [(0.0007541U ) + 0.05143]U ⎜ ⎟

⎠

C ⎞ d

⎟ Cd 2

(N)

For 46 < U < 84 (mph)

FD = [(0.00001514U )+ 0.002310 U ⎜

⎝

2 ⎛ Cd

⎜ Cd 2

⎟

⎠

⎞

⎟ (lb)

]

]
Appendix B 

230

FLOW OVER A CIRCULAR CYLINDER

----- (b) -----

Drag Coefficients at Various Reynolds Numbers over a Cylinder

in Two Dimensional Flow

Source: Hermann Schlichting, , Boundary Layer Theory 2000

Drag Coefficients for a Three Dimensional Cylinder at Various Aspect Ratios

C : drag coefficient in two-dimensional flow

b/d: aspect ratio

D2

CD2

Drag Coefficient

Reciprocal of Aspect Ratio, d/b

 Re 10

d: diameter

b: span

5

----- (a) -----

Reynolds Number, Re

Drag Coefficient, CD

Figure 85. Drag Coefficients for a Circular Cylinder with (a) Two Dimensional Flow (Schlichting 

and Gersten 2000) and (b) Different Aspect Ratios (Horner 1958) 
Appendix B 

231

CURVE FIT OF DRAG COEFFICIENT FOR A CIRCULAR CYLINDER

Reynolds Number

Drag Coefficient

0.1

1 x 104 1 x 105 1 x 106 1 x 107

1.0

10.0

Data

Curve Fit

x

x Measurement by C. Wieselsberger

Reference: Hermann Schlichting, , 2000 Boundary Layer Theory

Figure 86. Comparison between Data and Curve Fit of Drag Coefficients for a Circular Cylinder 
Appendix B 

232

CURVE FIT OF DRAG COEFFICIENT FOR A CIRCULAR CYLINDER

OVER CRITICAL FLOW REGIME

0.1

1 x 105 1 x 106

1.0

10.0

Reynolds Number

Drag Coefficient

Data

Curve Fit

x

x Measurement by C. Wieselsberger

Reference: Hermann Schlichting, , 2000 Boundary Layer Theory

Figure 87. Comparison between Data and Curve Fit of Drag Coefficients for a Circular Cylinder 

over the Critical Flow Regime 
Appendix B 

233
Appendix C 

234

Appendix C: Characterization of Locomotive and Rail Car 

C-1 Dimension and Dynamic Property 

The dimension and dynamic properties of rail cars and locomotives are shown in Table 

45, and the dimension and dynamic properties for the double-stack well car is shown in 

Table 46. 

Table 45. Dimensions of Rail Cars and Locomotives 

Locomotive and Car Length 

(Between Pulling 

Faces of Coupler) 

Extreme Width Rail to Extreme 

Height or to Roof 

Well Car TTX 456013 

(excluding containers) 

21.8694 m 

(71’ 9”) 

3.2004 m 

(10’ 6”) 

1.9558 m 

(6’ 5”) 

Acela Express Power Car 

TEL 

21.218525 m 

(69’ 7-3/8”) 

3.175 m 

(10’ 5”) 

4.318 m 

(14’ 2”) 

Acela Express Passenger Car 26.6446 m 

(87’ 5”) 

3.1623 m 

(10’ 4-1/2”) 

4.232275 m 

(13’ 10-5/8”) 

Horizon Passenger Car 25.9842 m 

(85’ 3”) 

3.2004 m 

(10’ 6”) 

3.86715 m 

(12’ 8-1/4”) 

TEL Train 

[TEL] + 2x[Horizon Passenger Car] 73.18 m 

(240’ 1”) 

Acela Express Trainset 

2x[Acela Express Power Car] + 

6x[Acela Express Passenger Car] 

202.34 m 

(663’ 8”) 
Appendix C 

235

Table 46. Dimensions and Dynamic Properties One Unit of an Articulated Double-Stack Well 

Car

Length 

Between 

Bolsters 

Mass of 

Carbody 

(Excluding 

Trucks) 

Height of Car 

Center of Mass 

from Top of 

Rail 

Moment of Inertia 

Roll Pitch Yaw

Empty 18 m 

(708 in) 

 21,420 kg 

(47,257 lbm) 

1.81 m 

(71.1 in) 

1.1x105 

2 kg•m

(9.8x105 

lbf•in•sec2) 

5.5x105 

2 kg•m

(4.9x106

lbf•in•sec2

) 

5.2x105 

2 kg•m

(4.6x106 

lbf•in•sec2) 

Loaded 61,243 kg 

(134,980 lbm) 

1.75 m 

(68.8 in) 

1.6x105 

2 kg•m

(1.46x106 

lbf•in•sec2) 

9.3x105 

2 kg•m

(8.27x106 

lbf•in•sec2) 

8.7x105 

2 kg•m

(7.71x106 

lbf•in•sec2) 

C-2 Roll Response of a Stationary Empty Double-Stack Well Car 

The dynamic properties for the carbody of the empty double-stack well car were 

computed from the measured roll response shown in Figure 88, Table 47, and Table 48, 

as follows: 

• Roll Natural Frequency: 1.6 Hz 

• Damping Ratio: 0.03. 
Appendix C 

236

FULL-SCALE TEST MEASUREMENT OF ROLL RESPONSE ON A 

DOUBLE-STACK WELL CAR FROM AERODYNAMIC INTERACTION 

WITH A PASSING TEL TRAIN

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

-2.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0

Time, (s)

Potentiaometer Trace of Car-Body Displacement (Positive when Well Car 

Moves Away from Passing Train)

Channel 15: East String Potentiometer

Average Value of Roll

Nose of Passing Train Reaches Container

Tail of Passing Train to Completely Pass Container:

Turbine-Electric Locomotive Pulling Two Horizon Passenger Cars at 177 km/h (110 

mph) Passing a Stationary Well Car with Empty Double Stacked Containers

Average Trace Value: -0.0289605441064639

Factor to Convert Potentiometer Trace to CarBody Roll Angle, (deg): 2.19101123595506

Time for Tail of Passing Train to Completely 

Pass Container, (s): 1.73624741735537

Figure 88. Roll Response of a Stationary Empty Double-Stack Well Car from Aerodynamic 

Interaction with a Passing TEL Train 
Appendix C 

237

Table 47. Periods and Logarithmic Decrements of Carbody Roll Decay of the Double-Stack Well 

Car after Tail Passage of a Passing Train 

Time, (s) Period, (s) Logarithmic Decrement 

Consecutive 

Maximum 

Peaks 

Consecutive 

Minimum 

Peaks 

Consecutive 

Maximum 

Peaks 

Consecutive 

Minimum 

Peaks 

2.0900 (+Peak 1) (+Peak 1) 

2.4540 (-Peak 1) (-Peak 1)

2.7660 0.6760 0.4022 

3.1090 0.6550 0.1371

3.4530 0.6870 0.2596 

3.7440 0.6350 0.0872

4.0870 0.6340 0.4234 

4.4090 0.6650 0.0717

4.6900 0.6030 0.2564 

5.0130 0.6040 0.1030

Table 48. Dynamic Properties of the Double-Stack Well Car from Measured Roll Response 

 From Maximum 

Peak Value 

From Minimum 

Peak Value 

From Maximum 

and Minimum 

Peak Values 

Average Damped Period, (s) 0.6500 0.6398 0.6449 

Average Damped Frequency, (Hz) 1.5385 1.5631 1.5507 

Average Damped Frequency, (rad/s) 9.6664 9.8213 9.7433 

Average Logarithmic Decrement 0.3354 0.0997 0.2176 

Average Damping Ratio 0.0533 0.0159 0.0346 

Average Natural Frequency, (Hz) 1.5407 1.5633 1.5516 

Average Natural Frequency, (rad/s) 9.6802 9.8226 9.7491 
Appendix D 

238

Appendix D: Instrumentation and Measurement 

D-1 Measurement on Double-Stack Well Car 

This instrumentation measures the time history of aerodynamic pressure and carbody roll 

motion for a double-stack well car. 

D-1.1 Aerodynamic Pressure 

Aerodynamic pressure on the near side of the container facing the passing train was 

measured by an Endevco 8510B-2 piezoresistive pressure transducer. Aerodynamic 

pressure on the far side of the container facing away from the passing train was measured 

by an PCB Piezotronics 103 A02 piezoelectric pressure transducer, modified for 10 s low 

frequency response. 

D-1.2 Carbody Roll Response 

Carbody roll motion was measured by two string potentiometers mounted between the 

carbody and truck frame on the left and right sides positioned at 0.930 m (36.625 in) 

from the car longitudinal centerline. 

D-1.3 Data Acquisition and Processing 

Train detection was provided by two methods. One method was by strain gages on the 

rail to detect of the axle of the passing train. A second method was by an optical beam 

directed across the track that detected the presence of a train when the beam is 

interrupted. 

Data was collected by a 12-bit analog-to-digital converter (ADC) sampling at 100 μs 

intervals. 

Data was processed by a 2 pole low-pass Bessel filter set a 1 kHz. 
Appendix D 

239

D-2 Airflow Velocity Measurement 

D-2.1 Single Peak Value Airflow Velocity Measurement 

This instrumentation provided a single peak airflow velocity measurement for each event 

using an Alnor Instrument velometer consisting of Alnor 6006AP meter, 6030CP range 

selector, and 6070P pitot tube. 

D-2.2 Time History Airflow Velocity Measurement 

This instrumentation measures the time history of airflow velocity. 

Airflow velocity was measured by a Dwyer Instruments model 160-8 pitot-static tube 

with a hemispherical tip geometry which gives accurate reading for pitot tube 

misalignments up to 15 deg. The pitot-static tube is connected to a Setra Systems model 

264 very low differential pressure transducer. 

GEOLOG Data Acquisition system provided excitation voltage, signal conditioning, and 

analog to digital (A/D) conversion for four channels at an A/D rate of 250 Hz (4 ms per 

sample). A photoelectric beam directed across the track detected the presence of a train 

when the beam is interrupted. 

A moving average low-pass filter was applied to the data with a minimum averaging 

duration of 0.032 s to remove high frequency noise. 

D-2.3 Yaw Misalignment of Pitot-Static Tube 

The pitot-static tube is designed to accurately measure airflow velocity when it is aligned 

with the direction of airflow, with increasing error as the misalignment increases. The 

effects of angular misalignment on pitot-static tube measurements of differential pressure 

and airflow velocity are shown in Figure 89. 

Resultant airflow velocity computed from airflow velocity components measured from 

two pitot-static tubes perpendicular to each other requires the differential pressure on the 

pitot-static tubes to vary with a specific trigonometric relationship. For a differential 

pressure PO at zero degree angular misalignment, and differential pressure Pψ at ψ degree 

P

angular misalignment, the differential pressure must vary as ψ = cos 2

ψ . An error is 

Po

incurred in computing the resultant airflow velocity when the measurement with angular 

misalignment from the pitot-static tube deviates from this relationship. 
Appendix D 

240

D-3 Force Measurement on CID 

This instrumentation measures the time history of force on the CID. 

D-3.1 CID 

The CID is an SNCF/VR Model 1993, which consists of a cylinder with a diameter of 

0.39 m (15.4 in) and an axial length of 0.92 m (36.2 in). The cylinder is supported on a 

post with strain gauges attached to the post to measure the unbalanced force acting on the 

cylinder along a horizontal plane. Any bending to the post is related to the unbalanced 

force applied to the cylinder. Data from the CID was processed through a Bessel second 

order 15 Hz low-pass digital filter to account for the muscular reaction time of a human 

being. The natural frequency of the CID is slightly higher than 15 Hz. The criteria for 

dynamic behavior of CID are as follows: 

• The peak value of the first oscillation following the release of load must not exceed 

45 percent of initial value. 

• The zero value with no load must be reached in less than 0.1 s. 

• The peak value of residual oscillation after 0.5 s must not exceed 10 percent of 

initial value. 

D-3.2 Weather Station 

Weather data was measured from a Campbell Scientific weather station, which consists 

of: 

• Barometer: 600 – 1060 mbar Vaisala. 

• Wind captor: 05103 (wind direction and speed). 

• Temperature and relative humidity: HMP45C. 

D-3.3 Data Acquisition and Processing 

Stain gages on the rail were used to detect of the axle of the passing train. 

Data was acquired at a rate of 1200 samples per second. 
Appendix D 

241

Acquisition data was processed with the LabVIEW (National Instruments) software. 

“Univers Soufflé” created by SNCF performed the application data processing. Data 

from the CID was measured at 1200 samples per second and was processed through a 

Bessel second order 15 Hz low-pass digital filter to account for the muscular reaction 

time of a human being. 

D-4 Moving Average 

The moving average is computed as a continuous series of mean values over a domain t 

as follows: 

( = ⎛ 1 ⎞ y t ∫

t

)

t t

= ⎜ ⎟ n +α n n 20

n t dt n =t f (t) n10 ⎝ 2α ⎠ tn −α

where 

t t • tn is the midpoint of the averaging window, t n1 + n2

n = , 2

t − t • α is one half the averaging window duration, α = n2 n1 , 2

• tn1 and tn2 are the initial and final values respectively of the averaging window 

endpoints, 

• and tn10 and tn20 are the initial and final midpoint values respectively over the 

domain from which the moving averages are computed. 

The moving average for discrete values is computed as a series of mean values over a 

domain t as follows: 

t +α

Y (t )

tn =tn 20 ⎛ 1 ⎞ n = ⎜ ⎟ tn =tn10 ⎜ ⎟∑

n

f (t)

⎝ Nt ⎠tn −α

where Nt is the number of values, which for equal intervals Δt between values, 

⎛t ⎞ = ⎜ 2 − t N 1

t ⎟ +1 ⎝ Δt ⎠
Appendix D 

242

0 5 10 15 20 25 30

0.85

0.90

0.95

1.00

1.05

1.10

1.15

EFFECT ON MEASUREMENT FROM 

PITOT-STATIC TUBE RELATIVE TO AIRFLOW DIRECTION

MISALIGNMENT OF A HEMISPHERICAL NOSE

----- (b) -----

0 10 20 30 40 50 60

0.5

0.6

0.7

0.8

0.9

1

1.1

Airflow Velocity, V /V@ O

Misalignment Angle, (deg) ψ

Effect on Airflow Velocity Due to Misalignment

----- (a) -----

Effect on Differential Pressure Due to Misalignment

Source: E. Ower and R.C. Pankhurst, The Measurement of Air Flow, 1977.

Airflow Velocity from Pitot-Static Tube

 Source: William J. Devenport,“AOE 3054

 Appendix 2: Further Information for

 Experiment #3,” 2001

Cosine of Misalignment Angle

Misalignment Angle, (deg) ψ

Differential Pressure, P/P` o

P = Differential Pressure at Misalignment

P = Differential Pressure at 0 Misalignment

` ψo

o

o

V = Airflow Velocity at Misalignment

V = at 0 Misalignment

` ψo

o

o Airflow Velocity

Figure 89. Effect of Angular Misalignment of a Pitot-Static Tube on (a) Differential Pressure (Ower 

and Pankhurst 1977) and (b) Airflow Measurement (Devenport 2001) 
Appendix D 

243
Appendix E 

244

Appendix E: Modeling Computation 

E-1 Impulse and Momentum in Shock Impact 

In a shock impact where a mass is struck by an impulsive force of very short duration 

relative to the natural period of the system, the impulse can be related directly to the 

change in momentum. This relation can be derived by using a model of a single degreeof-freedom mass/spring/damper system, 

d 2 y dy m 2 + c + ky = F(t) dt dt

where, 

m: mass, 

c: coefficient of viscous damping, 

k: spring constant, 

F(t): impulsive force. 

The equation can be expressed as, 

dv ( ) ( ) F(t) + ζ v + ω2

y = dt n m

where, 

c ζ: damping ratio, ζ = 2mω n

k

ωn: natural frequency, ω n = m

Integrating with respect to time, 

[ ] v v

ξ ξ ξ

( ( ) ( ) 1 ξ ) − (0) + 2ζω ∫ + 2

n vdt ω n ∫ ydt = 0 ∫ F(t)dt

0 m 0

If it is assumed that: 

• the mass is initially at rest, v(0)=0, 

• the damping is small, ζ ≈ 0 , and 
Appendix E 

245

• the pulse duration is short compared to the nature period of the system (pulse 

duration is about one tenth or less of the natural period) so that the displacement is 

small, ∫

ξ

ydt ≈ 0 , 0

then the initial velocity of the mass is approximately, 

1

v(ξ ∫

ξ

) ≈ F(t)dt

m 0

Under these conditions, the initial velocity of the mass from the impulsive force is 

directly related to the mass and impulse. 

E-2 Numerical Solution to Differential Equation by State Transition Method 

State transition method is a numerical integration of differential equation where the 

excitation term is assumed constant over each incremental time or spatial interval, and an 

analytical solution is found for each increment. The case of a second order differential 

equation with a constant excitation is, 

d 2

q dq 2

q

2 f ds 2 + 2ζωn +ω

ds n = ω n o , 

where, 

fo: excitation (held constant at each discrete step), 

q: response, 

s: spatial variable, 

ωn: natural spatial frequency, 

ζ: damping ratio. 

The solution to this differential equation for an underdamped case (ζ<1.0) is, 

for ζ < 1.0,

q = C e −ζωns cosω s + C e −ζωns

1 d 2 sinω d s + f o ,

dq = −C ( ) ζω cosω s +ω sinω s e −ζωns −C (ζω sinω s −ω cosω s e−ζωns

ds 1 n d d d 2 n d d d ) ,
Appendix E 

246

dq ⎛ dq ⎞ where,ω =ω 1−ζ 2

d n . Substituting initial conditions, q(0) = qo and (0) = ⎜ ⎟ , ds ⎝ ds ⎠o

the arbitrary constants C1 and C2 can be expressed as, C1 = qo − f o and 

⎛ 1 ⎞⎛ dq ⎞ ⎛ζω ζω = ⎟ + ⎜ n ⎞ ⎛ C ⎜ ⎟ − n ⎞

2 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟qo ⎜ ⎟ f

ω o . The numerical solution for the response (q) 

⎝ d ⎠⎝ ds ⎠o ⎝ ω d ⎠ ⎝ ω d ⎠

and the first derivative (dq/ds), are, 

for ζ < 1.0,

q = e −ζω ⎛ζω ⎞ ⎫ ns ⎧

⎨cosω s + ⎜ n

d ⎟ ω ⎜ ⎟sin s q

⎝ ω

d ⎬ o

⎩ d ⎠ ⎭

⎧⎛ 1 ⎞ ⎫⎛ dq ⎞ + e −ζωns

⎨⎜ ⎟sinω s

ω

d ⎬⎜ ⎟ ⎜ ⎟ ⎩⎝ d ⎠ ⎭⎝ ds ⎠o

−ζω s ⎧

e n ⎛ζω ⎞ ⎫ − ⎨cosω s ⎜ n

d + ⎟sinω d s f + ⎜ ⎟ ⎬ f

⎝ ω o o ,

⎩ d ⎠ ⎭

and, 

for ζ < 1.0,

dq ⎪⎧ 2

−ζω s ⎛ω n ⎞ ⎫ = − n ⎪

e ⎨⎜ ⎟sinω ⎟ d s q ⎜ ⎬ ds ⎩

⎪⎝ω d ⎠ ⎪⎭ o

− ⎧ ⎫ n ⎛ dq e s ⎛ ⎞ ⎞ − ζω ζω

⎨⎜ n ⎟ s ω s⎬⎜ ⎟ ⎟sinω

⎝ ω

d − ⎜ cos d

⎩ d ⎠ ⎭⎝ ds ⎠o

− ⎪⎧⎛

⎨⎜ n ⎞

+ e s ω2

ζωn ⎪⎫ ⎟sinω d s⎬ f . ⎜ ⎟ ⎩

⎪⎝ω d ⎠ ⎪⎭ o

E-3 Single Degree-of-Freedom Carbody Roll Model 

When a train passes by an observer car on an adjacent track, an aerodynamic pressure 

variation is swept across the observer car (Equation 1 and Equation 2). This produces a 

time varying force input to the car being passed (Equation 3 and Equation 4). The force 

depends on the position of the passing train relative to the observer car. Roll response to 

the single degree-of-freedom carbody roll model was computed from the equation of 

motion (Equation 5) by the numerical method of state transition using Mathcad software 
Appendix E 

247

E-4 Mannequin Stability Model 

E-4.1 Geometric and Inertial Properties 

The geometric and inertia properties for the mathematical mannequin are shown in Table 

49, Figure 90, and Figure 91. 

Table 49. Properties of a Human Body for an Average Adult Male 

 Value Source

Mass 78 kg

(0.445 lb•s2

/in) 

(Diffrient, Tilley, and Bardagjy 

1974) 

Pitch Moment of Inertia about Center of Mass 2 11.872 N•m•s

(105 lb•in•s2

) 

Computed from Mannequin 

Pitch Moment of Inertia about Bottom of Feet 2 84.2 N•m•s

(745 lb•in•s2

) 

Computed from Mannequin* 

(Relative to Human Body Center 

of Mass) 

2 90.0 N•m•s

(796 lb•in•s2

) 

Computed from Mannequin 

(Relative to Computed Center of 

Mass) 

Height to Top of Head 1.748 m (Diffrient, Tilley, and Bardagjy 

(68.8 in) 1974) 

Height to Center of Mass 0.963 m (Diffrient, Tilley, and Bardagjy 

(37.9 in) 1974) 

1.001 m Computed from Mannequin 

(39.4 in) 

Height to Center of Pressure 0.894 m Computed from Mannequin 

(35.2 in) 

Projected Frontal Area for Nude Body 0.577 m2

(894 in2

) 

Computed 

Projected Frontal Area for Lightly Dressed 

Person 

0.628 m2

(973 in2

) 

Computed from DuBois Formula 

*Simulation was performed using a pitch moment of inertia about the bottom of the feet of 82.1 N•m•s2 (727 lb•in•s2) while the 

revised value is 84.2 N•m•s2

 (745 lb•in•s2). 

E-4.2 Gust Profile 

The averages for each of the gust profiles for the airflow velocity can be found by 

1

− ∫

t2

f S (t)dt , while the root mean square for the corresponding drag is 

t t 2 t1 1
Appendix E 

248

1 2

( ) − ∫

t

f 2

S t dt , where f

t t 2 t

S(t) is a shape function which is a time varying waveform of 

1 1

unit amplitude that represents the gust profile and (t2 - t1) is the time over which the 

waveform acts. 

E-4.3 Statically Unstable Equilibrium Position 

The stability boundary at the SUE position for the single degree-of-freedom 

mathematical mannequin was computed using Mathcad software. A set of simultaneous 

equations is formed from the general solution to the second order differential equation for 

the mannequin stability model (Equation 15 and Equation 15(a to c)). The amplitude of 

the force pulse is computed for each time duration satisfying the conditions at the 

following points in time: 

• point of initial application of excitation force 

• point at which the moment from excitation force balances the moment from the 

gravitational force of the mannequin (for half sine and versine wave pulses only) 

• point of release of excitation force 

• SUE point 
Appendix E 

249

BODY SEGMENT REPRESENTED BY A BASIC GEOMETRIC SOLID

SUPERIMPOSED OVER PROFILE OF HUMAN BODY

Center of Mass of Human Body

----- (a) ----- ----- (b) -----

Front View Side View

Figure 90. Geometric Solids Superimposed over the Profile of a Human Body 
Appendix E 

250

MODEL OF HUMAN BODY WITH LOCATION OF CENTER OF MASS

RELATIVE TO GEOMETRIC CENTER

100%

50%

50%

100%

43.6%

56.4%

43%

57%

100%

100% 72%

28%

50%

50%

100%

Geometric Center of Body Segment

Center of Mass of Body Segment

Center of Mass of Human Body

100%

43.3%

56.7%

100%

43.3%

56.7%

100% 66%

34% 55%45%

100%

Source: Niels Diffrient, Alvin R. Tilley, and Joan C. Bardagjy. Humanscale 1/2/3. 1974.

Figure 91 Locations of the Center of Masses for Segments of the Human Body (Diffrient, Tilley, 

and Bardagjy 1974) 
Appendix E 

251
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252

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